X-RAY ANALYSIS AND PROTEIN STRUCTURE

By F. H. C. CRICK and J. C. KENDREW

The Medical Research Council Unit for the Study of the Molecular Structure
of BIologIcal Systems, Cavendbh Laboratory, Cambridge, England

CONTENTS

                                                      PAGES
I. Illtroductiorl.. ..........................................................  134
II. The Nature of X-Ray DifTraction. .......................................  135
  1. Diffraction from a Crystal ............................................ I35
   a. Crystal Lattice and Reciprocal Lattice. ............................  137
   b. Structure Determination ...........................................  I39
  c. Symmetry..........................................................l4 0
  2. Diffraction froma Fiber ...............................................  142
  a. The Interpretation of Fiber Diagrams ..............................  144
3. Stereochemistry and Molecular Packing. ..............................  I46
  4. General Remarks. . : ...... .: .......................................... I51
  5. Sulnmary .............................................................  153
III. Fibrous Proteins and Synthetic I'olypeptides ..............................  I54
1. Synthetic l'olypeptides (and Silk). ....................................  154
   a. a-l'olypcptides ..................................................  155
   b. &l'olyprptides and Silk. .........................................  158
   c. I'olgproline. .................................................  159
   d. I'olgglgcine ................................................  159
  2. Fibrous l'rofeins ....................................................  163
   a. The n-Kcral.in I':lf.tcrn .....   ...   .........................  lC3
   b. The fl-Kcratin l'attcw .........................................  165
   c. Coll:1gcrt ...................................................  IGG
IV. Crystalline I'rotcius. ....................................................  170
  1. The Nature of Protein Crystals ......................................  170
  2. Direct Information ...................................................  174
   a. Unit Cell and Space Group .........................................  174
   b. hlolecular Weight ..................................................  175
   c. Identification and Identity .........................................  176
   d. The Shape of Protein Molecules ...................................  Iii
  3. The Patterson Function.. ..  .........................................  Ii8
4. Methods Involving Heavy Atoms. ...................................  Ii9
   a. The IIcrvy Atom Method  .....................................  Ii!)
  b. The Mnthotl of Isomorphotls Rel~laccmcut. ....................  ISO
  c. Isnrnoq~l~nr~s Rcpl:~cmcut nntl the Strll(*turc of I~cmoglol~iu ........  ls3
  d. Isomorphous Rcplncemeut and t,hc Structure of Myoglobio. ........  18s

                          133


134             F. H. C. CRICK AND J. C. KENDBEW

X-KAY ANALYSIS ANL) J'JLOTISIN STILUCTURJC         1:El

   e. Isomorphous Rcplaccmcnt and the Structure of Ribonuclease. ........  182
   f. Requirements for Isomorphous Replacement ........................  193
  5. The Chain Configuration of Globular Proteins. ........................  197
V. Viruses. .................................................................  199
  1. Rod-shaped Viruses. .................................................. 200
    a. General Features of TMV. ......................................... 200
   b. X-Ray Results: Basic Features. .................................... 201
   c. X-Ray Results: the Internal Structure. ............................ 202
   d. Correlation between X-Ray and Other Results ...................... 206
  2. Spherical Viruses ..................................................... 207.
   a, TomatoBushy Stunt Virus ......................................... 207
   b. Turnip Yellow Virus. .............................................. 207
  3. General Principles of Virus Structure. ................................ 208
References. .................................................................. 210

I. INTRODUCTION

The last account of X-ray studies of proteins in Advances in Protein
Chemislry was written by Fankuchen in 1945 (apart from Corey's article
on Amino Acids and Peptides, in 1948). Dramatic progress has been
made since then, particularly in studies of synthetic polypeptides and
fibrous proteins; and although the goal of the protein crystallographer-the
complete determination of t.he structure of a globular protein-remains
unachieved, there have been considerable advances in method which should
shortly pay dividends.

In this review we shall not try to cover the whole field but only the
more successful and the more pregnant parts of it.  One major omission
is a description of the large-scale structure found in fibrous proteins such
as collagen, the muscle proteins, etc.  We have not discussed in detail
results from other techniques such as infrared, optical rotation, etc.,
althougb we refer briefly to the rcsult,s of such studies.  The comprehensive
articles hy Low (195X) and by Kendrew (1954b) in The Proteins should
be consulted for background material and for historical details, and for a
.summary of the most recent advances, a recent revielv by Kendrew and
PeJlJtz (1957).

We shall assume t,hat the reader is familiar with proteins, but unfamiliar
with c~rystallogr:~~)hy. Wc shall not, thcrcfort?, set ortt crystlallographic:
arguments in detail, l)ut shall 1 ry r:~t,lier to present a bird's eye view of
the sul,jcc:t.  This will c~lable the biochemist at kast t,o catch t.he drift of
crystallographic discussions; and also to gain some impression of which
parts of the subject arc spwula~ ivc and which park certain. Eksidcs,
protein (:rystaIlograI)flcrs iicctl help from hiochrmists; it, will he part of
our purpose to indicate wlirrr help is most nrcded.

M'e havn ~llrtl our revic!Iv ",Y-Ilny Rtmlysis arid J'rotciti Stzli(4urc."
In last, ypar's Adrwcfs irk Prokin Clwnislr~ nn excclletit arUe appeared

by Anfinsen and Redfield (1956) entitled "Protein Structure in Relation
to Function and Biosynthesis."  Here we shall use the term "protein
structure" in an entirely different sense-indeed, there is very little common
ground between the two articles.  Whereas Anfinsen and Redfield have
concerned themselves with the amino acid sequence and topological
interconnections of the polypeptide chains, we shall consider mainly the
geometrical aspects-the arrangement of the atoms in space.

As the complexity of molecules increases, the geometrical aspects of
structure become more and more impoktant, and it is less and less possible
to explain chemical behavior without taking into account dimensions and
exact geometrical relationships.  The strength of the X-ray approach to
protein structure is that it alone among all the techniques available can
hope to provide this precise quantitative information about molecules as
complicated and as delicate as proteins.  However, it is almost always an
advantage in obtaining the geometrical structure of a molecule to know $8
much as possible about its chemistry; in particular a knowledge of the
amino acid sequence of `b protein should be a very considerable, if hot
indispensable, help to the crystallographer. It is likely to be a very long
time before X-ray analysis can obtain by itself the amino acid-sequence of
a protein.  Both methods-amino acid sequence determination and X-ray
diffraction-will be necessary to obtain the complete structure, chemical
and geometrical, of a protein.

II. THE NATURE OF X-RAY DIFFRACTION   .

X-ray diffraction is not a difficult branch of physics: on the contrary,
it is easy to t,he point of t,ediousncss.  The widespread view that ii. is
litiiiit~elligihle has arisen because a cert,aiii intellectual rffort, is ric~lrd to
grasp it.s mnt~licniati~al foundat,ions, riud brrausr it, is supposrtl, infwr-
revtly, th:kt, sonic spwin! type of "thrrc~-dirncJiaiolinl imagination" is :I prc-
rrquisite for untlcrst:mding its methods and results.  111 this r;c4otl ~1
shll not attempt1 t,o cspound the I)nsic~ throry, Imt, rat,hcr to c~h:lr:lc+wizc~
sonar of thf? I)rond ffxturrs of ,X-ray dilTr:wtitrri, so tlwt ttiv rv:i,lvr 1113)'
Iwcwmc~ f:imili:tr with t,hc iiiiport:int, wiwclpts :ind with soin(' of OW j:~rg~it.
`I'0 tliosr who \visli to Imild on :I firnwr fouiitl:il ioll \w rwon~in~wl t I)(> 111fw~~
O~thOth :L~~r)t'O:ll'h ill SW11 il,TOUJlt S :LS ~hOSP Of' hlg~ (I!):{!)), .j:lJllW ( I!,:i()),
Rutiu (I!W), ant1 ltobcrtson (l!W).


1%             II`. Il. I'. CIU(:li ANI) J. C. KISNI,IiIF\V

X-RAY ANALYSIS AND PROTEIN STltUCTUllE        13i

distance behind the rrystal.  \i%at does the picture on t,he plate look like?
h rather nice example is given in Fig. 1. (To get this picture to look
SO pretty there had to be a good deal of "hokey-pokey"-complicated
movements of the crystal and of the photographic plate, as well as a special
screen.)

The reader will at once be struck by t,wo features of the picture: its
regularity and its symmetry. He should not be surprised by them,
however, because regularity and symmetry are among the most important
properties of crystals themselves. A crystal consists of a regular three-'
dimensional lattice of "unit cells," such that eGery unit cell has the same
relation to its neighbors; and the contents of every unit cell are the same,
namely a number of identical molecules related to one anot,her by sym-
metry elements, such as rot,ation or screw axes or planes of symmetry.

In an analogous manner, t,he X-ray picture exhibits regularity, which
lies in the positions of t.he spot,s.  They form a regular t,mo-dimensional
array or lattice. That is to say, the distance between a spot and its
neighbors is the same no matter where on the picture the spot may be.
The only exceptions are those cases where the spot is too weak to be
shown on the photograph; and this draws our attention to two other
features of the picture. First, while the positions of the spots are regular,
t,heir hlarknesses (their int,ensities, that is) differ--some arc strong, some
weak. Second, the pattern exhibits symmetry; that is to say, it can be
divided illt,o four ct~~:wl,crs which are ident.ical.  Other X-ray phot,ographs
of t,his sort might have shown dilfcrcnt types of symmetry, but some there
wnultl :hxys h?.

What, thc11, is the signilicatrcc~ of each particular spot at such and such
a position on the photograph and of such and such a blackness? What,,
iu fact, is it, that, sc:attcrs 1.1~: X-r:lys? To the last qur5tion we can give
a GInpie :IIM\VV: it is c:iec*trons which sontt,er X-rays, in this case tha
elec~l I'OIIS of thcx :ItSorns it1 t tic cbrystal.  Atoms have fin&e sizes and electrons
+st ril,utcb thctrnsc4ves ov(tr atoms and the bonds which join t,hem.  It is
couvetlicnt to think of a crystal as a three-dimensional pattern of electron
densit?/ whic41 reaches high values near the renters of atoms and tow or
zero WhlW in the SpUWS I)ct,!Vecll.  It can bc shown that t,hc X-ray picture
represc*nts a "wave analysis" (sometimes called Fourier analysis) of this
elertron tlcnsity. When we make a wave analysis of a carystal we think
of it as madc up of a very large number of waves of etcctron density,
running' in many different, directions through it.  If we hnve carried out
the analysis cnorrcctly, we shall find that when we add together all these
waves--c:arh of t,hc corrcrt, siza (amplitude) and to the right extent in or
out of step with its neighbors (phase)-we get back to the actual electron

density of the crystal.  This is a three-dimensional wave analysis, often
known as a Fourier analysis, and the reverse process is a wave (or Fourier)
synthesis. We are familiar with analogous processes involving only one
dimension. In music, a harmonic analysis of the profile of sound produced
by, say, a violin playing a steady note, gives us a fundamental and a series
of harmonics, each separately being a simple or sinusoidal wave, and all
of them adding up (synthesizing) to re-form the original profile.

The significance of a particular X-ray spot is that it corresponds to one
of these (imaginary) sinusoidal waves of electron density. The positim
of the spot on the picture shows us both the direction of the wave and its
wavelength. If the spot is near the center of the picture, the corresponding
wave of electron density is one having a large wavelength.  If it is far
from the center it corresponds to a wave of short wavelength.  Thus the
oicter purts of X-ray pictures are concerned with fine details of structure
(high resolution), the inner parts with broad features (low resolution).
The direction of the spot, relative to the center of the picture, shows the
direction of the electron density wave.  Thus a spot vertically above the
center corresponds to a wave of electron density in the crystal whose
direction is vertical-i.e., to horizontal layers of high electron density
separated by regions of tow electron density. The intensity of the spot
is related to the amplitude of the wave-in fact the square of the amplitude
is proportional to the intensit,y of blackening of the plate-and an intense
spot, implies that t,his particular electron densit,y wave must be of large
amplitude for the structure in question.

a. Crystal I,atticc and Reciprocal Lalticc.  In this sec4ion w\`c shall explain
t'he concept of the "reciprocal lattice," which is nothing more than an
abstract way of representing the diffrartion pattern.  A crystal is :I t.hrce-
dimansiollal sl.r~lcture, but the pic:t,ure in Fig. 1 is clearly a tn,o-dilllctlsioll:ll
atrair; and KC must now confess that, it coI&~ins not t.hc whole diffrac:t.iun
pattern of a cbrystal but. only part of it.  Thn reader is to imagine that the
complete pahtern is a three-dimellsioll:Il latbice of X-ray spot's, of which Fig.
1 is just one particular plane-actually a plane going through the origin.
This t.hree-dimensional lattice is known as the reciprocal lattice of the crys-
tal, and it, is import,ant to have a gencratl pict,urc of its propcrt,ies.  X-ray
cameras are merely devices which allow a part of t,he three-dimcnsioual
reciprocal Iat,tiee t>o be recorded on a two-dimel~sioual photographic plate in
a systematic way so that spots can readily be itlent,ified ("indexed").  IN-
fcrent t,ypes of cameras may therefore present t,he same array of refiec%ious
arranged in different ways; but whichever way one takes the picture thcrc
is one characteristic of an X-ray spot whitah can always be obtained di-
rectly from it. This is its "spacing"; that is t,o SRY, the wavtalcngth of I hi
imaginary wave of electron density (`I Fourier component") to which it. cor-
responds.


138           I<`. 11. I'. f'lfI(`li .\NIl J. (`. KI~:l\`l)lll':W

X-ILAY ANALYSIS AND I'IWTEIN STRUCTUIW         139

As WC have alr~tly point4 out,, the Zarger the distnuce of t,he spot
from the center of the pict,ure (t,hat is from the origin of the reciprocal
lattice), the smaller the "spac,illg'`--hellce the word reciprocal. And the
stronger a given spot, the larger the amplitude of the corresponding Fourier
component; in other words, t,he larger the number of electrons (and there-
fore of atoms) clustered near the anti-nodes of the wave.  For example, a

  FIG. 1. A txpir:d S-MY phol~c~gr:~J~h of :I l)rotcir~ crystal. Notirc that the spots
form 3 reg~d:w 1 \\o-tJirl~ollsir)ll:tl latlice; IIO(P :dso the symmct.ry.  The picture shows
only a smnll Jurt of 1.110 wmplrte X-ray diffrsrtion pattern of the crystnl.  (After
Kendrew and KradI: finlmk wh,zlc rnyoglobin, type F, c projection).

st ro~~g spot, above: thcl origin (meridional) with a spacing of 1.5 A. implies
ttiat in t.lica crystal there are c*ctrtain horizontal parallel planes 1.5 A. apart,,
near whic4l many atoms c4ustcr.  Fiually, from the regrllar dimensions of
t,he rec:iproc*al Iatticbc OIIP c'an tlirec+t.ly calculate t,he dimensions of t,hc
rc*pclating unit, or lulit. (VII of t hc c*ryst,al-Land ~WRIISC of the reriprocsal
rrlationship, thca smallor t hc ullit wII the grratrr the dist,ancc apart of the
spots in thr rc>c+l)roc4 Ml ice. To rccaapit ulatc our niusic~al analogy, t,lie
urlit, caell dimensions :IW 1110 t Ilrc'P-tlirrleltsiotlal analog of the wavelength
of the "furldamrlltal IOIIC~" in :t musical sound.

b. Strzlcfurr lletermination.  The relationships between the real lattice-
t.hat is, the real three-dimensional crystal or, rather, its three-dimensional
repeating pattern of electron density---and the reciprocal lattice (or X-ray
pattern) are very intimate ones.  Given the position of all the atoms in
the unit cell of a crystal it is a straightforward, if sometimes lengthy,
matter to calculate the entire diffraction pattern of the crystal.  This is
interesting, but not often useful.  It is the reverse process, given the
diffraction pattern to discover the structure, which one more often has to
contend with.  Unfortunately it is by no means so simple to carry out.
There is, in fact, a fundamental reason why one cannot calculate the
unknown structure from the experimental data merely by the use of some
mathematical sausage machine such as a high-speed computer.  In order
to combine correctly all the (imaginary) waves of electron density which
build up the correct structure it is necessary to know not only the amplitude
of each of them (which one obtains from the blackness of the corresponding
spot in the picture) but also its phase-that is to say, how far each train
of waves is out of step with its neighbors-and this information is not
given by the experimental data.  In other words, the experimental data
contain just half the required information. Onk has, therefore, the curious
situation that, if the structure can be correctly guessed one can check it
against the X-ray data in a str$ghtforward way; but t,he structure cannot
be deduced from the data in a routine manner except in certain special,
and very simple cases. There are, however, various stratagems which
allow one sometimes to make a rat,her good guess at the st,ructure-espe-
cially if one knows something about it bcforc one starts; but guesswork
is always involved, and it, is this whicbh makes c*ryst.allography sol~lc*thing of
an art.  l'h: pursuit, of a strucbt,urc is rather like huntSing: it recluircs SOIIW
skill, a knowledge of the vi&n's hahitP, ant1 II ccartaiii amount of !OM
(*mining.

A numlwr of lhc slr:~li~gcn~s uscfld for solvitlg striirturcs will t)c mcntionctl lclrr.
Often lhe most useful is sllccr intuition, txwxl 011 cxJxricmx zntl on nht 11~2 chemists
hwe :drc:~dy discovered about the formnl:~ of the molecule.  For structures of motl-
eratc comJ&sity the most J)owerful is J)robnbl?; the I':ltterson synthesis, whose pro,,-
ertics and aJq~lir:iliona in t.hc I,iologic:rl field IXLVC l)ccn fully dcscribcd 1,~ one of us
(Kendrcn- :~ntl I'crtitx, 1049; J<cndrrw, 305-1:~).  J3ricfiy, it is n method which tlcws not
involve guesswork, of Jwescnting all 1 he ?(-my dnt a in such :L form 3s to tJispl:ly I ho
relnline, Imt Ilot, the :LIw~I~I~A, positions of JxGrs of atoms in the strrwllcrc.  This ni:IJ
en:rl)lc one t,o ol)t:Lin iniport:tnl. clllcs rd101lt the strllctllrc.


140            F. I!. C. CRICK AND J. C. KENDREW

X-RAY ANALYSIS ANI) PROTEIN STItUCTURE         111

say loosely that the heavy atom acts as a marker in the crystal.  They will be de-
scribed more fully later in the article.

Recently a number of claims have been made that phases can be directly and de-
ductively obtained by certain complicated mathematical procedures.  This, if really
so, would take the guesswork out of crystallography and would make the italicized
sentence above untrue. These methods certainly work for simple structures, but SO
far no structure has been solved with their help which could not have been solved by
the older methods. Moreover, there are good reasons for believing that this approach
will not work when there are many atoms in the unit cell, aa there always are in pro-
tein crystals.

c. Symmetry. The reader will be familial: with the fact that most
crystals have symmetry elements, such as rotation axes and mirror planes.
The symmetry of protein crystals is simpler than that of crystals in general,
because certain types of symmetry elements-those which involve reflec-
tion (mirror planes, glide planes, and centers of symmetry)-are forbidden
to them. This is because proteins are made up of optically-active amino
acids all of which have the levo-configuration. A Zevo-compound, acted
upon by a mirror plane, a glide plane, or a center of symmetry, gives a
de&o-compound (just as a left-hand glove gives a right-hand glove) ;
since dextro amino acids are not present in the crystal, these symmetry
elements cannot be present either.  This leaves rotation axes and screw
axes as the only permitted symmetry elements for protein crystals.  These
two terms are formally defined as follows:

a. A crystal has an n-fold rotution axis if the structure appears identically
the same after bcirrg rotated through an angle of 3600/n about the axis.

b. A cryst,al has an n-fold screw axis if the structure appears identically
the same after first rot,nt,ing t.hrough an angle 3600/n about the axis, and
then tratwlating it, a wrtaiu distance parallel to thr axis.
It is well krmvii that for :I. crystal t,he only axes possible are 2-, 3-, 4, or
Ci-fold, whcthw thc~y b(l rotatiorl axw or swew axrs.
`I'hrre is a wry c*losc~ wl:tt ioii bckwccn the syinmctry of t,he wystal

size of the unit cell, but only on its symmetry elements.  It is possible to
show by quite general arguments that only 230 different space groups are
possible for crystals, and of these only 69 need trouble the protein crystal-
lographer-all the others involve forbidden symmete elements. An
analogous term-point group-is useful in discussing virus structure.  It
refers to the symmetry elements possessed by an arrangement which is
finite in all directions, and therefore clusters around a point.

There is one more piece of jargon which we must introduce at this

PIG. 2. ,411 example from everyday life to i!lu;itr:tte the tliffer~nce I)ef,ivceri iiiiit
WI1 and nsymmet.ric rmit.  There :WP two mermaids in the Ituit wII, IllIt only out iu
the asymmctrin unit.  Notice that this patt,ern is the same upside down.


142             IJ. II. f'. f'ltlf'ti ,\NIl J. (`. Kl~NI)IlI~:\\

S-H.\T ANALYSIS AND PROTEIN STIlUCTUl1E         143

asymmet tic unit may c~onlain two (occasionally more) moLecu\es not
related by symmetry clrmcnt.s of t hc space group (if they were so r&ted,
the asymmetric unit would be half t,hc size and would contain one molecule) ;
or, if the molecule consists of two identical subunits, earh subunit may be
a single asymmetric unit.  The latter state of affairs exists in horse hemo-
globin crystals.  Notice t,hat the environment of each asymmetric unit is
the same as that of any other (see Fig. 2), so that if it contains one molecule
it follows that every molecule in the crystal has an identical environment.
If, however, the asymmetric unit contains more than one molecule, it
follows that all the molecules do not have the same environments; and
the X-rays do not rerognize in a simple manner that these identical but
differently arranged molecules really have the same structure.  This will
only show up when such a structure is rompletcly solved.

2. I~<flraclion frnm a lVm

The diffraction of X-rays by a fiber is not different in prinriplc from
diffraction by a crystal, but there are a certain number of differences in
practice.

A fiber is not a single crystal.  It is best thought of as a collect.ion of
small crystallites, generally cmhcddcd in a certain amount of amorphous
material.  Fibers are uswdly hilt up of polymers, that is, of long molcculcs
constructed by t,tic indcfinil~c rcpctition of idciitiaal moncjmcr units.  Thus
a single chrmif4 molccwl~~ may rnn t,hrough sevcsral crystallit,es; t.he
monomer in fibers c'orrcsponds to the molecule ia single crystals.  In a well
orit~ntctl filw t)hr wyst.:tllitrs 211 lie \Ah oiw axis (the " liljcr axis") almost.
parallrl to t.hc Icngl.11 of I he lilwr, tjul 1.110 oriwjtat,ious around t,his dircct,ion
arc random or warly so; if Lhcir oricntat.ions were all t,he same the st.ruc-
turc w~nltl rwwt to a siiiglc cryshl.

It. follows that if w t.akr ail iX-r:ly pic+rire of n fiber thr rrsrdl~ will tic
similar to whut. w wo11lt1 get if WC photographed a siuglc crystal and
continually rotat.rd it abollt one axis during the exposure (Fig. 3).  This
means that, instead of photographing OIIC part, of the reciprocal latt.icc at
a time OIJC ol~taitjs alrr~ost~ the whole of the t.hrcc-diInrlrsiolIal reciprocal
Int tiw on the same (1\\-o-tlit~~c~rjsioll:LI) phatographic~ plate.  Thus it is not
always wsy to IIIISIT:~~I~J~~~ t ho X-ray picbrc and so to otit.:iin n,n cwwt
itlca of the rwiprw:~l Iat t iw whic41 prodrrcwl it.  Cwrlpurc the difficwlt,y
of visualizing :i person from a scrics of snpcrimposcd snapshots taken
while hc stood OII u twwl~~it~~ tahlc~, in spite of whicah c*ertain fcat,nrcs wnld
easily tjr rst:~Misi)wtl for cx:~~nplc one wuld see t,hat, the subjccl-`s eyes
wwc ahovc his nionl h."

The information which can most easily be obtained from a good fiber
photograph is the crystallographic repeat in the direction of the fiber
axis-this is shown by t,he sparing of the meridional reflections3; in favorable
cases it may be possible to deduce the other dimensions of the unit cell as
well.  The symmetry is often difficult to deduce directly, but can some-
times be inferred from the dimensions of the unit cell. Finally, it is
ushally possible to get some idea about where in reciprocal space the
strong reflections occur, and if the unit cell has been'identified, to locate
them precisely in the reciprocal lattice.

In a poor fiber the crystallites are only approximately parallel to the
fiber axis, and this will cause the X-ray spots to be drawn out into circular

a

arcs which mukrs it n~orc ditfiwlt to lwntc t hrm in rwiprwal apaw,
alt~hough thr spwing of the spot (given by the radins of the arc) can always
hr measured.  In prarticr all fiber photographs show this effect. which
also mnkrs it more difficult to get an accurate measure of the intensities
of the retkxtions.

What wc have so far I~CTII tlcscrihing is the best, t,ypc of fiber photograph.
Very oft,cn they we less ncll Iwhawd than the spwimcn illnstratcd itI
Fig. 3. For a start, fiber diagrams rarely extend so far in reciproral


144             I<`. II. f'. (!111(`1< ANI) .I. f'. Kl~:NI)I1EW

X-ItAP ANALYSIS AND PIWTEIN STIlUCTUllE         l-15

space as good single rrystai photjographs, the X-my inteusities fading
away it1 the outer parit of the picture.  The photograph is oft,en coufused
by difrusc background scatter of X-rays from amorphous parts of the
fiber. Even worse trouble comes if the crystallites themselves are dis-
ordered. We have so far considered the case where small regions of
fiber exist which, within themselves, are perfectly crystalline, in three
dimensions, and these we have called crystallites; or, in other words, we
have local three-dimensional order.  A common disorder is that of chain
direction-chains may run upward or downnjard at random within an
otherwise regular lattice. But there may be no three-dimensional order
at all-only one-dimensional order; that is to say, although the polymer
molecules all run (approximately) parallel to the fiber axis, there is no

~ot~rc~s~)o11tlc~11(~e Ijet wee11 11c+hhorir1g &ins, which may I)(> displaced up or
t1ow11 relative to one a11ot.hcr in a random 1va.y.  A fiber disordered in
.tliis way st iii shows t.lic c~rystnii~~grupliic~ repeat in the fiber direction, and
the X-ray scbatleritrg produc*es iagcr-iiues, or horizontal streaks, on the
photograph. l%ut t hcsrcl arc IIO tlisc774c sp0ls on the layers (with one
esc~c~ptioti) ; instead t li(~r(~ is :i caollt,illuous \.ariation of srat.terrd intensity
aloiig earl1 li11e.  S11rprisir1gly rirough in sonic (~irrumst,a1ic~rs this may he
a11 advantage rather fha11 the reverse, pro\-idi1ig cvcn more infor1natio11
th:111 :i phot ogrnph cBo11sist i1ig of tlisrrctc~ spots.  A11 example of surh a
photopraph is shoddy it1 Fig. 1.

n. 7'lw I~~twjvrcffllin~~ I![ lzihcr l)irup~?ls.  X-ray pirturrs of fihc>rs are
0ftf~1 too poor to allow 011~' t 0 IIS(' the nicbt hods of minlysis rriat,omary for
si1igi1~ rrystais: it1 p:11~Ii~~1il;1r 011~' 11suaiiy (%niiot hope to "see" t hr atoms
(`\.(`II ~~~I~!II 111~ f~or1M sl 17~4 11r(' 11:~ IIVV~I tliscfio\~c~rc~tl.  `1'111~ i1itf~rpr(+:il ion
of fitjclr diagrams is :I spcG1l art, t herc~forc~.  `1`1~~ mr~thotl of at tac*k is to

t,ry t.o deduce t.he symmetry of the fiber molecule from the X-ray picture;
then to build scale models having this symmetry; and finally to show that
only one of these models will fit all the available data, X-ray or other.
Thus unless one knows in advance the chemical formula, or at least its
most important features, the problem is almost hopeless. In addition,
information derived by other techniques such as measurements of infrared
dichroism is often invaluable.

The symmetry of a fiber molecule is almost always a screw axis.  The
reasons for this are explained in the next section, where it is pointed out
that there is no reason why a single fiber molecule should not have a
nonintegral screw axis. For example, 3.6 monomer residues per turn is
18 residues in 5 turns.  Such a structure will have a "true repeat" after
18 residues, but this is not a very fundatnental characteristic of it, since a
very small twist, of the molecule would give a diRerent "true repeat"
or even no true repeat at all.  (Th us in our example a twist from 3.60 to
3.61 residues per turn would lead to a repeat of 65 residues in 18 turns.)

It might be thought that.the absence of a short repeat distance would
make the problem impossibly difficult to solve, but fortunately helical
symmetry often produces striking effects in the photograph which imme-
diately reveal its exist,ence even when the screw axis is nonintegral.  Until
a few years ago t,he theory of the effects produced by nonintegral helices
in crystal diffraction patterns had not been worked out, simply because in
ordinary rryst,allography there is no occasion for it,.  It, was in fact only
developed (by Co&ran et al., 1952) in response to the proposal by I'auling
and Corey (1!)51:1) that. t,hr n-polJ.l)c`l)t,iclc's w(xr(: built. 1111 of 11o11i11t(!gral
helixes, narneiy t,hc now famous a-hriix wit,h its 3.0 residues per turn and
1.5 A. per residur to whirh n-c have already scvrral times implic~itiy refrrrrd.
Armed with the appropriate t,hcory it, is often possible to recogtlixc~ ihc:
hrlirai n:tt.urc of a fihcr structure at, a glaric*c, aiid sonietimrs to spcrify
t'he main parameters of the helix and it,s subunits with very little trouble
indeed.

There is a (hatch, however.  Imagine that a shc*ct of paper has hee11
fold4 around the strucbt.ure in t,he for1n of a cylinder, and a mark put WI
thp paper at. corresponding points in earh asymmctric~ unit.  If this paper
is uow openctl out we shall obtain a patter11 of the t,ype shown it1 Fig. 5,
whirh we shall rail a ne&diczgmm.  Now what. our helix t,heory is givit1g
us is iii CSSCII(`(~ the net-diagram of tlich st,ruc4,uro, or :it Ic~~4l, 0111: ol' :i s11lalI
number of posxihlo net-diagrams.  The posit io11s of t hc poirlts of a part ir-
uiar net arc 1111aml)igr1onsiy determi11rt1, Ijut Ilot, Ilow the at ems i11sitlo
earh of t.hcm are arranged, nor, what, is more importa11t from thr prcsc~~t
point. of virw, how cnrh net,-point is chcnuidl,y at taf4iccl to its iic~ighhors.
`1'1111s t lit 11ct4:1gr:1i11 of Fig 5 might c~~1~rrsp011d to ariy of the t hrccb arr:Ing(~-
nic11ts s110w11 by the arrows, or ir1dcctl to a11 irifi1iilr rir1nil)cr of ottic~rs.


146          F. II. C. CRICK AND J. C. KENDREW
Note that some of these possible arrangements have a single chain of
subunits winding upward, some more than one chain.

To solve the structure completely, and thus resolve this ambiguity in
the net-patt.ern, it is usually necessary to build models-the X-ray data
alone are not sufficiently restrictive, and one's knowledge of chemistry
must, be invoked to fill the gap. Generally the chemical nature of the
subunit is known (in polypeptides it is simply -NH-CO-CHR-),
and, as indicated in the next section, many detailed stereochemical data
are available from the literature. Armed with all this information, together

             --            @628 R
FIN;. 5. The helix-net derived from wide-angle diagrams of collagen.  Hack dot's
represent the relative Iorations of "centers" of equivalent grollps of atoms 011 a cy-
lindrical shell of radius l? (with axis vertical).  The vectors n to d show several
possil,ilities for connecting the l)Iack dots 1)~ 7 mcnns of polypeptide chains to rwm
hclirul structurw. The rcrrnt mod& of rollageu all use cnnncction c. As can be
sew by studyillg the figure this connection corresponds to three separate chains s-ind-
               .
iilg ro1tnd the s:mw nus. (OIIP c-hain joins 0, 3, 6, 9; another 2, 5, 8, and the third
1, -I, 7, 10.) (Ilc:w, 1055.3

\vith :niy d6~rivc~tl froni slll)sitlinry tc~chtliqrws, it is possible, with f>xpericncC,
10 tl(B\is:r :L s:c41wn(: of sgst(wa1 its n~otlrl building whkh will enable OIIC to
(~linlitlato nwrl~ all I IIV illlillile iiumbcr of throretiwl nays of joining up
thcl poilits oti the iwt-di:igr:lnl.  If alI bnt, one of tliew ways c&an be elimi-
ll:ltf~(l, :,ll(J if its t \w()rd ic*:ll tlill'rw1 ion pattorn gives rcasonnble agreement
\vith the ot,srrv(ad ,x-ray picature, tlrc strwtnre is essentially solved.

         X-RAY ANALYSIS AND PROTEIN STRUCTURE        147

In any postulated structure the bond distances and bond angles must
have acceptable values. The values to be regarded as acceptable are
those derived from X-ray studies of small molecules, such as amino acids
and small peptides, and the chance of any large deviations from the average
values is negligible. In the field of proteins much of the work of deriving
a canonical set of dimensions has been done at the California Institute of

VI<:. 6. A tli:~gi~nmm:ltic reprcscntation of a f111Iy cstcntleti ~~olyprq~titlc rhnin
with tJlc lwntl Iengt IIS and Imnd ntlgles derived from crystal structures and other ex-
perimelkd evidence. (Corey and Patlling, 1953.)

l'erhnology, nnd the standard values for t hc polypcplkle c+ain are those
given by Corey mid l'auling (1953) mtl sl10w11 ii1 Fig. 6. `I'hcir n1051,
import.:mt. featiire is that t.hr six atoms of t Iw prptide group (--C'- -Cl0 ---
NII-- Cm- ) inwriably lie ill a phmc, or wry nearly so.  This is attribllfc~tl
to IWOII:~INT, whkh is also rrsponaiblc for the r&l ivrly shori II N---(Y)
bond. The strntrt,nre rPt,ains freedom of motion in spite of thr plnllnrit~
of the prpt,ide bond, rotat,ion being possible about the two single bot~ds
at,tachrd t,o each C, at,om.


148           F. II. C. (:IlI(`ti i\NIJ J. C. KI~NIJILRW

X-RAY ANALYSIS AND PROTEIN STIiUCTUItE

14Y

Apart, from t hc c:ov:tlcrlt I,olltls---llsrlally known in advance from chemical
st,udies --t,he most important links in structures of the type we shall be
considering are the hydrogen bonds, such as NH. . .OC or OH. . . OC.
Experience has shown that in practice virtually all the NH, CO, OH or
similar groups which the structure contains are somehow linked up in
hydrogen bonds; but the particular groups paired to one another cannot
be predicted.  The stereochemical conditions which a hydrogen bond must
sat.isfy are not so restrictive as those governing covalent bonds, but the
bond distance and bond angle must fall nevertheless within certain limits,
which have been discussed by Donohue (1952). Finally there are the
van der Waals' contacts between neighboring atoms.  These are not
directional bonds, nor are the permissible distances very precisely deter-
mined. However, a structure must not have van dcr Waals' contacts
which are unacceptably short.  All in all the conditions imposed by
stereochemistry are very severe, and the number of configurations allowed
by them for a structure is oft,en very small. This does not necessarily
mean that all the allowed configurations can be simply discovered.

It is considered nowadnys good practice, when proposing a structure for a fibrous
molecule, to give coordinates for its atoms to the nearest 0.1 A., or preferably 0.01 A.
This does not implv thnt the nnthor thinks he knows the coordinates as accnrately as
this; it merely inciicates t,hat 3. confignration giving :xceptsble bond distances mid
angles i9 at lcnst possible. SIxxificntion of the exnct coordinates allows this to be
checked by others. The f:lct t.h:rt the coordinntes mny be slightly wrong is not a valid
excllse for fnilinn to present :I consint.rnt set, of them.

Apart from these st crooc~hcmi~nl ronsidcrations the most important
grnernl princ*iple in st,ructural lvork is symmetry. It is a good working
rlllth that whcrr possibh, the snrno pnc*king arrangements {vi11 be used over
. and ovw :rg:litl irl :L atrwturc.  11. follows that, generally thcrc: will be
symmet,ry dvtncwts of one sort, or another, and since the prcscnre of these
.can often be tlctln~ctl raf.her diret%ly from the X-ray dnt,a they are of
considerable impnrtancc in tJacakling a st.ruc%ure.  Of course, as we have
already indi&ed, true crystals almost alwa.ys possess symmetry elements.
But this is oftrn t.ruc CJf polymer molcru!es t,oo, especially if they have
been enrouraged to take up a regular configurat)ion by drawing them out
into fibers. Otherwisr they are called amorphous, and are then not very
suit,able for study by X-rays (S(V the next sert,ion).
If a fiber st rnc%rrr claw rrpmt, the most likely symmc+ry element is a
scbrew asis: a pure translalion WI be thought of as a special case of a s(`rew
axis n-ith zrro rot.atioH, and is comparatively rare.  Ot,her symmetry
elements (mirror nntl glide pl:lIIes) are theoretically possible but are most
improbnhhh in pr:lc*tic*c; indrotl they are impossible if t.hc polymer c*ontnins
asymmetric carbon atoms of only one hand.  There are only two excep-

tions-if there are several chains in the structural unit they may be related
by a rotation axis parallel to the axis of the fiber; and there is a possibility
of dyad axes perpendicular to the fiber axis (as in deoxyribonucleic acid
(DNA)). But, usually such symmetry elements occur, if at all, in addition
to a screw axis.

Unless it be a simple dyad, a screw axis generally gives a structure a
helical appearance. Helices are ubiquitous in biology precisely because
biological structures are very often made of small units linked together,
end to end, to make up a larger entity.  In recent years it has been realized
that a single isolated helix may have a screw axis which is noncrystallo-
graphic; that is to say, n (as defined on p. 140) is not restricted to 2, 3, 4,
or 6, but may assume any value, integral or nonintegral.  A nonintegral
value means merely that a single turn of the helix contains a nonintegral
number of subunits. Note that in an isolated helix the environment of
each subunit is the same whether n is integral or nonintegral; and there is
no reason why a nonintegral value, such as 3.6, should not be assumed if
packing relationships betweeii neighboring residues in the helix are best
satisfied in this way.

If, however, an attempt is made to pack such helices into a `regular
lattice, the relationship between asymmetric units in neighboring helices
will not be the same everywhere unless the screw axis is 2, 3, 4 or 6-fold;
in other words a true crystal rannot be formed unless this condition is
satisfied, because it can be shown that these are t,he only symmetry axes
(rotation or screw) which allow a pattern t.0 repeat indefinitely ii1 t\vo or
three dimensions. True, the chain molecule in a crystal may have a 3.6-
fold axis of symmetry, but t'his symmetry cannot, he apparent in the rela-
tions betn-ccn it and its neighbors-it is ,zccitle~ltnl from the point of vie\,
of ttic! cbrystal and c-antlot form part of t hc spare group.  Such a situation
could only arise if the interactions between neighboring chains were
relatively weak. n nonintegral screw axis is likely to appear when the
znteractions of a$ber molecule with itself are much stronger than its interactions
with its neighbors.
pseudo-axis.   In crystallographic jargon a nonintegral screw axis is a
     It need not even apply to the whole of t,he fiber molecule.
Thus the backbone of a polypeptide chain might have nonintegral screw
symmetry, but not the distal ends of the side chains which are largely
influenced by their neighbors.

If a small number of chains, each with a nonintegral screw axis, is plncacd
side by side, t,hcy may t.ry to interact in a regular manner, for example,
by forming interchain hydrogen bonds. If t,hey are to remain strictly
parallel, regular interact,ion will not usually bc possible since the nonint,cgral
axis will cause the interrhnin bonds to get, out of step.  Sometitnes, how-
ever, it may happen that if the individual (helical) chains coil slowly


150          F. It. C. CJlJCK l\NI) J. C'. KI<NJ)Itk%                             X-RAY ANALYSIS AND PROTEIN STRUCTURE         151

around each other there is again a possibilit,y of regular interlinking, the
small additional twist bringing the chains into step.  Such a distortion
destroys t,he exactness of the helical configuration of the individual chains,
but it is often so slight that t,he chemical bonds which brought that con-
figuration about are not appreciably distorted.  Such a structure is known
as a superhelix or coiled coil, and an example of it is probably a-keratin
(see Fig. 13). The smaller, primary, helix is referred to as the minor
helix, and the gently helical path followed by its axis is called the major
helix.

Nonintegral screlv axes arc not found only among fibrous molecules.
An interesting exantple, recently discovered, is the rod-shaped tobacco
mosaic virus (TM\`).  JI ere the asymmetric unit is liot a single atnino
acid residue, but the whole of a globular protein Jnoleculc of molecular
weight &bout 17,000. In other words the virus particle consists in the
main of a large number of identical protein molecules stacked in a helical
array. The asymmetric unit is a single one of these molecules, which
thus all have the same environment.

We have so far considered symmetrical arrangetnents of subunits which
are theoretically infinite in extent.  In other words, as far as their sym-
metries are cottccrttcd an cu-helix or a molcculc of 1'l'GV Inight go on forever.
111 fact,, (Jf (!OlJrSC, they (10 IlOt (10 SO.  It, is not clear what it is that causes
t,hem to t.ermittat,e at a particular point, but it c*ertaittly is bot the require-
mctti,s of sy~tttnc:t,t~y. Wo shall ~ottclutlc hy making brief reference to
synitnrt.ri~al arrtittgt~tncttts of subuttits which are jinitn iii rxt,ettt, sittc~e
sucah arrattgtmettts have hrett shown vc'ry rerctttly t.o bc relevant to the
st ructurcs of spheri~~at viruses, as we shall itidit~ate in Secttioti V. The
r~strict.iotts on tltcb sytnmrtry elements allowed in swh arrangement,s are
ttiorc st ritigctit tltatt rvcr; ot~ly rotat,iott axes arc pertnissihlr if the subuttits
arc ttottc~ttntttiotnorplt~)tts (optically artivc).  (It is not difficult1 t)o see that
srr(3v axes Rcttclratc new asymtnetric~ units nfl in$tbillcm---owing to the
ctemettts of trattstat,iott ittvolvctl-and must be itt:~dmissihlc in a fittit,e
systrtn.) Three gc>ttcral typos of point ~TOUI), or finite collect.ion of sym-
nict,ry clenicnts, (see p. 141) are possible: first,, those coJlsisting only of
                                                     . .
art n-fold rotatiott axis (n = any integer) ; second, those possessmg m
adtlit,iott tlyad axes pcrprtttticutar t,o the main axis; and Gtird, the cubic
pr)int groups.  It is thr Iattcbr which arc important in t,he present ronnet'-
tiott hec~ausc I ltry gc>ttc:rate isoditncttsiottal arrattgcnl~~tlt.s, sttcbh as spheric*nl
virtts;cs arc ktto\vtt to I,(>. `I'ltrrc are tltrcc c*ttbic poitit, groups which will
itttprest us. `Ilt(: first has four threefold axes, arrattgctl t(\trahrdrally, :uld
a ttumhrr of tlytul UPS. l'hr serond has fourfold, attcl the t.hird fivrfoltl
axes as 1vf.11 as thrrc- and twofold axes. The properties of these three

poiJJt groups, known as 23,432, and 532 respcctively,4 are set out in Table I,
together with the number of asymmetric units in each and the names of
the regular (or Platonic) solids which possess these symmetry elements
(among others).

                     TABLE I
     The Three Non-Enantiomorphous Cubic Point-Groups
Crystallographic
description   Number and type of    Number of
             rotation axes    asymmetric units Regular solids possessing the
                             same symmetry elements
    23     13 dyad           12       Tetrahedron

432

532

14 triad
i G dynd
4 triad
3 tetrad

15 dyad
IO triad
6 pentad

24

60

i Cube
Octahedron

Dodecahedron
Icosahedron

Q. General Remarks

In this section we shall briefly consider which aspects of a structure
are most clearly "seen" by the X-rays.
cultivat,c his "JX-r:ly eye,"       This should help the reader to
           lack of which has so often caused misunder-

standing in the past.

We have spoken so far as if X-rays are scattered only by rcpeat,ing
structures such as crystals; but this was a sitnplifiration, merely for didactic
purposes. The fact is that X-rays are scattered by e~cr?/ part of the
specitnen, but there will only bc sharp spots on the X-my photograph if the
electron demity is periodic in space.  Ot,ltermisc the photograph will show
smears, smudges, or merely diffuse blackcnittg.  If part, of the strucature
is periodic, part, aperiodic, then there will he sharp spots superposed on
smudges or diffuse background. Since a given amount, of blackening
shows up much more clearly if it is collected into a spot than if it is spread
over an area, and since spots are easier to interpret, our attention is usually
concentrated on them rather than on the smudges.  So when we "solve a
structure" we are generally describing those parts of it which are regular,
that is, which repeat. periodic~ally in space.

fh~ppose wc have a structure which dops for 11~: most part, rrpcat, rcagr~-
larly, with the exception that one small part, of the unit, cell is irregular,

' Pronounced two-three, four-three-two, and five-three-two.


F. II. C. (!IfI(!K ANJ) J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE

153

varying in a random manner from cell to wll. What will the X-rays see?
Strictly speaking, of course, they respond to the entire structure, but the
X-ray spots "see" only the average unit cell. Such a situation may be
met with in fibers, which may have a random arrangement of side chains;
and also in crystalline proteins, where much of the solvent in the unit cell
may have no regular structure. It is true in some measure of all X-ray
photographs owing to the random thermal motions of the atoms in all
crystals. All these effects to some extent smear out the average electron
`density and reduce the amount of fine detail which we can expect to see-
which means that those parts of the reciprocal lattice corresponding to
small spacings and fine details (the parts far from the center, that is to
say) are reduced in intensity. In protein work the trouble is particularly
acute, a?d the X-ray intensities from a protein crystal or fiber fall off
with decreasing spacing much more rapidly than do those from, an ordinary
organic crystal; so the atoms in the structure of a protein, if we eventually
succeed in "seeing" them, will certainly be smeared out somewhat.  This
will naturrilly make the interpretation of the results more difficult, even if
they are known to be correct.

What would be the effect on the diffraction pattern of minor variations
in the amino acid composition of the protein-a change in a single aide
chain, for example? Strictly speaking, almost every X-ray reflection is
influenced to some extent by every electron in the unit cell.  But a change
in the few atoms making up a single side chain represents a very small
change in the electron density distribution in the unit cell as a whole
(protein side chains all have about the same electron density, and we may
assume that they are generally packed close together without leaving any
gaps which cannot. at once be occupied by water molecules) ; hence the
average effect, of slrrh a change on any given reflection is slight, generally
. dell \rithin the error of measurement.  Small changes in a few reflections
may, however, bc just obscrvahlc. It follows that we cannot expect to
show by X-rays in any simple manner whether or not two very similar
`protrins are in fact idet&al.

X-rays see electron density, not, atoms and bonds.  Therefore they see
a structure in terms of clcatron density and not as a chemist would see it,.
For example, they cannot even distinguish in a simple way where one
molecule ends and t,he next boginP--one must deduce this indirectly from a
knowledge of bout1 dirnrusions.  On the other hand they are very sensitive
to FYCII slight cbhanges in the position or orientation of a molecule wit,hin
the unit cell; cshnnges of a killtl to which protein crystals are peculiarly
susceptible.  Difficulties of this kind arc not impottant when t,he correc*t
three-ditncrlsional clwtrorl tlerwity map of a struc+ure has been obtained,
but they have to be borne in mind during the early st,a.ges.

6. Summary

A crystal is made up by the indefinite repetition of a small three-dimen-
sional unit, the unit cell, consisting of a small number of chemical molecules.
It generally possesses symmetry elements, and the particular set of them
which is present is known as the space group of the crystal.  (Similarly
for finite, nonrepeating objects exhibiting symmetry the set of symmetry
elements is called a poin.8 group.)

X-rays are scattered by the electron density of the crystal.  The diffrac-
tion pattern can be thought of as a regular three-dimensional array of
spots, known as the reciprocal lattice. Each X-ray spot corresponds to bne
imaginary wave of a wave analysis, or Fourier analysis, of the electron
density. Ita position in the reciprocal lattice shows both the wavelength
(or spacing) and the direction of the wave. Its intensity is related to tht?
amplitude of the wave. Its phase is not given by the X-ray data.  There-
foie one cannot deduce the structure directly from the X-ray pattern,
except in very simple ms; but, given the stiucture, one can always
calculate the pattern.      -
What can we learn directly from the X-ray pattern of a crystal?  The
dimensions of the unit cell can be directly calculated from the dimensions
of the reciprocal lattice. The symmetry of the crystal is closely related
to the symmetry of the reciprocal lattice, and for protein crystals one can
almost always deduce the space-iroup from a study of the X-ray pictures.
Hence, knowing the volume of the unit cell, the size of the asymmetric
unit can be calculated.

Powder patterns are familiar from industrial practice, and are obtained
by passing a beam of X-rays through a crystalline powder. They can
be thought of as the superposition of a large number of single crystal
pictures of crystals in every possible orientation relative to the X-ray
beam. Their characteristic feature is a set of concentric and sharp but
continuous rings of blackening; the radii of these rings correspond to the
spacings of the priuaipal lattice planes in the crystal.  One can think of
them as generated by rotating the reciprocal lattice about all possil)lc
axes through its origin, and taking a central section of the resulting set of
concentric spheres.

A $ber is usually a collection of small erystallites, whose "fiber axis" is
nearly parallcl to the length of t,he fiber. X-ray pictures of fibers arc
generally more confused and less perfect than those of single crystals,
because the structure of most fibers is only partly ordered, so that, some of
t,he X-ray intensity is thrown into regions of difruse scattering and not
into discret,e spots.

Fibers often possess nonintrgral screw nxcs of symmetry, and thr prrs-
ence of these can often be deduced by inspection from the X-ray phot,o-


154             F. II. C. CIII(`K ANI) J. C. KENIIIlEW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        155

graph. Nhcrc adequate st,crcorhemic:al information has been made
availahlc by studies of the sWctures of small molecules, it is sometimes
possible to guess the structure of a fiber by careful model building, using
accurate scale models.

X-ray diffraction is only really useful for studying that part of a struc-
ture which repeats regularly in space.  By X-ray techniques it is easy to
show that two structures are similar, but very difficult to show that they
are identical, at any rate when the molecules are large.
The importance of symmetry, whether in a crystal, in a fiber, or in a
virus, is that it allows the same subunits to be' used in identical environ-
ments, repeatedly in the same structure.  Presumably for reasons of
economy in manufact,ure, Nature is addicted to the mass production of
identical small units for building up large constructions.  These tend to
aggregate in a symmetrical manner which can be "seen" by X-rays.  This
is why X-rays are useful in studying biological structures. And this is
why symmetry is t,he most important of all crystallographic ideas for
biochemists.

III. FIBROUS PROTEINS AND SYNTHETIC POLYPEPTIDES

In this section WC shall give a brief account, of recent work on the small-
scale strurturc of fibrous proteins and syuthctic polypeptides.  The latter
serve as model stru&rcs, simpler than naturally occurring materials
because they car1 if desired have uniform side chains; and they have pro-
vided some of the most important clues to the configurations of collagens
and kcral,ius.  A more dcl,ailcd account of X-ray st,udics of fibrous prot,cins
up to 1954 has been published by Kcndrew (1954b), while the most recent
advances have bctrn reportrd hy Kendrew and l'erulz (1957). As stat,cd
in the introdllction WC shall not discuss in t,his review the large-scale
structure of fibrous proteins.

1. Synthetic Polypeptides (and Sillc)

The polypcptidcs which have proved most useful from the present point
of view arc those in which all the side chains arc identical, though random
copolymers having two or more types of side chain have also been synthc-
sized. The dcgrcc of polymerization is gcncrally fairly high-several
hundred residues would be a typical value-so that the molecules are
genuinely `I fibrous."  Oriented films or fibers can be produced by various
simple techniques and these have occasionally given astonishingly good
X-ray fiber diagrams.

It was tliscovcrcd rarly that, synthetic polypcptidcs form two main
types of st rlu+urc, kuown as the (Y- and the @- forms bccausc they are
analog()us to the a- and &forms of kcratin.  By appropriate choice of

solvent either one or the other can be precipitated from solution at will.
Thus m-cresol usually gives the a-form, while the &form is precipitated
from formic acid.  The two forms give quite different X-ray patterns and
they can also be distinguished by means of their infrared absorption spectra
(as shown by the extensive studies of Elliott and his coworkers, 1956; see
the review by Doty and Geiduschek, 1953).

a. cr-Polypeptides.  The best X-ray photographs of polypeptides in the
a-form have been obtained from poly-L-alanine (Bamford et al., 1954;
Brown and Trotter, 1956) and from poly-r-methyl-L-glutamate (Bamford
et al., 1952, 1953).  These photographs have very characteristic features,
and so far all polypeptides in the a-form have given similar X-ray patterns,
though with varying degrees of perfection.  The most detailed studies of
them are those carried out by Bamford and his colleagues at Messrs.
Courtaulds Ltd (Bamford et al., 1956) and described in their recent book.

The main features are a strong meridional reflection of 1.5 A., discovered
by Perutz (1951); a strong "layer line" of reflections with layer linespacing
5.4 A.; together with a strong reflection, spacing about 10 A. (depending
on the side chain), on the equator.

It now seems certain that the configuration of the a-polypeptides is
based 011 the a-helix of Pauling et al., (1951).  This is a folded configura-
tion of the mniu chain; the positions of the atoms in the side chains beyond
Cp are not specified by it. A diagram of the a-helix is given in Fig. 7.
The polypeptide chain backbone follows an approximately helical path
having a pitch of 5.4 A. and containing about 3.6 amino acid residues per
turn.  The translation per residue in the fiber axis direction is thus 5.41
3.G = 1.5 A.  The C, carbou atoms, to which the side chains are attached,
are all at a radius of 2.3 A. The whole structure is held together hy
hydrogen bonds running from the NH of one pcptidc group to the CO of
another peptidc group on the next turn of the helix.

The arguments in favor of the a-h&x have already heen rather fully
set out elsewhcrc (Crick, 1954) and will bc only very briefly rccapitulatcd
here.  From the X-ray pattern it is possible to deduce unambiguously the
parameters of tlhc nonintegral screw axis: thcsc are a rotation of about
100" and a translation of 1.5 A.  From the density of the specimen and
the dimensions of the unit cell it can be shown that the asymmetric unit
consists of a single amino acid residue.  The positions of the strong reflec-
tions, together with the fact that a-polypeptides can be stretched into a
p-form, show that thcrc is only oue polyppptidc chain per lattice point,,
rather than two or more intertwined.  Only two st,ructures can he built. to
this specificaat,iou: one, the cu-h&x, has the same paramctcrs as those
observed; the other (described by Bamford at al., 1952) is very much less
satisfactory stereochemically.


156            F. II. C. CRICK AND J. C. KENDHIGW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        157

A quite different approach is to build models without assuming any
particular screw axis.  It can be shown that if a polypeptide chain is to

        I                                         I

FIG. 7. I)r:twings of the Icft-handctl and right-h:~nclcd a-heliccs. l'hc 11 :tnd II
groups on the a-carbon atom are in the correct position corresponding to the known
conligur~tiw of the I.-:mrino nrids iu proteins.  (I,. I'nrding and 11. B. Corey, unprtb-
lished drawings.)

be folded ht~lieally :ml st~al~ilizc~tl l)y internal hydrogen l)onds, as l.hc infrared
evidence suggests (;1int)roac: and Elliott,, 1!J51), 011ly a few siniplc arrnngc-
mrllts are stcrco~l~c~i~~ic~:~lly possihh~.  Alorcovcr thcbsc ran bc cn~unrr:~t~rtl
systematically so that OIIP (WI bc ccrtaiu that none have bocn ovcrlookcd.

All of them have been built by Donohue (1953) and arranged in a stereo-
chemical order of merit.  By any criteria the o-helix is the best, though
one or two of the others cannot be totally excluded.
The strength of the case for the a-helix lies in the fact that both of these
approaches give the same answer.

As originally described the a-helix was really two structures, since its
backbone could follow either a right-handed or a left-handed helix.  These
are mirror images of each other; but there are two possible ways of adding
side chains to the C, carbon atoms of each, giving in all four structures, of
which two are mirror images of the other two.  Thus if we confine our-
selves to t-polypeptides there are two possible structures, one with a
right-handed helix, the other with a left-handed helix, but not mirror
images of one another.

Until recently it was not known which of these two was more stable,
but it now seems likely t,hat the right-handed one is the more common for
L-polypeptides. This had, been suggested much earlier on structural
grounds (Huggins, 1952); the newer evidence comes in part from studies
on optical rotation, both experimental (Elliott et aZ.,1956; Yang and Doty,
1957) and theoretical (Moflitt, 1956 a,b; Fitts and Kirkwood, 1956a,b).
In addition, a critical reconsideration of the X-ray data for poly-L-alanine
(Elliott and Malcolm, ,1956a). has shown t,hat the agreement between
calculated and observed X-ray intensities is greatly improved if the assump-
tion is made that t,he chains are polarized at random either llpmard or
downward in the strurturr; and that if this is done the right-handed
a-helix fits the data muc*h better than the left-handed.

Thcrc is a need for still more detailed comparisons between observed
and calculated data for a-polypcptides, and these should make it) possible
t)o refine t)lie structure even further.  The presence of "forbidden" rcflcv-
tions, albeit weak, on the meridian of the poly-L-alanine pattern illdicatcs
that the a-helix must he slightly distorted in t.he solid state, probably
owing to the mutual interference of neighboring chains.  There must also
1~ distortion in mixed m-copolymers, since t,hcse give a I.5 A. rCflW!~i~Jll
whose spacing is slightly less than usual, and ahnorma.lly broad infrared
ahsorption bands (Bamford et al., personal communication). filotl(4
building suggests that in this case the distortion is due to occasional steric
hindrance bet,ween CB atoms of side chains (of difrering hands) belonging
to rcsiducs on adjacent turns of the same helix (CricLk, 1'J.W)).

There is IIOW c*onsiderable evideucae that the a-helix exists in solution
ill ccrt.aill solvellts, sr~h as m-cresol, dimrt,hyl-fornlallliCle, and c~hlorofortu-
formamidc, provided that the polymer be lollg enough (say 100 residues),
since surh solutions bchavr as if t,hcy contained rigid rods ill whic*lr c:L($
residue occupirs 1.5 A. of lengt Ii (Ijoty et al., I!)%).  Rlixal nr+)lytncrs


158             F. II. C. CRICK AND J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        159

also form a helical configuration, but it is less stable than that of the pure
D- or L-material.  Thus it is clear that each enantiomorph of the monomer
prefers its natural sense of helix (Doty and Lundberg, 1956; Elliott et al.,
1956). The stability of the a-helix in solution, in various solvents, has
been discussed theoretically by Schellman (1955).
b. P-Polypeptides and Silk.  It has been known for many years that in
the so-called P-configuration of keratin and synthetic polypeptides, and
also in silk whose X-ray pattern shows it to be a close relative, the poly-
peptide must be very nearly fully extended. A fully extended chain has a
twofold screw axis, and repeats after two residues in a distance of 7.3 A.
The observed repeat in all known B-structures is less than this-usually
between 6.6 A. and 7.0 A.-so the chains must be somewhat puckered.
In general plan the features of a @structure follow from the disposition
of the hydrogen bonds.  The hydrogen bonding groups (CO and NH) of
a single extended chain all lie in a plane, or nearly so, and project, in a
direction roughly perpendicular to the chain direction; it follows that the
polypeptide chains can easily be hydrogen bonded into infinite plane
sheets. The side chains project alternately on either side of the sheet.
Neighboring sheets must be held together by bonds of various types between
opposed side chains.

The main difficulty in making this general plan more precise is to know
the relative directions of neighboring chains in the same sheet.  Pauling
and Corey (1953b) have described two possible regular arrangements:
in the "parallel pleated sheet" all the chains in oue sheet have the same
direction, while in the "anti-parallel pleated sheet" alternate chains have
opposite directions (see Fig. 8).  They claim that if the structures are
built so as to conform to the best values of bond dimensions the former
arrangement gives a repeat of 6.5 A. and the latter a repeat of 7.0 A.  It
has not hcen rigorously established, however, that the two models can be
distinguished mcrcly by observing the exact value of the repeat, and it
stems quibe as likely that iu the syntJhetic polypcptides the directions of the
chnius arc randomly in one direction or the other (see Brown and Trotter,
1950).

\\`c shall tlist*uss silk only briefly: for a more cxteudcd account of recent
work see Kendrew and I'crutz (1957). For the silk of Bomb2/z mori,
which cont,ains 44% glycinc residues, Marsh et al. (1955a,b) and also
Warwirker (1954) have srlggclstctl a structure based on the nntiparallcl
pleat.etl sheet, in whirh it is supposed that crcry alternate residue along
tile cllains is glyc4nr; ill (:oI1sc(III(LIl(`c~ gly&c r&dues :~ll projrct (or rather,
siIi(nc tliclir "si& &ins" consist, mrrrly of hydrogcu atoms, fail to project)
011 fmr si&: of 2. given shwt.  `ho such she&s are packed hacbk t,o bncuk
\vitli their gtyciuc 4th togdhr; arId t.he whole structure is supposed to be

built up of pairs of such sheets (see Fig. 9). Chemical evidence on the
amino acid sequence supports these ideas, and it seems very likely that

/I:c'-0
H-N,'   `. H--d\
            `(-p-O'
  \
  K3c
  /
0-C
   a      /+H..
   `,,,-,-, o-e&
        \
           Hcpc
         /
/.C'=ao. . k--N\
H-N'     ~(yyo "

            64
   I
  pea
   \      ac/
         7
   &?-=o *
                  -0 .
H-N            p-o.. .
                `H-N"

  \
  f-WC     \
  /        HCPC      \
         /        Hcpc
0-q             /

    `N-t-t
PC&  oec;"N-H o=-c:\N-H,. .
         I
  \       PCcH
H-Ncc'==o    \   PCJH
               \
    H-N"`c'==o

\
HCflC
/

ITIf:. 8. Di:Igr:wun:rtic reprcscnt:~tions of tlrc two plcnted sheet, strlu:tllrcs pro-
posed by I':ruling :LIICI Corey (1951~ and 1053h).  (n) The anti-parallel ple:~trd sheet,
mith chains running alternntely 11p md down.  (b) The parallel pleated sheet, with
all chains trmuing in the mme direction.

much of the strurturc does possess the double-sheet strrict.urc.  rht, 1llC
details, for example t.hc direction of run of the chains and the iuterplctation
of the longer equatorial spacings (Marsh et al., 1955a), seem to us less
certain.


1GO          F. II. C. CIIIC'K ANI) J. C. KENI~IWW

X-ItAY ANALYSIS AND I'IWTIFIN STIIUCTUILE         161

In the more uncommon Tussah silk only 27 % of the residues are glycine
so the arrangement must be somewhat different.  Marsh et ~2. (1955c)

Fro. 9. The basic structure proposed by Marsh el aI. (1955a) for the silk fibroin
of Bambyz mori. The figure shows the view looking down the fiber axis, so that the
polypeptide chains are running toward the reader.
cut the figure in vertical lines.         The sheets of polypeptide chains
            Notice two sheets close together, back-to-back, in
the center of the figure, with alanine side-chains on the o&side of the pair of sheets.

Fro. 10. The basic structure proposed by Marsh el al. (1955b) for Tuss:A silk,
and also for the P-form of poly-r.-nl:mine. Again the view is clown the fiber asis.
Notice that in cont.rast to Fig. 9 sheets of polypoptide chains do r~ol occur in pairs but
are equally spaced.

have suggested a simple struct.IIrc, also based on the nnt,iparallel pleated
sheet; here it supposed that the glycines are arranged at random so t)hat
the two sides of any sheet are equivalent and all sheets pack at t'he same
distance from one another, i.e. as singlets rather than doublets (see Fig. 10).

They propose a similar structure for the @-form of poly-L-alaninc whose
X-ray picture is remarkably similar (Bamford et al., 1954; Brown and
Trotter, 1956).

Finally it should be noted that by using appropriate solvents "soluble
silk" can be made to take up the a-configuration (Ambrose et al., 1951;
Elliott and Malcolm, 1956b).

c. Polyproline.  We now come to two materials which fall outside the
classification of cr- and /3-structures.  The first of these is poly+proline,
which is interesting because of its relationship to collagen and because,
having no NH group, it is incapable of donating hydrogen atoms for hydro-
gen bond formation. Cowan and McGavin (1955a,b) have studied its
X-ray diffraction pattern, using material prepared by Katchalski. The
X-ray pattern can be indexed in terms of a relatively simple unit cell of
space group P32 and dimensions a = 6.62 A., c = 9.36 A.; in other words
with a threefold screw axis.  The asymmetric unit contains one residue,
making the distance per residue in the fiber axis direction 3.1 A., a value
which indicates that the polypeptide chain must be somewhat folded.

Model building shows that,`if the peptide group is both trans- and planar,
only a very limited number of configurations is at all possible, owing to
the severe restrictions imposed by the steric hindrance between neighboring
residues and by the fact that there is only one bond per residue about
which rotation can take place.. Only one of these configurations (see
Fig. 11) has a triad symmetry axis.  These considerations establish the
general nature of the structure, although at the time of writing. neither
the exact dotails of t,lic configuration nor !.!ic position of the molecule in
the unit cell have been deduced unambiguously from the X-ray data-
probably because, once again, the chains are running up and down at
random in the structure.

There is no reason to suppose that the integral threefold axis is an
especially favored configuration for the polypeptide chain.  It probably
arises in this case because of strong van der Waals' interactions between
neighboring chains, which discourage the formation of a nonintegral
screw (see p. 149).

d. PoZ2/gZ@ne. I'olyglycine can be precipitated from solvents in two
different forms having different X-ray patterns. That of polyglycine I
is a trypica P-pattern; but polyglycine II gives a new kind of pattern not
hitherto obtained from any other material, although so far oriented speci-
mens have not been obtained and the only photographs available are
powder patterns (Meyer and Go, 1934; Bamford et al., 1955).

Polyglycine II is of interest because of it,s relationship to collagen (see
p. 168). It is prepared hy precipitat.ion from aqueous solutions in the
presence of salts such as lithium bromide or calcium chloride.  The struc-


162            F. If. C. CMCK AND .I. C. KENDREW

ture turns out to be based on an integral threefold screw axis; the powder
diagram can be indexed in terms of a trigonsl unit cell, space group P31

FIG. 11. A single chain of the model proposed for poly-L-proline, seen in projcc-
tion, below, along the threrfold screw axis, and, above, perpendicular to this axis and
along the direction indicated by the arrow.  (Cowan and McGavin, 1955b.)

or P3*, a = 4.8 A., c = 0.3 11., one residue per nsyrmnetric unit. The
configuration proposed for polyglycjnc II by Crick and Rich (1955) (see
Fig. 12) has a backbone configuration very similar to that of poly-L-
proline. But in this substance, unlike the latter, the? prptide groups all
contain hydrogen atoms suitable for hydrogen bond formation, and in

         X-RAY ANALYSIS AND PROTEIN STRUCTUBE        163

the proposed structure neighboring chains are joined together to form an
infinite three-dimensional network by three sets of hydrogen bonds running
perpendicular to the fiber axis.  The diffraction data are not sufficiently
detailed to enable a decision to be made whether all the chains run in the

Fro. 12. The I):Lsic strwtnrc proposed for polyglycinc II.  A project,ion down t.he
threefold screw axis, showing seven chains.  Hydrogen bonds, drawn as dashed lines,
run in a number of directions linking neighboring chains together.  (Crick and Rich,
1955.)

same directiou or whet(her they rutI randomly up and down; either arrangc-
ment would lead to a stereochemically plausible structure.
Further confirmation of the threefold character of the structure comes
from the observations of hleggy and Sikorski (1956), who have found
hexagonal crystals of polyglycine II in electron micrographs.

               9. Fibrous Proteins
a. l'hc a-Kcralirr. P&v-u.  11` .lir epidermis, porcupine quill, rnyosin,
tropomyoxin, fibrinogen, and ot,her naturally occurring materials give


164             F. H. C. CRICK AND J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        165

diffraction patterns resembling one another in broad features, and known
as alpha-patterns (for details see Kendrew, 1954a).  The most striking of
these features are strong meridional reflections with spacings of 5.1 A.
(Astbury and Woods, l!M) and 1.5A. (Perutz, 1951).  The latter strongly
suggests that the structure is based on the a-helix.  However, an array of
parallel o-helixes would not give a 5.1 A. meridional reflection, but, as
pointed out by Crick (1952, 1953a) and by Pauling and Corey (1953s) a

*
I     Jb
  (h)

FIG. 13. To illlwt,rnte the genernl idea of a "coiled-coil" or "compound helix."
The figure on the Ml shows :I single polypcptide chain.  The small helix is supposed
. to be an a-helix whose axis has hecn distortedso that it follows a larger, more gradual
helix. The figure on the right. show two possible ways of combining helices into
ropes. (After I'wling and Corey, 1953x.)

system of a-hc~liccs twistc*tl togcthrr into coiled coils is capable of cxplainirlg
both the meridional rcflcctions.

It. seems probable that this suggestion is correct in princaiplc, but the
details are still very uncaclrtain.  Panting and Corey (1953h) proposed a
complicated st,ructure bast~l on a 7-st,randcd rope, composed of a central
straight a-helix with six others twisting slowly around it (see Fig. 13),
together with additional int,rrstitial a-hrlircs; and they made the suggrs-
tion that thr super coiling might be prodo~rtl by a repeating sequcncc of
residues. Cric*k (195Ba) tentatively proposcltl two simple models- --the
double rope and the triple rope--which could be derived from simple

packing considerations: for reasons of symmetry two right-handed cr-helices
might be expected to pack together, not parallel, but at an angle of 20" to
one another, when the side chains of one fit into the spaces between the
side chains of the other. By a slight deformation this would yield a
structure resembling a piece of twin lighting cable; the triple rope is similar.
Recently Lang (1956a,b) has shown that this kind of structure would
probably give an X-ray pattern simpler than that observed, although his
argument is not entirely rigorous, since he made no allowance for side
chains.

Not only are the details of the configuratiori unknown, but it seems
likely that they may be different in different materials giving the a-keratin
pattern. Tropomyosin, for example, with no proline and little cystirie,
and a molecular width corresponding to only two polypeptide chains, is
unlikely to have precisely the same structure as porcupine quill, which
contains large amounts of both proline and cystine and gives an X-ray
pattern of considerable complexity.

In spite of these reservatibns it seems almost certain that a stibstantial
part of these proteins is folded into the a-helix configuration, so we may
be reasonably confident that the a-helix is not restricted to synthetic
polypeptides but can also occur in genuine proteins.

b. The &Keratin Pat&p. It. was shown many years ago by Astbury
and his colleagues (1930, 1931, and 1933) that when hair is stretched its
X-ray diagram changes from what is now called the a-pattern to a radically
different one called the &pattern; he concluded that this change reflected
a change in t,he configuration of the polypeptide chain from a folded form
t.o one which is almost fully extended.  This interpretation is still con-
sidered to be correct; but t,he details of the /%configuration have eluded
discovery, although its general nature is not in doubt. What we have
said above (p. 158) in corm&ion with /3-polypcptides and silk applies also
t,o the other P-proteins, which include the stretched forms of ma.ny of the
proteins we have listed above as a-prot,eins, as well as feather keratin,
which exist,s only in what is presumably a &configuration.

Thr most important fraturcs of the X-ray pat,tcrn of fl-keratin are
equatorial rcflcct'ions of spacing 9.7 and 4.65 A., and a meridional rcflcc-
tion of spa.ring 3.33 A.; there is no reflection of sparing 1.5 A., but inst'ead
one of 1.1 A.  Pauling and Corey (1953b) have sugge&d that t,he structure
is essentially a parallel pleat,ed sheet, with repeating unit 6.5 A., in contra-
distinrtion to @-polyalanine and silk to whi&, it will be rememl~ered, t hry
have attributed the antiparallel plcatcd sheet. Tn our view the cxpcri-
JllCllkt~ evidcnrc dots not yet permit the deduction of so precise a modrl;
but in grneral terms it does stem likely that the strurturc coilsi& of
pleated sheet,s or something very like t,hcm.  It is to be hoped that more


103            F. II. C. CRICK AND J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        167

definite conclusions can be reached by working on the few p-proteins which
give diffraction patterns rich in detail: among these is feather keratin, on
which a preliminary note has been published by Kdmm and Schor (1956).

One of the problems still to be solved about the structure of kerstin is the exact
nature of the a-8 transformation.  This process is reversible and takes place under
relatively mild conditions.  Keratin contains a very large number of S-S bridges,
and the chemical evidence suggests that these are not ruptured during extension.
It is not easy to see how a process which, we must presume, involves the pulling out
of (possibly intertwined) helices into pleated sheets, could leave so many interchain
bridges intact; the suggestion that all the S-S bridges are in&a-chain also raises
formidable stereochemical difficulties. Nor is it clear how all the side chains can
readjust themselves easily, since in some cases one would expect them to rotate
through large angles during the extension.

c. Collagen.  In this review we shall be concerned only with the struc-
ture of collagen at the atomic level, although it also exhibits features of
great interest at a higher level which can be studied in the electron micro-
scope.  For a recent discussion of the latter see Schmitt et al. (1955).
Collagen has been studied by X-rays for many years.  As Anfinsen and
Redfield have said in the review to which we have already referred (1956),
"perhaps for no other protein has such a multitude of structures been
proposed, or, to use a term more common among X-ray crystallographers,
`discovered'."  It must be admitted that the jibe was not unjustified; the
structure was in fact unknown until recently, when several groups of
workers suggested CSSCII t,ially similar solutions.  Thcso suggestions have
radically altered t,he situation, which now is that the structure is almost
certainly "discovered" in a final sense of the term.  It is unlikely that the
recent models mill require modification except in detail. There have
been several reviews of the earlier efforts (Bear, 1952; Kendrew, 1954a),
which need not be described here.

It is well known that collagen has an unusual amino acid composition
(see Tristram, 1953).  Its main peculiarities are the high glycine content
(just over one-third of the residues are glycines); t,he presence of hydroxy-
proline and hydroxylysine, amino acids which occur in no proteins other
than collagen and its near relat,ions; and the large amounts of proline and
bydroxyproline, lyhirh toget,hcr make up about 22 % of the residues of
beef collagen.  There have been tmo important studies of the amino acid
sequence in collagen. The first, by Schroeder et al. (1954), showed that
the sequence Pro-Gly was rare and Gly-Hypro absellt,, whereas Gly-Pro
and IIypro-Gly Ivere common.  The provisional ron(*lusioo, that Gly-Pro-
ITypro-Gly might, be n common secluence in caollagcn, mas coufirmed by
Kroner et al. (1955), who identified this tetrapeptide among t,heir hydrolysis
products, as well as t,he t)ripcptitle (:ly-Pro-Hypro.  It, seems very probable

that the conclusion may be accepted, in spite of the rather low yields
obtained in both studies,

The X-ray pattern of collagen is of a type given by no other protein.

Its main features are a strong meridional arc of spacing 2.86 A. and near-meridio-
nal spots with spacings about 4 and 10 A.  There are also equatorial reflections, the
principal among which is humidity-sensitive, having a spacing of 10.4 A. in dry and
up to 17 A. in wet collagen.  Finally there is a diffuse patch on the equator in the
4% A. region, especially strong in the dry material (see Fig. 4).

  Certain electron micrographs (Schmitt el al., 1942; Mustacchi, 1951)
have suggested that collagen fibers may be able to stretch by large amounts
(up to several hundred per cent) ; but no one has been able to reproduce
this phenomenon except under electron bombardment, so it seems probable
that it is an artifact.  There is no doubt, however, that collagen can be
stretched reversibly by small amounts (up to about 10 %) and that during
stretching there is an increase in the spacing of the principal meridional
reflection, normally 2.86 A. .-This effect was discovered by Cowan et al.
*-  (1953), who found that it was accompanied by a considerable improvement
in the definition of the X-ray pattern, and thus made an important. techni-
cal advance.  They suggested (1953), as did Cohen and Bear (1953), that
the structure was based on a nonintegral helix. There is now general
agreement with this view and that the approximate parameters of the
screw axis are a rotation of 108" and a translation of 2.86 A.

To bc more correct, the structure might have an n-fold relation axis, parallel to t)he
fiber axis, in addition to the screw, whose paramctcrs would then be 108"/n and 2.86
A.  Consideration of the distribution of strong int,ensit,ies in the diffraction pattern,
and of the probable mean radius of the helix, makes it very likely that in fact n = 1
(Cowan et al., 1955).

The net-diagram implied by this screw symmetry is shown in l?ig. 5,
but it cannot tell us which way the polypeptide chains run, nor how many
of them there are, even though there is independent evidence that the
number of amino acid residues per asymmetric unit is three (this follows
from a consideration of the density of the structure).  Various possibilit,ies
are shown in Fig. 5.  In fact there is evidence from studies of light scat-
tering, etc., on collagen in solution (Boedtker and Doty, 1956), as well as
from the model-building approach which me shall now discuss, that the
number of chains in the helix is most probably three.

The structures recently proposed, which are all closely related t,hough
not identical, spring from an earlier suggestion by Ramachandran and
Kartha (1954).  Their first model (whose synnnctPry is nof t hc same as
that discussod above) c~onsistcd of thrrc parallel polyprptitln (*haills,
joined by hydrogen bonds, not twined around a common axis but running


168             F. II. C. CRICK AND J. C. KENDREW

side by side in a compact, group.  Each chain had a threefold screw axis
with a translation of 9.5 A. (containing three residues) in the fiber axial
direction.  The backbone configuration of these chains was, in fact, very
similar to that subsequently est,ablished for polyproline and polyglycine II,
whose axial repeats are almost the same. Ramachandran and Kartha
later (1955) modified their structure by causing the three chains to twist
slomly around each other, thus giving the model a nonintegral screw axis
in conformity with the net-diagram discussed above.

The other structures suggested recently have all been of this form, but
have differed in the way the three chains are linked together.  Since the
asymmetric unit contains three residues one can conceive of three different
types of interchain hydrogen bond.  Rich and Crick (1955) have shown by
exhaustive model building that only one of t.he three types can be made
sysfema~icaZZy, between atoms of the polypeptide backbone: all structures
with more than one type are stereochemically unsatisfactory.  Moreover,
there are only two ways of making a single set of hydrogen bonds, and
these they have described as Structure I and Structure II. The same
conclusion has been reached by Bear (1956), also from systematic model
building, but to a slightly different set of postulates.

It will hc rcmcmhcrcd I.h:~t. in polyglycinc II an ir1finil.n &work of hexagonally
nrrauged chain8 is linked together hy hydrogen bonds (Fig. 12). We might imagine
the collagen structure as derived by isolating R group of three chains from this infinite
network.  It cnn easily hc shown hy mean8 of models that there are juet two types of
groups which aau hc isolated in t,his way, tlifTcring in the wny their hydrogen bonds
arc a.rr:mgctl.  One of t,hcsc lypcs corrcaponds to Structure I for collagen, the other
to Structure II.

Structure II (Fig. 1.4) turnctl out t,o bc much easier to bu Id than Struc-
ture I, in that it gave more ac~ccptnble values of bond dimensions and
' angles and of interatomic: distancacs; also its difTrac%ion pattern is in better
agrcemeut with the obscrvcd patt,crn (ltamarhandran, 195F; Bear, 1956;
`Cowan rt al., I!)%; Ili& autl Crick, unpubliuhcd). For stereochemical
rcusons St,ructurc 11 will accommodate only t,he amino acid sequence
-G--t~1--1'2-, rcpcat.ctt indefinitely; G must be glycine, while I'1 and
Pz could bc any rcsiducs, in(+lding proline and hydroxyprolinc.  The
arninn acid sctluencc tlat,a t,o whicbh we have already referred indicate that
in fact all the hytlroxyproline must be at I'*.  This site is located far from
the axis of the st.ruct,ure, and thus in Struct.ure II the hydroxyl group of
hydrosyproline vannot form hydrogen bonds with CO groups in the
tmckhonw of the salne group of &ains.  It follows t,hat if it is used for
illt,crcahniil liukagcs at. all, it, must scrvc to link toget,hcr neighboring groups
of c4iai ns, :ts suggrstrtl I),y Ila~~i:~c~tia~itlra~i aild Kart~lia, mthcr than to
link chains within one group, which was the case in the less satisfactory

          X-RAY ANALYSIS AND PROTEIN STRUCTURE        169

Structure I (Rich and Crick, 1955). The data collected by Gustavson
(1955), suggest that the thermal stability of collagen is greater the greater

Glycine

Hydroxy-
proline
Proline

,
`a
' .
: ,

, I

   .*
6 $>
d

FIG. 11. To illustrate bhe basic idea of the proposed collagen structure (Coll~~gcu
II of Rich nrltl Crick, 1055). For clarity only the C., carbon nloms are shown. The
pept,ide groups connecting them are drawn simply as short straight lines. On the
left the dotted lines show the general run of the three polypeptide chains about fhe
fiber axis (full line). In t.he middle one of the three chnins is shown, to illustrrtte how
it coils round the dotted lint.  On the right all three chains nre included.  The small
circles show the sites which must he glycine.  The large circlcR xhow where prolinc
and hydroxyproline (shaded) are mainly found. Note the repenting sequence of
sites.

it,s cont,ent of hydroxyproline; but. as yet t,herc is no chemical evidence
whether t,hc bonds it forms arc with a group of three &ains, or hetwecn
groups, or bot.11.

It should be noted that in t,hese structures rclativcly few hydrogen


170            F. II. C. CRICK AND J. C. KENDREW

X-RAT ANALYSIS AND PROTEIN STRUCTURE        171

bonds are made between backbone atoms.  There seems to be no intrinsic
objection to this, however; indeed it may be that the solution of the struc-
ture has been delayed by an overemphasis on backbone-backbone hydrogen
bonds. It cannot be said that there is yet general agreement that Rich
and Crick's Structure II is correct.  There is, however, general .agreement
that all other structures so far proposed are unsatisfactory, and that
Structure II is the best suggestion yet. In our opinion it is likely that it
will turn out to be correct. Nevertheless it is necessary to add a note of
caution to the effect that different parts of the collagen molecule may have
different configurations. It is well known that collagen fibers have a
banded structure which can be seen in great detail in electron micrographs,
and that the bands differ in certain respects from the interbands.  More-
over collagen has to be stretched in order to give a good diffraction pattern;
it may be that the effect of stretching is to alter the configuration of part
of the fib&. It is not impossible, in fact, that in unstretched collagen
part of the chain has a different configuration, Structure I for example.
If it were shown that the collagen molecule is inhomogeneous in some
such sense as this, the force of some of the avents used to deduce the
structure would naturally be weakened.

IV. CRYSTALLINE PROTEINS.

More work has been done to determine the structures of the globular
proteins by means of X-rays than has been done in any other area of the
field, and with fewer results.  By and large, globular proteins are meta-
bolically active, and fibrous proteins are not. From the biochemist's
point of view, therefore, any results obtained with globular proteins should
be the most interesting of all.  This branch of protein X-ray studies has
in fact just reached a critical point.  For the first t,ime there is a real
-prospect of getting definite and incontrovertible results.  None to speak
of have yrt been published-the achievements so far are spect,aculnr from
the technical standpoint,, but not from the point of view of t,hc interested
outside observer-bnt there is now for t8he first time a real promise fat
the immediate fnt,ltrc. The t,ransformation of the fichl is largely a con-
scquencne of the sucrrssfril applioat.ion, by l'erntz and his colleagues, of
the mct,hod of isomorphous replaccmcnt to a prot,ein crystal. We shall
speak of this in its placnr; in the meantime WC must make a preliminary
survey of some basic facts about. protein crystals.

1. The Natwe of Protein C'rpfals

`I`he maill tlil1crc~rrc~e I~t.~c:n prolcin c*rystals and the cryst'als of mnrh
smaller orgatlic 11~0lcc1~lf~s is I hat they (contain a (~onsi(lcratJIc quantit,y
of solvent, actually within each unit cell.  Typically half the volume of

t,he crystal will be mater (or, more often, the salt solution with which the
crystal is in equilibrium).  If such a crystal is removed from its mother
liquor and exposed to the air, water is lost and the crystal can be seen to
shrink somewhat; its optical properties usually deteriorate at the same
time. X-ray measurements would show that the visible shrinkage is a
consequence of the shrinkage of the unit cell itself.  In this condition a
crystal is conventionally described as "dry," in contradistinction to the
original "wet" crystal-though in fact it can be dried still further if placed
in a desiccator.

All the evidence suggests that most of the water in the crystal is in a
"liquid" state-that is to say, it has no regulai structure like ice oh like
the hydrated layer around an ion; and it is permeable to small ions.  Thus
considerable amounts of salts can often be diffused into a brystal tithaut
changing the dimensions of the iinit cell, and indeed, since many prdt&s
are crystallized by "saltihg out," the salt concentration in the liquid ihside
the crystal may reach sev@al moles per liter. Proteins such as ribo-
nuclease, which are crystallized from strong solutions of organic solvents,
exhibit similar behavior in that the cell dimensions hardly change when
the organic solvent is changed, a typical alteration (for ribo&lease)
being 0.i A. in 30 A.  In all these cases, the fact that ions or other small
molecules have gone right into each unit cell can be demonstrated in several
ways. For example, if sodium dithionite is diffused into a crystal of
methemoglobin the spectrum of the protein can be directly obgerved to
change from that of ferrihemoglobin to that of ferrohemoglobin, as the
process of diffusion t,akes place.  Again, changes in the low order X-ray
reflections (t,hat is, the reflections of long spacing near the center of the
phot,ograph) show clearly t,hat these small molecules have penetrated
the unit cell.  This is demonstrated in Fig. 15 which shows the reflections
of finback ~+alc myoglobin in four different, salt. solutions.  Note that
while the inner refiertions alter dramatically, the outer ones are ~n~hnngcd.
This shows that. whereas the $;lae sfrucfurr of the contents of ihc unit wII
is nr~altered, thr f~cnc~71 disfribufion of c,lccstroil density, as sron at IO\\
resolution, has altrrcd greatly; and t.he cf'frct is romph~tcly rxplninc~tl I)\-
snpposing that, the clcctron density of the strnrtnrrlcss but, c?ttttl.Gi.(*
(and, in regard to their bonndnrics, somcnhat. ill-tlcfinctl) rrgions c*ont:tirr-
ing mother liqrmr has IJWII stcppcd up or down, while lhnl of tlrc prol(4ll
mol~~(~nl~s, with t,hcir pre&? and drfinitc strnf4,nre, has rcnlainc~tl IIn-
chllrgcd.


1'72             F. Ii. c. CIlICK ANI) J. C. KENDJtEW

X-RAY ANALYSIS AND PROTEJN STRUCTURE        173

favorable cases the extra molecules have no effect on the dimensions of
the unit cell; but sometimes small changes in dimension do take place, and
sometimes the crystals may become disordered or perhaps break up alto-

ferent space groups, suggesting that the process of oxygenation may involve
an appreciable change in the shape of the molecule, possibly by altering
the relative positions of the two subunits of which it is composed (see p.
175). It is noteworthy that in myoglobin, where the indications are
that the molecule is not made up of subunits, no such phenomenon has
been observed: oxy- and reduced myoglobins crystallize isomorphously.

These observations leave no room for doubt that some of the water
(or other solvent) within the protein crystal is "liquid;" and the question
arises whether it is all liquid. Only in horse hemoglobin has it been fully
answered, by Perutz (1946), who measured the density of the crystals after
they had been equilibrated in salt solutions of various concentrations.
His results are in accordance with the assumption that part of the water
is "bound" to the protein, that is to say, held in a rigid or pseudocrystalline
arrangement, so that salt cannot diffuse into it; on the other hand, the
rest of the water is continuous with the external medium and contains
the same concentration of salt.  The amount of "bound water" was found
to be 30 % of the proteifi (by weight). Whether this simple picture has
any physical reality remains to be seen: but at least it summarizes the facts
in a very compact way. On the other hand, despite earlier 8uggestions,
the X-ray data clearly show that it is an oversimplification to conclude
that the bound water consists of a uniform unimolecular layer covering
an ellipsoidal protein molecule (Crick, 1953a).

The shrinkage of protein crystals can also be studied by X-rays. It
is oftctl fount1 that wc:ll-tlcfincd shrinkage stages exist bctwccn the wet
and dry extremes. These stages have been carefully studied in horse
hemoglobin (Huxley and Kendrew, 1953). The cell dimensions change
quite sharply as the humidity is varied at a fixed temperature.  In this
protein it is even possible to obtain an "expanded" stage by altering the
pH. Shrinkage st,ages have also been reported for various myoglobins
(Kendrew, 1950; Kendrew and Pauling, 1956; Kendrew and Parrish,
1956), and also for ribonuclease (Magdoff and Crick, 1955b). For the
latter protein it has been shown that the wet lattice can be "strained"
by what appear to be small humidity variations; that is, the cell dimensions
can be altered by about 0.3 A. in 30 A. in an apparently continuous man-
ner (Mngdoff and Crick, 1955b).  It is not known whether this is true of
any other protein.

All these phenomena can be understood if we regard a protein as a
large molecule of relatively fixed size and shape.  It would be surprising
if such molecules (as opposed to smaller and relatively more flexible organic
molecules) nere able t.o pack t,ogether without leaving considerable space
bctmcen them. This spncc is naturally filled with water, or other solvent,
as in many crystals of smaller organic molecules; but it is bigger, and there


174           F. Ii. C. CJtICI< AND J. C. KENDItEW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        175

is room for a larger number of solvent molecules, which therefore find it
easier to retain their "liquid" state-in other words they distribute them-
selves over the rather large space in a random manner.  The protein
molecules presumably touch one another at a rather small number of
specific points of contact; and at least some of these are changed abruptly
when the crystal goes from one shrinkage stage to another, although minor
humidity changes may strain the arrangement a little without causing
large and discontinuous changes.  As more and more water is removed
the molecules pack down together as best they can, alld the structure often
becomes disordered. If the crystal is, finally,' dried thoroughly most of
the water comes out of the interstices and empty spaces are left between
the closely packed protein molecules.

In some proteins, 8-lactoglobulin for example, it has been reported
(McMeekin et al., 1954) that shrinkage is continuous; though of course
the truth may be that even here shrinkage stages do exist, but that their
dimensions are so similar that they elude detection.
The X-ray pattern of wet protein crystals usually extends to spacings
of about 144 or 2 A, the average diffracted intensity falling rapidly with
increasing spacing in this region.  In this respect protein crystals differ
from crystals of ordinary organic molecules, which produce diffracted
beams of much smaller spacing. The absence of fine detail in protein
diffraction patterns sets a limit to t.he resolution of the structure we can
hope to obtaiu even when X-ray methods reach their ultimate power,
although in some small proteins it may just be possible to resolve individual
atoms. Some protein crystals arc better t,han others from this point of
view; thus ribonuclease is particularly good, with spots extending out to
about 134 A. In general the smaller the protein the further out into
reciprocal spare its ditYraction pattern extends.
Dry crystals are always more disordered than wet, ones, and generally
give few reflections with spacings less than 5 A, though there are exceptions
(in both dir&ions). Thus t.hc diffraction patterns of wet crystals contain
more information, and it is usual to study proteins wet rather than dry.
To do so one must mount them in sealed capillaries, as thin as possible
to minimize loss of X-rays, and containing a few drops of mother liquor
to stabilize the humidity.

2. Direct Information.

In this section we shall describe the sort of information which can bc
obtained from the preliminary examination of a protein crystal. Most
of it (except that, discuusscd under d) can be got in only a few days.
(1. [*nil C:C~U no! Spacr Group. In most, CRSCS tho dimensions of the
unit cell and the nature of the space group (i.e. the symmet,ry elements)

can be derived unambiguously from two or three suitably chosen X-ray
photographs. Reference. to the International Tables of CrystuZZogruphy
at once gives the number of asymmetric units in the unit cell; and from
the volume of the latter it is simple to calculate the volume of the asym-
metric unit. If the molecular weight of the protein is approximately
known one can calculate the maximum number of molecules which the
asymmetric unit can contain. To obtain the actual number one must
estimate the relative proportions of protein and solvent in the crystal.
This usually presents little difficulty since in general only an approximate
estimate is required; in fact in almost all cases the proportion of solvent
is 40-60%. The most usual number of molecules in the asymmetric
unit is one, but two are found quite commonly, and larger numbers oc-
casionally. It may even happen that the number is a fraction. Thus
in the most common form of horse hemoglobin, whose space group is C2,
the number is one-half, showing that the "molecule" found in solution,
of molecular weight 67,000, must consist of two identical halves.  In the
crystal these halves are related by the dyad or twofold rotation axis of
symmetry which in this space group relates two neighboring asymmetric
units. It is most likely that the same is true of a hemoglobin molecule
in solution (it will be realized from what has so far been said that the
environment of a protein in a crystal is rather like its environment in
solution). In conditions of extreme dilution or in presence of high con-
centrations of urea the horse hemoglobin molecule dissociates into two
halves in solution.

The contrary proposition-that a molecule possessing internal symmetry
must exhibit it in the crystal-is not necessarily true.  Sometimes a
protein with internal symmetry may crystallize in two different forms,
in one of which the internal symmetry forms part of the symmet,ry of
the cell, while in the other it is not revealed.  Thus X-ray evidence alone
cannot tell us the minimum structural unit of the prot.ein (at least from
the preliminary examination).  Insulin, for example, which has a chemical
molecular weight of 6000, has a crystallographic molecular weight of 12,000
in both its known crystal forms, and this is also the lowest value so far
found in aqueous solution.  It will be interesting to see how the two halves
of the 12,000 molecule are related, but this we shall not discover without
a full-scale analysis of the crystals.  Recent work has shown that dissocia-
tion of the 12,000 unit into "monomers" of molecular weight 6000 is
promoted by urea and guanidine (Kupke and Linderstrgm-Lang, 1954;
Trautman, 195G); this suggests Chat hydrogen bonds play an important
role in holding the two parts toget.her.

b. dfolecztlar Weig~~t.  In favorable cases it, is possible to obtaiu a mthcr
good value of the molecular weight of the asymmetric unit of the protein


176          F. II. C. CRICK AND J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        177

by X-ray studies; as we have just indicated, this may he a multiple or a
submultiple of the "molecular weight" found by other methods. As
this subject has been reviewed elsewhere very recently (Crick, 1957) it
will only be briefly alluded to here.  In essence the method is to measure
the volume of the asymmetric unit (by measuring the cell .dimensions),
and to calculate its weight by measuring the density of the crystal.  To
determine the molecular weight of the protein it is then only necessary to
establish the composition of the asymmetric unit in terms of protein, solvent,
and salt (if any). This is easiest when salt or organic solvent is absentzif
salt is present there will be difficulties due'to the fact that part of the
water is "bound" and salt-free, so that the overall salt concentration in
the internal medium is less than that in the external medium.  Usually
therefore one works with salt-free crystals if these are available.  Under
favorable circumstances the errors should not exceed l-2%, and even a

TABLE II

Molecular Weights of Some Proteins, ae Determined by X-Rays

Protein        Molecular weight       Determined by

Ribonuclease            13,466
Lysozyme            13,906 zk 600
u-Chymotrypsinogen      25,966 f 806
&Lactoglobulin         35,006 f 406
Iiumnn serum albumin     65,266 f 1,360
Human mercnptalbumin    65,600 f 706

Harker (1956)
Palmer et al. (1948)
Bluhm and Kendrew (1956)
Green et al. (1956)
Low (1952)
Low (1952)

very rough estimate will usually be within 5-10%. Considering its ac-
curacy, the method has been somewhat neglected in the past; partly
perhaps because it requires collaboration between a protein chemist and
crystallographer.  In Table II we have collected some of the more recent
and more accurate results obtained by this method.

c. Identification and IdeMit?/. It might be thought that the X-ray
diffraction pattern, being so intimately related to the structure of the
protein producing it, could be used like a finger prhlt for identification
purposes.  IJttfortunatcly this is true only to a limited extent.  The same
protein, crystdlizetl under slightly difrcrent conditions, may give various
cBrysta1 forms with totally difirrent space groups and diffractiott patterns.
l'htts the fact8 that, t.hc X-ray pictures of two protein crystals are radically
tliffcrrttt does not mean that the proteius themselves are different. On
the other hand, two protAts kt~onn to br different (though the differences
are slight) may sotnat irnrs wystxllizr in the same unit. ~11, attd give almost
irletttical tlifl'rartiott patterns.  The reason why this is possible has already
been discussed (see p. 152).

The various crystal forms of myoglobin provide some very good examples
of this (Kendrew et aZ., 1954).  Thus the form known as Type A has been
obtained from sperm whale, finback whale, blue whale, sei whale, lesser
rorqual, and common porpoise; the crystals are isomorphous and the dif-
fracted intensities very similar though not identical. Again, crystals of
the form called Type C have been obtained from the horse, common seal,
and gray seal. Nevertheless the myoglobins of the different species differ
immunologically and (wherever analyses have been made) chemically,
albeit slightly.  Changes in the diffracted intensities, of the same order of
magnitude as those found in these examples, can also be produced by sini-
ple chemical modification of the protein, as for example by convetiing
CO-myoglobin to metmyoglobin. It seems very probable, by analogy;
that the changes produced by varyink the species are a consequence of a
few variations in the side chains (cf. the species variations in insulitl
investigated by Brown et al., 1955).

Thus while the X-ray pattern is not a safe guide to strict idehtity, it
remains true that if two pt'oteins from different sources give very similar
unit cells and diffraction patterns, it is virtually certain that they have
the same major structural features, and therefore that their amino acid
sequences are closely related.

d. I'he Shape of Pro@n MoZe+Zes.  In certain special cases it is possible
to learn something about the shape of the protein from the dimensions
and symmetry of the various unit cells in which it occurs.  It is-rare that
straightforward deductions can be made, however, and the information
obtained is not generally very precise, so we shall only touch on it briefly
(for a more extended account see Kendrew, 1954a).

The cell dimensions put upper limits t,o the diameter of the molecules
itt certain directions, but the restrictions arc not often severe enough to be
ititrrrstitrg. If the same protein rrystailizcs in many difrcretit fortns it
ma,y bc possil)lc t'o dadwe a unicfuc shape for the "cquivalcttt cllipsoitl"
sudi that good close-pnckittg is achieved itt all the forms.  The tnost, full!,
worked ottt esarnplc of t,his approach is hcwoglohitl, nttd those ittt,ewstc~l
in it, sltortld consult, the origittal papers (Rrngg and Perutz, 19521,; Hragg
et nl., 1!)54).

A sottrw of ittfortnatiou whic*h is tnorc of'tett profitable is the itltnosl'
rrgion of twiptwal spare--the rrflec~tiorts of lwy low ortlw -cspw~i:tll~
when the clwt 1'011 dcttsity of the solvcttt, is wry dif~crettt frotn that of t,lw
s0l1w1t.  These reflectSions, which corrcqottd to a view of the st,rwtrtw
at wry low resolttt ion, depetttl on the gcttcral wtttrast, bctwectt the prot.c:itt
molrc~~tlc and the solvettt,, and wry lit t.lr OH thr: ittterttxl structurr of the
proteitt.  Allctwttively, whert fhc salt, rottwtltrntiott ittside the St rrt~tttt'c~
is high, ottc wn tnwsure the changes in X-ray itttSwsit,y produced by chn~tgcs


178            F. 11. C. CRIVK AND J. C. RENDREW

X-RAY ANALYSIS. AND PROTEIN STRUCTURE        179

in salt conccntrat~ioti (WC Fig. 15).  Uy methods of this sort Bragg and
Perutz (1952a) derived a shape for t,he molecule of horse hemoglobin
which agreed well with that deduced from packing considerations: namely
an ellipsoid with dimensions 71 X 53 X 53 A. consisting of hydrated
protein. This shape, however, can only be regarded as a .first rough
approximation to the truth-the molecule is almost certainly more asym-
metrical and more "knobbly" than an ellipsoid.  In our view the method
of isomorphous replacement offers a more general and more reliable method
for discovering the shape of a protein; and its application for this purposti
will be discussed on page 195.

3. The Pa.tterson Function

The basic principle of the Patterson synthesis has already been men-
tioned.  In the past it was, for lack of anything better, the main tool for
the exploratory studies of protein crystallographers.  The newer methods
have reduced its importance and we shall refer to it only very briefly
here.  The subject has been dealt with rather fully by one of us (Kcndrew,
1954a), and a simple explanation of the ideas involved in its application
to protein crystals has been set out in an earlier article (Kendrew and
Perutz, 1949).

It will be recalled that in this method the experimental data are manip-
ulated mathematically without any assumptions about the structure
being made.  This treatment gives a map which shows not the structure
itself but the relative positions of all possible pairs of atoms in the structure,
all superposed.  It can be shown that, if a structure, even so complicated
a one as a protein, possesses certain strong features, such as parallel "rods"
of high electron density (e.g. polypeptide rhains in suitable configuratJion),
the Patterson synthesis will possess analogous featurcs. The actual
intcrpretat#ion is ?ont,roversial in almost all cases.  It suffices to say that
the Patterson approach has clearly demonstrated that the structures of the
.few proteins so far examined are not of extreme simplicity in the sense of
consist,ing essentially of bundles of parallel &might polypeptide chains;
on the other hand they are caertainly not completely isotropic.  Some
proteins, such as myoglohin, show more obvious signs of regularity than
do others, SW% as ribonuclcnsc.

Another application of the Patterson synthesis is t,o obtain relative
orientations of the same prot,ein in different unit cells, by considering the
relative orientation of the strong features of their Patterson syntheses.
This c&an be a powerful method in favorable cases, espcrially if three-
dimensional data are avnilahlc- but the computation of three-dimensional
Patterson synt,lrcscs is at, best, a very tcldions bnsillcss, and it. is doubtful
if the effort is well spent, now that more powerful, though eq~~ally t,edious,

methods of analysis are available. Again, it may be possible to obtain
some knowledge of the relative positions of the molecules in the unit cell
by looking for "pseudo-origins"-that is, for regions where the Patterson
function appears to repeat within the unit cell. These methods have
been used for ox hemoglobin (Crick, 1956) and for various types of myo-
globin (Kendrew and Pauling, 1956; Kendrew and Parrish, 1956). But
in all cases the results are suggestive rather than conclusive, and SO far
there has been no opportunity to check them by more certain methods.

The Patterson synthesis, then, will always be a powerful tool in the
hands of the crystallographer, but for the present any results obtained by
its use should be accepted with reserve.  The use of the Patterson syn-
thesis in the isomorphous replacement method (see p. 181) is in a different
category, however.

4. Methods Involving Heavy Atoms

These methods, which involve the addition of heavy atoms to the protein
molecule and studying the dbnsequent alteration in the diffraction pattern
of the crystals, are the only ones so far discovered which give any secure
hope of solving the structure of proteins.  For this reason, and- because
they are intimately connected with the chemistry of proteins, we shall
describe them at length.  There are two distinct methods, both of which
have been used for a number bf years in the study of small molecules.
The first has not yet been applied to proteins, while the second was so used
for t#hc first time in 1953.

a. The Heavy Atom Method.  The first is the Heavy Atom Method
proper.  This was used by Carlisle and Crowfoot (1945) in their deter-
mination of the structure of rholcsterol iodide; and also hy Crowfoot-
Hodgkin and her collaborators (Hodgkin et al., 1956) in the first, stages of
the study of Vit)amin Nlz .  In this method a heavy atom is introduced
into t,he molecule, sufi&ntly heavy for it&s contribution to dominate the
X-ray intensities.  It is then an easy matter to find its position in the unit
cell by computing a Patterson synthesis, which will clearly show heavy
atom-heavy at,om vectors. One proceeds to calculate the diffraction
pattern, both amplitude and phase, which such an atom would produce if
it were the o?aZ!/ atom in the unit cell.  The result will resemble the observed
pattern, but naturally will not be identical to it, since the contribution of
the rest of the molecule has been omitted.  Now the observed diffraction
pattern gives us the correct amplitudes for the whole structure, but not the
phases. One employs, therefore, as the next best thing, the calc7Urd
phases-based on the llcal:y atom alone-together with the observed
amplit.ndcs, t,o c~alculntc a Fourirr or electron density synthesis.  This will
show the heavy atom and in addition a "ghost" of the rest of the molecule


180             I'. II. c. f:ltl(`l< ~\Nll J. (:. I<P:NI)IIISW
(ITl0l.C; dtcll, i.Wo ghosts srlJ~~!~~~oScttl~~~o~l~ Icft-handcd, & Other @ht-
handed). With IrIck t,his rather confused picture enables one to guess
the positions of the atoms making up the molecule.  A new set of phases
can then he calculated, based on them as weI1 as on the heavy atom.  From
then on the process is one of refinement,, of making successive small shifts
in the atomic positions to improve the overall agreement, of calculated and
observed amplit'udes.

The major difficulty in applyiug this method to proteins would be that
no single atom is heavy enough to control the majority of the phases be:
cause of the large size and scattering power of even the smallest, protein
molecule. Nevertheless, as we shall see, it may prove possible to circum-
vent this limitation to some extent by using a large number of heavy atoms
attached simultaneously to the protein molecule.

b. The Method of Isonlorphous Rep2acement. This method is often
loosely referred to as the Heavy Atom method, but, should be clearly
distinguished from the foregoing; it is bet,t,er described as the method
of isomorphous rcplaremcut,. It is not' too much t,o say that the subject
of protein crystallography has been transformed by the pioneer application
of this method to hemoglobin by Perutz and his collaborators.  It requires
Iwo practically identical unit, cells, one caontaiuing a heavy atom (preferably
one per asymmct ric unit, but, see p. l!M below) such as mercury, and the
othrr having all the atoms in the same places as in I trc first,, \\-it,h t,he ex-
ception of one or two light atoms (oft.cn a wat,cr mnlccule) in the place
where the heavy atom was bcforc.  This requirement is not easy to meet
in proteins. One nants suhstit,ution at a unique sit,e cm the surface of
niolwulcs whic41 ill ~f~l~w:d tlo 1101 cwli,:litl ~II:I.II~ Iiniquc sites--- it, is only iu
special cases, suc*h as proteins with prost)hetic groups or sulfhydryl groups,
that. they are obviously pr(`srllt On the other hand protein crystals
,prtscnt advnntagrs from auothcr poirIt of \iew, bcc~nuse of I he considerable
volume of t tic unit cell oc*f~upiccl I)y sol\w1t,, providing many pl:lc~~ whore
pxtra molcculcs caii be addctl wil~hout dist,urbiug the arrangcmcnt of the
protcitt.

As ill t.hc Il~:tvy l\lot~~ .%lctllotl, the proscn(*c of our mercury atom
(for cxamplc) will (*haugc the itltcnsitics of the rcflccat,ions in the difrraction
pat~tcrir . In clonsidcring the nat.urc of the cahaugcs produced, and how
they may IN> used to iuvcstigatc t hc strucature of t,hc protein, we shall in
the first instan~c rrstric*t, ollrsclvcs as follows.  It, has been explained (see
1~. 136) tlta~, :III~ pnrt icbul:lr rc+l(~c+iou has :L rcrtain arnplit~utlc :ttd phase.
It (`:I ii 1 hr~rc~forc~ IX: rq:1r(1(`(1 3s :I \.cxc$or; niorcov~~r, the cont~rihutions to it
of :III the atolns it1 tllcl Ittlit ~11 :IIY thrmsclvcbs vectors, which must,, of
r011tw. tw coinbill(~(l ~3~x1 ori:lIl?..  llowr~~~r, ill c3~rt:liri phm of the rccsip-
rocal Iatticbc (dcpoudiug OII the symmetry of the c*l,ystal), corresponding

X-RAY ANALYSIS AND PROTEIN STRUCTURE        181

t,o certain special projections of the structure, these vectors are all either
parallel or antiparallel, and can therefore be added arithmetically. We
may speak of such reflections as being real, i.e. having no imaginary vec-
torial component,; as having phase angles of 0 or rr; or as being positive or
negative. The corresponding projection is known as a real projection.
Our first discussion will confine itself to these reflections.

Consider, then, a certain (real) reflection, and suppose that its intensity
(on some arbitrary scale) is 100 for the case where'there is protein only,
and 64 for the case where there is the same arrangement of protein and in
addition one mercury atom per asymmetric unit. The amplitudes will
be the square roots of these numbers, that is 10 and 8 respectively; but
since we do not know whether the phases of the reflections are 0 or A we
must write these as f10 and +8. The mercury contribution must be
the difference of these two numbers, that is to say either f 18 or f2.  For
most reflcct,ions the contribution of the mercury is smaller than that of the
protein, so the correct value, will be the smaller one of the pair, that, is f2
in our example. We are still left with an ambiguity of sign, however:
that is to say we have, to correspond with

    protein + heavy atom = (protein plus heavy atom),
either   (+10) +   (-2) =      t+f9
or    (-10) + (+2) . =      t-8)

Which of these is correct, we cannot yet tell.  What we do know,-however,
is that the amplitude due to the heavy atom is ~2; and thus if we could
have a unit, crll with all thr prot,cin sribtrart,cd, empty cxcrpt for t,he
heavy atom alone, the illtcnsity of the reflection we are considering in its
diffraction patt.crn would bc (f2)2 = 4.  \\`c can thus calculate, wit,hout
making assumptions, the intrnsit,ics in the diffraction pattern due to the
heavy atom aloilc-the so-(*atled diflircnce i&~~itira.  To find the positioli
of the heavy atom we carry out a l':tt,terson synt,hesis, known as a dz"cr-
cncc I'attcrson synthesis or (AF)2 synthesis.  This shows LIS the vectors
betn-c>en the heavy atoms in rarh of the asymmetric units of the cell,
all t,he vectors involving atoms ot.hcr t.han the heavy at,om having been
canceled out; and from it one ran simply obtain the posit,ion of the heavy
atom rclativc to the symmetry elements of the cell.  Examples arc given
in Figs. 16 and 18.

Having found t,hc heavy at,om we cm calculate its rontribut,ion to WIJ
particular refiect,ion.  I,et us suppose that, it, comes out to $1.7 for the
reflection we have been considering.  Allowing for experimental err01
this ngrces with the second of our two nlt)ernativcs; it. follows that the
protein reflcctioii must bc - 10 and not +lO. That is to say, WE hnv~
dctcmincd the phase of this particular wjlectiou.  If we can do this success-


182             17. II. C. CRICK AND J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        183

fully for all the reflections in the reciprocal lattice plane we have been
studying, the way is open to calculate an electron density map of that
particular projection of the structure.
So much for the real projections.  For those regions of the reciprocal
lattice where the reflections are complex (that is, of genera1 phase) and
which comprise its major part, we follow an analogous but more compli-
cated procedure, whose results are less definite.

We cannot do as we did before, that is &tract the two amplitudes, because tkk  -

corresponding vectors are not parallel.  It turns out' thnt to find the heavy atom we
have to calculate another variety of Difference Patterson, called a (AI) synthesis,
in which the terms are simply the difference in inlen&& between (protein + heavy
atom) and protein alone.  In algebraic terms we use

               AI = Ip+n - Ip

where P = protein; P + H = protein plus heavy atom, whereas before we used

(AIV = (d/IP+A - X&J*

The AI type of Difference Patterson synthesis gives us as before the vectors be-
tween the heavy atoms, from which we can calculate their co-ordinates in the unit
cell; but superposed on them are all the vectors between heavy atoms and every other
alom in Ihe unit cell, i.e. atoms of protein or liquid (although our procedure does
remove those between protein and protein).  The diagram thus has a confused bsck-
ground and it may be difficult to locate the heavy atom-heavy atom vectors.

Even when we have successfully done this there are still further difficulties.
Without going into det,ails me may say that:

1. With one single isotnorphous replacement we cannot hope to find t,he
phases of all the reHecat ions dircc%ly.  What WC get, is two values for the
phase ntlgle of each reflection, and t)o remove this ambiguity a second
isomorphous replnc~etnent in a dif~crent place in the unit cell is necessary.
To be on t,hc safe side it would be better to have at least three separate
isomorphous reptacctncr~t.s.

2. The accuracy is less than in the case of real reflections, since me have
to assign a cluantitativt: valor t,o the phnsc angle-a value which Gtl bc in
error-whereas in the rral case all we have to do is to decide between two
alternatives, plus or tninus.

111 J)ractice, therefore, working wit,h rcficctions of con~plcx phase is quite
a differtnt proposition from working with real ones.  It is less acacurate and
more troublesotrrc; besides, the acat ual number of gcncral reHections of general
phase is far grealer.  011 the other hand, experictice with the few proteins
where electron density maps have been produced indicat)es, as we shall see,
that a two-dimensional projecation of the unit. ccl1 is very lit.tle use even when
it is knonu to he caorroc,t--t hc thickness of protein and solution t,hrough
which the projection tnust, be tnade (never less than 30 A., represent.itlg

15-20 atoms) is so great that all the features of interest are obscured and
the result is an uninterpretable confusion. To make real progress the
third dimension must be broken into, even though the labor involved is at
best formidable.

It should be added that one of the inescapable difficulties of protein
crystallography is that it is impossible for all the reflections from a protein
crystal to be real. This could only happen if the mirror-image protein
molecule (made up of de&o residues, and related to the real molecule as
a right-hand glove is related to a left-hand glove) were also present.  So
three dimensions mean solving the genera1 phase problem.  On the other
hand some space groups are more favorable than others for studying
projections; thus monoclinic unit cells have one real projection, whereas
orthorhombic ones have three, mutually perpendicular.

To illustrate the use of the method we shall now describe some of the
results obtained by it so far.

C. Isomorphous Replacement and the Structure of Hemoglobin.  This was
the first appliiation of the-method.  Perutz and his collaborators (Green
et al., 1954) made use of the fact that hemoglobin contains free sulfhydryl
groups by causing it to react with p-chloromercuribenztiate (PCMB), a
standard reagent for SH groups.  In this way they obtained a hemoglobin
molecule with two mercury atpms attached to its surface at specific and
definite sites. After crystallization the dimensions of the unit cell were
found to be quite unchanged, but the X-ray photographs showed unmis-
takable changes in the intensities of the reflections.  The reflections cor-
responding to a projection along the b axis, which in this space'group are
all real, were measured carefully for both normal and mercury-substituted
hemoglobin.  The two sets of intensities were adjusted to the same scale
by a stat,istical rnet.hod and the difference between t#heir square roots
(i.e. t,hcir amplitudes) gives 1 AP (, the c*hange in amplitude producBc:d hy
t,hc mercury atom. A difference l'at,tcrson projection was computed
using values of (AF)2; it is shown in Fig. 16.  It will he noticed that apart
from the prak at t,he origin (always present in l'attcrson synthcsc~s, and
mcrcly rrprcscnting the fact that every atom in the unit cell is at zero
distnncc .from itscy), there is one other peak much larger than a.11 the rest.
It has the coordinates (14.8, 31.6).  It follows that in t,he mlit c*ctI t,hc: R
and z coordinates of the heavy atoms are (+7.4, + 15.8) and (-7.1, - 15.X)
relative to an origin at the dyad axis of symmetry by which they arc rcl:Ltetl.


As il happens l'crutz W:LS :~l)lc 1,o tlcci(!c which solution was correct !)y making use
of the extensive expcrirnsntnl rcsult.s on thr shrinltngc and expansion of the crystal.
Horse hemoglobin crystals arc II~II~II:~! in Imlcrgoing :I p:~rtinulnr!y simple type of
shrinkage.  The molecules lie in sllnets and tlrtring slninkagc each sheet remains quite
unchanged in itself, !)nt moves rclstive to its neighljors, in a direction always per-
pendicular to the b axis.  Using this fact it can be shown (Bragg and Per&z, 1952c;

  FIG. 16.  A I JilTcwtwc !`a1 fcrson, tn show how I.!Ic position of :L heavy atom is t!is-
covcret! Iwing the iso~norpl~o~is rc!~l:xemc~~ 1 mel hot!.  The origirl is shown twice, at
the to!) alit! bottom Icft~hant! corrw~. The pe:~k rc!,rcscntirlg the end of the vccto~
. behuee~t hc:~.v,y ntmns is nr:tr t,!le mitltllc of lho ma!) (I:~!~!ot! f 24). The
ot,!lcr (smaller) peaks :~II(! hollows :~rc s!)uriolls I):tckground ~IIIC t,o errors of measure-
menl, etc. (!Iorse I~cniogl0~~in: tlilTcrcnces dire to I'CMR. Green et al., 1954.)

X-RAY ANALYSIS AND PllOTEIN STIlUCTUIlE        185

discussed: t,hat is to say, if the X-ray picture showed that the mercury
had increased the intensity of a reflection, then it was given the same sign
as the calculated mercury contribution; if the intensity had been decreased,
then the signs were made different.  In some cases the mercury contribu-
tion happened to be so small that no decision could be made, but in the
great majority of reflections the signs could be definitely allocated.
The earlier studies, predicting that certain reflections would be of like or unlike

sign, were confirmed wherever they made definite predictions.  Some of the weaker
predictions were not confirmed, however, and it is because of this, and because this
method of linking signs is only possible in very special cases, that we have not de-
scribed it in detail.  It was nevertheless a technical tour deforce at the time.
Recent work, which mill be mentioned shortly, has increased the number

of definite sign determinations, and confirmed those allocated earlier,
with the result that 88 reflections out of a total of 94 whose spacings exceed
G A can now be taken as certainly established.  From these data an elec-
tron density map has been computed, showing the contents of the cell
projected parallel to its b axis.  By combining the results of the various
shrinkage stages Perutz was able to calculate his electron density projection
corresponding to an imaginary superexpanded stage in which -the layers
of molecules have been, as it were, floated apart, so that there is open
water between them.  (Note that this procedure is only possible in very
special cases, as we have indicated above.  In general one cannot separate
out the molecules from their overlapping neighbors.)  The result, showing
the projection of a single layer of hemoglobin molecules, is reproduced
in Fig. 17. This has been drawn in such a way that the zero contour
represents the electron density of water: protein is, on the average, more
deuse t.han t,his.

Looking at Fig. 17 one experiences two feelings: admiration for the
very c~onsiderable technical achievement which it represents, and disap-
point~mcnt that the result appears to give us so little information. Its
obscurity is due mainly t'o the very great thickness of the projection-the
unit cell is 63 A thick in this view-and partly to the rather low resolution.
* Nevertheless there are some interesting features.  For example, the outline
can be fitted roughly t,o the ellipsoidal shape deduced by earlier methods
(see p. 178), but is markedly more irregular.  Again, the molecule appears
to have a waist, or rather a dimple, close to the dyad axis; presumably
this is related to the fact that it consists of two identical halves.  None of
the other features suggest anything in part,icular, though the "hole" marked
`w is surprisingly, though not impossibly, deep. The features which a
biochenlist, might first, searrh for-the iron atoms and the heme groups-
would not. iu my case be expected to show up in projection at this resolu-
tion.


J8G            F. H. C. CIlICK ANli J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        187

The one feature which can be identified with certainty is the position
(in projection) of the heavy atom, although even this could not be picked
out if we did not have two views, one with and one without it (the figure
shows the latter).  Since we know that the mercury atom is attached to a
sulfhydryl group, it is possible to draw some conclusions about the position
of sulfhydryl groups in the hemoglobin molecule by a correlation of chemi-

      ,'       ,' r -\
,--.
.P. `,  l.-.
        ,'     :  I :           8'
                        ,.-._ .-_.    : :
                          ' i
    \_e---       L_' .--._a'  : \_*,_._. *I     -.._a ---. .

  FIG. 17.  A Fourier projection of a row of hemoglobin molecules sllspended in salt-
.free water.  The rolltours nrc contours of (project&) electron density, the zero COW
tour corresponding to the density found where the whole depth of the unit cell is
filled with water,  The dgad axis between the two halves of the molecule is in the
center of the figure. (Bragg and I'erute, 1954.)

cal and X-ray studies.  We shall enlarge on this topic since, one hopes, it
provides the pattern for much future work.

It is convenient to summarize the chemical work first (Green et al., 1954;
Ingram, 1%5), fixing our attention for the moment on native horse hemo-
globin.

Ingram used the technique of ampcrometric titration with silver nitrate: thus the
protein would first he made to react, with a known quantity of PCMD, and the SH
groups remaining unhlorked would be titrated with AgN& The results showed
that all the available cinlfhg~lrgl grorlps of a single hemoglobin molecrde (molecular
weight 67,000) could he saturat,ed either by 4 molecules of AgN03 , or by 2 of PCMB,

or by 2 of HgClz (the experiments were carried out under conditions such that combi-
nation of the reagents was probably with SH groups, though t,his is not certain).
If the molecule was first saturnted with AgNOa or with PCMB subsequent reaction
with HgClr displaced the first substituents.  If on the other hand one mole of either
PCMB or HgClr were added first the protein would subsequently take up only Iwo
moles of AgNOs , the reagent first added not being displaced in this case.  The sur-
prising thing is that stoichiometrically PCMB and HgClr are equivalent, although
one would expect the former to be univalent relative to SH, and the latter divalent.

The results suggest that native horse hemoglobin contains four available
sulfhydryl groups, arranged in tzoo close pairs.  One molecule of HgC12 or
PCMB will saturate both the SH groups of one pair, the former by com-
bining directly with both of them, the latter by combining with one ahd
inactivating the other by steric hindrance.  On the other hand a silver
atom, being much smaller, saturates only one SH of a pair, and Iwo are
required to inaat.ivate t,he pair altogether.  One would expect, therefore,
that there would be only two regions on the hemoglobin molecule where
mercury or silver would go, each corresponding to one of the pairs of SH
groups.  The X-ray results confirm this, at least as far as the z and .z
coordinates are concerned. Difference Fourier projections have been
prepared, showing the positions of the heavy atoms, for the cotiplexes of
hemoglobin with (a) 2 moles of I'CMB, (b) 2 moles of HgClz , (c) 2 moles
of AgNOz , and (d) 4 moles of AgNOn .  The resulting projections all
show heavy atoms combined at approximat,ely the same positions in the
cell.  It is especially significant that when four silver atoms are combined
the unit cell cont,ains only two peaks, showing that they are present, in two
pairs, each pair being so closely spaced that at 6 A. resolution the two
silver atoms composing it carmot be seen as separate peaks.

This is not, the whole st,ory, however.  Analytical dat,a for horse hemoglobin (Tris-
t8ram, 1953) show that, it, actu:dIy rontnins 6 sulfur atoms in the form of cystine or
cystcine. Other experiments by Ingram have shown that, when denatured, hemo-
globin ran react with siz moles of AgNOa , in contrast to the native protein which,
as we have said, reacts with four.  This result, toget,her with others on blocking by
HgCl2 and by PCMB, suggest that the SH groups actually occur in two groups of
three, but, that one member of each group is unavailable in the native prot,ein.  Ox,
sheep, and human hemoglobin have also been studied wit,h similar (but. not identical)
results; Ingram'* paper (1955) should be consulted for details.

Careful study of the X-ray data shows that although in all the deriva-
tives we have mentioned the heavy atom is attached to the same part of
the molecule, there are in fact minor differences in position, amounting to
a few Angstrom unit,s.  The reason for these small differences is unknown;
they may be due perhaps to rotations about the bonds of the cysteine
side chain.  Tbry were in fact, of great assistance in sign determination;
the signs of some of the rrflert,ions could not be decided from the I'CRiIR
derivative alone because the mercury happened to be in such a position


X-RAY ANALYSIS AND PROTEIN STRUCTURE        189

and isocyanides were all investigated, but for various reasons none of
them was wholly successful-generally the reason was that myoglobin has
so high an affinity for gaseous oxygen (much higher than that of hemoglo-
bin), with the result that unless the most strictly anoxic conditions were
maintained the heme group ligand was promptly replaced by an oxygen
molecule.

In the end success was achieved by an entirely different approach,.
namely to crystallize myoglobin in the presence of various inorganic ions
containing heavy elements.  Naturally ions were chosen which on general
chemical grounds might be expected to have some affinity'for one ok more
of the types of side chain present in proteins.  But of course & protein
nearly always contains more than one of any given side chain; the hope ivas
that in some cases steric or other factors might induce the ion td be at:
tached preferentially or even specifically at a single site. In effect this
hope was realized in a number of in&&es.  The criteria for success tPefe
crystallographic rather than chemical:' that is to say, atl X-ray picture
showing changed intensitie3 was the &dence that combination had taken
place; and a difference Patterson, computed from the intensity changes
in the same way as we have described above, indicated that combination
had been specifically at a single site if it was found to contain only one
peak per asymmetric unit. we may take as an example the first ion that
was successfully attached in this way-namely mercuriiodide HgId--.
This was investigated because it was known to form complexes. with thio
ethers; myoglobin contains two residues of methionine whose side chain is
-CH,-CH,-S-CHa .  Myoglobin crystals prepared in presence of po-
tassium mercuriiodide gave an X-ray pattern substantially different from
normal, and tdie Difference Patt,erson projection calculated from it is
shown in Fig. 18.  (We shall be dealing throughout with myoglobin derived
from sperm whale and crystnllixcd from ammonium sulfate.  It is known as
Type A and is mnnorlinic, wit,h t,wo molecules in the unit cell; the space
group is 1'21 , n-hicah means to say that the only symmetry elements present
in the unit, cscll are srrew dyad axes parallel to b.)  Figure 18 cont,ains ody
one peak per asymmetric unit (i.c. per half cell) apart from the origin
peak, and it may t~hcr~~fore be taken that caombination has occurred at OIIC
site per molcculc.  This is not, an exprctrd result since sperm whale myo-
globin csontnills two mrthioninc sitlc &ins, IIO~ one; it must be sr~pposct]
that, one of them only is stcri?ally av:lilnl)lc for c~orribir~ntion-if ir~JC~r:d
the mcthioninr side (*hain is the sit.c of attachment,.  The difYercncr Pat-
terson is cnomputcd from rrficcttions of sparing greater than 4 A. ; the
mercuriiodidc group is thcreforr not rcsolvrd int,o its cornponcnt at 0111s.
A later projt~c*liorr wit,b all t,crms out, to 2 A. (not illustrated here) sho\vs
t.hc group part i:rlly rcsnlvcd.

From the known position of t!hc Iucrt'llriiotlitlc group many of t,hc signs

that its contribution to their amplitudes was almost zero, while the silver
atoms were displaced sufficiently to ensure that in such a case their con-
tributions would be quite substantial.

At the t.ime of writing nothing further has been published on hemoglobin.
Sign determination has, however, been extended to a resolution of 3 A.
and a Fourier projectioh wit'h this resolution has been caltiulated; as might
have been anticipated it does not reveal any additional features of the
structure which can be interpreted, at present at. least (Perutz, personal..
communication).

  Peruts (1956) has worked out the theory of a method for determining the difference
' in I/ coordinates between two heavy atoms used in two separate isomorphous replace-
ments (the minimum requirement for three-dimensional work-see p. 182); in a mono-
clinic cell there is no simple way of establishing this difference, since there are no
symmetry elements perpendicular to r/ which can act 89 reference points,
Work has also been in progress on ox hemoglobin; Green and North
(personal communication) have obtained several isomorphous replace-
ments, again using the sulfhydryl groups, and have determined a substan-
tial proportion of the signs of the a and c projections of the (orthorhombic)
unit cell. They have also derived a tentative Fourier projection along 2,
a view of the molecule already known to have interesting features (Crick,
1953a, 1956). In both species of ,hemoglobin the most pressing problem
is to obtain further isomorphous replacements at radically different places
on the surface of the molecule-in this endeavor some success has been
achieved by the use of two reagents developed for the work on myoglobin
(see p. 191), namely mercuriiodide and aurichloride, but, it cannot be said
that the problem is yet entirely solved.  Its solution would open the way
for determining the exact shapa of the molecule in a fairly short time, and
in the long run for a full t hrec-dimensional analysis.
d. Iso~norpho~l.s R'cplmvw~t nnd th Stmctwc qf Alpqlobin Frown
several points of view myoglol)irl is an attractive objcrt, for study by the
protein crystallographer.  It has :1 small molecular weight. (I 7,000) and it
can readily he cq%allixctl in at lcnst a ~IOZCII dilYcrcnt' spacsc groups (Ken
drew ct al., 1954). It, c~otrf:~ins a proslhc~t ic: group of I~IIOWI~ c~llcmi~al
structure and dcfinctl physiological rule, and il is arudogous ill function
and so perhaps in structure to :Lnother protein which is being intensively
studied by X-ray mrlhods, nar~~dy hcrnoglobin.  On the other h:lnd it
is more intractable from the poirlt of T+tw of i~omorphous rc~placrment,,
berausc no myoglol)irl is k~~r~\vn to cv111ait1 ftw snlfhytlryl grou1)s, whcrc:ls
these groups arc to IIO found it1 ~11 I~rmoglobit~s so far csamil&. The
other obviolis uniql~c site ili tlicl niolt~~lllc i?: the hcrnc group i&If', :.ind
varioils attempts wcrc m:rdc (l<cIidI'c\v, Rotlo, l)illtxis, atic Ingrmn, illi-
publishrd data) to prc'p:lrc ligantls for the hcmc grollp whicah csoritairicd
heavy atoms such as mercury aud iodine.  In~idazolcs, nil 1.0~0 compounds


190        F. 11. C. CRICK .4ND J. C. KENDREW
                   .
of the reflections could be deduced in exactly the same way as was done
with hemoglobin. To be certain of all of them, however, more than one
isomorphous replacement was required.  In fact several other methods
have been discovered; in most of them the chemistry involved is even more
obscure than it is in the case of mercuriiodide. Figure 19 shows the posi-
tions of the different replacements in the unit cell. In each case they were
located by means of a difference Patterson or difference Fourier projection.
In some cases the method of achieving isomorphous replacement was

X-RAY ANALYSIS AND PROTEIN STRUCTURE        191

Difference Patterson projections, any more than the other specific heme
group reagents which were tried; but once all the signs of the reflections
had been established by other means it was possible, making use of them,
to locate the heavy atoms in these combinations by Fourier methods.
As the figure shows, they are in almost identical sites.  Since the two com-
pounds react specifically with the iron atom of the heme group, we may
conclude that the latter is situated about 6 A. from this site.

The next contour map (fig. 20) is a Fourier projection of the protein
with a resolution of 6 A. A Fourier projection with resolution 4 A. has

a

111 II,
0       10A.
FIG. 18. hdhr rxnmplr of n l)iffprrnre I'attcrson. This t.imc the origill is in

the middle of (.he figure. `l'hr vector I~LWCCII he:rvy atoms produces the peak near
the top left-hand corner (and also, hy tiymmetry, near the hottom right-/mad corner).
It can be seen that, the dist,ance between either of these peaks and the origirl is ahout
23 A, showing that in projection each heavy atom is II!4 A from a twofold (screw)
a,xis, and thus 23 A from the other heavy atom.
heavy atom due to K211gI,         (Sperm whalr myoglohin, Oype A;
           Bode, IIintzis and Kendrew, unpublished data.)

extremely simple--for example, the silver atom indicated in the figure was
introduced by the simple expedient of crystallizing myoglobin in the
presence of 1 mole of silver nitrate. Each of the replacements provides
an independent check of some 80% of the signs; and this means that all
reflections except a few weak ones are at least triple checked. Out to
spacings of 6 A. there are no discrepancies: beyond this the analysis has
not been carried in detail.

Two of the ligands shown in the figure are specific reagents for the heme
group, namely p-iodonitrosohenzene and a compound made by combining
the mercury atom of p-chloromcrcuribellzellc sulfonate wit,11 the sulfhydryl
group of p-mercaptophenylisocyanide.  Neither of these gave interpretable

LI PCMBS   I                                  4 ,

a Au,Ag           c7                            o
? ?????
? ? ? ???????       ???

El PCMS-S.C,H,.NC   Myoglobin, type A: positions of heovy-atoms.
- I
m Hg di-ommine
FIG. 19. To show the seven different isomorpt1ou.s rcp1acement.s so far achieved
in myoglobin, type A. The symbols indicate the pwdtions of the diflerent heavy
atoms in the unit cell. (Bodo, IXntzis and Kendrew, unpublished data.)
also been computed, but is almost identical, indicating that the confusion
of peaks and hollows in the projection which makes it virtually uninter-
pretable is a consequence not so much of inadequate resolution but of the
great depth of protein (31 A. in myoglobin) through which the projection
is necessarily made. We have here one more example of the fact that
two-dimensional projections of protein unit cells are not at all informative,
and once again it is clear that a three-dimensional approach, with all that
is involved of tedious computation and greater error, is quite essential.
Resides the work on Type A myoglohin crystals, attempts have been
made t,o ac+icve isomorphous replacement in several other crystalline
forms of the protein. The most successful of these is seal myoglobin


192          F. 11. C'. (:111(`1C AND J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN 3TRUCTURE         193

(Type C; Scouloudi and Kendrew, unpublished data), a monoclinic form
of which a preliminary Fourier projection, based on signs deduced from
isomorphous replacement with mercuriiodide, has been computed.  Not
all the ions used with Type A are equally successful with Type C, however;

. Ftn. 20. Fourier prfJjcc:tiorr of JJl~O~lOlIiJJ, t,ype A.  This show the projcrted
electron density of the JnorJovlinic: rJrJit ccl1 (which cont.:GJJs two rnolec#JJlcs), looking
down the b axis, i.e. through 81 li of protein and Jnothcr liquor.  Ilcsol~Jtion 13 A.
The I)osition of two heavy grol~lw are S~OKJI :*&,T4--; X lfg in p-chloro-mercnri-
benzene SJJlfOIJate. Thn two molcc~~les ovrrl:rp and it is not easily possil)lc to tell
where one begins :tnd the other cndn. (Bode, IAntzis :Lnd Kendrew unpublished
data.)

and this suggests that in sornt: crises at least, the "combination" between
protein and ion may be intrrstitial rather t,hQn st,rictly chemical; difIcrent
methods of packing virtually the same molecules ill crystalline array would
lead to the formation of different "cozy corners," apt, for the harboring of
different small ions.

e. Isomorphow Rcplaccmrut nnd ihc Structure of I?ibonuclerrse.  3~ ilw-
nuclease is anot,her favorable pr~Jk?iiL for X-ray studies because of its

low molecular weight (about 13,500), because of its ready availabilit,y,
and because a great deal is already known about its amino acid sequence
(for a summary of the present position see Anfinsen and Redfield, 1956);
indeed it is likely that the whole sequence will shortly be established.
There ape several different types of crystal (King er al., 1956), but most
work has been carried out on a monoclinic form (space group P21, two
molecules per cell). Earlier tentative interpretations of the Patterson
projections of this form (Carlisle and Scouloudi, 1951; Carlisle et al., 1953)
have not been widely accepted by other workers in the field.  The three-
dimensional Patterson syntheses (Carlisle and co-workers, unpublished
data; Magdoff et al., 1956) in fact show less "regularity" than those of
hemoglobin, myoglobin, and insulin.  It, is thus not very likely that the
structure will be solved without the help of either the isomorphous fe-
placement or the heavy atom method, even when the amino acid sequence
is known.

No completely successful isomorphous replacement has yet been reported
in print, but Dr. David Harker and his co-workers (personal communica-
tion) have succeeded in introducing into the crystal a uranium complex of
the dye alizarine cyanone RC, in such quantity that the tinit cell contains
four dye molecules and eight uranium atoms. A preliminary Fourier
synthesis of the b projection qf the unit cell has been obtained (Barker,
1956).  It, is understood that furt,her isomorphous replacements are being
attempted both on the monoclinic crystal form (Carlisle and co-workers)
and 011 an orthorhombic form (1Iarkcr and co-workers).

f. Rrquircments jar Isnmorphous Replacement. Having described some
applications of isomorphous replacement to proteins we shall tt0W Std
the basic requirements of t.he mct,hod.  The first, of these is the obvious
one that the heavy atom should he hcnvp: but,, WC may ask, how ht;:~~?
The parameter measuring the ef'fective "heaviness" is approximately given
by

where ?L  = number of heavy atoms per protein molcculc
   ill* = atomic weight of heavy atom
   nl, = molecular weight of protein.

Two poiut,s must he made about nr,, .  The first is that irr practice the
heavy atom rrplarrs a light, molccul~~, probably of solvent,, so that some-
thing should 1~: subtrac*tcYl to allow for 1 his.  `l'ho scc~nrl is t Ii:it, wry ofI (91
the Harry :ltom (10~ not, fully saturate ils sitr; if wly 80 % of' the sit,(`s
are occtupied then the heavy atom will appear to t,he X-rays to bc less


191          F. II. C. CIIICK AND J. C. KENDHEW

X-KAY ANALYSIS AND PROTEIN STRUCTURE        195

heavy, in proportion.  Our formula is therefore better written

k(M,, - 25)

where Ic = occupancy by the heavy atom (= 1 if all sites occ.upied).  (If
the n heavy atoms are very close together compared with the spacing of
the reflection being considered, it can be shown that l/n should be re-
placed by n in the above expression).

As an example we may take the case of mercury added to horse hemd-
globin, where n was 2 per molecule of molecular weight 68,000 and k was
believed to be 0.8.  Our parameter is then

0.8(200 - 25)

1f we add. one atom of mercury to one molecule of myoglobii, with 100%
occupancy, the parameter works out to be 1.35.

It is still not clear what is the lowest useful value of the parameter, but
there is no doubt that a value 1 is satisfactory for real structure factors,
while one of 0.5 would be marginal; for complex structure factors higher
values are desirable-l.5 or 2.0 or even larger. Thus in practice a single
bromine atom, for example, is near the lower limit even for a small protein.
For complex phases it is an advantage to have more than one heavy atom
at a t,ime, but multiplicity of heavy atoms raises new problems which we
shall now consider.

To specify the most desirable number of heavy atoms is not a simple
problem. Jn the first instance it is probably best to have only one heavy
atom per asymmetric unit, since it can be located with great ease.  Never-
theless it may be possible t,o find two, or even more, especially if some of
.thctn arc linked together chctnic~ally so that their distance apart is known.
It is tlifli4tJ to 1)~ dogmnt~ic~, hut. four or more would cacrtainly be difficult
to loratc, t~horrgh if the atoms were really heavy, e.g. mercury or uranium,
the rliflicirlt its would bc rctlurod somewhat.

Ilr~a-ever, onrc the sians of (he prolcir~ reflections iu a given projection have hecr~
cstn~Aishctl by an initial sirn~)le isomorphorts replacement, more complex replace-
ments can Ix dealt wit,h rcllat,ively simply, since one can then work in real space by
computiug difference Fourier projertions, showing directly where the heavy atoms
are, rather than diflerence Pat,terson projections which becomc very complicated if
it is much ahove ntle (the nrlniher of pc:tlts in :I Patterson projection is the square of
the nrlmhcr of atoms in real ~p:~e).  Under these oircumst,ances there should be no
difficulty ill Iocalirrg qltilc a nurnlxr of heavy at,oms, say 10 or even 20, assuming that
isornorphisni is maintained \vitll so Iargr :I nllmher of foreign at.oms in t,he unit cell.
For mllltiplc r.~~~I:~c~~:rneft~s of (his kirltl 111~ grca(csl dif5cult.y would be to find theit
u coordinates irt a morto~litlin c*cll. So Iargo :I rrumI)cr of heavy atoms, if arcrlral.ely

located, would be of the greatest value for three-dimensional work, and it might even
become possible to use the Heavy Atom Method proper (see p. 179).
We may summarize the requirements for isomdrphous replacement as
an aid to structure determinations:

a. A substantial degree of saturation is desirable at all sites which are
occupied at all. It makes every kind of application difficult if, in addition
to some sites being fully occupied, there are others slightly occupied-for
the latter cannot readily be distinguished from experimental error.

b. It is a great advantage to have several di$erent isomorphous replace-
ments on the same protein; that is to say, replacements on diffei+ent parts,
of the molecule.                                          I
The minimum useful separation between two sites, if they ate tb be consideted as

"different," depend8 on the spacing of the X-ray reflections being studied-fop long
spacings they must be further apart than they need be for shott spacings; but tt
separation of as little as 6 A. can give much usefut information, though not abotit the
inmost reflectiqns. It follows_ that there is scope for adding different molectiles, kdh-
taining heavy stoma in different places, to the same point of attachment ori the pro-'
tein.

c. At least `one of the isomorphous replacements should give a large
value to the parameter discussed above. That is, the atoms should be
really hea y.

If these criteria can be satisfied there seems at present no insurmountable
obstacle in principle against proceeding toward a complete structure
determination of a crystalline protein.
will be a very long and tedious business. At the very best, however, this
                 It may be asked whether in the
short run there are any quick returns which can be expected from an
investment in heavy atoms, in advance of the long-term dividends which
protein crystallographers patiently hope to rereivc. There appear to be
two ways in which quick answers, of direct use to biochemists, can IC
obtained by means of isomorphous replacement; the determination of the
shape of the molecule, and the localization of interesting groups on its
surface.

We think that met,hods involving isomorphous replacement are 1ikclJ
to become the standard ones for determining the shapes of all except pcr-
haps the very large protein molecules. Since only t,he low order X-raj
reflections are involved (high resolution is not needed) strict isomorphism
is not necessary, and t,he amount of expcrimcntal dat,n which has t,o bc
collected is not very large; on the other hand at lcnst two and probably thrccx
separate isomorphous replacements are needed. If these are available,
and especially if the elect,ron density of the solvent car1 he mrietl---ns is
usually the rasc-it should be possible to obtain a good low rcsolutiutl
three-dimensional picture of the molecule.


1%;             I?. Il. f'. f'l!ll'li :\NIl J. (`. I<ENIJI~I~:\\

X-IIAT ANALYSIS ANI) I'IWTF:IN STI1UCTUIlE        1 97

\Vc do not :ltt:wh m~~v11 in~~m4:~mc 10 1 Ilc ol~jrc:~ ion th:d prolcitls ma). nlt:lnge Iheir
slxll~2 while pwsirlg from strllll iolb III Ihc crystal, n-ilh the implioation thnt, results
ol~tui~~rtl I)y r~~st:llIogt~:~l)Irr:~s :II`P 1101, rrlevat~l, in 1111: intew3t.s of biochemists; as
we Iiavc oul)l:Gtietl, tlic enviwr~rncnt~ of the J)roloin iu a crystal is very similar to its
environmcut iti wIlllion.  WC do agree, l~owcvcr, that some changes may sometimes
occur (see Yang and J)oly, 1957); but even so, lirm information about a slightly al-
tered shape is very milch more useful than dubious information about the actual shape
under physiological conditions.

A more import,ant difficulty is that, where two neighborittg molecules-.
are touching it may not be easy to discover from a low resolution picture
where otte ends and the other begitts.  However, such ambiguities can
probahly be resolved by the comparison of different shrinkage stages
or different crystalline forms of the same protein.
The second type of quicnk answer which ottc may hope t,o obtain by the
help of heavy atoms is the position of side chains or active &tt,crs which
can be "marked" by spccifio atItarhmcttt of groups cont,aing heavy atoms.
This procedure, wltilc at first, sight, very attractive, may not always prove
to be of real value, sinw the position of the heavy atoms is found in the
first insta1tce only in relation to the symmetry elements of the crystal.
That it can sometimes give useful information may be gathered from one
example that we have already cwttsidered-the location of sulfhydryl groups
in hemoglobin. 111 any (vase, as isotnorphous replacemettts on the same
protein ntult~iplg, the ittterrclatiotts of dif~erettt groups begin to emerge
and arquirc significannce; nttd itt ndtlitiott the shape of the molecule and t'he
positions of the heavy at,oms within it should become available. The
kind of ploblrtn \vhi& might. (wily fw wlwd, for wtntplr, would bo the
Csl.:ilJlislttttrttl, of 111~ rcl:11 ivc IJositiotts of the wlive wtiter of an enzyme
and fJf a sulfttydryl group in 1 hc molrcwlc: the former might be `Ltnarkcd"
by tttratw of a spcvih irtltit)ilor csotttaittg a heavy at(om, the latter by
ntct lryltwrcwt~y or IY~MS.  `I'hrrc tn:ky also bc a poittt in adding heavy
atoms to loc:tIizc particwlar side c+:titts or wtivc wtitcrs, eve11 if the rc-
sttllattt, c:otnplcx d0cs not crysl ullixc isontorphously wilh the ttormnl pro-
tcitt.  Thus if the (yrosittc twiducs in a protein wcrc to bo iodittsted, the
result might IIC: that the rcll dintensions of tltc crystal chattged substantially,
or ~VCII that. tlw apwc group w:w altered; butI it, might ttcvertheless pay to
work with the iodinai od pt*otc\in in ot)hcr isomorphorts replacctncnt studies,
since cwttually it, wJult1 bc easy to locate the ioditte atoms, and these
would innnediatc~ly reveal the position of the Lyrosine residues. If the
amino acid src~uwwc of tltc protcitt were k1towt this would be of consider-
able help in building trial nrodnls of the structttrc.
`I'ttcre arc thus scvcwl w:~ys in which heavy atoms may bc added to a
prtJtf+i so as to I)(! ttwfttl for X-ray tlil'ftwtiott st,rtdies.  JGwlt case has to
bc cxnrttittrd it~tlividtt:rlly 01t its mcrils, csprc+tlly sitter there is 3s yet 110
meatts of pr.cdictitlg wlte(hc~r a particular addcttd will alt,er the size of the

uttit cell.  It seems to us that, these requiretnettts present, a challenge to
the protein chemist.  To attach heavy atoms at relatively few sites and in
high yield, without denaturing the protein, is not an easy task; nevertheless
since the information which can be obtained if success is achieved is po-
tentially very great the expenditure of considerable effort, is justified.  We
hope that our short outSline of the problem will stimulate other workers to
devise new methods to this end.

6. !l'he Chain Configurakon in Globular Proteins

As wc saw in a previous section, there is good evidence that the synthetic
polypeptides, in their folded form, assume the n-helix configuration of
Pauling and Corey; further, it is very probable that certain fibrous proteins
contain the cu-helix; among t,hese may be mentioned cr-keratin, tropomyo-
sin, myositt, fibrin, and intact bacterial flagella. The question which me
shall now discuss is how strong are the many claims that t,he a-helix is also
the main st.ructural featttre of the globular proteins. These claims are
controversial, and in our view the case is 1tot yet proved.  We shall s&t-
marize t,he evidence briefly.

Similarit& between t,he X-ray pattern of cY-kerntin and the Patterson
synthesis of hemoglobin were pointed out by I'erutz (1940): parts of the
three-dimensional vector structure contain rods spaced 10 A. apart with
maxima at 5 A. ittt,ervals along their lengt,h, and the suggestion was that
these rods corresponded to polypeptide rhains in real space, liThose dimen-
sions ~vould rorrcspond to those in wkeratin.  Similar rods have bcwi
found in tttyoglohitt (liwtdrcw, 1950; l<cntlrcw and 1'. J. I'aulittg, 1956).
When the a-helix was discovered J'auling and Corey (305lb) n-orltcd out,
t,hc radial average vcrtor density of I'errttz's Patterson sytttttcsis of hcmn-
globin, and sl~owrtl that it was ttot, rtrtlikc what. ottc might cxpcct, from :ttt
nssc~mbly of cu-hrliccs.  Their c*otttparisort was in clrwt a cottiparisoti IJr-
twccn thcorctical and espcrintcntal versions of the powder pnttcrtt of thn
protein--that is t)o say, the pat,tcrrt which would be o!Jtaittcd by irradiatjittg
a random assctnbly of hemoglobin tnolwulcs.  This rotnpnrisott has becrt
made dircc:t.ly by hrudt and I<iley (1!155), who mensurrd the itttcnsity of
X-ray scnt,t,ering as a function of rl.ttglc for a large ttutnher of amorphous
protein specimens, and concluded f,hat the cu-helix was an important
constituent of most of t,hetn, hcmoglobitt and myoglobin included.

In order t,o J~OVO, by this method, that the n-helix is a predomitt:tttt8
st~rurtural fw,t~ttre of a protcirt, t.wn witwin would have to be sal isfictl.
Firsts, the ~~otiittiott fmt~utw itt the powtlrr patt~ctrtts of tltow protritts fot
whic4t the ltypot.hrsis is tiiaclc: ~li0111t1 wtwspottrl c3:wtly, or ncnrly rx:wf ly,
wit'h t,hosc known to bc produced by thr c*-ltrlix (as shown citltw 11.1' KII~~II-
lnt,ion or by c*otnpnrisott with a. vat+ty of sytttltrl ic* polypcptidcs knowtt f.o
be in the a-form).  Second, no other possible rhain configuration should


198             F. II. C. (!ItICI< AND J. C. KJ3NDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE         199

give these features.  The matter is a highly technical OJW, but in our view
the evidence presented is unsat,isfactory on both these counts. Besides,
Arndt and Riley conclude that their observed curves are best fitted by the
left-handed e-helix; very recently, as we have already pointed out (p. 157),
evidence has been forthcoming that the stable form of an a-helix of L-
residues is right-handed.

There have been various attempts (mostly unpublished) to discover a
1.5 A. reflection in the diffraction pattern of globular proteins, this being ,
a diagnostic feature of the X-ray pictures of fibers containing the a-helix
(see p. 155). Apart from a very diffuse "spot"`in the diffraction pattern
of horse hemoglobin (Perutz, 1951), no such reflection appears to have
been found, although searches have been made in insulin (Low, 1955),
ribonuclease (Bernal and Carlisle, personal communication), and myoglobin
(Kendrew and P. .J. Pauling, unpublished data).

A number of rather fragmentary observations of the infrared absorption
spectrum of globular proteins, and of the infrared dichroism of protein
crystals, have been held to provide some evidence for the presence of
cu-helices (for a summary of this evidence, see Doty and Geiduschek, 1953).
This evidence was never very strong, and has now been shown to be vir:
tually worthless by the discovery that those values of the absorption fre-
quencies which had been held to be characteristic of the a-helix are also
given by materials now known definitely not to possess this configuration.
It would appear, in fact, that there may he no characteristic and diagnostic
infrared frequencies for the a-fold, though such probably do exist for the
&fold (see Elliot,t and Mal~~olrn, 1956~).

Measurements of optical rotation have recently been taken as an indi-
cation of t.he presence of cu-heliccs in proteins and synthetic polypeptides.
This dcvclopment has resulted from the theoretical studies of Fitts and
Kirkwood (1956 a, b) and of Moffitt, and Yang (Moffitt, 19,56a; Moffitt and
Yang, 1956) and from the experimental investigations of Doty and his
colleagues (Dot,y et al., 1957) and of Elliott and his colleagues (Elliott et al.,
1956).  In a recent paper Yang and Doty (1957) have found that the spe-
cifc rotation and rotatory dispersion of a number of proteins are in ac-
cordanre with the hypothesis that cY-helices are present, and in t,he right-
handed conligurat,ion, but, by no means uZZ the polypeptide chain in the
molecule could have helical configuration. They quot#e, for example,
35-38 % in insulin and 14-20% in ribonuclease-figures which may
change considerably if the solvent is altered. In our view this type of
evidence is suggestive but falls far short of being conclusive.  It leads to
a strong presumption that some sort of helical configuration is present,
and of a single hard, but as far as wc know does not discriminate between
the a-helix and other helical configurations of a similar kind which have
from time to time been proposed (e.g. the r-helix of LOW and Baybutt,

1952; Low and Grenville-Wells, 1953).  It may be remarked that there is
an encouraging parallelism between the X-ray and optical results. For
example, tropomyosin gives a strong 1.5 A reflection, and is one of the
few proteins believed to contain a rather high percentage of a-helix (70-
80%; Cohen and Saent-Gyorgyi, 1957); again, the X-ray results suggest
that ribonuclease contains an unusually small amount of a-helix or other
regularly folded structure (see p. 178), and similarly this protein is put
well down the list on the basis of its optical rotation.

We conclude that, although it is plausible and attractive to suppose
that globular proteins are made up in part of ar-helices, the case is not yet  :
proved. On the other hand it is undoubtedly useful as a working hypothe-
sis, although it is virtually certain that if a-helices form the major part of
globular proteins they are not all strictly parallel, or at least not in hemo-
globin, myoglobin, or ribonuclease; otherwise the fact would have been
apparent long ago.  Whether certain globular proteins contain nonparallel
rr-helices-and we have seen that this is a plausible way of packing them
(p. 165)-remains to be seen.  Readers interested in the more controversiai
aspects of the subject may wish to refer to the papers of Bragg et pl., (1952)
on hemoglobin; Carlisle and Scouloudi (1951) on ribonuclease; and Ken-
drew and P. J. Pauling (1956) and Kendrew and Parrish (1956) on myo-
globin. Interesting models of. insulin, based on mixtures of left-handed
and right-handed a-helices, have been proposed by Linderstrgm-Lang and
Schellman (1954), Lindley and Rollett (1955), and Low (1955). These
are structurally plausible, but it is not yet known which is favored by t,he
X-ray evidence, and to what extent.

It is generally assumed that since regular folds, including the a-helix,
cannot accommodate proline residues (which, being imino-acid residues,
have no spare hydrogen atom on the peptide bond to form a hydrogen
bond), the polypeptide chains may kink or bend where the prolines occur.
Another possible way of turning corners has been proposed by Lindlcy
(1955).  The fact is that although it is almost certain that the chains in
globular proteins do turn corners-myoglobin, for example, consists of
only a single polypeptide chain, so it must certainly be folded back OJI
itself several times-there is no direct evidence how this occurs.  The solu-
tion of the structure of one or two globular proteins will inject some life
into these rather pale and wandering speculations.  It may well be that
the next review article on these topics in these volumes will be mainly
concerned with such problems.

v. VIRUSES

Twenty years ago it was a matter for surprise that one could somet.imes
make crystals of viruses. The implications of the detailed difrraction
patterns given by such virus crystals have not, always been realized.


200             F. II. c.  CI:ICK AND J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE      2oi

Cryst,als large enough to be seen have so far been obtained from compara-
tively few viruses, perhaps hccausc t,hc small amounts of material usually
available have discouraged attempts at crystallization.  This may be the
reason why few c*ryst:ds of animal viruses have been reported, although it
seems unlikely that the larger and more irregular viruses, such as vaccinia,
                                             .
will ever be crystallized.

But even if only minute quantities are available a virus can be studied
by the electron microscope (see the review by Williams, 1954). The
remarkable fact has emerged that almost all smaZ2 viruses have a fixed
size and are, in shape, either rods or "spheres" (recent work had indicated
that the "spheres" may be more nearly polyhedra; see, for example,
Kaesberg, 1956). It is convenient to discuss the X-ray diffraction of
virus particles under these two headings.

1. Rod-shaped V&uses

The most important rod-shaped virus, and the first to be examined by
X-rays, ii tobacco mosaic virus (TMV).  This virus has been extensively
studied by many different techniques and illustrates v,ery well their various
advantages and limitations.  Here we shall naturally concentrate on the
X-ray results, describing first of all the main features of the virus, then
summarizing the X-ray studies, and finally commenting on the relation
between the X-ray results and those obtained by other techniques.
a. General Features of lljllv. The TMV particle is approximately
cylindrical in shape.6  Its length is 3000 A. and its mean diameter 150 A.
It, is made up of about G% ribonucleic acid (RNA) and 94% protein.
Chemical results strongly suggest that the protein component of the virus
consists of ralher over 2000 identical subunits, each of molecular weight
ahout 18,000. Various straiils of the virus are known ; they generally
. tlifrrr slightly irl the :unino acid cornposit.ion of their protein components.
The JlNA ant1 the pro((~itl P:I.I~ 1)~: stparatctl, and under favorable rondit,ions
t IIPSP srpnratctl rwnpotlcuts GIII be rccornbincd to give rodlikc particles
similar to that rriginal virlci.  nlorcovcr some of them appear to be infcc-
ti1.11 (E'rnc:~~l~c~l-~lo~~r~:~t~ alit1 Williams, 1955).  `I'hcrc is ovidencse, further-
more, ihat the srpnrnt~ctl 11Nh has some infcrtivit,y on its own (Giercr
ant1 Pl~lllxmrtl, I!M).  `1'hc llrotcill (~oinpoi1cn~, known as "A" protein,
usr~ally has a molc(~ul:tr \\-eight around 100,000 (and therefore must, consist
of :,,I aggrrgntc of srlvrral of thr al)ovc-mentioned &mica1 subunits).
Tt lvill polynic~riw at, lo\v 1'11 1 o form rods similar to the iutact virus, but
of iiltlcfinilc lctigth (S(+rarnrll, l!)-l7).  The virus protein is ncwr infective
  5 `rl,c sfj(lmy for mwf. of lhc s~:~lcn~fmt.s nn~tlc in this srrljion c:m hc found in the
vol,~lnca of ..I&t~rlr.~,~ ill L'irm /~~~.sc~arc~/~ (I<. RI. Sinith :md RI. A. Id:lllffcr, c&i., Ac:L-
tlplnic I'rrss, New ~<,l,l<) :IIIII wlwvi:llly in the adides by C. A. Knight antI Jt. C.
William3 in Vol. 2, 1051.

in the absence of RNA.  Recently it has been found that RNA from sources
other than TMV, and also vllrious kinds of synthetic polynucleotides,
can be co-aggregated with "A" protein to give (noninfectious) rods (Hart
and Smith, 1956).

True crystals of TMV, with sharp faces, are found within the cells of
the host plant.  They are too small to be examined by X-rays, but they
have been studied in visible light by Wilkins et al. (1950) using a variety
of techniques. These workers suggested that. within the crystal the
virus rods are arranged in rows with their ends in line, afid that altek%at&
rows of rods have slightly different orientations. This ingenious picture hd
recently been conformed by electron microscopy (Steere, 1957). '

No one has so far succeeded in producing true crystals from e%tMcted
virus particles, but they easily form birefringent gels which ate bata;
crystalline: that is to say, the virus rods are all parallel and in hexagonal
array, but their ends are not lined up.  These gels C&II swell and shtinkg
and the X-ray evidence strongly suggests that this behavior is a con-
sequence, nbt of a change within the virus particle, btit of change6 &-I the
distance between them.
b. X-ray Results: Basic Features. The most striking conblusion from

the pioneer X-ray studies of Bernal and Fankuchen (1941) was that the
virus is made up of spbunits,  This followed from the demonstration that
the repeating unit in the direction of the virus axis was only 69 A. long,
whereas the part,icle was known to be 3000 A. in length.  The exact ar-
rangement of these subunits was not clear at the time, but the essential
feat,ure was later suggested by Watson (1954), who pointed out that the
X-ray pattern (in particular the region near the meridian where reflec-
tions are absent) could be most easily explained if the virus had a nonintcgcr
screw asis. The screw axis post,ulat,cd had (n + >$) subunit,s per tlrrn,
one coinplctc turn ocbclipyilrg 23 A.  11, is tlifIic~rllt to tletcrminc tlic: v:tluc
of n from the tlilYrnction dat:), and early suggestions that it, might, IIC l(J 01
12 jrerc based on a vrr.y irisec~ure argument.  Itercut work, (l(~sc~ril)c:tl
below, make it likely that n is Ifi.


202           F. Il. C. CRICK AND J. C. KENDREW

A number of other "strains" of Th$V have been studied by X-rays
(Franklin, 1956a). They all give extremely similar X-ray pictures,
though minor differences can be detected. In particular the so-called
cucumber virus 4 has a structure very close to that of TMV, though it
has a slightly smaller mean diameter (146 A. instead of 152 A.). It is
clear that all these "strains," including cucumber virus 4, are structurally
related, but exactly how close this relationship may be biologically is
another matter (Knight, 1955).

The X-ray pattern of reaggregated "A", protein (without RNA) is
similar to that of TMV but less perfect, suggesting that the structure is
basically the same but a little more irregular (Franklin, 1955b). The
small differences between the patterns, probably due to the RNA, are
discussed below. The change in the birefringence, from low positive for
the intact virus to low negative for reaggregated protein, shows that the
RNA makes a positive contribution to the birefringence of TMV.  This
result is compatible wit,h earlier studies on the ultraviolet dichroism (Seeds
and Wilkins, 1950), which established that the nitrogen bases of the RNA
were arranged with their planes roughly parallel to the fiber axis, rather
than perpendicular to it. It is interesting to note that when gels of
reaggregated "A" prot,ein are dried the layer line spacing shortens from
69 A to 62 A, whereas in the virus itself it! does not change, presumably
because the structure is constrained by the R.NA (Franklin 195513).

We cannot do mnre than barely mention the fact that certain globular proteins,
immunologically and otherwise related to TMV, are found in infected plants (Rich
et al., 195.5; Franklin and Commoner, 1955) and that these too are capable of aggre-
gation into rodlike particles which give X-ray patterns somewhat resembling those
from TMV.

c. X-ray resulls: the Internul Structure.  A knowledge of the screw
' symmetry does not, by itself tell us anything about the shape of the asym-
metric unit, Or the location of the RNA. Some information on these
points has come from investigations using other methods of attack.
The first of lhesc is the very careful work of Caspar (1955, 195Bb) 011
the intensities of the equatorial reflections, leading to a direct deduction
of their signs.                                      .

It can be shown that these reflections correspond to the cylindrical average of the
electron density of the virus (at least if reflections of short spacing are excluded)
and that the amplitudes of the reflections must be either positive or negative (i.e.
the phase nnglc must I)c 0 or r). Caspar studied the first ten maxim& of theintensity
distribution, and showctl t h:tt all sign combinations but two were very unlikely, in
that t,hey indicated :I particle of too great, IL radius, and that of the two, one was dis-
tinctly belter than the 01 hpr.

Jlis next, approach was totally diflcrent,, caonsisting in the application
of the method of isomorphous replacement to a virus for the first time.

X-RAY ANALYSIS AND PROTEIN STRUCTURE        203

Lead was bound to TMV by adding to the mother liquor an amount of
lead acetate corresponding to about 2500 lead atoms per virus particle
(greater lead concentrations produced a curdy agglomerate).  It could be
deduced that the lead atoms were bound at two distinct radial distances
from the virus axis, namely 25.3 A. and 84 A.  Using this information it
was possible to determine the signs of the reflections, and the result was

Radius, R (angstroms)

FIG. 21. Radial electron-density distribution in the tobacco mosaic virus par-
ticle, plotted as a function of distance from the axis of the particle.  The density is
the mean density in excess of that of water.  Note the hole (filled with water) near
the axis (R less than u) A), and the large peak at the radius of 40 A.  (Caspar, 195613.)
identical with the preferred sign combination derived by the first method.
Though the agreement between observed and calculated data was very
good, some doubt might have been felt about Caspar's result because of
the necessity of invoking two sites for the lead; however, recent work (see
below) has confirmed his choice of signs.

The Fourier synthesis computed from the observed amplitudes, to-
gether with Caspar's chosen signs, shows the radial distribution of averago
density in the particle and is given in Fig. 21.  Its most important features
are the central minimum, representing a hole down the middle of the virus


204             I<`. II. f'.  (`ltl(`l< ANI) .I. (:. KlCNI)ItIC\\

X-RAY ANALYSIS AND PllOTElN STIIUCTUIIE        205

(occupied by wai,er), the peak :tO a radius of 24 A. together wit(h the even
larger peak at 40 A., and finally t.he fn.ct that t.ho radius of the part,icle
appears to exceed the mean value of 75 A which had been deduced from
earlier data.

Another important advance (Franklin, 1956b) has resulted from a
second successful isomorphous replacement on the virus. Franklin
studied a mercury substituted TRZV, prepared by Fraenkel-Conrat, and
containing one mercury per 20,000 molecular weight of protein.  This .
proved to be isomorphous with uusubstituted .TMV and a study of its

I.""""1

                  I * I . I , I
          0 20      40      60      80      100
             Rodius, R (angstroms)
Frn. 22.  Ilwli:J clwl.rr)n tlcusit,y tlislril~~~t,ion for rcpolymcrixctl, RNA-frcr, "A"
prolcin from ThlV. Cornlwc Kg. 21, which sliow~ the corresponding function for
intact ThIV.  The main difference is the absence here of a peak at 40 A radius.  This,
hnd other evidence, suggests that the RNA of the virus is located at a distance of
40 A from the axis of the virus particle.  (Franklin, 1956b.)
&ffrartion pattern has confirmed Caspar's allocation of signs for the
equatorial rcflcctions, bcsidcs showing that the number of asymmetric
units per turn is probably 16.  It has also proved possible to allocate
signs to the quatoria1 reflections of the aggregated "A" protein (free of
RNA),  The Fourier syntheses prepared using on the one hand the ampli-
tudes of the equatorial reflections of the complet,e virus, and on the other
those of the repolymeriecd "A" protein, show clearly that the RNA
must be located at a radius of 40 A., since the only major difference between
the two syntheses is that the large peak at 40 A. in the former is absent in
the latter (see Figs. 21 and 2'2). hloreover the nature of the intensity
differences in the first eight nonequatorial layer lines of the pattern all
confirm that the RNA is located at a radius of about 40 A.  Further work

is in progress which may reveal the general disposition of the RNA chain
(or chains).  Notice that the inner peak of Fig. 21, at a radius of 25 A.,
st,ill appears when no RNA is present (Fig. 22) and must therefore be due
to protein; but little so far is known about the disposition of the protein,
in particular the arrangements of the polypeptide chains, though the dif-
fraction data suggest that they may run perpendicular to the axis of the
virus. The infrared dichroism of oriented TMV (Fraser, 1952) is
compatible with this idea.

Franklin and Klug (1956) have reached some interesting conclusions
about the external shape of the' virus by making an entirely different
approach to the data.  When the virus particles are pdcked closely td-
gether (i.e. at a distance apart of 150,A.) the nature of the diffuse reflections
in the pattern suggests that the virus surface is not smooth, but grooved
or serrated; this produces helical disordering, as if one were packing to-
gether a set of screws.  Moreover the intensity distribution on the third
layer line suggested to them that there was some matter outside the
noerage radius of 75 A.  Their arguments, though not entirely compelling,
are very suggestive and are moreover compatible with the conclusions
reached by isomorphous replacement.

In summary, then, the X-ray studies of TMV have shown: (a) the virus
is made up of identical (or at least very similar) protein subunits, related
by a noninteger screw'axis; (b) the surface of the virus is probably not
smooth, but is grooved or serrated; (c) there is a hole of radius 20 A.
down the center of t,he virus.  The RNA is located near a radius of about
40 A.; some of the protein is at a smaller radius t,han this.

It is indeed remarkable that two successful isomorphous replacements
should have been nrhieved in a virus at this relatively early stage in the
application of the method to large molecules.  Part of this success must
be attributed to the high technical quality of the work of Caspar and
Franklin.

The only rod-shaped virus unrelated to TMV whicnh has been studied
by X-ra.ys is potato virus X. This gives much poorer X-ray pattarns;
and although thry snggost that the structure is helical, better pictures
will be nrcdcd hefore this can be established with certainty (Watson,
unpublished data).

.d. Correlation between X-ray and Other Results. We shall restrict
onrselv& to a comparison with electron microscopy and the chemical
methods.

The electron microscope shows that the length of the virus is close to
8,000 A.  This distance is too great to be resolved as a long-spacing X-ray
r&e&ion, but by using Bragg reflection of visible light Wilkins et al. (1950)
have found that a spacing of this order does exist in intracellular virus


206         F. II. C. CRICK AND; J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        207

crystals. The packing diameter of TMV, measured on electron micro-
graphs, is 150 A., but it is now realized that the diameter of individual
virus particles in electron micrographs is a little greater than this.  This
agrees with the X-ray results which also show that the maximum diameter
is a little greater than the mean diameter, and that the virus particles
pack closely together by intermeshing.

By studying partially degraded virus in the electron microscope it
can be seen that the RNA is near the axis of the particle (Hart, 1955;
Schramm et aI., 1955). This does not, agree with the X-ray results, ac- ..
cording to which the RNA is at a radius of 40 `A.: the discrepancy is prob-
ably due to the RNA collapsing toward the center when some of the sup-
porting protein is removed preparatory to making electron micrographs.

On other electron micrographs pieces of "A" protein, shaped like disks,
can be seen to have a hole in the middle (Hart, 1955; Fraenkel-Conrat
and Williams, 1955). More recently Huxley (1957) has "stained" intact
TMV with salts such as KCl, and has been able to demonstrate the hole
down the center of the virus.

Although various claims have been made, no satisfactory demonstration
of surface structure has yet been given by electron microscopy.

The chemical studies have showrl that the protein of the virus is made
up of small protein molecules whose molecular weight is about 18,000
(see the review (1956) by Anfinsen and Redfield).  It has not yet been
shown that all the subunits in a virus are identical, but they are certainly
similar, for the amino acid sequences near the two ends of the single poly-
peptide chain show no signs of inhomogeneity. It has also been found
that (with one possible exception) the various strains differ in their amino
acid composition, sometimes quite strikingly; on the other hand, as might
be expect,cd, t,he X-ray results reveal only very minor differences between
most strains, and these are in any case hard to interpret.

To summarize, the elcrtron microscope has the advant#age in studying
1,argc featlures. It is also a very valuable auxiliary tool since it needs
such smali amounts of material.  The X-ray approach is unrivaled in
st,utlyirtg strwtrwc nt :I sorr~ewl~:~t high resolution, and can also pick
up features itisidc the int,actj virus.  To detcrt differcttces at the amino
acid lcvcl the c~hctnic~al tc&ttiqrtc~s arc utqttnlcd. The three m&hods,
when properly used, give rrsults whirh fit together iuto a coherent, picture.

In particular we can combine dat,a from all three to estimate the molec-
ular weight. Accepting that thcrc are 49 subuttit,s per 69 A. of length,
as indirated IJy the X-ray data, then in the total leugth of 3000 A. (meas-
ured itr elect ran micrographs) t hcrr mud hc 21 ZO subunits, assuming no
shrinkage in Icttgth Tvhctt (hc virtts tlrics itt t.hc cIc&rott mic*rosc:opc.  The
chemical met hods suggest, that t hc molecular weight of the protein subunit

is about 18,000. Allowing for 6% RNA these figures lead to a molecular
weight of 40 X 10s for the whole virus.  This figure should be compared
with the value previously regarded as the best,, namely 50 X lo", found
by particle counts in electron micrographs (Williams et al., 1951); actually
earlier determinations by other methods had given figures nearer to 40
x 106. The agreement, is only fair, but subsequent work may improve it.
           2. Spherical Viruses
X-ray studies of spherical viruses are less advanced than those of TMV

which we have just described, mainly because up to now no isomorphous,
replacement has been achieved. Merely noting that single brystal X-&y."
photographs of a spherical virus (Rothamsted strain of tobdccll h&fosis:
tirtls) were taken as early as 1945, by Crowfoot and Schmidti tpB shall
at once proceed to describe recent work on tomatd bushy stunt virtis atid
turnip yellow mosaic virus. For electron mitiroscope studies see
(1954) and Kaesberg (1956).          -       Wilki&tig 1
                                                  L    I *
a. Tomato> Bu$hy Stun? ViTtis. This virus contains 17 % of ithA by
weight, the remainder being protein. Early X-ray &u-dies (see Cariisle:
and Dornberger, 1948) showed that the unit cell was cubic in shape (u =
386 A.), but did not establish definitely that its symmetry was cubic.
Caspar (1956a) has recently produced new evidence which suggests very
strongly that the symmetry is indeed cubic, the space group being 123.
There is only one molecule in the (primitive) unit cell; it follows that
the yirus particle itself must have cubic symmetry, its point group being
23, and therefore that it is made up of 12 identical subunits (see Table
I). Following a careful study of the distribution of the strong reflections
in reciprocal space Caspar has put forward very suggestive arguments
that the point group may actually be of higher symmet,ry than the space
group demands, namely 532 rather than merely 23: the 532 point group
has 60 subunits, or a mult,iple thereof.  Nothing has so far been discovered
about the location of the RNA.

b. 9'7mtip Yellow Virus.  T1 iis material is of c*ottsid~~rablc inttrrrst.
because it was discovered (Markham, 1!)51) that the ittfwtive virrts is
accompanied in the plant by particles whicah, though ot'herwise sin1il:t.r
to it, are nottinfective and RNA-free.  The infective virus contaius about
40% RNA, t,he remainder being protein.  The associated noninfect,i\-e
particle is 40% lighter, lacking as it does a11 RNA, yet its diameter is
approximately the same (about 280 A.); its protein is similar immuttologi-
tally to t,hc protein component of the romplete virus.  The two particlw
form similar rrystals, atld will indeed form mixed cry&Is (Rcrnnl :wd
Carlisle, 1918).  Furt~hcrmorc, the low nnglr X-my scal,tcring of the RNA-
free particle in solution, unlike that, of the ittfectivc virus, is what one


208            F. 11. C. CRI(`K AND J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE        209

would cxpcct, f'rorn :I sphcri~:~l shnll rather thnu florn :L solid xphcro (Schmidt
et al., 1954).  `l'akitlg all Oris cvidruce togclhcr t,hc conclusion is clear
that by and large the protein is outside and the RNA inside the virus
particle.

Some early electron micrographs of a few layers of virus (Cosslett and
Markham, 1948) suggested that the lattice was of the diamond type,
and the first X-ray studies were thought to confirm this.  The problem
has recently been taken up again by Ktug, Fincnh, and Franklin, who kindly
allowed us to see their manuscript prior to publication.

Their new data show clearly that the Intt,icc has cubic symmetry, but are difficult
to reconcile with the idea of a diamond lattice: the alternative would be a body-
centered cubic lattice. A diamond lattice is a very open one, containing exnctly half
as much virus as would a body-centered cubic Iattice in which the distance between
neighhoring virus particles was the same.  It is thus possible to decide between the
two alternatives simply by finding how much virus there is per unit volume of crystal.
This has been done (in collaboration with Dr. Peter Walker) using a combination of
ultraviolet absorption and interference microscopy; the result shows clearly that the
more dense lattice is correct, at least as far ns large crystals are concerned.

However a straightforward body-centered lattice cannot adequately explain the
X-ray pattern except at low resolution.  It is suggest,ed that the centers of the virus
particles fall on a simple body-centered cubic lattice, but that the particles may have
either of two orientations which alternate in a regular manner; this means that the
true unit cell in larger than the simple one.  The same authors find that most of the
strong inten.ritios are lncntrd iu posit,ions in rcciproc:tl space which correspond to the
virus particle having the point group symmetry 532. Nevertheless one or two re-
flect,ions are present which are quite incompatible with the virus having such a high
symmetry, and Klug nnd his colleagues arc driven to conclude that although the virus
ns R whole can only have 23 symmetry, some pnrt of it may have the higher 532 sym-
metry.

This ingenious itlt,erpretation is too intricate to bc completely accepted
pithout further work, but there seems to be little doubt that turnip yellow
virus has cubic symmetry of some sort. Results from the ItNA-free
protein component are eagerly awaited.

3. General Principles of Virus Structure

The fact that certain small viruses form crystals, and that these crystals
in some cases give X-ray diffraction patterns extending to relatively small
spacings (say 5 A.), shows quite clearly that such viruses can be loosely
considered as "molecules" in the sense used by protein crystallographers;
namely as entities in which t,he majority of the atoms are arranged in
fixed (relative) positions. As we have indirated earlier, this does not
carry the implication t,hat the posit,ions of all the atoms are fixed, nor that
they arc exactly the same in en& virus; but it does imply that there is a
very considerable similarity between the atomic arrangements of any

two sist.er virus particles. In t,he same way the existence of internal
symmetry elements in the virus particle shows that one of its subunits
must resemble any other subunit, though once again it is structural simi-
larity rather than chemical identity which is proved by the X-rays.

The fact that small viruses are either rods or spheres (and not, for
example, ellipsoids or plates) has suggested the hypothesis (Crick and
Watson, 195Ga) that they are all made of subunits, related by symmetry
elements; This is a very natural idea to a crystallographer and had been
proposed earlier in special cases (Hodgkin, 1949; Low, 1953), but it had
not been sufficiently appreciated by virus workers themselves.

Reasons can be given why small viruses are made of subunits, but the
arguments are speculative (see Crick and Watson, 1956b); however given
that subunits do exist it is natural that we should find them to be related
by symmetry elements.  Such an arrangement means that every subunit
has the same contact points with its neighbors-points at which it must
be assumed that the same chemical groups are available in each of the
identical subunits.        ,.
Apart from its approximate location in TMV and in turnip yellow virus,

very little is known about the way the RNA is arranged iti virus& or how
it combines with the protein, except that the combination is unlikely to
involve primary chemical bonds.  It is nevertheless a very reasonable
surmise that the RNA in the virus has the symmetry elements, or at least
some of the symmetry elements, of the protein.  In TMV this idea leads
to the prediction (Crick and Watson, 1956a) that it is the backbone of
the RNA which will follow-this symmetry, not the sequence of the bases.
Tllis has been confirtned by the recent experiments of Hart and Smith
(1956) who have shown that viruslike rods (of indefinite length) can be
made by co-aggregating "A" protein from TMV with synthetic poly-
ribotides having an RNA-like backbone, no matter what bases are attached
to it. (That these polyribotides occupy the same sites in the "virus"
particle as the native RNA does in the true virus is so far only an inference.
It should be possible to prove it by X-ray methods.) It seems likely
that the same prediction-that the backbone of the RNA possesses the
same symmebry elements as the virus protein--will also be proved cor-
rect for the spherical viruses, but so far there is no evidence to support this.

Since symmetry elements can be discovered relatively easily by X-ray
methods, and since they have been detected in all three plant viruses so
far studied, it now becomes a worthwhile subject of inquiry whether any
small virus under investigation has symmetry elements, and if SO, what
they are. However there is no law which says that a virus must have
symmetry, and the hypothesis can only be evaluated by examining more
and more types of virus; it remains to be seen whether the surmise of


210         F. H. C. CRICK ANb J. C. KENDREW

X-RAY ANALYSIS AND PROTEIN STRUCTURE       211

Crick and Watson that most small "spherical" viruses have cubic sym-
metry will he confirmed or not.

Meanwhile the search for symmetry and the hope of isomorphous
replacements (which would hardly be practicable if the virus did not
contain identical subunits) are likely to stimulate an increa,sing amount
of work in this field. Moreover X-ray investigation shows that at least
certain viruses are simpler than their molecular weight might lead one to
expect, and this should encourage further chemical studies, especially on
the proteins of the spherical viruses.                            . .
It is not improbable (Crick and Watson, 1956b) that microsomal par-
ticles-the small compact particles in the cytoplasm which are perhaps
the sites of protein synthesis-may also have cubic symmetry. They
contain about the same amount of RNA as do the small spherical viruses,
and have a similar (or perhaps slightly smaller) diameter, and they appear
to be approximately spherical.  It would not be surprising if the arrange-
ment of the RNA were very similar in small viruses and in microsomal
particles.

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