Kinky helix ~

F. H. C. Crick & A. Klug

Medical Research Council Laboratory of Molecular Biology. Hills Road, Cambridge, UK

DNA in chromatin is highly folded. Is it kinked? And
does it kink in other situations?

CHROMATIN ia the name given to chromoaomal material
extracted from the nuclei of calls of higher organisms. It
ccmsists mainly of DNA and a sat of small rather basic
proteiax caHed histones. Other meins and RNA am
present in :lesser z3momts (sq ,for example ref. 1). Early
X-ray work (for review see mf. 2) suggested that there was
a structuw h ohromatin which repeated at h.tervals of
abom 100 A. More `recent work using nucleaaes'*' has
shown .t.hat the DNA in ohnomatin exists in some regular
fold which repeats entry 200 base pairs, the best value
currently being 205f 15 base @rs'.
The most 0ogm.t model for chromatin has been put
forvmrd by Komberg' who suggested that the basic struc-
ture consists of a string of beads eaoh contaiaCng two each
                                            

Fig. 1 General view of a model of a kink, taken from the side.
For this model d = 0, a = 98', D==8A and 0=23" (see
text). The two short lengths of backbone, connecting .Ihe two
stretches of straight helix, can he seen at A. The region of van
der Wadis' contacts between baekboncs, which limit the kink
          angicrx,isnearB. . .._ _     . .

of t,he four major histones, each bead being associated with
a,bout 200 base pairs of DNA. Linear arrangements of
beads (in a partly extended form) were first seen in the
elect,ron microscope by Olins and Olins' a,nd called by them
v-bodies. The exact diameter of a bead in the wet state is
rather uncmain but it is probably in the ,re@un of 100 A.
Kornberg's model suggested that DNA, when associated
wish histone, is folded to about one-seventh of its length.
This is the value deduced by Griffith" from dect.rcm m~icro-
graphs of the mini-ch.romosome of the virus SV40. A
similar value has been obtamed by Oudet er al.* from
measurements on adenovirus 2. Other cumpac.t models
have been proposed by van Holde et af.`" and Baldwin
et al.".

Thus ,the DNA in chromatin, even at this first level of
structu.re, must be folded conside.rably since its length is
contracted to about one-seventh. Moreover, the basic .repea,t
of 200 base pairs (which is 680 A long in the B form of
DNA) must be folded into a fairly limited space bavmg the
dimensi,ons of about 100 A" (rep. 6).
-We have found it very difficult to estimate just ,how much
energy is' ieouired to `bend DNA "smoothly" to a sma1.l
radius of curva.ture, say 30-50A, bearing in mind that
these numbers are not many t,imes greater than the diameter
of the DNA double helix, which is about 20 A, and that
bending a ,helix destroys ,its symmetry. We have formed
the im~pression tha.t the energy might be rather high. We
therefore asked ourselves whether the folded DNA may
consist of relatively straight stretches joined by large kinks.
Tlhis #paper descri,bes a certain type of kink which can be
built rather nicely and has i'nteresting properties.

The stereochemistry of a kink

No doubt other types of kink could be built, but we have
concentrated on one special type which we consider to be
.r&her plausible. We have assumed .tha.t all the base pairs
of the double hel.ix are left intact (so that no energy is lost
by unpaisring them), that the stmight parts of the DNA on
each side of the kink remain in the normal B form, but
that at We kink one base pair is comlpletely unstacked from
the adjacent one. Thus at each kink the ene,rgy of stacking
of one #base pair on another is lost. Naturdtly all bond
distances and angles (including dihedlral angles) have to be
stereochemically accelptable.

We find that, given these assumptions, one can con-
vincingly build a neat kink, having a large angle of kink,
in one way only; or, more strictly, in a family of ways all
ve.ry sim.ilar to each other. The double helix is bent towards
the side of the minor groove. This can be seen in the photo-
graph of one such model shown <in Fig. I.


Nature Vol. 255 June 12 1975

531

Fig. 2 View of part of the model of Fig. 1 taken approximately
looking down the pseudo-dyad. It shows two base pairs, one
on either side of the kink. The rest of the model has been blanked
out for easier viewing. The two arrows point to the C,`-Cs' bonds
at which the chain conformation is changed by kinkmg-see
Fig. 3. The letters A correspond to the region marked A in

Fig. 1.

The structure can be built with an approximation to a
dyad axis passing through the kink, though we cannot see
any strong reason why such symmetry is essential in
chromatin. A partial view #looking along the pseudo-dyad is
shown in Fig. 2.

To our surprise the configuration of the backbone at the
kink can be made similar to that of the normal backbone
of the B form except that the conformation at the C,`-Cs'
bond in the sugar is rotated 120" about this bond, going
from one of the possible staggered configurations to another
one as shown in Fig. 3. (We haye arbit.ratily kept the same
pucker of the sugar ring as is found in the B form of
DNA.)

The structure of the backbone at the kink is not one of
the preferred configurations that have been listed"~" since
these involve a weak CH . * . 0 close contact between the
hydrogen attached to ei.tsher G; of a `pyrimidine or Ca of a
purine and the OS' of the sugar, and by its very nature ,the
type of kink we have assumed cannot have this at every
position. In our model this contact is absen.t for one base
of each of the base pairs immediately adjacent to the kink.
As explained above, however, the backbone configuration
is sufficiently close to that of the B form of DNA (except
for the torsion angle about Cl'&`) that we feel it is
acceptable stereochemically.

The nature of the base pairs on either side of the kink
is immaterial to the model though presumably the energy
required to unstack these base pairs will de,pend to some
extent on their compositi,on. We have found ijt difficult to
estimate the free energy involved. It is probably a few
kilocalories. It is obviously desirable that this figure should
he determined as accurately `as possible scince the ease of
making kinks depends on just how big it is. Another
impor'lant question is how much a DNA double helix can be
bent before it kinks. If we denote the mearicurvature by K
(where K equals the reciprocal of the radius of curvature)
then we would cspect the energy of deformation of a
uniformi!~ hrnt helix. per unit length, to increase at least
;1s fast ;IS K'. For ;L kinked helix, i)n rhc other hand, this
energy increases only ~1%  K. In this case K `is the mean
`iur\;tture' of the scgmcnlcd douhlc helix which is propor-
rional to the numhcr of kinks per unit length. Thus, as is

intuitively obvious, at small K the double helix will bend,
while at large K it will kink. The value we should like to
know is the radius of curvature at which it changes from
bending to kinking.

There is probably an appreciable activa,tion energy to
the process of making a kink since the C,`-Cj' bond must
pass through *the eclipsed configuration. For th'is reason
we consider kinks of this type with a kink angle of about
half the full 100" to fbe unlikely.

Common features of the family

A nmnber of very similar structures can be built along
these lines and it is not obvious which is to be preferred.
They all have certain ,features in common.

(1) The axes of the two st,raight parts of the DNA do
not necessarily intersect exactly, but may be separated by
only a small distance, d, typically about 1 A or less. Note
that d has a sign. (2) The angle between the two axes, Q
(projected, if necessary, on to a plane perpendicular to the
line joining their points of nearest approach) is easily made
more than 90" bu,t approaches 100" with difficulty. The
model shown in Fig. 1 ,has or=98". At t'he maximum angle
(for any particular model) the backbone of one straight
part starts to touch t,he backbone of the other chai,n of t,he
other straight part. This contact, marked B in Fig. 1 has
:a (local) dyad axis. (3) If we define the kink point as the
point where the local he,lix axes, on either side of the kink,
intersect (or, if they do not intersect, then the midpoint of
the shortest straight line between the axes) then the dis-
tance, D, from the kink Ipoint to the plane of the nearest
base pair is appreciable and typically in the .region of 7-8 A.

To introduce our fourth (point we must first consider the
relationship between three successive straight portions; that
is, two khks Q succession. We assume that every kink is
exactly the same. The structure formed will depend on the
precise number of base pairs ,&between the kinks. (It should
be remembered that the B form of DNA has an exact
repeat after ten pa&.) For example, if there are ten (or a
multiple of ten) base pairs between two ki,nks, the structure
will bend round into, very roughly, three sides of a square.
If there are five base *pairs between kinks (or an odd mul-
tiple of five) the,n the structure will approximate to a zig-
zag. In short the dihedral angle for three successive straight
portions will depend on the exact number of base pairs
between the iwo adjace,nt kinks.

We can now state our fourth point. (4) The kink imlparts
a small negative twist to the DNA. This is most easily
grasped `by imagin$ing that the kink is made in two steps;
first, the two base pairs to be unstacked are unstacked
in the axial direction without kinking the backbone-this

Fig. 3  Diagrams of the deoxyribose ring showing the approxi-
mate conformation at the C,`-CS' bond (a) in the normal straight
B form of DNA, and (b) in the proposed kink; the two sugars
       affected are marked in Fig. 2.

Xb


532

Nature Vol. 2.55 June 12 1975

a smaller angle of kink and seem rather awkward to build.
We have not explored them further. A rather different
type ,of kink, `in which a sbase pair is undone, (has been
suggested by Gourevitch et aL1.".

F  . 4
vlx  Each cylinder represents a length of strai& double
he ' . When there are ten base pairs (or an integer multiple of
ten base pairs) in the middle stretch the kink has a left-handed
contiguration, as shown. The dihedral angle used in this paper
is zero for the cis conformation. Its sign agrees with the usual
convention that positive values less than 180" correspond to a

right-handed confIguration.

reduces Athe twist of 36" between these residues to about
lO-20"-and second, that this extended structure is then
kinked. The result L that if successive kinks are made at
intervals of 10n base pairs (where n is an integer) the DNA
instead of folding back ,t.o fcnm a %5rcle' follows instead a
l&&handed helix, #though naturally a kinked helix made of
straight segments (see Fii. 4).

The exact dihedral angle associated with three successive
straimght stretches depends somewhat on the precise details
of the kink but is typically about (m.36" -6) where m is the
number of base pairs between the two kinks and 8, the
dihedral correction angle, is not far from S-20". A very
small mtational deformation of t.he straight portions could,
howevm, alter .&is figure a little so the exact value in
chrmmtin (if it clccs iMud cmsist of kinked hdices) will
pddAy a& imposed by the histones.

(5) For any model there is a smallest number of base
pairs between two adjacent kinks. For models of this
fa&ly this ntrmber is usually #three. In ocular, the model
illustrated in Fig. 1, for which a=98', can be built with
three base pairs ,between two kinks but not with only two
base pairs there. This is probably true for all models of
this type for which a is gre&er %han 90". A model with
&fee base pairs between two kinks exposes these base pairs
Ilather effectively.

It is easy to see &at six ~patametem ate needed to
d&be ohe rela~tionship between any two (equal) stre,tches
of stmight double helix. If these stretches are related by
a dyad &is through the kmk puint then only four para-
meters are requi:red. These can conveniently be taken to
be the four used above: d,. a, D and 8.
Another family of models can be made w,ith ihe kink
on the side of the major groove, but such structures have

The occurrence of kinks

The idea that the fold of DNA in chromatin was based on
a tmit of 10 .&se pairs was ori@nally suggested to us by
experimental evide.nce discovered by our colleague, Dr
Markus Nell. Nell" has shown that the digestion of native
chromatin with the nuolease DNase I produces nicks in
the DNA which tend to be spaced multiples of 10 bases
apart. This suggests that the DNA is folded in a highly
regular way and is prabaMy mainly on the outside of the
structure'*". Mwm recent work by Nell and Komberg
(unpublished) using mic roco0~1 nuclease pomts to a struc-
tural repeat itt'mtervals of 20 *base paus. Thus a rather neat
model for the most compact (wet) form of `chromatin can
be ma& in which `the DNA is kinked through about
95-100" every 20 base p&s, g&%g a shallow kinked helix
having 10 straight stretches of DNA in each 100 A repeat.
The middle stretches of this repeat would be la.rgely pm-
tected by the histones of the bead, the flanking stretches
less so. Whethe.r this very simple model is basically correct
remains to be seen.

Obviously we should ask whether DNA is kinked in
other situations. One interesting possibility is that when
the lac ~repressor binds .to the operator site on the DNA the
double helix becomes kinked. It has been shown by Wang,
Barkley and Bourgeois" t,hat this binding unwinds the helix
by a small angle, eithe'r about 40", or, more likely, about
90" (@he value depending on the amount of unwinding
assumed to be produced by the standard agent, ethidium
bromide). As they point out, this is too small to allow
the formation of a Gierer-type loop". It is, however, just
whrtt one would expect from a small number of kinks since
each kink of the kind we have described unwinds the,
double helix by about 15" to 25". For example, an attrac-
tive zig-zag model can be imagined with four kinks, each
spaced about five base pairs apart. T1hi.s model places the
two sequences related by a dyad, each of six consecutive base
pairs, on either side of the first and last kinks (see Fig. 5).
In this position, being near a kink, they are more exposed
than they would be in a stretch of unkinked DNA.

In essence, kinking may be a way of `partly exposing a
small group of base pairs wi.thout too great an expenditure
of energy. T.he exposed side of each of these (base pairs is
that ,normally in the major groove. The ki.nk has the effect
of displacing one of the phosphate-sugar backbones which
normally make up the two sides of this groove. T,he specific
pattern of qhydrogen *bonding sites in the major groove is
thus made more accessible for a few base .pairs on either
side of a kink. A kink may therelfore turn `out to be a pre-
femed configuration of DNA when it is interacting
specifically with a protein.

Kilnks may be suspected in all cases where double-
stranded DNA has been shown to adopt a more compact

Fig. 5 The minimal base sequence of the /UC operon. taken
from Gilbert and Maxam'". The dotted line marks the pseudo-
dyad in the base sequence. The two sets of consccutivc base
pairs, related by the dyad, are boxed, The arrows show one

choice of positions where kinks might occur.


Nature Vol. 255 June I2 I975

state than the normal double h&ix. Obvious examples are
the folded chromosomes of Escherichia coli""O (and no
doubt other prokaryotes), the folded DNA in viruses, the
ti phase of naked DNA discovered By bernan" and the
shortened form of DNA in alcoholic solutions as described
by Lang". '

One should also .ask whether kinks occur spontaneously,
as a result of thermal motion, in double-stranded DNA in
soluticrn. The frequency at which this occurs clearly depends
on the free energy difference involved. If <this were, say,
about 4 kcalorie then there should be one kink in about
800 base pairs which could `be appreciable. Such kinks
would occur mainly between A-T pa&. If the free energy
were as high as 6 kcdorie this would mute one kink in
about every 22,000 (base pairs, whioh would .be more
difficult to detect.

At the present we have no compelling evidence which
shows #that DNA in chromatin `is kinked <rather than bent
nor that kinks exist in DNA in other contexts. Nevertheless
our model seems to US sufficiently attractive ti !be worth
presenting now for consideration by other workers in the
field. Kinks, if they occur, Ihave at least stwo possible
advantages. It has always been a puzzle how to construct
hilerarchies of helices in a neat way, since .bending an exist-
ing helix necessarily distorts iits regular structure. This
distortion becomes more acute as the basic helix is coiled
at higher and higher levels. A kink allows such deforma-
tions to ,be local rather than diffuse and makes it easier to
build hierarchical models which are neat stereochemically.

533

The other advantage .is *that, at a kink, several base pai,rs
may be more easily available for specific interaction with a
protein. If kinks in DNA exist they will surely prove to be
important.

We thank our colleagues Drs R. D. Kornberg, M. No11
and J. 0. T,homas for communicating their results to us
before ,publication. We also thank them and our other
colleagues for many useful discussions on chromatin
structure.

Received April 25; accepted May 6. 1975.

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