IOP PUBLISHINGNANOTECHNOLOGY

Nanotechnology 19 (2008) 384009 (9pp)

doi:10.1088/0957-4484/19/38/384009

Anisotropic diffusion of point defects in a
two-dimensional crystal of streptavidin
observed by high-speed atomic force
microscopy
Daisuke Yamamoto, Takayuki Uchihashi, Noriyuki Kodera andToshio Ando1
Department of Physics, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan
andCore Research for Evolutional Science and Technology (CREST) of the Japan Science andTechnology Agency (JST), Sanbon-cho, Chiyoda-ku, Tokyo 102-0075, Japan
E-mail: tando@kenroku.kanazawa-u.ac.jp

Received 29 March 2008, in final form 29 April 2008
Published 12 August 2008
Online at stacks.iop.org/Nano/19/384009
Abstract
The diffusion of individual point defects in a two-dimensional streptavidin crystal formed on
biotin-containing supported lipid bilayers was observed by high-speed atomic force microscopy.
The two-dimensional diffusion of monovacancy defects exhibited anisotropy correlated with thetwo crystallographic axes in the orthorhombic C 222 crystal; in the 2D plane, one axis (thea -axis) is comprised of contiguous biotin-bound subunit pairs whereas the other axis (theb-axis) is comprised of contiguous biotin-unbound subunit pairs. The diffusivity along theb-axis is approximately 2.4 times larger than that along the a -axis. This anisotropy is ascribedto the difference in the association free energy between the biotin-bound subunit–subunit
interaction and the biotin-unbound subunit–subunit interaction. The preferred intermolecular
contact occurs between the biotin-unbound subunits. The difference in the intermolecularbinding energy between the two types of subunit pair is estimated to be approximately
0.52 kcal mol−1 . Another observed dynamic behavior of point defects was fusion of two point
defects into a larger defect, which occurred much more frequently than the fission of a point
defect into smaller defects. The diffusivity of point defects increased with increasing defectsize. The fusion and the higher diffusivity of larger defects are suggested to be involved in themechanism for the formation of defect-free crystals.

of semiconductors [1, 2] and limit the resolution of protein
structures obtained by diffraction methods [3, 4]. Therefore,
the behavior of lattice defects both in two-dimensional (2D)
and three-dimensional (3D) crystals has been a subject of greatinterest in many fields.
Streptavidin is a homotetrameric protein with dihedral
D 2 symmetry, and each subunit specifically binds to one
biotin [5, 6]. Streptavidin is easily crystallized in 2D forms
on biotinylated lipid layers, which is considered to be an
ideal model system for investigating 2D crystals grown on
lipid layers [7, 8] and protein crystallization in general. On
the biotinylated lipid layers, two of the four biotin binding

1. Introduction
Crystals, which are ordered lattices of colloids, molecules
or atoms, have attracted much attention because of theirwide range of applications in material science, biology andengineering.
Although the constituents are assumed tobe perfectly ordered in an ideal crystal, real crystals havenumerous imperfections such as point defects, incorporated
impurities, dislocations and grain boundaries. These crystal
imperfections significantly affect, for example, the properties
1 Address for correspondence: Department of Physics, Kanazawa University,

Kakuma-machi, Kanazawa 920-1192, Japan.
0957-4484/08/384009+09$30.00

1© 2008 IOP Publishing Ltd Printed in the UKNanotechnology 19 (2008) 384009

D Yamamoto et al

molecule level. For example, the attachment and detachmentof apoferritin molecules at the growth steps on the crystal occur
in a few seconds or less [19], while conventional tapping mode
AFM requires at least a minute to obtain one image.
Here, we report defect diffusion in the orthorhombic
C 222 crystal of streptavidin formed on biotin-containing
supported lipid bilayers. The 2D migration of defects was
successfully traced by our high-speed AFM [20–23] at an
imaging rate of 0.5 s/frame. The defects showed anisotropic
diffusion with respect to the two crystal axes. An analysisof this anisotropic diffusion of monovacancy defects revealed
different intermolecular binding affinities between a pair of
biotin-unbound subunits and between a pair of biotin-boundsubunits. In contrast to the result of a previous study by Wanget al [11], the preferred intermolecular contact in the crystal
was between biotin-unbound subunits, which is consistent withthe result obtained by Ku et al [9]. This conclusion was further
confirmed by the observation that the ordered crystalline
arrangement was immediately disrupted by the addition of
biotin to the bulk solution. The difference in the intermolecularbinding energy between the two types of subunit pair was
estimated to be approximately 0.52 kcal mol−1 . In the AFM
observation of the C 222 crystal, we also found anotherinteresting dynamic process: fusion of two point defects intoa point defect. Its analysis suggested that the fusion andthe higher mobility of the resulting larger defect are involvedin the mechanism for the formation of defect-free crystals.
In addition, we resolved the molecular arrangements in the
C 222/P 2 coexisting crystals, which clarified the mechanism
by which the C 222/P 2 coexisting crystal preferably grows in
the same direction [11].

sites face the lipid layers and are occupied by biotin, while
the other two are exposed to the aqueous environment andtherefore are biotin-free. Thus far, it has been reported thatordered 2D arrays of streptavidin molecules are formed on
biotinylated lipid layers at both the air–water [7–14] and solid–
water [15–17] interfaces, the molecular arrangements of whichhave been investigated by transmission electron microscopy(TEM) [8–13] and atomic force microscopy (AFM) [14–16].
These studies have revealed that streptavidin molecules selfassemble in three distinct crystalline arrangements ( P 1, P 2
and C 222 symmetries), depending on the crystallization
conditions such as pH [11, 13], ionic strength [12], andbiotin concentration in the lipid membrane [16]. Here,the crystallographic symmetries are named following thenomenclature used in the literature [9, 13, 15]. It should
be noted that C 222 is the symmetry of the 2D crystal itself.
In projection, the in-plane 2-fold rotational axes become
mirror axes, and the symmetry of the projection map is
cmm . As already mentioned, the streptavidin molecule itself
possesses D 2 (222 in the international system) point groupsymmetry [5, 6].
Streptavidin 2D crystals exhibit macroscopic morphologies resulting from the growth anisotropy. The dependenceof the growth rate on the crystallographic axes has been attributed to a structural difference between biotin-bound andbiotin-unbound subunits, which would result in heterogeneousintermolecular contacts in the crystals [9]. The relationship between the preferred crystal growth direction and the orientationof streptavidin molecules has been investigated by the combination of optical microscopy and electron microscopy. This
relationship was first studied by Ku et al [9]. They proposedthat the growth of the C 222 crystal preferably occurs along
the crystallographic axis along which biotin-free subunits arecontiguously aligned. Therefore, the preferred intermolecular
contact was assigned to be that between biotin-unbound subunits. Later, this model was revised by Wang et al [11]. They
concluded that the faster growth of the C 222 crystal occurs
along the crystallographic axis in which biotin-bound subunits
are contiguously aligned. Hence, the preferred intermolecular
contact was assigned to that between biotin-bound subunits.
Although this conclusion has been adopted in the literature,
this issue still remains controversial.
The anisotropy of intermolecular interactions is expected
to affect the dynamic behavior of individual constituent
molecules and lattice defects in the crystal. The analysis of
the dynamic behavior of individual point defects would offer
insights into protein–protein interactions in crystals and crystal
growth mechanisms. AFM is one of the most appropriate
tools for the analysis of such dynamic behavior in protein
crystals because of its applicability in liquid environments.
Thus far, several attempts have been carried out to directly
visualize the morphological changes in protein crystals by
successive AFM imaging. For example, the crystal growth
kinetics of a virus [4], lysozyme [18] and apoferritin [19]have been measured at a resolution close to the size ofthe molecules.
However, because of its slow imaging
speed, conventional AFM lacks the ability to track dynamic
phenomena taking place on the 2D crystals at the single

2. Materials and methods
2.1. Materials
All lipids used in this study were purchased from Avanti Polar
Lipids (Alabaster, AL, USA). Streptavidin was purchased from
Wako Pure Chemical (Osaka, Japan). Biotin (vitamin H) was
purchased from Sigma (St Louis, MO, USA). These materials
were used without further purification.
2.2. Sample preparation
Streptavidin 2D crystals were formed on the supported lipid
bilayer (SLB) by slight modification of the method describedin [15]. The lipid composition used in this study wasdioleoylphosphatidylcholine (DOPC), dioleoylphosphatidylserine (DOPS) and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine- N -(cap-biotinyl) (biotin-cap-DOPE) (7:2:1, weightratio). Dried lipid films were obtained by mixing appropriate
amounts of lipids dissolved in chloroform followed by evaporating the solvent with argon. The lipid films were further
dried in a desiccator by aspirating for more than 30 min. To obtain multilamellar vesicles (MLVs), the dried lipid films were
resuspended by vortexing in a solution (buffer-A) containing
10 mM HEPES-NaOH, 150 mM NaCl, and 2 mM CaCl2 (pH7.4). Small unilamellar vesicles (SUVs) were produced from
the MLV suspension by sonication with a tip-sonicator.
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To evaluate the effect of biotin binding on theintermolecular association in the crystal, biotin molecules
were bound to all the available subunits of streptavidin. For
this purpose, a buffer-A solution containing 1 mM biotin
was injected to the AFM sample chamber while successively
imaging the streptavidin 2D crystal sample, which resulted
in the immediate disruption of the crystalline arrays (seesection 3.3). Then, the excess biotin molecules were washedout with buffer-A. To test whether the crystal disordering
upon full biotin binding is due to the lowered intermolecularbinding affinity or partial dissociation of streptavidin fromthe lipid layer surface, the sample was further incubated for
1 h in a buffer-A solution containing 0.1 mg ml−1 of biotinfree streptavidin. For the chemical fixation of the crystals,
a buffer-A solution containing 10 mM glutaraldehyde wasadded, followed by incubation for 5 min.
2.3. High-speed atomic force microscopy
The observations of streptavidin 2D crystals were performed
in tapping mode using a laboratory-built high-speed atomic
force microscope [20, 24, 25]. Small cantilevers designed
for high-speed AFM were used, which have a spring constantof 0.1–0.2 N m−1 , a resonant frequency of 0.8–1.2 MHz inwater, and a quality factor of ∼2 in water [26]. The cantilevertips were grown by electron beam deposition. The condition
for imaging defect diffusion was typically as follows. The
cantilever’s free oscillation peak-to-peak amplitude was set
to 5 nm, while the set-point peak-to-peak amplitude during
imaging was 4–4.5 nm. The scan area was 150 × 150 nm2 ,and the number of pixels was 200 × 200. The imaging rate
was 0.5 s/frame. The amplitude error signal was negligibly
small during scanning, indicating that the feedback speed issufficiently high to precisely trace the surface topography. The
substrate-tilt effect was removed from the AFM images by aflattening software program. The scan size in the x - and y directions was calibrated using purple membranes as a standard
specimen, which are 2D crystals of bacteriorhodopsin with aspacing of 6.2 nm between unit cells [27].

Figure 1. Streptavidin 2D crystal formed on a mica-supported lipid
bilayer. (a) High-speed AFM image of a streptavidin crystal with
C 222 symmetry. In the inset, a calculated diffraction pattern of the
AFM image is shown. The peak positions at (1, 1) and (−1, 1) areindicated by circles. The weakest measurable diffraction spot at(−1, 3) (1.9 nm resolution) is indicated by an arrow. (b) Schematicof a streptavidin molecule on a biotinylated lipid bilayer. Two biotin
binding sites occupied by biotin are indicated by the closed circles.
The open circles indicate biotin binding sites facing the aqueous
solution and are biotin-free. (c) Schematic of streptavidin arrays in a
C 222 crystal. Unit lattice vectors are indicated: the a -axis includes
rows of contiguous biotin-bound subunits, while the b-axis includes
rows of contiguous biotin-unbound subunits.

SLBs were prepared by depositing 0.1 mg ml−1 SUVs
onto a freshly cleaved mica surface, followed by incubationfor 30 min in a chamber with saturated humidity at room
temperature. Then, the excess lipids were washed out with alarge amount of buffer-A.
The 2D crystallization of streptavidin was performed byplacing a streptavidin solution (0.1 mg ml−1 ) on the biotincontaining SLBs, followed by incubation for 2 h in a chamberwith saturated humidity at room temperature. The buffer
solutions used for the streptavidin crystallization were bufferA for the C 222 crystal and buffer-B (10 mM HEPES-NaOH,
300 mM NaCl and 2 mM CaCl2 (pH 7.4)) for the C 222/P 2
coexisting crystal. The excess streptavidin molecules were
washed out with the same buffer solution as that used forcrystallization. By AFM observation, we confirmed thatthe streptavidin 2D crystals were uniformly formed over a∼1 μm2 area. Although a small amount of particles wasfound on the crystals, completely flat regions of ∼200 ×
200 nm2 area were observed elsewhere on the crystal samples.
Therefore, this incompleteness of the crystal had no effect on
our measurements.

3. Results
3.1. Streptavidin 2D crystal with C222 symmetry
Figure 1(a) shows AFM images of a streptavidin 2D crystal.
The periodic structure exhibits C 222 symmetry with lattice
constants of a = 5.9 ± 0.1 nm, b = 5.9 ± 0.3 nm, and
γ = 92 ± 3◦ . These values are consistent with the previously
reported result of a = 5.8 nm, b = 5.8 nm, and γ = 90◦
for a C 222 crystal prepared at the air/water interface [13]. The
calculated diffraction pattern indicated lateral resolution better
than 2 nm (figure 1(a), inset). With this lateral resolution,
the orientation of the rectangular streptavidin molecules wasclearly identified. Owing to the dihedral D 2 symmetry oftetrameric streptavidin, the two biotin binding sites facing
the lipid membrane are occupied by biotin, while the othertwo are unoccupied (figure 1(b)). Thus, the arrangement of
biotin-bound and biotin-unbound subunits in the crystal axis
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D Yamamoto et al

Figure 2. Migration of monovacancy defects in streptavidin 2D crystal. (a) High-speed AFM images of streptavidin 2D crystal andmonovacancy defects therein. The monovacancy defects are enclosed by dashed squares and circles. The directions of the lattice vectors of
the crystal are also indicated. Successive images were obtained at an imaging rate of 0.5 s/frame with a scan area of 150 × 150 nm2 , and thenumber of pixels was 200 × 200. (b) Trajectories of individual monovacancy defects. Closed squares and circles correspond to defects
indicated by open squares and circles shown in (a), respectively.

Then, the diffusion of point defects in the crystals wasobserved. Figure 2(a) shows images of the streptavidin 2D
crystal and monovacancy defects therein, which are clippedfrom successively captured high-speed AFM images. In
figure 2(b), the trajectories of two monovacancy defects
are shown. The mobility of the monovacancy defects was
obviously anisotropic with respect to the two axes of thecrystalline lattice. These defects have larger mobility along
the b -axis than along the a -axis. Occasionally, the defects
stopped diffusing at lattice sites. While observing the crystal
for several seconds, the stopped defects started to diffuse
again. This behavior may arise from the discontinuity of the
SLB underneath the streptavidin crystal. The total time inwhich the defects are arrested at lattice sites was ∼3% of thetotal observation time, which is negligibly small to affect ouranalyses of the defect diffusion.
The mobility of monovacancy defects along each axis of
the C 222 crystal was quantified by measuring the mean-squaredisplacements (MSDs) at various intervals (figure 3). From thelinear increase in MSDs with time, the diffusion rate constantsof migrating monovacancy defects were Da = 20.5 nm2 s−1along the a -axis that includes rows of contiguous biotin-boundsubunits, and Db = 48.8 nm2 s−1 along the b -axis that includes
rows of contiguous biotin-unbound subunits. Da and Db are
similar even for other samples that have different orientationsof the crystal axes relative to the raster scan direction. Thus,
we conclude that the anisotropy in diffusivity is an intrinsic
property of the lattice defects in the streptavidin C 222 crystal.
The monovacancy defects sometimes fused into abivacancy defect. Through several fusions, larger multivacancy
defects were formed. The multivacancy defects also diffused in
the C 222 crystals during the successive imaging. In figure 4,
the diffusion constants of the multivacancy defects are shown
as a function of the defect size. As the size increases, thediffusivity of multivacancy defects increases for both crystal
axes, although the diffusivity of divacancy defects is similar

Figure 3. Plot of mean-square displacements (MSDs) ofmonovacancy defects against time. The MSDs as a function of time
were measured from 94 trajectories. Error bars indicate standard
error. The MSDs of defects along the a -axis and the b-axis in the
C 222 crystal are compared. Data fitted to a linear function yielded
diffusion constants Da = 20.5 nm2 s−1 and Db = 48.8 nm2 s−1 forthe directions along the a -axis and the b-axis, respectively. Closed
circle, MSDs with the a -axis that includes rows of contiguous
biotin-bound subunits; open circle, MSDs with the b-axis that
includes rows of contiguous biotin-unbound subunits.

shows a schematic of the molecular arrangement in the C 222
crystal. In the C 222 crystal, the intermolecular contacts
between biotin-bound subunits are contiguously aligned along
one crystal axis (the a -axis), while the contacts between biotinunbound subunits are contiguously aligned along the other axis
(the b -axis).
3.2. Diffusion of point defects in crystal
Monovacancy defects in the streptavidin 2D crystals were
produced by increasing the tapping force onto the sample fromthe oscillating tip, similarly to a method used previously [28].
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Figure 4. Diffusion constants of multivacancy defects for each axis
as a function of the defect size. Each number (as an index of thedefect size) indicates the number of unit vacant sites contained ineach multivacancy defect. Error bars indicate standard error.

Figure 6. Molecular arrangements at the boundary of C 222 and P 2
domains. (a) High-speed AFM image of a streptavidin C 222/P 2
coexisting crystal, which was grown in a high ionic solution(buffer-B). The lower region of the image shows C 222 arrangement,
while the P 2 lattice is seen at the upper region. (b) Schematic ofstreptavidin arrays in the C 222/P 2 coexisting crystal. Unit cells in
the C 222 and P 2 regions are indicated by a square andparallelogram, respectively. The C 222 and P 2 crystals are connected
through the interaction between biotin-bound subunits at theirinterface.

3.3. Influence of biotin binding to ordered arrays of
streptavidin
When the crystals were exposed to free biotin in the bulk
solution, the ordered lattices were immediately disrupted.
After the disruption, the individual streptavidin molecules
were undetectable without chemical fixation because of therapid diffusion of the streptavidin molecules on the SLBs.
After the fixation with glutaraldehyde, the surface structures
could be observed owing to the elimination of the lateral
movement of streptavidin molecules. From figure 5(a), it
is clear that streptavidin molecules are densely packed on
the mica-supported lipid membranes but are arranged in adisordered structure. The disordered structure, which was nottreated with glutaraldehyde, failed to recover to an ordered
lattice after incubation in a biotin-free solution containing
streptavidin (figure 5(b)), indicating that the streptavidin had
never dissociated from the biotinylated lipids by the additionof biotin to the bulk solution.

Figure 5. Disruption of crystalline lattice of streptavidin on fullbinding to biotin. (a) Molecular arrangements of streptavidin after
biotin binding at all available binding sites. (b) Moleculararrangements of streptavidin after incubating the sample shown in (a)in the presence of biotin-free streptavidin.

to that of monovacancy defects. Interestingly, the reverse
reaction, i.e., fission of a large multivacancy defect to smaller
multivacancy or monovacancy defects, was rarely observed.
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3.4. Molecular arrangements in C222/P2 coexisting crystal

E b − E a = G u–u − G b–b . Therefore, the observed relationship Db > Da indicates G u–u < G b–b ; namely, the u–u
bond affinity is higher than that of the b–b bond. The ratioof the two diffusion rate constants ( Db /Da ) can be expressedby Db /Da = exp[−(E b − E a )/(kB T )], where kB is the Boltzmann constant and T is the absolute temperature. Thus, fromthe observed value of Db /Da ∼ 2.4, the free energy difference G u–u − G b–b is estimated to be approximately −0.88kB T(T ∼ 300 K), which corresponds to −0.52 kcal mol−1 .
In previous studies, the anisotropy of protein 2D crystal growth has been evaluated from the crystal morphologies. The streptavidin C 222 crystals formed under biotinylated lipid layers show X-, H-, and rectangle-shaped morphologies [8, 9, 11, 13] that arise from asymmetric growth rates
along perpendicular axes. The anisotropy estimated from the
aspect ratios of the C 222 crystals is reported to be 2–3 (about 2
at neutral pH) [13], coinciding with the diffusion constant ratio( Db /Da ∼ 2.4). We think that this coincidence is accidental.
However, it is obvious that the diffusion constant ratio is intrinsically related to the anisotropic growth rate through the freeenergies associated with the attractive intermolecular interactions between the subunits [30]. Supposing that the aspect ratioof a crystal is proportional to the ratio of the free energies of attractive interactions that occur along the crystal axes (Wulff’s
rule [31]), G u–u /G b–b is approximately 2. This relationshipand G u–u − G b–b ∼ −0.88 kB T result in G b–b ∼ −0.88 kB T
and G u–u ∼ −1.76 kB T . These values seem consistent withthe fact that 2D protein crystallization requires lateral interaction energies between −1 and −5 kB T . Although this estimation of the interaction energies cannot be validated at present,
it will be cleared by systematic studies on the monovacancy
defect mobility in the other types of streptavidin 2D crystals
formed under various conditions.

By increasing the ionic strength of the crystallization buffer,
C 222/P 2 coexisting crystals were obtained. Figure 6(a) showsan AFM image of the boundary between the C 222 and P 2
regions in a coexisting crystal. The lattice constants of the P 2
crystal domain were a = 5.8 ± 0.1 nm, b = 11.2 ± 0.3 nm, and
γ = 104◦ ± 1◦ , which agree with those reported in a previous
work [10]. Figure 6(b) shows a schematic of the moleculararrangements in the C 222/P 2 coexisting region modeled fromfigure 6(a). Streptavidin molecules in the C 222 domain appear
oriented in the same direction as that in the adjacent P 2 crystal.
This result is consistent with the fact that the C 222 and P 2
regions grow in the same preferred direction [11].

4. Discussion
4.1. Observations of point defect diffusion in a crystal by
high-speed AFM
The migration of monovacancy defects in the streptavidin
2D crystals was visualized by high-speed AFM, as shown infigure 2. The linear relationship between MSDs and time
(figure 3) of this migration indicates that the migration ofmonovacancy defects occurs by a random walk. The onedimensional diffusion constant D is expressed as D = δ 2 /2τ ,where δ is the step length and τ is the time for each step
(stepping time) [29]. In the C 222 crystal of streptavidin, thestep length δ is 5.9 nm in both two axes because the minimum
step length corresponds to the lattice constant. Therefore, thestepping time τ for the movements along each axis can be
estimated to be τa = 0.85 s and τb = 0.36 s for the a -axis
and the b -axis, respectively. In this study, the imaging rate
was 0.5 s/frame, which is comparable to the stepping rates
of monovacancy defects in the crystal. Thus, the trajectories
of individual monovacancy defects diffusing in the 2D crystal
were well traced.

4.3. Fusion of point defects
Fusion of two point defects into a larger point defect wasoften observed. On the other hand, fission of a multivacancy
point defect into smaller point defects was rarely observed.
We think that the fission often occurs but cannot easily beobserved because the two point defects formed immediately
after the fission are quickly fused again. Immediately after
the fission, a streptavidin molecule becomes facing both theresulting two smaller point defects. This streptavidin moleculecontains only two intermolecular subunit–subunit contacts, andtherefore quickly detaches from the lattice and moves intoeither of the two adjacent point defects. The imaging rate weused (0.5 s/frame) was not sufficiently high to observe thistransiently occurring fission.
During the formation of streptavidin 2D crystals in thepresence of free streptavidin in the bulk solution, small point
defects such as monovacancy and divacancy defects would
not easily have access to the free streptavidin molecules, andhence, they have a tendency to remain in the crystals. However,the fusion of small point defects into a larger point defectfacilitates its access to the free streptavidin molecules andthereby promotes the removal of small point defects from thecrystals.

4.2. Anisotropic diffusion along two axes
In the C 222 crystal of streptavidin, the two-dimensional diffusion of monovacancy defects showed significant anisotropy
correlated with the two crystal axes, as indicated infigures 2 and 3. This anisotropy in the lateral mobility (i.e.,
Db > Da ) arises from a free energy difference between thebiotin-bound subunit–subunit interaction and biotin-unboundsubunit–subunit interaction. When a streptavidin molecule adjacent to a monovacancy defect moves to the defect site along
the a -axis, two intermolecular bonds between biotin-unboundsubunits (‘u–u bond’) and one intermolecular bond between
biotin-bound subunits (‘b–b bond’) are broken. On the other
hand, when it moves to the defect site along the b -axis, one u–u
bond and two b–b bonds are broken (see figure 1(c)). Therefore, the difference in the activation energies E a and E b forthe step movement of a monovacancy defect along the respective a - and b -axes simply corresponds to the difference between the free energy changes G u–u and G b–b produced by theformation of the respective u–u bond and b–b bond; namely,
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Figure 7. Pathways for the step movement of a cross-shaped tetravacancy point defect to the +b direction. The defects are schematicallyindicated with broken lines. (I): the initial state of a cross-shaped tetravacancy point defect; (II) and (III): the initial transient states; (IV): thesecond transient state; (V) and (VI): the final states. In state (V), the step movement in the +b direction is attained, while state (VI) is thesame as the initial state (I).

The higher mobility of larger point defects increases theirprobability to encounter other point defects to form larger
point defects with further higher mobilities. During the crystal
growth in the presence of free streptavidin in the bulk solution,
this acceleration effect also promotes the removal of point
defects from the crystalline regions.

4.4. Increased diffusivity of multivacancy defects in a crystal
As shown in figure 4, the defect mobility increases withincreasing defect size. It does not seem easy to interpret thistendency intuitively as more than three intermolecular bonds
between streptavidin molecules are involved in the diffusion of
the multivacancy defects. The total number of intermolecularbonds to be broken for the defect step movement increases
with increasing size of vacancy. This fact seems contrary to
the observed tendency (faster diffusion with larger defect).
This conflict could be resolved by considering two factors.
One factor is that there are multiple paths along which a
multivacancy defect migrates to one of their nearest-neighbor
positions. For simplicity, let us consider the step movementof a cross-shaped tetravacancy defect in the +b direction(figure 7). In the initial step, one of the two streptavidin
molecules, which face the defect and locate in the +b direction
relative to the defect, detaches from the surrounding crystal
region (steps from (I) to (II) and from (I) to (III) in figure 7). In
this detachment, three intermolecular bonds are broken. Once
detached, one of streptavidin molecules, which had been incontact with the detached streptavidin molecule, loses one b–b bond, resulting in two intermolecular bonds. Therefore, it
quickly detaches from the surrounding crystal region (steps
from (II) or (III) to (IV) in figure 7). The two detachedstreptavidin molecules rapidly diffuse in the void and quickly
reach the stable configurations ((V) or (VI) in figure 7). In
these pathways, the initial steps, from (I) to (II) or from (I) to(III), limit the rate of the defect step movement. Comparedwith the step movement of a monovacancy defect, the step
movement of a cross-shaped tetravacancy defect has twoparallel paths for the initial rate-limiting step. Therefore,
its diffusivity is approximately twice as fast as that of amonovacancy defect.
Another factor to be considered for the movement of amultivacancy point defect is the stability of the crystal regions
surrounding the point defect. By a collective effect, thestability of the crystal regions adjacent to a larger point defectmust be lower than that of crystal regions adjacent to a smaller
defect. This lower stability gives higher diffusivity to larger
point defects.

4.5. Discrepancy in preferred intermolecular interaction withprevious study
In the study by Wang et al [11], the preferred crystal
growth direction was examined by the observation of themacroscopic crystal morphology by fluorescent microscopy,
while the molecular arrangement in the crystal was analyzed
by TEM and electron diffraction. In this manner, the preferredintermolecular contact was determined. In our study, themolecular arrangement and the diffusion of point defects in the
crystal were simultaneously visualized by high-speed AFM,
and the preferred intermolecular contact was determined byanalyzing the anisotropic diffusion of monovacancy defects inthe lattice structure. As proposed by Ku et al [9], the resultsof our study indicate that the preferred intermolecular contact
in the C 222 crystal is between biotin-unbound subunits,
contradicting with the report by Wang et al. Unfortunately, it islikely that Wang et al have incorrectly assigned the streptavidin
orientation in the C 222 crystal. As shown in figure 1(a)(inset), the calculated diffraction pattern of the C 222 crystal
exhibits a higher intensity at the (1, 1) peak than at the (−1, 1)
peak. The vectors (1, 1) and (−1, 1) correspond to thedirections of the long and short axes of the rectangle-shaped
streptavidin, respectively. This result was confirmed by thecalculated diffraction pattern of a C 222 lattice of an artificial
rectangle molecule constituted in a computer. In contrast to
our observation, in the report of Wang et al, the electron
diffraction intensities and the determined molecular orientation
are inconsistent with each other.
Further support for our conclusion as to the preferredintermolecular contact is first provided from our observationthat the C 222 crystal is immediately disordered upon the
addition of biotin to the sample solution. Second, it isprovided from the observation of the C 222/P 2 coexisting7

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crystal. The high-speed AFM imaging of the C 222/P 2
coexisting crystal showed that streptavidin molecules in the
C 222 and P 2 domains are oriented in the same direction(figure 6). From this result, we can anticipate that the C 222
and P 2 domains preferentially grow in the same direction by
sharing the same orientation of the preferred intermolecular
contact between biotin-unbound subunits. In fact, it has
been observed that the C 222/P 2 coexisting crystal grows
in the same direction [11]. In a model provided by Wanget al, this fact was interpreted based on (1) in the coexisting
crystal, the orientations of streptavidin molecules in the C 222
and P 2 regions are different by 90◦ , and (2) the preferredintermolecular contact in the C 222 region is between biotinbound subunits while that in the P 2 region is between biotinunbound subunits. It is very unlikely that, under the same
solution condition, the preferred intermolecular contacts aredifferent at the two crystal regions.

to the asymmetric crystal growth along the crystal axes.
Quantitative evaluation of this relationship and finding its
general rule remain important issues to elucidate. From thevisualized anisotropic diffusion of monovacancy defects andthe molecular arrangement, the difference in the free energy
between the biotin-bound subunit–subunit interaction and thebiotin-unbound subunit–subunit interaction was determined tobe 0.52 kcal mol−1 ; the contact between biotin-bound subunits
is weaker than that between biotin-unbound subunits. In
addition, the rapid disruption of the ordered lattice upon the
addition of free biotin was observed. The fusion of point
defects occurs much more predominantly over the fission ofa point defect into smaller point defects. The higher mobilityof larger point defects increases the probability of the fusion
event and thereby accelerates the removal of point defects
during crystallization in the presence of free streptavidinin the bulk solution. The molecular arrangements in the
C 222/P 2 coexisting crystals were revealed, which cleared
the mechanism by which the C 222/P 2 coexisting crystal
grows in the same preferred direction. These results showthat high-speed AFM developed by us for the studies ofdynamic behavior of biomolecular machines at work [21] isalso useful for studying various dynamic processes in protein
2D crystallization, such as the nuclear formation, the initial
growth process, the fusion of small crystal patches, the defectexclusion process and the growth process of a differentsymmetries-coexisting crystal.

4.6. Implication for intermolecular contact in a C222 crystal
Among various 2D crystals of streptavidin and its mutants
formed on lipid layers, symmetric square-shaped crystals with
C 222 symmetry have been obtained. For example, they areformed on biotin-containing lipid layers using streptavidin
mutants (T20A [32] and N23A [33]). In these crystals, theaffinity of the intermolecular contacts between subunits is
considered independent of the biotin binding. Since the aminoacid residues T20, W21 and Y22 are involved in hydrogenbond interaction at the intermolecular contact interface in the
C 222 crystal, the mutation (from T20 to A20) is consideredto suppress the structural changes in the interface induced bybiotin binding. N23 is a key element for hydrogen-bonding
to biotin, and therefore, the mutation (from N23 to A23)
significantly lowers the affinity for biotin [33]. In addition,
N23 is adjacent to the intermolecular contact interface in
the C 222 crystal. This significantly low affinity for biotin
is likely to decouple the biotin binding and the structuralchanges in the intermolecular contact interface; namely, thebinding of biotinylated lipid to N23A streptavidin does not
weaken the intermolecular subunit contact in the C 222 crystal.
This decoupling results in the symmetric crystal growth in
the two orthogonal directions. In fact, the square-shaped
C 222 crystal of N23A streptavidin exhibits a significantly
low critical surface concentration for crystallization, whereas
different mutants with relatively high affinities for biotin
produce asymmetric C 222 crystals with higher critical surface
concentration [33].

Acknowledgments
We thank Hayato Yamashita for providing us with a purified
purple membrane sample. This work was supported by the
CREST project (to TA), the project of Development of System
and Technology for Advanced Measurement and Analysis (toTA), and Strategic International Cooperative Program (to TU)
of the Japanese Science and Technology Agency, and a Grantin-Aid for Basic Research (S) from the Ministry of Education,
Culture, Sports, Science, and Technology of Japan (to TA).

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