Kinesin motion in the absence of external forces characterized by interference total internal reflection microscopy.

Abstract

We study the motion of the kinesin molecular motor along microtubules using interference total internal reflection microscopy. This technique achieves nanometer scale resolution together with a fast time response. We describe the first in vitro observation of kinesin stepping at high ATP concentration in the absence of an external load, where the 8-nm step can be clearly distinguished. The short-time resolution allows us to measure the time constant related to the relative motion of the bead-motor connection; we deduce the associated bead-motor elastic modulus.

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Kinesin motion in the absence of external forces characterized by interference total internal
reflection microscopy
Giovanni Cappello,* Mathilde Badoual, Albrecht Ott, and Jacques Prost
Physico Chimie Curie, UMR CNRS/IC 168, 26 rue d’Ulm, 75248 Paris Cedex 05, France
Lorenzo Busoni
Physico Chimie Curie, UMR CNRS/IC 168, 26 rue d’Ulm, 75248 Paris Cedex 05, France
and Department of Physics, University of Florence and INFM, Via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy
?Received 14 February 2002; revised manuscript received 15 April 2003; published 15 August 2003?
We study the motion of the kinesin molecular motor along microtubules using interference total internal
reflection microscopy. This technique achieves nanometer scale resolution together with a fast time response.
We describe the first in vitro observation of kinesin stepping at high ATP concentration in the absence of an
external load, where the 8-nm step can be clearly distinguished. The short-time resolution allows us to measure
the time constant related to the relative motion of the bead-motor connection; we deduce the associated
bead-motor elastic modulus.
DOI: 10.1103/PhysRevE.68.021907PACS number?s?: 87.15.?v, 87.80.?y, 07.79.Fc
I. INTRODUCTION
Many beautiful techniques which allow in vitro studies of
single biological molecules such as DNA, RNA, and proteins
have been developed over the past ten years. These tech-
niques often involve observing mesoscopic objects such as
beads or nanoneedles, to which the biomolecules are grafted.
Current nanomanipulation techniques ?i.e., atomic force mi-
croscopy, micropipettes, optical and magnetic tweezers? al-
low single molecules to be localized with nanometer preci-
sion and manipulated with forces down to a piconewton
?1–4?. Using these techniques, several studies have been
successfully conducted on biological machines, such as mo-
lecular motors and enzymes. However, the simultaneous con-
trol of force and position requires one to conjugate the mol-
ecule to a micrometer sized bead, which limits the time
resolution of the experiments to the millisecond range. If a
small bead ?bead radius ? 100 nm? is used, the bandwidth
can be significantly improved ?5,6?.
We describe an evanescent wave microscopy technique
for imaging small particles with high spatial and temporal
resolutions. This method is based on the detection of light
scattered from a single particle ?i.e., bead? moving through
an interference pattern generated by two identical laser
beams undergoing total internal reflection at the glass/water
interface. Measuring the temporal variations of the total scat-
tered light allows us to estimate the position of an object
moving in the fringes. In our experimental setup, we can
reach a spatial resolution of a few nanometers (?1% of
fringe periodicity?. Time resolution can be excellent
(?microseconds) using a fast detector, such as a photomul-
tiplier tube, but it is limited by the detector rise time and
photon flux. Using this technique to observe molecular motor
movement allows us to work in the absence of any external
force. Moreover, we can measure the velocity, randomness,
kinesin step length, bead-motor elastic modulus, and the
bead friction coefficient in a single experiment.
The experiments described in this paper are performed on
kinesin with a very small cargo ?50-nm bead? and without
any external load. The kinesin microtubule is a protein com-
plex, which catalyzesATP hydrolysis: ATP⇒ADP?Pi. Dur-
ing the enzymatic reaction, the kinesin-microtubule complex
converts chemical energy into mechanical work. Together
with dynein-microtubule and myosin-actin complexes, it is
responsible for intracellular transport, mitosis, and many
other biological processes. Kinesin is a dimer of two identi-
cal subunits; it contains two motor heads and a coiled-coil
tail. This two-headed motor moves processively ?7? along
microtubules towards the plus end, and travels over a mean
distance of more than 1 ?m without releasing from the mi-
crotubule. The fastest kinesins ?Neurospora Crassa ?8,9??
can reach speeds up to 2–3 ?ms?1. Optical tweezers ex-
periments have shown that kinesin develops a force of a few
piconewtons ?stall force ?6–7 pN) and that the motion is
achieved by discrete steps of 8 nm ?1,10?. This distance cor-
responds to the periodicity of the ??-tubulin arrangement in
microtubules. Each step requires the hydrolysis of one-ATP
molecule ?11?.
II. EXPERIMENTAL SETUP
A. Interference total internal reflection microscopy
As discussed previously, we localize the kinesin-coated
bead with a precision of a few nanometers, in the microsec-
ond range, by using a spatially modulated light ?12?. This
technique bears some similarity to earlier ones designed to
study the proximal hydrodynamic behavior of polymers
close to a surface ?13?. A sinusoidal light modulation is ob-
tained by interference of two laser beams, with opposite
wave vector k?x?the x direction being parallel to the micro-
tubule long axis?, with a fringe periodicity of
d?
?0
2nglasscos?,
*Electronic address: Giovanni.Cappello@Curie.fr
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where ?0is the laser wavelength, ? is the incidence angle at
the glass/water interface ?Fig. 1?, and nglassis the glass re-
fraction index. As the bead scatters the light proportionally to
the local electromagnetic field, its position x(t) can be ex-
pressed as a function of the scattered intensity:
2?sin?1?
x?t??
d
I?t???Imax?Imin?/2
?Imax?Imin?/2?.
?1?
The laser source wavelength currently used in the experi-
ments is 532 nm, which implies that, with nglass?1.518, the
fringe periodicity can be tuned down to 178 nm by changing
the incidence angle ?. In our experiments, a typical value of
? is 24°?3°, corresponding to an interference periodicity of
192?5 nm. This period can be experimentally measured by
fixing a subwavelength single colloid on the slide and mov-
ing the sample holder by means of a calibrated piezoelectric
stage. The measured mean value agrees with the expected
one to within 4% ?Fig. 2?. The two beams, identical in diver-
gence (?0.2°), intensity, phase, and polarization, are ob-
tained using a flat beam splitter. The split beams are reflected
on the sample, respectively, by mirrors M? and M?. In order
to obtain fringes with a well defined wave vector ?direction x
in the following?, we set the same incidence angle ? for both
the beams, with a precision greater than 0.5°.
If we take into account the laser polarization, the local
intensity of the electric field at z?0 can be written as
2?cos2??sin2???sin?
I?x??E2??Ey
2?Exz
2?
dx?,
where Exzand Eyare, respectively, the components of the
electric field perpendicular (P polarized? and parallel (S po-
larized? to the glass/water interface. We note from this equa-
tion that the fringe contrast,
C?
Ey
2?Exz
2?cos2??sin2??
E2
,
has a maximum when the polarization vector is along the y
axis (Exz?0). In order to maximize the contrast, the laser
polarization is set parallel to the glass/water interface.
The resolution of this setup has been calibrated using a
piezoelectric stage, which moves a bead stuk to the cover
glass. Figure 2 shows the signal from a 40-nm bead, moving
through the fringes in 5-nm steps. We observe that the mea-
surements are accurate to within 2 nm. Eventually, we also
verified that the drift of the pattern does not exceed 5–10
nm/s. This value is small enough to allow for the measure-
ment of single-step events with ATP concentrations greater
than 50 ?M. At this concentration, the uncertainty in the
average velocity is smaller than 8% ?3% in most cases?.
These figures could be improved, if necessary. With a 50-nm
bead and our experimental conditions, one can expect to col-
lect at most ?109photons s?1per bead ?14,15?. Experimen-
tally, we measure up to 108photonss?1per bead. We choose
to work at grazing incidence in order to reduce the scattering
volume, in which we collect only the intensity scattered from
the beads near the interface ?location of the microtubules?.
The penetration depth ? can be tuned by adjusting the inci-
dence angle. In our experiments, ? is usually set to 100
?20 nm. The decay length of the evanescent field is mea-
sured by observing the optical signal due to the Brownian
FIG. 1. Schematic of the experimental setup. The prism is re-
quired for total internal reflection.
FIG. 2. Fringe calibration: a single colloid ?diameter 40 nm? is
fixed on the slide. The sample holder is moved in 5-nm steps by
means of a calibrated piezoelectric stage. ?a? The position of the
bead is calculated from its luminosity according to Eq. ?1?. ?b?
Histogram of pairwise distances calculated from curve ?a?.
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motion of free beads in and out of the scattering volume. The
same experiment provides an independent measurement of
the bead diffusion constant, as discussed in Sec. III B.
The laser beam is focused on the sample slide over
?100?100 ?m2. Since the laser beam waist is much larger
than the distance between fringes (?200 nm), we approxi-
mate the intensity I(x,z) as
I?x,z??I0?1?sin?qx??e?z/?,
?2?
where z is the direction orthogonal to the glass surface, the
origin is chosen at the interface, and q?2?/d.
The external load due to the optical force can be deduced
from Eq. ?2? and the laser power. For a 1-W laser and a
50-nm-radius bead, the force is estimated to be 1000 times
smaller than that which is exerted by optical tweezers. In our
experimental setup, the ‘‘trapping’’ energy associated with
the intensity gradient is 10?3kBT, which is clearly negligible
compared to the energy from Brownian motion.
Experiments are carried out using an inverted Zeiss Axio-
vert 100 microscope, equipped with an oil 100X DIC Plan
Apochromat objective and a charge-couple device ?CCD?
camera. The laser source is a second-harmonic YAG ?Coher-
ent Verdi?, with a wavelength ?0?532 nm and a longitudinal
coherence length of several hundreds meters. Its power is
typically set to 400 mW. The scattered intensity is measured
by a photomultiplier tube ?Thorn-Emi 9125B? with a band-
width of 100 kHz. Data are acquired using an analog-digital
converter ?Keithley instruments?, with a sample rate up to
300 kHz. Any constant background is electronically sub-
tracted by rejection of the DC component.
B. Bead assays
Bead assays are made with a biotinilated kinesin from
Drosophilae: HAtag KinBio401. The biotinilated HA-kinesin
is purified from transformed E. Coli as described in Refs.
?16,17?. Kinesin is then conjugated with streptavidin-coated
latex beads (r?50?10 nm, Bangs laboratories?. Beads are
incubated for a few minutes in ultrasound bath with 5-mg/ml
casein. This procedure prevents the beads from clustering.
Microtubules are assembled by polymerization of tubulin
purified from pig brain and they are stabilized with 10-?M
Taxol.
The flow chambers are built with a cover slip and a float
glassmicroscope slide,spaced
(?30 ?m) of vacuum grease. Microtubules stick to a poly-
L-lysine coated slide. Microtubules are injected into the
chamber and incubated for a few minutes. The chamber is
then rinsed with BRB80 buffer (80-mM K-pipes, 1-mM
MgCl2, 1-mM EGTA, pH 6.8? and flushed with a 5-mg/ml
casein solution, in order to avoid nonspecific interactions be-
tween the beads and poly-L-lysine. The chamber is rinsed
again and the kinesin-coated beads are injected into the
chamber, together with the motility buffer ?BRB80, 1-mM
ATP, 1-mM GTP, and 10-?M Taxol?.
After injection of kinesin-coated beads into the chamber,
the beads randomly come into contact with the microtubules.
Preliminary observations are performed by DIC microscopy.
At room temperature, the kinesins move at 340?40 nm/s.
bytwothinlayers
This speed is appreciably slower than the velocities reported
for analogous constructions ?18,19?. However, many experi-
ments have confirmed that the speed of this construction
strongly depends on the buffer and on its pH ?20?.
In order to observe a single motor, the kinesin/bead ratio
has been decreased to slightly above the limit where no
beads move processively. Nevertheless, it is impossible to
exclude the possibility that several motors interact simulta-
neously with the microtubules.
III. RESULTS
A. Kinesin steps
Bead motion is recorded by a CCD camera ?25 frames/s?
while the light intensity is measured by the photomultiplier
tube. Figure 3 shows a kinesin-coated bead moving along the
microtubule, from the left to the right, through the interfer-
ence pattern ?white arrows point toward the bead?. We ob-
serve a strong variation of the scattered light when the bead
moves from an antinode ?Fig. 3?a?? to a node ?Fig. 3?b??. In
Fig. 3?c?, the bead is localized between these two positions.
Figure 3?d? illustrates in which way the bead position can be
determined from its brightness.
Figure 3?a? also shows that no photons are scattered by
the microtubule itself, even if it is 30 nm thick ?and therefore
FIG. 3. ?a?–?c? A kinesin-coated bead blinks moving through
interference fringes in the near field. ?d? Schematic view of the
relationship between bead brilliance and its position.
FIG. 4. ?a? Scattering from a microtubule parallel to the wave
vector k?in: the momentum transfer is zero and k?out?k?in. (a?) The
two arrows point towards the end of the microtubule, which is
invisible in this geometry. ?b? and (b?) Scattering from a microtu-
bule perpendicular to the wave vector: the scattered beam must
satisfy ?k?out???k?in? and k?outperpendicular to the microtubule axis.
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not much smaller than the bead?. In fact, we observe scatter-
ing from the microtubules only when their axis is perpen-
dicular to the incident beam k?in. This effect has a simple
geometrical reason: the microtubule is much longer (1
?10 ?m) than the wavelength while its radius is 20 times
smaller than the wavelength. Therefore, there is no momen-
tum transfer along the microtubule axis ?Fig. 4?a?? in the
experimental geometry, and no light is transmitted through
the objective. On the contrary, the light can be scattered if
the incident wave vector is perpendicular to the microtubule
?Fig. 4?b??.
The total scattered light collected by the photomultiplier
tube is plotted in Fig. 5?a? as a function of time. The dots
represent I(t), acquired with a bandwidth of 100 kHz. No-
tice the low signal/noise ratio: rms noise is 33% of the aver-
age peak-to-peak signal modulation. This noise is essentially
due to the Brownian motion of the bead and to the shot
noise. In order to improve the signal/noise ratio, the signal is
averaged by convolution with a box function. The continu-
ous black line in Fig. 5?a? corresponds to the smoothed sig-
nal, where the cutoff frequency of this low-pass filter is set to
1 kHz. The bead position x(t) is calculated according to Eq.
?1? over intervals of half a period. The position vs time func-
tion ?black line? presents sudden jumps with discrete steps
and plateaus in between. The discontinuities can be inter-
preted as the single steps of the kinesin, where the plateaus
are the waiting time between two ATP hydrolysis events ?1?.
These steps have been statistically analyzed from several se-
ries of data. For each pair of points, x(ti) and x(tj), we
calculate the distance dij??x(ti)?x(tj)?, with i?j. The his-
togram of pairwise distances dijis plotted in Fig. 6. The
histogram shows peaks around 8, 16, 25, 33, and 41 nm,
which suggests a kinesin step of 8.2?0.5 nm. This length is
consistent with the periodicity of the microtubule and it re-
produces, in the absence of external forces, the results ob-
tained using optical tweezers. The histogram for a fixed bead
moved by the mean of a calibrated piezoelectric stage does
not exhibit any peak at all. This is to our knowledge the first
observation of steps at high ATP concentration (1 mM), and
without external forces.
B. Autocorrelation analysis
The I(t) signal is extremely noisy when acquired with a
bandwidth of 100 kHz ?dots in Fig. 5?. Two main sources of
noise have been identified: the Brownian motion of the bead
around the motor position and the shot noise. For a single
bead, we collect up to 108photons/s per bead, over a back-
ground of 5?108photons/s, whereupon the shot noise is
?14% of the bead signal for a sample time of 3 ?s. Both of
these noises can be reduced by decreasing the bandwidth.
The main disadvantage of this solution is that it simulta-
neously reduces the time resolution. However, the shot noise
is uncorrelated, and computing the intensity-intensity auto-
correlation function removes the shot noise while retains the
useful information. With this procedure, the average over
long acquisitions preserves the time resolution.
The autocorrelation function is defined as
???j???I?ti??I?ti?j??
?I?ti??I?ti??
??N?j??1
?I?t?2???
i?1
N?j
I?ti?I?ti?j?,
where ?j?ti?j?ti.
FIG. 5. Measured intensity as a function of time. ?a? Data re-
corded with a bandwidth of 100 kHz ?dots? and with a low-pass
filter at 1 kHz ?black line?. Notice discontinuities in intensity varia-
tions. ?b? Bead position calculated from curve a according to Eq.
?1?. The mean velocity of the motor is 340?40 nm/s ?19? at room
temperature and 1-mM ATP. We choose a section of the curve with
long plateaus.
FIG. 6. Histogram of pairwise distances dij??xi?xj? for i?j,
calculated from curve in Fig. 5?a? over four half periods.
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In Fig. 7, we give an example of autocorrelation function
characterizing the Brownian motion of a free 70-nm-radius
bead in the buffer solution. The intensity-intensity autocorre-
lation functions correspond, respectively, to the bead motion
through the evanescent fringes ?Cxz(?)? and to the motion in
the evanescent field without fringes ?Cz(?)? ?Fig. 7?.
Both Cz(?) and Cx(?)?Cxz(?)?Cz(?) can be calculated
analytically:
Cx????e?Dq2?,
?3a?
Cz?????
D?
??2?
1?2D?
?2
2
eD?/?2erfc??D?
?2?. ?3b?
With independent measurements of Cx(?) and Cz(?), the
diffusion coefficient D and the penetration depth ? are mea-
sured independently. D is obtained directly from Eq. ?3a? and
? can be estimated by fitting the curve Czwith Eq. ?3b?.
Experimentally, we find ??85?10 nm and a diffusion
coefficient consistent with the viscosity of pure water.
Figure 8 shows the autocorrelation function for kinesin-
coated beads moving on a microtubule in 50-?M ATP buffer.
The curves correspond to a total observation time of 21 s.
Because of the limited processivity of kinesin ?a few mi-
crometers?, autocorrelation functions are limited in time and
the curve is not significant much further than a few seconds.
The autocorrelation function can be described as an expo-
nentially damped cosine ?21?:
?????cos?qv0??e?q2D˜??C,
?4?
where C is a constant value and v0is the mean velocity of
the bead, which was measured ?Fig. 8? as 120 nms?1?three
times smaller than the speed measured in the same experi-
mental environment, but at 1-mM ATP concentration? ?11?.
The exponential envelope of the autocorrelation function
corresponds to velocity dispersion and can be classically de-
scribed by the effective diffusion coefficient D˜. This point
was detailed for molecular motors by Svoboda et al. ?22?. A
randomness parameter r was introduced as
r?lim
t→?
?x2?t????x?t??2
??x?t??
?2D˜
?v0,
where ? is the kinesin step.
For a Poisson enzyme, r?1 and r?1/2 for a one-step and
a two-step sequential process, respectively. The continuous
line in Fig. 8 represents the best fit between experimental
data (?) and Eq. ?4?. The best agreement was obtained for
D˜?315 nm2s?1, which corresponds to r?0.66?.07. This
value is consistent with earlier experiments ?22?, although
somewhat large compared to more recent ones ?5?. Under the
same experimental conditions, but in different runs, we ob-
serve a dispersion of r of ?0.25. This dispersion is probably
due to the short run lengths, which do not exceed a few
seconds. This value is consistent with numerical simulations
which give a variation of r of ?0.15 for runs of 250 s ?21?.
Figure 9 shows the autocorrelation function measured for
beads interacting with a microtubule in the presence of ATP
at short time: ??1/D˜q2and ??1/v0q. We observe that the
experimental data (?) depart significantly from ?(?), as
expected for small values of ? from Eq. ?4? ?dashed line in
Fig. 9?.
The origin of this mismatch can be understood by com-
paring with the autocorrelation functions measured, respec-
tively, for a bead attached to the microtubule in the absence
of ATP (?) and for a single bead stuck on the coverslip
(?).
The correlation function of the last curve (?) is domi-
nated by the intrinsic noise of the experimental setup, which
includes the motion of the free beads diffusing through the
fringes. We observe that the amplitude is weak compared to
FIG. 7. Intensity-intensity autocorrelation function measured for
70-nm beads diffusing through the evanescent fringes, Cxz(?) (?),
and in the evanescent field without the fringes, Cz(?) (?). Con-
tinuous lines correspond to the best fit with Eq. ?3?.
FIG. 8. Long-time autocorrelation function. Oscillations are due
to the light modulation when the bead passes from a maximum to a
minimum of the fringe pattern; their frequency is proportional to the
kinesin speed as shown in Eq. ?4?. The cosinelike function is expo-
nentially damped because of the motor randomness. The continuous
line is the best fit between data and Eq. ?4?.
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the curves with molecular motors (? and ?). Furthermore,
we do not observe an appreciable difference between the
curve with ATP and the one without ATP. Therefore, the
experiments suggest that the submillisecond behavior is nei-
ther due to the motion of the free beads nor to the kinesin
motion.
The Brownian motion of the bead, tethered to the micro-
tubule via the kinesin, probably gives rise to the short-time
correlation decay. This decay contains information about the
motor-bead linkage: if the linkage is weak and no external
forces are applied, the bead wiggles as a Brownian particle
attached to a spring in a viscous medium. In this framework,
we expect Eq. ?4? to be modified in the following way:
??????exp??q2kBT
?
?cos?qv0??e?q2D˜??C,
?1?e?(?/?)????
?5?
where ? is the bead-motor linkage elastic modulus, ? is the
friction and R is the bead radius. The fit yields ??0.1
?0.02 pN/nm and ??(2.8?0.8)?10?5pNs/nm.
Current estimates of the kinesin-microtubule stiffness, un-
der load, range between 0.3–1 pN ?6,23?. The value mea-
sured in the absence of external load is rather lower, which is
probably dueto thehighly
microtubule compliance found by Svoboda et al. ?24?. At
zero force, we might explore the entropic elasticity of the
microtubule-kinesin-bead linkage. Applying a force of a few
piconewtons would increase the stiffness by a factor of 5 and
allow a 40 ?s bead response time. The value of the friction
coefficient is high, but comparable with the values found by
Nishiyama et al. ?6?. Indeed they find a response time ?
?72 ?s and ??0.3 pN/nm,
?10?5pNs/nm. An interpretation in terms of viscous drag,
using Stoke’s law, yields a viscosity 30 times greater than
that of water. Such a high value cannot be accounted for by
standard corrections due to the proximity of a substrate ?25?.
It might be due to high friction on the thick casein passiva-
tion layer or by nonspecific absorption on the microtubules.
nonlinearbead-kinesin-
which yield ?????2.1
IV. CONCLUSION
In this paper, we illustrate, with the example of the kine-
sin molecular motor, the potential of an experiment based on
the use of interference total internal reflection. We show that
in a single run one can extract not less than five characteris-
tics of the motor and bead-motor linkage: average velocity,
dispersion ?hence randomness?, step size, bead-motor elastic
modulus and bead friction coefficient. The step is identified
in the absence of any external force and in physiological ATP
concentration: the obtained value, 8 nm, is consistent with
values obtained in low ATP concentration and with picone-
wton external forces. The detection speed allows, in prin-
ciple, for microsecond ?or better? resolution, but for now the
bead response time limits the resolution to 200 ?s. Reducing
friction and stiffening the bead-motor elastic linkage should
allow microsecond time resolution. Such a resolution is
needed for a complete analysis of the motor stepping dynam-
ics.
ACKNOWLEDGMENTS
We warmly thank F. Ne ´de ´lec for the gift of the expression
vector of kinesin from E. Coli, M. Schliwa for providing
kinesins from Neurospora Crassa, P. Chaikin for help with
the initial setup, and A. Roux and B. Goud for their essential
and continuous help in molecular biology.
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FIG. 9. Short-time autocorrelation function measured for a bead
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