Supplement 2.
Stochastic oscillation by a single KIF1A monomer and rapid, kinesin
dimer-like movement by the clustering of KIF1A.
Some of the beads coated with KIF1A in a large excess (30 - 100:1 in molar ratio at
mixing) showed two modes of movement.
Typically, they first showed repetitive small
amplitude plus-end biased stochastic oscillation (Fig S2a, red bar), essentially the same as
the movement observed with a bead coated with a low concentration of KIF1A (mixing
ratio <3:1, Fig 1b). Then, the same bead suddenly started to move rapidly toward the
microtubule’s plus-end and stalled for a while before full detachment (Fig S2a, blue bars).
This movement is apparently similar to that of the beads coated with two-headed
conventional kinesin.
Its velocity at a low force (<0.1 pN) was 800 nm/s, which is close
to the velocity determined in the microtubule-gliding assay (Table S1) and in the bead assay
with an artificially dimerized KIF1A molecule1.
This mode of movement was never observed with KIF1A-beads mixed at lower
KIF1A/bead ratios (<10:1 molar ratio at mixing).
Such low mixing-ratio beads only
showed stochastic oscillatory movement as shown in Fig 1b.
Therefore, this stochastic
oscillation is expected to be supported by a single KIF1A monomer, and the rapid,
conventional kinesin-like run will be supported by multiple KIF1A molecules.
To confirm this, we examined the number of motor molecules required for the stochastic
oscillatory movement and the rapid run. We have first analyzed the fraction of the beads
that bound to the microtubule in the presence of AMPPNP as a function of the KIF1A/bead
mixing ratio2, 3, because a single kinesin-type motor domain is sufficient for the binding to
the microtubule in the presence of AMPPNP. We, then, compared the results with the
fraction of the moving beads (2 mM ATP). Each bead was tested three times on different
microtubules for 1 min each, since the positive bead typically shows the binding or the
movement within 10 s after contacting to the microtubule. The binding of the bead to the
microtubule was detected by the decrease of the fluctuation of the bead position.
In the
presence of AMPPNP, the binding was much stronger than the optical trap, which enabled
unambiguous detection of the binding events.
Only the beads that showed repetitive
movement whose duration was longer than 1 s were counted as moving bead.
The
observed values were fitted with the Poisson distribution: n  1 : 1- exp  C  (red in Fig
S2b-f) and n  2 : 1-(1  C) exp  C  (blue), where C is the molar mixing ratio of the
motor to the bead. The fitting parameter  indicates the efficiency of the functional
binding between the motor and the bead.
The best-fit curve for the fraction of the binding
beads was n  1 with  = 0.05 ~ 0.1, confirming that a single KIF1A monomer is enough
for the binding to the microtubule. Furthermore, the same curve fits well to the fraction of
the moving beads (Fig S2b,c), demonstrating that one KIF1A molecule is sufficient for the
movement of the bead on the microtubule. The best-fit value of the fitting parameter 
agrees well with the binding efficiency of KIF1A to the bead. Around 90% of KIF1A
remained in supernatant after mixing with the beads, indicating that only ~10 % of the
added KIF1A bound to the bead surface.
This relatively low binding efficiency might be
caused by the efficiency of the in vivo biotinylation (10~50%) and the conformation around
the biotinylated residues.
However, there remains a possibility that the biotinylated KIF1A binds to the multivalent
binding sites of streptavidin in a cooperative manner. To exclude this possibility, we used
a monovalent ligand-receptor pair for the immobilization: His-tag and anti-His-tag Fab
fragment (Fig 1a). The A382-His bead and the His-A382 bead showed the same motile
properties as shown in the main text (Fig 1b).
The Poisson analysis as above indicated
that the movement is supported by a single KIF1A molecule. The observed probability for
the movement was well-fitted with the Poisson distribution with n  1 and  = ~0.2 (Fig
S2d,e). The binding efficiency was limited by the numbers of the active Fab fragment
on the bead, as indicated by the titration experiment (Fig S2f). The active Fab fragment
was diluted by mixing with the control Fab fragment (Fab fragment of a non-specific
mouse IgG with the same heavy chain and light chain isotypes) so that the total
concentration of the Fab fragment was constant.
The Fab-coated beads were, then,
incubated with the 30-times molar excess A382-His protein, and the fraction of the moving
beads was analyzed as above against the relative concentration of the active Fab fragment
(Fig S2f). The result supported that the efficiency of the KIF1A binding to the antibody
bead is limited by the number of the active antibody fragment on the bead.
The Poisson statistics analysis above has demonstrated that a single KIF1A monomer is
sufficient for the stochastic oscillation-type movement of the KIF1A-bead. Based on this
analysis, we analyzed the fraction of the beads that showed the kinesin-like run as a
function of the KIF1A/bead mixing ratio (Fig S2g).
Although the experiments with
higher mixing ratios are difficult due to technical limitations, the results clearly show that
more KIF1A motors are required for the kinesin-like run than for the stochastic oscillation
or the binding to the microtubule. The probability that the bead has two (or more) motors
close enough to allow them to simultaneously interact with the microtubule can be
calculated from the Poisson statistics. The probability that a bead has two or more motors
is given by 1-(1  C) exp  C  , where C and  denote the molar mixing ratio and
efficiency of the binding, respectively.
The binding efficiency for A382-BCCP was ~0.1
(Fig S2b). This value reflects the binding efficiency of the motor to bind anywhere on the
bead surface. The geometrical constraints to allow the two motors to simultaneously
interact with the microtubule will significantly decrease this efficiency.
For example, if
we assume that a motor can interact with a microtubule within 5 nm from the bead surface
(an assumption based on the structure of the A382-BCCP construct), the distance of the two
motors should be less than 60 nm due to the curvature of the bead (100-nm radius). Then,
the two motors should bind within 10% of the area of the bead surface, which will result in
a 10-fold smaller  value.
Based on this calculation, the Poisson probability curve
1-(1  C) exp  C  was drawn in Fig S2f with blue) This curve agrees well
with the observation, supporting the hypothesis that the kinesin-type run requires more than
two motors as reported previously 1, 4, 5 .
References
1. Tomishige, M., Klopfenstein, D., R. & Vale, R., D. Conversion of Unc104/KIF1A Kinesin into a
Processive Motor After Dimerization Science. 297,2263-2267 (2002).
2. Block, S.M., Goldstein, L.S. & Schnapp, B.J. Bead movement by single kinesin molecules studied with
optical tweezers. Nature 348, 348-352 (1990).
3. Endow, S.A. & Higuchi, H. A mutant of the motor protein kinesin that moves in both directions on
microtubules. Nature 406, 913-916 (2000).
4. Berliner, E., Young, E.C., Anderson, K., Mahtani, H.K. & Gelles, J. Failure of a single-headed kinesin to
track parallel to microtubule protofilaments. Nature. 373, 718-721 (1995).
5. Inoue, Y., Toyoshima, Y.Y., Iwane, A.H., Morimoto, S., Higuchi, H. & Yanagida, T. Movements of
truncated kinesin fragments with a short or an artificial flexible neck. Proc. Natl. Acad. Sci. U. S. A. 94,
7275-7280 (1997).
Figure S2.
Movement of KIF1A beads coated with many KIF1A molecules. a.
Displacement of the KIF1A beads at a high mixing ratio (30:1) in the presence of 2
mM ATP, showing two modes of movement: oscillation (red bars) and run (blue
bars).
Trap stiffness, 6 fN/nm. To simultaneously show the oscillation and the run,
the bead is trapped weakly.
Therefore, the displacement by the run-type
movement exceeds the region where the load force by the optical trap is linearly
related to the displacement from the trap center (±300 nm). Furthermore, the
vertical component of the load force by the optical trap is not negligible with such
large displacements. Thus, the stall force could no be determined in this trace, but
was measured as ~2.5 pN from experiments with higher trap stiffness (not shown).
b-g. The Poisson statistics of KIF1A-beads’ behavior.
The probability of the
movement (run + oscillation) and the best-fit curves are plotted.
See text for detail.