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Biophys J, June 2001, p. 2515-2526, Vol. 80, No. 6
and
*Physics Department, and Center for Interdisciplinary Research on
Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA and
Departamento de Física, Facultad de Ciencias Exactas
y Naturales, Universidad de Buenos Aires, RA-1428 Buenos Aires,
Argentina
A two-dimensional stochastic model for the dynamics of
microtubules in gliding-assay experiments is presented here, which includes the viscous drag acting on the moving fiber and the
interaction with the kinesins. For this purpose, we model kinesin as a
spring, and explicitly use parameter values to characterize the model from experimental data. We numerically compute the mean attachment lifetimes of all motors, the total force exerted on the microtubules at
all times, the effects of a distribution in the motor speeds, and also
the mean velocity of a microtubule in a gliding assay. We find
quantitative agreement with the results of J. Howard, A. J. Hudspeth, and R. D. Vale, Nature. 342:154-158. We
perform additional numerical analysis of the individual motors, and
show how cancellation of the forces exerted by the many motors creates a resultant longitudinal force much smaller than the maximum force that
could be exerted by a single motor. We also examine the effects of
inhomogeneities in the motor-speeds. Finally, we present a simple
theoretical model for microtubules dynamics in gliding assays. We show
that the model can be analytically solved in the limit of few motors
attached to the microtubule and in the opposite limit of high motor
density. We find that the speed of the microtubule goes like the mean
speed of the motors in good quantitative agreement with the
experimental and numerical results.
Biophys J, June 2001, p. 2515-2526, Vol. 80, No. 6
© 2001 by the Biophysical Society 0006-3495/01/06/2515/12 $2.00
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