The influence of chromosome flexibility on chromosome transport during anaphase A

Abstract

The role of protein flexibility in molecular motor function has previously been studied by considering a Brownian ratchet motor that is connected to its cargo by an elastic spring, with the result that the average velocity of the motor͞cargo system is increased by reducing the stiffness of the linkage. Here, we extend this investigation to the case of chromosome transport during anaphase A, in which the relevant flexibility is not primarily in the motor͞cargo linkage but rather in the cargo itself, i.e., in the chromosome. We model the motor mechanism as an imperfect Brownian ratchet with a built-in opposing load and the chromosome as a collection of discrete segments linked by an elastic energy function that discretizes the potential energy of an elastic rod. Thermal fluctuations are produced in the model by random forces, as in Brownian dynamics. All of the parameters that characterize the chromosome are known or can be estimated from experimental data, as can all but one of the motor parameters, which is adjusted to give the correct transport velocity of normal-length chromosomes. With the parameters so determined, we then reproduce the experimental finding of Nicklas [Nicklas, R. B. (1965) J. Cell Biol. 25, 119 -135] that chromosome speed is essentially independent of chromosome length, even though our model contains no ''velocity governor.'' We find instead that this effect is a consequence of chromosome flexibility, as it disappears when stiffer than normal chromosomes are considered.Brownian ratchet ͉ molecular motors ͉ protein elasticity ͉ velocity governor ͉ thermal fluctuations

Self-induced stochastic resonance for Brownian ratchets under load

“…In particular, the meaning of ǫ ≪ 1 means that the work involved in one step of the motor is a significant multiple of k B T . It is observed [20] (see also [21]) or inferred [19] for multiple examples of motor proteins that the activation energy required to move the motor one step in the ratchet is about one order of magnitude greater than k B T , but comparable to the energy released in the hydrolyzation of one ATP molecule. This means that α is O(1), and ǫ is small enough so that ǫ ≪ 1, but, perhaps more importantly, it is not too small.…”

“…This is important because non-smooth potentials (e.g. piecewise-linear) are used in several applications [19,9].…”

“…Rectified thermal diffusion, or the Brownian ratchet, has been used in many contexts as a model for processes at the molecular level; a few examples include RNA polymerase [23], chromosome transport [19], protein translocation [22], and ATP hydrolysis of kinesin [18] (see [9] for a comprehensive list).…”

Several Issues in Modeling Molecular Motors

“…It is clear that Laurent expansions (71), predicted from the Laplace transform, are invalid for this discrete cycle time distribution. The equivalence between R N and R T , however, still holds.…”

“…The motor and the cargo are linked by an elastic element. 71 Over long time, the cargo must follow the motor and they must have the same average velocity and the same effective diffusion coefficient. Under the framework of twodimensional Fokker-Planck equations, we derive that the Stokes efficiency is bounded by 100% for motor-cargo systems.…”