Realistic models of biological motion

Abstract

The origin of biological motion can be traced back to the function of molecular motor proteins. Cytoplasmic dynein and kinesin transport organelles within our cells moving along a polymeric filament, the microtubule. The motion of the myosin molecules along the actin filaments is responsible for the contraction of our muscles. Recent experiments have been able to reveal some important features of the motion of individual motor proteins, and a new statistical physical descriptionoften referred to as "thermal ratchets" -has been developed for the description of motion of these molecules. In this approach the motors are considered as Brownian particles moving along one-dimensional periodic structures due to the effect of nonequilibrium fluctuations. Assuming specific types of interaction between the particles the models can be made more realistic. We have been able to give analytic solutions for our model of kinesin with elastically coupled Brownian heads and for the motion of the myosin filament where the motors are connected through a rigid backbone. Our theoretical predictions are in a very good agreement with the various experimental results. In addition, we have considered the effects arising as a result of interaction among a large number of molecular motors, leading to a number of novel cooperative transport phenomena.

“Burnt-bridge” mechanism of molecular motor motion

“…The stochastic burnt bridge model is a simplification of models proposed to mimic classical molecular motors [3,4,5,6] with energy coming from ATP hydrolysis [7]. Recently it has been shown [8] that the stochastic burnt bridge model with two weakly coupled tracks (the walker moves on the ladder and the hopping rate between the tracks is small compared to the hopping rate along the tracks) accurately describes experimental results on the motion of an activated collagenase on the collagen fibril.…”

Breaking of general rotational symmetries by multidimensional classical ratchets

“…Massive (underdamped) ratchets exhibit a parametric current reversal that could be useful for continuum mass separation [10] and designing 'molecular shuttles' [11]. Furthermore, ratchet motion is considered to be a possible explanation for the longrange cellular transport of motor proteins [12]. On the experimental front, Brownian ratchets have been demonstrated in the rectified motion of polystyrene spheres and a drop of mercury [13], and in current rectification in a DC SQUID [14].…”

Multiscale Modeling and Time-Scale Analysis of a Human Limb

“…These processes are generally modeled by dynamic equations. For example, in [9] ATP dynamics was modeled, and in [6, 14] a fatigue mechanism is modeled.…”