Physical analysis of a processive molecular motor: the conventional kinesin

Models of protein linear molecular motors for dynamic nanodevices

Protein molecular motors are natural nano-machines that convert the chemical energy from the hydrolysis of adenosine triphosphate into mechanical work. These efficient machines are central to many biological processes, including cellular motion, muscle contraction and cell division. The remarkable energetic efficiency of the protein molecular motors coupled with their nano-scale has prompted an increasing number of studies focusing on their integration in hybrid micro- and nanodevices, in particular using linear molecular motors. The translation of these tentative devices into technologically and economically feasible ones requires an engineering, design-orientated approach based on a structured formalism, preferably mathematical. This contribution reviews the present state of the art in the modelling of protein linear molecular motors, as relevant to the future design-orientated development of hybrid dynamic nanodevices.

Dynamic stability versus thermodynamic performance in a simple model for a Brownian motor

Homeostasis allows living organisms to perform in optimal conditions despite ever-changing surroundings. Dynamically, it corresponds to a stable steady state, and so its quality can be judged by the volume of the corresponding basin of attraction and/or the length of the relaxation time. Motivated by the fact that the vast majority of intracellular processes involve enzymatic reactions and, as some people have suggested, models similar to those of Brownian motors can be used to study them, here we introduce a simple Brownian motor model and use it to gain insight into the relation between efficiency and stability properties previously observed in macroscopic systems. For this, we analyze the existence, uniqueness, and stability of the motor's steady state; study its thermodynamic process variables, their relation, and their dependence on the model parameters; and compare the Brownian motor relaxation time and thermodynamic properties. Finally, since the steady state is unique and globally stable, we discuss our results from the standpoint of the energetic costs of maintaining a homeostatic state with short relaxation times.

Kinesin as an electrostatic machine

Kinesin and related motor proteins utilize ATP fuel to propel themselves along the external surface of microtubules in a processive and directional fashion. We show that the observed step-like motion is possible through time-varying charge distributions furnished by the ATP hydrolysis cycle while the static charge configuration on the microtubule provides the guide for motion. Thus, while the chemical hydrolysis energy induces appropriate local conformational changes, the motor translational energy is fundamentally electrostatic. Numerical simulations of the mechanical equations of motion show that processivity and directionality are direct consequences of the ATP-dependent electrostatic interaction between the different charge distributions of kinesin and the microtubule.