A general network theory for the molecular motor kinesin is developed that is based on the distinct chemical states of the motor and on recent observations about its mechanical steps. For small concentrations of adenosine diphosphate (ADP), the motor's behavior is governed by the competition of two chemomechanical motor cycles which determine the motor's stall force. A third cycle becomes important for large ADP concentrations. The theory provides a quantitative description for the functional dependencies of different motor properties as observed in single molecule experiments.

PACS 05.70.Ln-Nonequilibrium and irreversible thermodynamics PACS 87.16.Nn-Motor proteins (myosin, kinesin, dynein) PACS 82.39.-k-Chemical kinetics in biological systems Abstract-Molecular motors and nanomachines are considered that are coupled to exergonic processes which provide energy input to these motors and allow them to perform work. The motor dynamics is described by continuous-time Markov processes on a discrete state space, which can contain an arbitrary number of cycles consisting of two dicycles with opposite orientation. For the steady state of such a motor, the statistical entropy produced during the completion of each dicycle is expressed in terms of its transition rates. Identifying this statistical entropy with the heat released by the motor and using the first law of thermodynamics, we derive steady-state balance conditions that generalize the well-known detailed balance conditions in equilibrium. Our derivation is rather general and applies to any nonequilibrium system described as a Markov process. For molecular motors, these balance conditions depend on the external load force and can be decomposed into a zero-force and a force-dependent part.

Molecular motors are considered that convert the chemical energy released from the hydrolysis of adenosine triphosphate (ATP) into mechanical work. Such a motor represents a small system that is coupled to a heat reservoir, a work reservoir, and particle reservoirs for ATP, adenosine diphosphate (ADP), and inorganic phosphate (P). The discrete state space of the motor is defined in terms of the chemical composition of its catalytic domains. Each motor state represents an ensemble of molecular conformations that are thermally equilibrated. The motor states together with the possible transitions between neighboring states define a network representation of the motor. The motor dynamics is described by a continuous-time Markov process (or master equation) on this network. The consistency between thermodynamics and network dynamics implies (i) local and nonlocal balance conditions for the transition rates of the motor and (ii) an underlying landscape of internal energies for the motor states. The local balance conditions can be interpreted in terms of constrained equilibria between neighboring motor states; the nonlocal balance conditions pinpoint chemical and/or mechanical nonequilibrium.

No abstract

The velocity and the adenosine triphosphate (ATP) hydrolysis rate of the molecular motor kinesin are studied using a general network representation for the motor, which incorporates both the energetics of ATP hydrolysis and the experimentally observed separation of time scales between chemical and mechanical transitions. Both the motor velocity and its hydrolysis rate can be expressed as superpositions of excess fluxes for the directed cycles (or dicycles) of the network. The sign of these dicycle excess fluxes depends only on two thermodynamic control parameters as provided by the load force F and the chemical energy Deltamicro released during the hydrolysis of a single ATP molecule. In contrast, both the motor velocity and its hydrolysis rate depend, in general, on the load force F as well as on the three concentrations of ATP, adenosine diphosphate (ADP), and inorganic phosphate (P), separately. Thus, in order to represent the different operation modes of the motor in the (F,Deltamicro) plane, one has to specify two concentrations such as the product concentrations [ADP] and [P]. As a result, we find four different operation modes corresponding to the four possible combinations of ATP hydrolysis or synthesis with forward or backward mechanical steps. Our operation diagram implies in particular that backward steps are coupled to ATP hydrolysis for sufficiently large ATP concentrations, but to ATP synthesis for sufficiently large ADP and/or P concentrations.