Operation modes of the molecular motor kinesin

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 Delta mu 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,Delta mu) 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.