Nonequilibrium Fluctuations and Mechanochemical Couplings of a Molecular Motor

Abstract

We investigate theoretically the violations of Einstein and Onsager relations and the thermodynamic efficiency for a single processive motor operating far from equilibrium using an extension of the two-state model introduced by Kafri et al. [Biophys. J. 86, 3373 (2004)10.1529/biophysj.103.036152]. With the aid of the Fluctuation Theorem, we analyze the general features of these violations and this efficiency and link them to mechanochemical couplings of motors. In particular, an analysis of the experimental data of kinesin using our framework leads to interesting predictions that may serve as a guide for future experiments.

Generalized Einstein or Green-Kubo Relations for Active Biomolecular Transport

“…Moreover, it goes beyond similar relations obtained for genuine diffusive spatial transport [9,10] since we require no Euclidean metric and hence the notion of a locally co-moving frame is not available. Our results will therefore be applicable not only to any discrete model for a molecular motor or ion pump (see, e.g., [11][12][13][14] and references therein) but also to driven (bio)chemical reaction networks and their response to changing chemical conditions [15,16]. As a simple illustration will show, a misguided rewriting of our additive relationship between mobility and dispersion in terms of a multiplicative "effective temperature" could easily lead even to negative values for the latter as found for various active biomolecular systems, see, e.g., [17,18].…”

“…As one example consider the observation made in [11] for a particular two state motor model that at stalling conditions, j = 0 at f = f s , the usual Einstein relation between mobility and diffusion constant holds true, even though idle chemical currents dissipate energy. Our expressions (6), (13) and (14) show that, in general, the validity of the Einstein relation requires not only that j = 0 but moreover that any link carrying a non-zero probability current K mn be not sensitive to the force f , i.e.…”

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

“…The model can be simplified by merging the states corresponding to a kinesin head strongly bound to the MT (states K and KT in Fig 11 -state KDP has a too short lifetime to be considered) and those where the kinesin head diffuses freely along the MT (state KD). This results into a two-state 6 model [181,276,219] that already captures important features of the stepping cycle.…”

“…A theoretical frame for fluctuation analysis has been provided in [219]. Due to the generic non-equilibrium features of the motor dynamics, generalized fluctuation theorems have to be applied where the Einstein and Onsager relations are violated.…”

“…Some rates also depend on the ATP concentration. Estimating these contributions allows to calculate a number of experimentally testable quantities, for example the stall force and the load dependent velocity of the molecular motor, or the dependence of velocity on the ATP concentration [125,181,219].…”