Quantifying the Heat Dissipation from Molecular Motor’s Transport Properties in Nonequilibrium Steady States

Abstract

Theoretical analysis, which maps single molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and diffusivity. Unlike passive Brownian particles in equilibrium, the velocity and diffusion constant of molecular motors are closely inter-related to each other. In particular, our study makes it clear that the increase of diffusivity with the heat production is a natural outcome of active particles, which is reminiscent of the recent experimental premise that the diffusion of an exothermic enzyme is enhanced by the heat released from its own catalytic turnover. Compared with freely diffusing exothermic enzymes, kinesin-1 whose dynamics is confined on one-dimensional tracks is highly efficient in transforming conformational fluctuations into a locally directed motion, thus displaying a significantly higher enhancement in diffusivity with its turnover rate. Putting molecular motors and freely diffusing enzymes on an equal footing, our study offers thermodynamic basis to understand the heat enhanced self-diffusion of exothermic enzymes.Together with recent studies [1][2][3][4], Riedel et al. [5] have demonstrated a rather surprising result, from a perspective of equilibrium statistical mechanics: Diffusion constants (D) of exothermic enzymes, measured from fluorescence correlation spectroscopy (FCS), increase linearly with their catalytic turnover rates V cat , so that the enhancement of diffusivity at maximal activity (maximum V cat ) is as large aswhere D 0 and D max are the diffusion constants measured by FCS at V cat = 0 and maximal V cat , respectively. Their enigmatic observation [5] has called much attention of biophysics community to the physical origin of the activity-dependent diffusivity of a single enzyme. Golestanian [6] considered four distinct scenarios (self-thermophoresis, boost in kinetic energy, stochastic swimming, collective heating) to account for this observation quantitatively; however, the extent of enhancement observed in the experiment was still orders of magnitude greater than the theoretical estimates from the suggested mechanisms. Bai et al.[7] also drew a similar conclusion by considering hydrodynamic coupling between the conformational change of enzyme and surrounding media. The experimental demonstration of enzymes' enhanced diffusion with multiple control experiments in Ref.[5] is straightforward; however, physical insight of the observed phenomena is currently missing [5,6,8,9].While seemingly entirely different from freely diffusing enzymes, kinesin-1 [10-15] is also a substrate-catalyzing enzyme. Conformational dynamics of kinesin-1, induced by ATP hydrolysis and thermal fluctuations, is rectified into a unidirectional movement with a high fidelity [16,17]; hydrolysis of a single ATP almost always leads to 8 nm step [18]. Every step of kinesin-1 along 1D tracks, an outcome of cyclic chemical reaction, can be mapped (2)µ, ..., (N )µ denote distinc...

Allocating and Splitting Free Energy to Maximize Molecular Machine Flux

“…11,19,[34][35][36][37][38] Unlike in our model, all other models we have found assume that rate constants only explicitly contain splitting factors for force, with no splitting factors for other free energy components (though one other model has implicit splitting of the effect of chemical potential 11 ). Splitting factor analysis has largely been done in the context of 'canonical' molecular machines, such as the walking motors kinesin, [35][36][37][38] myosin, 11,19 and dynein, 39 or the rotary motor F1-ATPase. 34 Splitting factors δ are not always robust, with distinct data sets for kinesin motility 40,41 leading to substantially different inferred values of 0.3 and 0.65.…”

“…We have shown that both low and high splitting factors can maximize flux, and that the optimal splitting factor value depends on the allocation of free energy. Experimental fits of splitting factors find both low splitting factors 11,19,[34][35][36] and high splitting factors. 35,37 These fits use several models for the dependence of rate constants on resisting forces.…”

“…In SI: Experimental splitting factors, we describe in more detail the fitted splitting factors for various models. 11,19,[34][35][36][37][38] Flux can also be maximized by varying free energy components ω k ij , with flux significantly decreasing away from the optimal ω k * ij . For a scenario with two distinct free energy components, one variable and one fixed, the flux is maximized by allocating the variable free energy component to compensate for any departure from optimal of the fixed free energy component allocation.…”

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

“…305 Recent work has argued that enzyme diffusion enhancement due to catalysis fits within the same framework that describes the diffusion enhancement of traditional motors, such as kinesin, due to dissipation. 176…”

How kinesin waits for ATP affects the nucleotide and load dependence of the stepping kinetics

“…The binding and hydrolysis of ATP are the events associated with the NL docking (19). Based on these observations and other key experiments probing the variations of the stepping characteristics of the motor as a function of ATP concentration and applied load, several theoretical models for motors in general and the the catalytic cycle of Kin1 in particular have been proposed (15,(20)(21)(22)(23)(24)(25), although issues such as the mechanism of inter-head communication (gating) continue to be topics of interest (26)(27)(28).…”