Exact dynamic properties of molecular motors

Abstract

Molecular motors play important roles within a biological cell, performing functions such as intracellular transport and gene transcription. Recent experimental work suggests that there are many plausible biochemical mechanisms that molecules such as myosin-V could use to achieve motion. To account for the abundance of possible discrete-stochastic frameworks that can arise when modeling molecular motor walks, a generalized and straightforward graphical method for calculating their dynamic properties is presented. It allows the calculation of the velocity, dispersion, and randomness ratio for any proposed system through analysis of its structure. This article extends work of King and Altman ["A schematic method of deriving the rate laws of enzyme-catalyzed reactions," J. Phys. Chem. 60, 1375-1378 (1956)] on networks of enzymatic reactions by calculating additional dynamic properties for spatially hopping systems. Results for n-state systems are presented: single chain, parallel pathway, divided pathway, and divided pathway with a chain. A novel technique for combining multiple system architectures coupled at a reference state is also demonstrated. Four-state examples illustrate the effectiveness and simplicity of these methods.

Fluctuating currents in stochastic thermodynamics. II. Energy conversion and nonequilibrium response in kinesin models

“…This is in agreement with recent experimental results and theoretical predictions from an alternative model [17]. Our method to calculate the second scaled cumulant and thus the diffusion constant avoids all of the combinatorial complexity of previous approaches [41,42]. Ref.…”

“…• Current statistics correspond to experimentally observable quantities, like the average motor velocity or its nonequilibrium diffusion constant. Our systematic approach thus extends and unifies previous approaches for calculating these quantities [41][42][43].…”

“…Our method to calculate the second scaled cumulant and thus the diffusion constant avoids all of the combinatorial complexity of previous approaches [41,42]. Ref.…”

Fluctuating currents in stochastic thermodynamics. I. Gauge invariance of asymptotic statistics

“…Ref. [24] for explicit considerations of the combinatorics involved in a scaled cumulant of second order). In other words, the relevant information about the steady- state distribution is hidden in the coefficients a k (q).…”

Are Two‐Station Biased Random Walkers Always Potential Molecular Motors?

“…More sophisticated networks can be studied by the present approach. [14,15] It will be interesting to apply Equation (9) to the development of artificial molecular machines and to verify experimentally how variation of friction and temperature can turn a random walker into a biased one.…”