Unraveling on kinesin acceleration in intracellular environments: A theory for active bath

A single-molecular motor kinesin harnesses thermal and nonthermal fluctuations to transport various cargoes along microtubules, converting chemical energy to directed movements. To describe the nonthermal fluctuations generated by the complex environment in living cells, we propose a bottom-up model which combines a Markov model of the kinesin and a mean-field model for the active bath, to mimic the kinesin movements in the intracellular environment. Simulations of the model system show that the kinesin and the probe attached to it are accelerated by such active bath. Further, we provide a theoretical insight into the simulation result by deriving a generalized Langevin equation (GLE) for the probe with a mean-field method, wherein an effective friction kernel and fluctuating noise terms are obtained explicitly. Numerical solutions of the GLE show very good agreement with simulation results. We sample such noises, calculate their variances and non-Gaussian parameters, and reveal that the dominant contribution to probe acceleration is attributed to noise variance.