Michaelis-Menten dynamics of a polymer chain out of a dichotomous ATP-based motor

TL;DR

This paper models an ATP-driven molecular motor pushing a polymer through a pore, revealing Michaelis-Menten dynamics in translocation velocity and stall force, aligning with recent biological experiments.

Contribution

It introduces a novel model linking ATP concentration to motor activation and translocation dynamics, deriving Michaelis-Menten laws for velocity and stall force.

Findings

Velocity follows a Michaelis-Menten law.

Translocation time varies monotonically with activation frequency.

Results agree with recent biological experiments.

Abstract

We present a model of an ATP-fueled molecular machine which push a polymer through a pore channel. The machine acts between two levels (working-waiting), and the working one remains active for a fixed time giving a constant force. The machine activation rate can be put in relationship with the available ATP concentration in the solution, which gives the necessary energy supply. The translocation time shows a monotonic behavior as a function of the activation frequency and the velocity follows a Michaelis-Menten law that arises naturally in this description. The estimation of the stall force of the motor follows a corrected Michaelis-Menten law which still is to be checked in experimental investigation. The results presented agree with recent biological experimental findings.