Muscle Crossbridge Theory With Internal Crossbridge Dynamics

TL;DR

This paper introduces a novel muscle crossbridge model with internal dynamics, where crossbridges behave like springs with force-dependent detachment, fitting experimental data and explaining different time-scale behaviors.

Contribution

The paper presents a new crossbridge model incorporating internal dynamics and force-dependent detachment, aligning with experimental force-velocity data and enabling stochastic simulation of muscle behavior.

Findings

Model reproduces Hill's force-velocity curve

Detachment rate decreases linearly with force

Explains different properties on fast and slow time scales

Abstract

We describe in this paper a crossbridge model in which an attached crossbridge behaves like a linear spring with a variable rest length. We assume in particular that the rest length has a linear force-velocity relation, and that the force and rest length are both zero at the moment of crossbridge attachment. Crossbridges that are not attached in our model have a fixed probability per unit time of attachment, and attached crossbridges have a probability per unit time of detachment that is a function of the crossbridge force. This detachment rate is uniquely determined by the requirement that a limiting form of the model should reproduce the force-velocity curve and heat of shortening discovered by A.V.Hill~\cite{AVHILL}, and the detachment rate turns out to be a linearly decreasing function of the crossbridge force. The parameters of the model are determined by a fit to steady-state experimental data; and then an event-driven stochastic simulation methodology is introduced in order to study the behavior of the model in a simulated quick-release experiment. The model explains how the crossbridge can act like a linear spring on a fast time scale but have very different properties on a slower time scale.