Understanding crossbridge dynamics from a modeling perspective

A new computer modeling system for determining crossbridge cycle dynamics is described. The transition rates from one state to another are defined by rate coefficients that can either be constant or vary with the position of the crossbridge relative to the thin-filament attachment site. This leads to a system of differential equations defining the rates of change for the fractions of bridges in each state. Solutions for this system of equations are obtained at specified times during and after a length change using a method for systems with widely varying time constants (C.W. Gear, 1971, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs. NJ). Crossbridges are divided into discrete populations that differ both in their axial displacement with respect to thin filament attachment sites and with respect to the twist of the actin helix. Separate solutions are made for the individual populations and are then averaged to obtain the ensemble response