Shorten, O'Callaghan, Davidson, Soboleva, 2007

Model Status

This cellML model is known to run in both PCEnv (0.4), JSIM and COR to recreate the published results. The units have been checked in COR and they are consistent in as much as they are known to be equivalent. This particular version of the CellML model represents fast twitch muscle.

Model Structure

Abstract: The ability for muscle to repeatedly generate force is limited by fatigue. The cellular mechanisms behind muscle fatigue are complex and potentially include breakdown at many points along the excitation–contraction pathway. In this paper we construct a mathematical model of the skeletal muscle excitation–contraction pathway based on the cellular biochemical events that link excitation to contraction. The model includes descriptions of membrane voltage, calcium cycling and crossbridge dynamics and was parameterised and validated using the response characteristics of mouse skeletal muscle to a range of electrical stimuli. This model was used to uncover the complexities of skeletal muscle fatigue. We also parameterised our model to describe force kinetics in fast and slow twitch fibre types, which have a number of biochemical and biophysical differences. How these differences interact to generate different force/fatigue responses in fast- and slow- twitch fibres is not well understood and we used our modelling approach to bring new insights to this relationship.

Schematic diagram of the muscle membrane electrophysiological model. There are descriptions of K+, Cl- and Na+ transport in the sarcolemma and t-tubules membranes. The model includes descriptions of an inward rectifier K+ current (IIR), a delayed rectifier K+ current (IDR), a Na+ current (INa), a Na+/K+ pump (INaK) and a Cl- current (ICl). Currents in the t-tubules are denoted by a subscript t.

Schematic diagram of the Ca2+ dynamics model. Ca2+ binds to parvalbumin and ATP myoplasmic buffers, is transported and buffered to calsequestrin in the SR and bind to tropinin to generate force.

Schematic diagram of the crossbridge dynamics model. Two Ca2+ ions must bind to the troponin-tropomyosin regulatory unit (RU) to permit crossbridge cycling (XB) kinetics. Open circles denote Ca2+ binding sites, the black circles represent the number of Ca2+ ions bound to troponin and the black bar represents the tropomyosin block.

Schematic diagram of the phosphate dynamics model. Phosphate is generated during crossbridge cycling and SR Ca2+ pumping, feeds back to slow crossbridge cycling and is transported into the SR to precipitate with Ca2+ and reduce Ca2+ release from the SR.

The complete original paper reference is cited below:

A mathematical model of fatigue in skeletal muscle force contraction, Paul R. Shorten, Paul O’Callaghan, John B. Davidson and Tanya K. Soboleva, 2007, Journal of Muscle Research and Cell Motility , 28, 293-313. (Full text and PDF versions of the article are available to journal subscribers on the Journal of Muscle Research and Cell Motility website.) PubMed ID: 18080210