Mathematical modelling of the half-sarcomere from a human skeletal muscle
Guest, Kay P.
mesheuropmc: macromolecular substances
The character of the functional output of a motor unit within skeletal muscle has been linked experimentally to the proteins found in the sarcomere, the smallest contractile unit of muscle fibre. Current mathematical models focus on either individual chemical reactions or the bulk properties of muscle with limited reference to the internal processes and structures within the muscle. Without an understanding of those internal properties, the normal function of muscle cannot be simulated and consequently muscular diseases and their treatments cannot be accurately modelled.\ud \ud In this project, a mathematical model has been developed which relates the chemomechanical cycle of individual events (crossbridges) to the transfer of mechanical\ud energy through an actin filament, myosin cofilament and, by incorporating the protein titin, the mechanical properties of the interconnecting proteins in a section of\ud sarcomere. Evaluation and parameterisation of the model were made by comparison with in vitro test data from the published literature at the level of a single crossbridge\ud and single filaments. At the single filament level, the model was evaluated against two conditions: a low load high displacement (concentric contraction) and a high load low displacement (isometric contraction).\ud \ud In isometric loading the peak force level per unit length of actin filament was higher than that observed in vitro, the difference being attributable to the greater compliance\ud in the substrate used in vitro to hold the myosin fragments (~37pN compared to ~12pN). The mean number of concurrent crossbridges was consistent between the model and in vitro data. Under low load the model demonstrated filament movement at speeds comparable to those measured in in vitro motility studies, although longer filaments in the model were required than those in vitro to reach the higher speeds (7μm vs. 2μm for ~8μm/s).\ud \ud By making the pre-lever reaction duration of the crossbridge cycle strain dependent it was possible to obtain long reaction cycles in low load scenarios comparable to those observed for fragments in solution while generating the actin filament speeds observed\ud in vitro. It was necessary to have a distribution of attachment times across the filament in order to generate and maintain filament movement in the model; the variation being governed by the tension distribution in the filament. By applying a passive loading as generated by the titin protein the filaments moved more rapidly, with an increased contribution from each crossbridge to filament movement.\ud \ud Initial results indicate examination of the strain dependency of the post-lever reaction duration may modify filament speeds and will increase the proportion of each crossbridge movement that contributes to the actin filament propulsion (increase crossbridge efficiency). Examination of a selection of the model’s parameters gave an initial evaluation of how the model could be ‘tuned’ to change the number, reaction state and distribution in time of crossbridges to achieve changes in filament contraction speed, isometric force generation and the efficiency with which crossbridges are used; noting that one desired output may conflict with another.\ud \ud The interaction of the passive components in the structure of the sarcomere with the strain dependent reaction cycle at each crossbridge demonstrated the potential limitations of scaling and averaging localised events without consideration of the passive structures present in the fibre and muscle bulk. The model provides a means to examine the mechanisms and parameters of the sarcomere’s function and how those parameters may be adjusted to achieve different output characteristics. The model provides a foundation for the emulation of muscle fibres and a motor unit in health and disease.
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