Energy-based Modelling of Single Actin Filament Polymerisation Using Bond Graphs

Bond graphs provide an energy-based methodology for modelling complex systems in a hierarchical fashion; at the moment, the method allows biological system with both chemical and electrical subsystems to be modelled. Herein, the bond graph approach is extended to include chemomechanical transduction thus extending the range of biological systems to be modelled. Actin filament polymerisation and force generation is used as an example of chemo-mechanical transduction and it is shown that the TF (transformer) bond graph component provides a practical, and conceptually simple, alternative to the Brownian ratchet approach of Peskin, Odell, Oster & Mogilner. Furthermore it is shown that the bond graph approach leads to the same equation as the Brownian ratchet approach in the simplest case. The approach is illustrated by showing that flexibility and non-normal incidence can be modelled by simply adding additional bond graph components and that compliance leads to non-convexity of the force-velocity curve. Energy flows are fundamental to life; for this reason, the energy based approach is utilised to investigate the power transmission by the actin filament and its corresponding efficiency. The bond graph model is fitted to experimental data by adjusting model physical parameters.