Mathematical Modeling

Figures from modeling papers Muscle weakness - an inability to develop normal force - has a significant impact on public health but the molecular mechanisms that underlie the dysfunction are not yet clear. This project integrates mathematical, biophysical and proteomic techniques to improve quantitative understanding of force generation in skeletal muscles. The research will determine which structural and/or molecular changes are most detrimental to contractile performance and use synergistic in silico and in vitro experiments to identify and test potential new treatments for muscle weakness. Muscles develop force when myosin heads protruding from 'thick' filaments interact with binding sites on 'thin' actin filaments. Most existing models treat all myosin heads as identical motors but this is an over-simplification because some myosin molecules will be located too far from an actin site to generate force at a given instant. Myofilament architecture therefore influences force generation but has been largely discounted in previous work. This research uses newly developed computer programs which implement spatially-explicit stochastic techniques to simulate actin-myosin interactions. The new model is more useful for simulating diseased muscle than most previous frameworks because its calculations incorporate information about the geometrical constraints on actin-myosin interactions imposed by the filament architecture and the specific behavior of individual protein structures. At the completion of this work, the model, full documentation describing how to use it and all relevant computational data will published on the internet for unrestricted download by academic researchers. Aim 1 uses a high-performance distributed computing system (DEngine) previously developed by the Principal Investigator to model the contractile behavior of permeabilized rat soleus muscle fibers. This will establish baseline parameters for the model. Aim 2 uses the computer model to investigate contractile dysfunction in two relevant animal models: hindlimb suspension unloaded rats and genetic deletion of the Bmal1 gene in mice. Experiments will establish the myofilament lattice structure (using automated analysis of electron micrographs) and the amount and isoform profile of titin, myosin and regulatory proteins (using gel electrophoresis) in each animal model. Posttranslational protein modifications will be assessed using mass spectrometry. This data will be integrated into the basal computer model which will then be iteratively refined by testing its ability to predict the results of new biophysical and proteomic experiments and adjusting the computational framework as required to reproduce the real data. Once a suitable computer model has been developed, the simulation parameters will be systematically manipulated to search for in silico interventions that raise contractile force. Some of these interventions could be potential therapies for muscle weakness. The most promising approaches will be tested using proteomic and biophysical experiments.