Modeling the Cell Muscle Membrane from Normal and Desmin- or Dystrophin- null Mice as an Elastic System

Two of the most important proteins linking the contractile apparatus and costameres at the sarcolemma of skeletal muscle fibers are dystrophin and desmin. We have developed an elastic model of the proteins that link the sarcolemma to the myofibrils. This is a distributed model, with an elastic constant, k, that includes the main protein components of the costameres. The distributed spring model is composed of parallel units attached in series. To test the model, we performed experiments in which we applied negative pressure, generated by an elastimeter, to a small area of the sarcolemma from single myofiber. The negative pressure formed a bleb of variable height, dependent on the pressure applied. We normalized our measurements of k in dystrophin-null (mdx) and desmin-null (des-/-) mice to the value we obtained for wild type (WT) mice, which was set at 1.0. The relative experimental value for the stiffness of myofibers from mice lacking dystrophin or desmin was 0.5 and 0.7, respectively. The theoretical k values of the individual elements were obtained using neural networks (NN), in which the input was the k value for each parallel spring component and the output was the solution of each resulting parallel system. We compare the experimental values of k in control and mutant muscles to the theoretical values obtained by NN for each protein. Computed theoretical values were 0.4 and 0.8 for dystrophin- and desmin-null muscles, respectively, and 0.9 for WT, in reasonable agreement with our experimental results. This suggests that, although it is a simplified spring model solved by NN, it provides a good approximation of the distribution of spring elements and the elastic constants of the proteins that form the costameres. Our results show that dystrophin is the protein that contributes more than any other to the strength of the connections between the sarcolemma and the contractile apparatus, the costameres.