Active gel theory for cell migration with two myosin isoforms

Myosin II molecular motors slide actin filaments relatively to each other and are essential for force generation, motility, and mechanosensing in animal cells. For nonmuscle cells, evolution has resulted in three different isoforms, which have different properties concerning the motor cycle and also occur in different abundances in the cells, but their respective biological and physical roles are not fully understood. Here we use active gel theory to demonstrate the complementary roles of isoforms A and B for cell migration. We first show that our model can be derived both from coarse-graining kinetic equations and from nonequilibrium thermodynamics as the macroscopic limit of a two-component Tonks gas. We then parametrize the model and show that motile solutions exist, in which the more abundant and more dynamic isoform A is localized to the front and the stronger isoform B to the rear, in agreement with experiments. Exploring parameter space beyond the isoform parameters typical for animal cells, we also find cell oscillations in length and velocity, which might be realized for genetically engineered systems. We also describe an analytical solution for the stiff limit, which then is used to calculate a state diagram, and the effect of actin polymerization at the boundaries that leads to an imperfect pitchfork bifurcation. Our findings highlight the importance of including isoform-specific molecular details to describe whole cell behavior.