Insights from Graph Theory on the Morphologies of Actomyosin Networks with Multilinkers

We investigated the role of multivalent actin-binding proteins (ABPs) in reorganizing actin filaments into higher order complex networks via a computer model of semiflexible filaments. We characterize the importance of local connectivity among actin filaments as well as the global features of actomyosin networks by first mapping the networks into graph representations, then implementing network-theory order parameters that provide principles for combining multiple local models into a joint global model accounting for heterogeneous observations. We find that ABPs with a valency greater than two promote filament bundles and large filament clusters to a much greater extent than bivalent multilinkers. We also show that active myosin-like motor proteins promote the formation of dendritic branches from a stalk of actin bundles. Our work motivates future studies to embrace network theory as a tool to characterize complex morphologies of actomyosins detected by experiments, leading to a quantitative understanding of the role of ABPs in manipulating the self-assembly of actin filaments into unique architectures that underlie the structural scaffold of a cell relating to its mobility and shape.