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Quantifying the influence of microscopic details on the dynamics ofdevelopment of the overall structure of a filamentous network is important in anumber of biologically relevant contexts, but it is not obvious what orderparameters can be used to adequately describe this complex process. In thispaper, we investigated the role of multivalent actin-binding proteins (ABPs) inreorganizing actin filaments into higher-order complex networks via a computermodel of semiflexible filaments. We characterize the importance of localconnectivity among actin filaments as well as the global features of actomyosinnetworks. We first map the networks into local graph representations and then,using principles from network-theory order parameters, combine properties fromthese representations to gain insight on the heterogeneous morphologies ofactomyosin networks at a global level. We find that ABPs with a valency greaterthan two promote filament bundles and large filament clusters to a much greaterextent than bivalent multilinkers. We also show that active myosin-like motorproteins promote the formation of dendritic branches from a stalk of actinbundles. Our work motivates future studies to embrace network theory as a toolto characterize complex morphologies of actomyosin detected by experiments,leading to a quantitative understanding of the role of ABPs in manipulating theself-assembly of actin filaments into unique architectures that underlie thestructural scaffold of a cell relating to its mobility and shape.

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