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

Abstract

Quantifying the influence of microscopic details on the dynamics of development of the overall structure of a filamentous network is important in a number of biologically relevant contexts, but it is not obvious what order parameters can be used to adequately describe this complex process. In this paper, 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. We first map the networks into local graph representations and then, using principles from network-theory order parameters, combine properties from these representations to gain insight on the heterogeneous morphologies of actomyosin networks at a global level. 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 actomyosin 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.

arXiv comment10 figures

References in corpus (23)

• Statistical mechanics of complex networks
• Community detection in graphs
• Finding community structure in very large networks
• A nonequilibrium equality for free energy differences
• Assortative mixing in networks
• The spread of epidemic disease on networks
• Identification of influential spreaders in complex networks
• Mixing patterns in networks
• Community detection in networks: A user guide
• Nonlinear Elasticity in Biological Gels
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Community detection in complex networks using Extremal Optimization
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Graph Neural Networks: A Review of Methods and Applications
• Elasticity of Semiflexible Biopolymer Networks
• Generalizations of the clustering coefficient to weighted complex networks
• Centrality Measures in Spatial Networks of Urban Streets
• Stochastic thermodynamics: Principles and perspectives
• Are randomly grown graphs really random?
• Collective Langevin Dynamics of Flexible Cytoskeletal Fibers
• Size, shape, and flexibility of RNA structures
• Scaling behavior in steady-state contractile actomyosin network flow
• Self-organization of stress patterns drives state transitions in actin cortices