  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.
