Forecasting Avalanches in Branched Actomyosin Networks with Network Science and Machine Learning

Abstract

We explored the dynamical and structural effects of actin-related proteins 2/3 (Arp2/3) on actomyosin networks using mechanochemical simulations of active matter networks. At a nanoscale, the Arp2/3 complex alters the topology of actomyosin by nucleating a daughter filament at an angle to a mother filament. At a subcellular scale, they orchestrate the formation of branched actomyosin network. Using a coarse-grained approach, we sought to understand how an actomyosin network temporally and spatially reorganizes itself by varying the concentration of the Arp2/3 complexes. Driven by the motor dynamics, the network stalls at a high concentration of Arp2/3 and contracts at a low Arp2/3 concentration. At an intermediate Arp2/3 concentration, however, the actomyosin network is formed by loosely connected clusters that may collapse suddenly when driven by motors. This physical phenomenon is called an "avalanche" largely due to the marginal instability inherent from the morphology of a branched actomyosin network when the Arp2/3 complex is present. While embracing the data science approaches, we unveiled the higher-order patterns in the branched actomyosin networks and discovered a sudden change in the "social" network topology of the actomyosin. This is a new type of avalanches in addition to the two types of avalanches associated with a sudden change in the size or the shape of the whole actomyosin network as shown in the previous investigation. Our new finding promotes the importance of using network theory and machine learning models to forecast avalanches in actomyosin networks. The mechanisms of the Arp2/3 complexes in shaping the architecture of branched actomyosin networks obtained in this paper will help us better understand the emergent reorganization of the topology in dense actomyosin networks that are difficult to detect in experiments.

Graph identification of proteins in tomograms (GRIP‐Tomo)

“…Graph‐based representations of structurally complex biomolecules extend the learning of chemical and molecular data by transforming the connectivity and morphology of physical structures into graphical maps for advancing discoveries in protein‐ligand binding (Knutson et al, 2022 ), protein structure–function prediction (Gligorijević et al, 2021 ), and actomyosin networks (Eliaz et al, 2020 ; Li et al, 2021 ). In these studies, the connectivity is inspired by the determination of chemically bonded and non‐bonded contacts, allowing the transformation of 3D structures into 2D contact maps.…”

“…Among the limited example of misidentified protein structures, we note that hierarchical helical structures (e.g., four helix bundle, calmodulin) prove to be challenging to correctly classify. This can likely be remedied with more hyperparameter tuning as well as a greater emphasis on global or higher order hierarchical structure such as the number of communities and assortativity (Li et al, 2021 ). Also, while the network order parameters are in theory rotationally invariant, we found some variation in the similarity scores with the proteins randomly rotated in the 3D volumes (Figure 4 ).…”

“…The network theory order parameters are sorted into three vantage points: (a) the topology of a node, which is illustrated in Figure S5 ; (b) the centrality of a node, which quantifies the connectivity or reveal the “importance” of the node in a local network; and (c) the detection of a distinctive community in a global network. In our prior work, we have introduced several network‐theory order parameters in great details as they collectively describe the hierarchical features of a network rich with biological information (Eliaz et al, 2020 ; Li et al, 2021 ). Here, we have used a set of 12 network theory order parameters, such as number of nodes, number of edges, density, diameter, average path length, average clustering, max closeness centrality, max eigenvector centrality, max betweenness centrality, degree assortativity, max clique number, and number of communities (using the Clauset‐Newman‐Moore method) (Clauset et al, 2004 ), to capture the topological and hierarchical features of protein complexes as structural networks in a mathematical graph.…”