Actin filaments are polymers that interact with myosin motor proteins and play important roles in cell motility, shape, and development. Depending on its function, this dynamic network of interacting proteins reshapes and organizes in a variety of structures, including bundles, clusters, and contractile rings. Motivated by observations from the reproductive system of the roundworm C. elegans, we use an agent-based modeling framework to simulate interactions between actin filaments and myosin motor proteins inside cells. We also develop techniques based on topological data analysis to understand time-series data extracted from these filament network interactions. These measures allow us to compare the filament organization resulting from myosin motors with different properties. Recently, we have also studied how different models of myosin regulation predict actin network organization during the cell cycle. This work also raises questions about how to assess the significance of features in common topological summaries.