Numeric reconstruction of 2D cellular actomyosin network from substrate displacement

Introduction: One of the fundamental structural elements of the cell is the cytoskeleton. Along with myosin, actin microfilaments are responsible for cellular contractions, and their organization may be related to pathological changes in myocardial tissue. Due to the complexity of factors involved, numerical modeling of the cytoskeleton has the potential to contribute to a better understanding of mechanical cues in cellular activities. In this work, a systematic method was developed for the reconstruction of an actomyosin topology based on the displacement exerted by the cell on a flexible substrate. It is an inverse problem which could be considered a phenomenological approach to traction force microscopy (TFM). Methods: An actomyosin distribution was found with a topology optimization method (TOM), varying the material density and angle of contraction of each element of the actomyosin domain. The routine was implemented with a linear material model for the bidimensional actomyosin elements and tridimensional substrate. The topology generated minimizes the nodal displacement squared differences between the generated topology and experimental displacement fields obtained by TFM. The structure resulting from TOM was compared to the actin structures observed experimentally with a GFP-attached actin marker. Results: The optimized topology reproduced the main features of the experimental actin and its squared displacement differences were 11.24 μm2, 27.5% of the sum of experimental squared nodal displacements (40.87 μm2). Conclusion: This approach extends the literature with a model for the actomyosin structure capable of distributing anisotropic material freely, allowing heterogeneous contraction over the cell extension.