Bayesian Cell Force Estimation Introducing Cell Shape Prior

Abstract

Cell morphogenesis and migration are essential for various physiological and pathological processes. To elucidate their mechanisms, it is necessary to observe the mechanical force generated by the cells. Traction force microscopy (TFM) uses fluorescent nanobeads that are embedded in the surface layer of an elastic gel substrate. When cells cultured on the substrate generate traction force, the beads change their locations due to the force-induced deformation of the gel substrate. Various algorithms for estimating traction force from bead displacement have been proposed. Higher bead density is better for accurate force estimation. However, substrates containing high-density beads have several problems such as heterogeneous distribution of beads, fusions of condensed beads on the image, and influence on the effective Young's modulus of the substrate. Therefore, it is important to develop an algorithm to estimate accurate traction forces under the condition of a small number of beads. In this study, we proposed the traction force estimation algorithm introducing the force priors: force is more likely to occur near the edge of a cell and is directed from the edge to the center of the cell. Using synthetic condition with 3∼8 beads per one um2, we estimated traction force by employing Bayesian framework. We also estimated the minimum density of the beads against the cell size that guarantees the accuracy of force estimation. The proposed algorithm showed better performance than other regression-based methods such as Ridge regression or LASSO. Furthermore, we applied the algorithm to the traction force estimation of neuronal growth cone.