Traction forces control cell-edge dynamics and mediate distance-sensitivity during cell polarization

SUMMARYTraction forces are generated by cellular actin-myosin system and transmitted to the environment through adhesions. They are believed to drive cell motion, shape changes, and extracellular matrix remodeling [1–3]. However, most of the traction force analysis has been performed on stationary cells, investigating forces at the level of individual focal adhesions or linking them to static cell parameters such as area and edge curvature [4–10]. It is not well understood how traction forces are related to shape changes and motion, e.g. forces were reported to either increase or drop prior to cell retraction [11–15]. Here, we analyze the dynamics of traction forces during the protrusion-retraction cycle of polarizing fish epidermal keratocytes and find that forces fluctuate in concert with the cycle, increasing during the protrusion phase and reaching maximum at the beginning of retraction. We relate force dynamics to the recently discovered phenomenological rule [16] that governs cell edge behavior during keratocyte polarization: both traction forces and the probability of switch from protrusion to retraction increase with the distance from the cell center. Diminishing traction forces with cell contractility inhibitor leads to decreased edge fluctuations and abnormal polarization, while externally applied force can induce protrusion-retraction switch. These results suggest that forces mediate distance-sensitivity of the edge dynamics and ultimately organize cell-edge behavior leading to spontaneous polarization. Actin flow rate did not exhibit the same distance-dependence as traction stress, arguing against its role in organizing edge dynamics. Finally, using a simple model of actin-myosin network, we show that force-distance relationship may be an emergent feature of such networks.

Dynamics of gene regulatory networks with stochastic propensities

Gene regulatory networks (GRNs) control the production of proteins in cells. It is well-known that this process is not deterministic. Numerous studies employed a non-deterministic transition structure to model these networks. However, it is not realistic to expect state-to-state transition probabilities to remain constant throughout an organism’s lifetime. In this work, we focus on modeling GRN state transition (edge) variability using an ever-changing set of propensities. We suspect that the source of this variation is due to internal noise at the molecular level and can be modeled by introducing additional stochasticity into GRN models. We employ a beta distribution, whose parameters are estimated to capture the pattern inherent in edge behavior with minimum error. Additionally, we develop a method for obtaining propensities from a pre-determined network.