Scale bar is 50?m. Click here to view.(3.7M, mp4) Supplementary video 2: Transmitted light microscopy video of the migration of UC-1728 CHO-K1 cells expressing paxillin-EGFP after treatment with 10?M Y-27632. highlights of this study: ? Cellular polarity (and hence directionality) did not form spontaneously when simulating a stochastic spatiotemporal model of Rac, Rho and paxillin in a 2D domain name representing a randomly moving CHO-K1 cell. This result of the simulation was verified experimentally by inhibiting ROCK in these cells, which was previously shown to increase directionality in fibroblasts . Although polarity was not formed, hysteresis was still preserved by the model.? Imposing activation gradients around the 2D domain name of the model produced polarity in a manner similar to that observed experimentally.? Experimentally inhibiting ROCK led to phenotypes similar to those seen following Rac hyperactivation, including increases in ANGPT2 cell motility speeds and a reduction in adhesion size.? Cells treated with Y-27632 also had decreased localization of paxillin at adhesions but increased association between PIX and paxillin, as predicted by the model. 2.?Methods 2.1. Mathematical model and simulations 2.1.1. Model formalism We adopted the same spatiotemporal model presented in  (see Fig. 1), which was originally developed from the experimental findings of . This molecularly explicit model consists of six equations governing the dynamics of the following key proteins: inactive Rho or RhoGDP, active Rho or RhoGTP, inactive Rac or RacGDP, active Rac or RacGTP, unphosphorylated paxillin and paxillin phosphorylated at serine residue 273 (S273). Other proteins involved in the dynamics of this system include p21-Activated Kinase 1 (PAK), G protein-coupled receptor kinase InteracTor 1 (GIT) and beta-PAK-Interacting eXchange factor (PIX). The main assumptions of this model are (see Fig. 1): 1. Active PAK mediates the phosphorylation of paxillin at S273, allowing the protein complex GIT-PIX-PAK to subsequently bind to it . 2. Rac and Rho activation and inactivation are mediated by GTPase-specific Guanine Exchange Factors (GEFs) and GTPase-specific GTPase-Activating Proteins (GAPs), respectively , . 3. Rac and Rho mutually inhibit each other through the inhibition of each other’s Rho- and Rac-GEFs, respectively , , , . 4. Active Rac (RacGTP) activates PAK by forming the intermediate PAK-RacGTP, while PIX and its intermediates can act as Rac-GEFs , , . For the remaining set of model assumptions, see . Rescaling the concentrations of the key proteins Rho, Rac and paxillin (Pax) by their total corresponding concentrations within the cell, we obtain is the ratio of total active PAK (PAK-RacGTP and all complexes made up of it)-to-total PAK concentrations, given by and represent the feedback loops involving PAK, RacGTP and Paxp (along with their complexes) and result from the quasi-steady state assumptions imposed on various intermediates as well as other proteins, including GIT, PIX and PAK. Specifically, represents the role of active PAK complexes (assumed at steady state) in driving Rac activation, Rho inactivation and paxillin phosphorylation , while (which is a function of by matrix. The total copy number of protein molecules in the cell for both Rho and Rac was estimated to be 2,250,000, whereas the initial copy number of paxillin molecules was estimated to be 690,000. These values were obtained from model parameters presented UC-1728 in . Here, we have reduced these copy numbers by a factor of 10 UC-1728 to decrease computation time. In order to verify the validity of this approach, a simulation was done with the estimated copy number of molecules and no qualitative differences were observed (results not shown). The stochastic simulations were performed step-by-step, based on the following set of conditions/decisions: 1. The six species of proteins could undergo 34 different possible reactions, which included: I. Rac inactivation (RacGTP to RacGDP).II. Rac activation (RacGDP to RacGTP).III. Rac complexing (formation\de-formation of [PAK-RacGTP], [PIX-PAK-RacGTP], [Paxp-GIT-PIX-PAK-RacGTP]).IV. Rho inactivation (RhoGTP to RhoGDP).V. Rho activation (RhoGDP to RhoGTP).VI. Paxillin S273 dephosphorylation (Paxp to Pax).VII. Paxillin S273 phosphorylation (Pax to Paxp).VIII. Paxillin complexing (formation\de-formation of [Paxp-GIT-PIX-PAK], [Paxp-GIT-PIX-PAK-RacGTP]).IX. Four directional movements within the 2D domain name for each of the six-protein species (24 possible reactions). 2. Reaction propensities were calculated for each of the eight reactions in I-VIII based on Eqs. (8), UC-1728 (9),.