Fig. 2.

The proposed molecular mechanism and associated mathematical model can quantitatively account the observed dynamic polarity patterns. (A) Mechanism schematic (Top) and classification of cell behavior (Bottom). RhoA–ROCK signaling and Rac1–PI3K signaling are mutually inhibitory in coupled signaling networks activated at the front or rear of a cell. Signals from the ECM activate RhoA (and possibly Rac1–PI3K; see text). Rac1–PI3K-induced cell spreading increases contact with (and signaling from) ECM. RhoA–ROCK-induced cell contraction decreases the contact with (and signaling from) ECM. The model accounts for the three main classes of behaviors: random (no Rac1–PI3K-dominated hot spots established), oscillatory (cycling between hot spots in the front and rear), and persistent (polarization of hot spot to one lamellipodium). (B) The mathematical model emerging from the mechanism described in A leads to the bifurcation diagram specifying parameter domains leading to each of three different polarity patterns (the bifurcation parameters are the intrinsic activation rates of GTPases, RhoA, and Rac1; see the model description in SI Appendix). Outboxes at the Top show the dynamics of a lammelipodium–ECM contact at the front (Cell–ECM contact_front) and at back (Cell–ECM contact_back) lamellipodia of a model cell for random, oscillatory, and persistent polarity patterns. Deterministic and stochastic simulations are shown to illustrate the effect of noise, particularly on the random polarity dynamics. The details of models are in SI Appendix. (C) Cell populations cultured in different nanopost density zones are mapped onto the bifurcation diagrams as described in the text. Intensity of gray shading corresponds to three zones of distinct density of posts in nanofabricated substrata (lightest gray represents densest post region). The mappings are inferred based on experimentally determined fractions of cells with different polarity patterns, as explained in detail in SI Appendix. Variation of ECM (FN) density is predicted to shift the oscillatory/persistent bifurcation boundary, thus changing fractions of cells adopting these patterns in a population. (D) Comparison of modeling predictions (in silico) and experimental results (in vitro) for the dependence of fractions of different cell polarity patterns on surfaces with varying post and FN densities. Dashed lines indicate the fraction of cells having polarized focal adhesion (FA) localization (see details in SI Appendix, Fig. S2, and Materials and Methods). (E) Variation of migration persistence metric, D_y/T_y, that correlates with the polarity patterns (D_y is the distance traveled by the cell along the y direction, and T_y is the total distance traveled by the cell along the y direction) over 3 h for different post and FN densities. *Statistical significance of D_y/T_y among each group, *P < 0.05 and all paired Student’s t test.