Figure 2. Areal strain-dependent PG elongation quantitatively predicts shape recovery dynamics.

a, MreB molecules are modeled as points that move circumferentially along the PG mesh with a spot velocity v and unbind as a Poisson process with rate 1/τ. The growth at an angle θ at a given time depends on the number of initiated glycan strands also at θ, which in turn depends on the strain profile of the cell in the past (see also the growth equation in Supplementary Note 2). b, A sensitivity analysis of the theoretically predicted straightening rate for several material properties, assuming a large MreB processivity of M τ = 6 radians. The elastic snapback and material parameters determine the value of the areal strain-coupling parameter α self-consistently, as discussed in Supplementary Note 2. The predicted straightening rate is consistent with the experimental data shown in Fig. 3c. c, Numerical solutions of the growth equation agree with the theoretical prediction for the straightening rate. Here the aspect ratio is defined as the product of arclength and curvature, L(t)C(t), which does not decay without areal strain-coupling in the limit of infinite processivity (dashed lines; see also Supplementary Video 11). The normalized time is defined with units of 1/λ = t_d/ ln(2). d, There is an intermediate value of the processivity, measured in units of time for a constant rate of PG subunit insertion, for which mechanical strain-sensing confers the largest effect on straightening. Empirical values of MreB processivity, intriguingly, lie close to the optimal value at which a cell straightens fastest.