Figure 7. Mathematical model of... | Rockefeller University Press

Figure 7.

$Figure 7. Mathematical model of Rdi1-dependent symmetry breaking and parameter validation. (A) Schematic of analytical model for Rdi1-dependent polarization. Distribution of Cdc42 across the cortex is given by u(x,t) (blue curve), of which a constant fraction a1 is activated. Cdc42 extraction is proportional to free Rdi1, Rf (purple crescents), and u(x,t) by a constant β. Targeting of Cdc42 to the cortex is assumed to be proportional to the squared distribution of active Cdc42GTP, (a1u)2, the profile of which is represented by the filled orange curve. Cytosolic diffusion Dv and cortical diffusion Du are shown in black. (B) Simulation of cell polarization via the Rdi1-dependent mechanism. Initial distribution of cortical Cdc42 at the time of perturbation is shown in red, with steady-state shown in black and intermediate time points given in blue. The parameter values used in the simulation shown are C = 1, γ = 0.4, β = 0.2, Dv = 0.1, Du = 0.01, ub = 0.05, L = 3, A = 1.75, and R = 0.6. (C) Simulated data for Rdi1-dependent polarization, showing dependence of polarization strength umax on R, and Rdi1 concentration relative to Cdc42. Gray dashed lines indicate cortical Cdc42 concentration in unpolarized states, whereas the red curve indicates mean umax over 25 simulations for parameter values in which polarization is allowed. The parameter values are as in B, with changing value of R. (D) Experimental assessment of the impact of Rdi1 expression level on polarization without actin. Expression of Rdi1 was induced under the GAL1 promoter for the indicated amounts of time (x axis) concurrent with a 1-h G1 pheromone arrest followed by a 0.5-h pheromone arrest in glucose media before release into LatA-containing media (see diagram in Fig. S3). The percentages of polarized cells were counted at 50 min after release. P = 0.06, comparing polarization in wild type with that of 60-min galactose (Gal) induction. The plots show means from three experiments, and error bars correspond to SEMs (blue shading indicates error bars for controls). More than 80 cells were counted per time point per experiment. (E) Simulated data for Rdi1-dependent polarization, showing dependence of polarization strength umax on A. Gray dashed lines indicate cortical Cdc42 concentration in unpolarized states, whereas the red curve indicates mean umax over 25 simulations for parameter values in which polarization is allowed. The parameter values are as in B, with R = 0.6 and changing value of A.$

Mathematical model of Rdi1-dependent symmetry breaking and parameter validation. (A) Schematic of analytical model for Rdi1-dependent polarization. Distribution of Cdc42 across the cortex is given by u(x,t) (blue curve), of which a constant fraction a₁ is activated. Cdc42 extraction is proportional to free Rdi1, R_f (purple crescents), and u(x,t) by a constant β. Targeting of Cdc42 to the cortex is assumed to be proportional to the squared distribution of active Cdc42^GTP, (a₁u)², the profile of which is represented by the filled orange curve. Cytosolic diffusion D_v and cortical diffusion D_u are shown in black. (B) Simulation of cell polarization via the Rdi1-dependent mechanism. Initial distribution of cortical Cdc42 at the time of perturbation is shown in red, with steady-state shown in black and intermediate time points given in blue. The parameter values used in the simulation shown are C = 1, γ = 0.4, β = 0.2, D_v = 0.1, D_u = 0.01, u_b = 0.05, L = 3, A = 1.75, and R = 0.6. (C) Simulated data for Rdi1-dependent polarization, showing dependence of polarization strength u_max on R, and Rdi1 concentration relative to Cdc42. Gray dashed lines indicate cortical Cdc42 concentration in unpolarized states, whereas the red curve indicates mean u_max over 25 simulations for parameter values in which polarization is allowed. The parameter values are as in B, with changing value of R. (D) Experimental assessment of the impact of Rdi1 expression level on polarization without actin. Expression of Rdi1 was induced under the GAL1 promoter for the indicated amounts of time (x axis) concurrent with a 1-h G1 pheromone arrest followed by a 0.5-h pheromone arrest in glucose media before release into LatA-containing media (see diagram in Fig. S3). The percentages of polarized cells were counted at 50 min after release. P = 0.06, comparing polarization in wild type with that of 60-min galactose (Gal) induction. The plots show means from three experiments, and error bars correspond to SEMs (blue shading indicates error bars for controls). More than 80 cells were counted per time point per experiment. (E) Simulated data for Rdi1-dependent polarization, showing dependence of polarization strength u_max on A. Gray dashed lines indicate cortical Cdc42 concentration in unpolarized states, whereas the red curve indicates mean u_max over 25 simulations for parameter values in which polarization is allowed. The parameter values are as in B, with R = 0.6 and changing value of A.