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A Predictive Model for Yeast Cell Polarization in Pheromone Gradients
Fig 3
Model behavior and model parameters value selection.
A and B) Increasing the strength of pheromone stimulation (S) leads to increasing levels of spatial segregation and for a given S, depending on the spatial correlation length χ and the endocytosis rate koff the cell will polarize or not. Shown are kymographs from simulations (y axis, membrane position; x axis, time). Particle density is in absolute value. On the left we see an unpolarized cell and a polarized one on the right. C) Representation of mean time polarization isovalues for S = 1 nM as a function of the spatial correlation length χ and the endocytosis rate koff. If the numerical simulations did not lead to a polarized state before 10 hours, we considered the cell to be non-polarized. D) Representation of the cost function (labeled as fit quality) depending on χ and koff, allowing us to determine the optimal pair of values (χ, koff that fit the data (Fig 2C). E) For the optimal values of χopt = 2.5 × 105 μm2/s, 
s−1 and δopt = 0.2, we show the simulated timing of polarization for solutions to our model under varying pheromone concentration compared to the experimental data for polarization timing. The inset shows the standard deviation of the timing of polarization for solutions to our model under varying pheromone concentration compared to the experimental data for polarization timing. F) For the same optimal parameters 
, we represent the numerical fraction of cells which polarize under varying pheromone concentration. Before fitting the model parameters with the data, we defined the numerical criterion for polarization. Following [42], we considered that polarization occurred when more than 50% of the total membrane protein pool was located in a window of 10% of the membrane. Hence, a numerical simulation corresponded to a polarization state if there existed a time for which more than 50% of the total membrane Cdc42 was located in less than 10% of the perimeter of the cell boundary (S1 Text).
doi: https://doi.org/10.1371/journal.pcbi.1004795.g003