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We study the non-linear stability of a coupled system of two non-linear transport-diffusion equations set in two opposite half-lines. This system describes some aspects of yeast pairwise cellular communication, through the concentration of some protein in the cell bulk and at the cell boundary. We show that it is of bistable type, provided that the intensity of active molecular transport is large enough. We prove the non-linear stability of the most concentrated steady state, for large initial data, by entropy and comparison techniques. For small initial data we prove the self-similar decay of the molecular concentration towards zero. Informally speaking, the rise of a dialog between yeast cells requires enough active molecular transport in this model. Besides, if the cells do not invest enough in the communication with their partner, they do not respond to each other; but a sufficient initial input from each cell in the dialog leads to the establishment of a stable activated state in both cells. [ABSTRACT FROM AUTHOR]

Budding yeast cells exist in two mating types, a and α, which use peptide pheromones to communicate with each other during mating. Mating depends on the ability of cells to polarize up pheromone gradients, but cells also respond to spatially uniform fields of pheromone by polarizing along a single axis. We used quantitative measurements of the response of a cells to α-factor to produce a predictive model of yeast polarization towards a pheromone gradient. We found that cells make a sharp transition between budding cycles and mating induced polarization and that they detect pheromone gradients accurately only over a narrow range of pheromone concentrations corresponding to this transition. We fit all the parameters of the mathematical model by using quantitative data on spontaneous polarization in uniform pheromone concentration. Once these parameters have been computed, and without any further fit, our model quantitatively predicts the yeast cell response to pheromone gradient providing an important step toward understanding how cells communicate with each other. [ABSTRACT FROM AUTHOR]