Disentangling signaling gradients generated by equivalent sources

Abstract

Yeast cells approach a mating partner by polarizing along a gradient of mating pheromones that are secreted by cells of the opposite mating type. The Bar1 protease is secreted by a-cells and, paradoxically, degrades the α-factor pheromones which are produced by cells of the opposite mating type and trigger mating in a-cells. This degradation may assist in the recovery from pheromone signaling but has also been shown to play a positive role in mating. Previous studies suggested that widely diffusing protease can bias the pheromone gradient towards the closest secreting cell. Here, we show that restricting the Bar1 protease to the secreting cell itself, preventing its wide diffusion, facilitates discrimination between equivalent mating partners. This may be mostly relevant during spore germination, where most mating events occur in nature.

Keywords: Gradient; Mating; Yeast.

Fig. 1

Mating in the presence of alternative mating partners. α-cell preparing for mating signals its position by secreting mating pheromone (α-factor). a-cells polarize their growth according to the resulting spatial gradient of α-factor. A problem may arise when the a-cell is surrounded by a number of α-factor secreting cells. In this case, the cell needs to polarize towards one particular partner, whereas the pheromone gradient is influenced by all other partners and may point towards some midpoint between the cells

Fig. 2

α-factor gradient in germinating spores. As explained in the text, the diffusion of α-factor in the medium can be mapped to the problem of defining an electric field. In this analogy, α-factor secreting cells can be viewed as positive charges, whereas cells that locally degrade α-factor can be viewed as negative changes. The α-factor flux is analogous to the electric field. a Electric field lines of a quadrupole: two positive charges and two negative charges. b Electric field lines due to two positive stationary charges of equal magnitude in a dipole arrangement. c Diffusive field lines for localized degradation model. The system is composed of two α-factor secreting cells and two a-cells which locally degrade a-factor. We assumed that local degradation on the a-cell is strong enough, that the cells can be viewed as perfect sinks with zero concentration on the boundary. D Diffusive field lines for simple diffusion model. The system is composed of two α-factor secreting cells and two responding a-cells. Since in this model a-cells do not degrade α-factor locally, they are assumed to be reflective with a normal flux of zero. Field lines are similar for the uniform degradation model, where degradation is assumed across the field. e The α-factor flux along the perimeter of an a-cell in the presence of localized degradation. Note the two peaks, corresponding to equivalent maxima pointing towards the two alternative partners. f The α-factor concentration in the absence of local degradation. Note that only a single peak is present, pointing midway between the two secreting cells

Fig. 3

Mating in the presence of alternative partners: a Germination-inspired topology with two a-cells and two α-factor secreting α-cells positioned in close proximity. Simulations are performed in three dimensions (see Section 4 for details). b Illustration of α-factor (concentration of flux) around the perimeter of the a-cell, as shown. For good recognition, the amount of occupied receptors should peak at two angles, corresponding to the direction of the two α-cells. “max” stands for the maximal receptor occupancy, “mid” is the receptor occupancy at the midline between the two expected maxima, and “min” is the minimum receptor occupancy. c Based on the definitions of “max,” “mid,” and “min,” we define three measures for the ability to locate mating partners, sensitivity, relative peak strength, and relative sensitivity, as shown. d Relative peak strength vs. diffusion coefficient for three models: uniform degradation, simple diffusion without degradation, and localized degradation on cell borders. Results are plotted for diffusion coefficient of 1 μm²/s (black) and 300 μm²/s (gray). e Relative peak strength vs. secretion rate for three models as in a. Results are plotted for secretion rate of 1 molecule/second (gray) and 10 molecule/second (black). f Relative sensitivity vs. diffusion coefficient for three models as in a. Results are plotted for diffusion coefficient of 1 μm²/s (black) and 300 μm²/s (gray). g Relative sensitivity vs. secretion rate for three models as in a. Results are plotted for secretion rate of 1 molecule/second (gray) and 10 molecule/second (black)