Fig 1.
Yeast mating: experiments and simulations.
(A) Time-lapse microscopy of mating yeast cells. Wild-type bar1Δ a-cells (left) and α-cells (right) were imaged over a two-hour period starting at t = 90m. The polarisome was labeled with Spa2-GFP (a, first row, cells outlined in green) and Spa2-mCherry (α, second row, cells outlined in red). The GFP and mCherry channels are merged (third row) with the three a-cells and four α-cells labeled. The DIC images are shown in the fourth row. The pairs a1-α1 and a3-α2 mated successfully. The presence of Bar1 over time will degrade the α-factor in a mating mix, and so to maximize the mating response we employed a bar1Δ strain. Scale bar = 5 μm. (B) Schematic diagram of yeast mating simulations. At the start, two cells are separated by 4 microns. The two mating pheromones (a-factor and α-factor) diffuse from their respective sources (a-cell and α-cell) which are sensed by the respective partners. The spatial dynamics of the biochemical reaction network are triggered resulting in the polarization of the membrane species. The boundary of the cell moves in response to the concentration of the polarized species resulting in the growth of a mating projection. Mating ends when the tips of the projections contact one another.
Fig 2.
Effect of external and internal noise on yeast mating simulations.
(A) Varying a-factor diffusion rates under no-noise simulation conditions. The diffusion constant for a-factor Da was set to 0.1, 1, 10, and 100 μm2/s; the diffusion constant for α-factor was Dα = 100 μm2/s. The cell centers were separated by 4 μm at the start. In all cases the cells were able to grow toward each other successfully. (B) External and internal noise disrupt mating. External (κ1) and internal (κ2) noises were added to the simulations using a range of values (0, 5, 10, 50 for κ1; 0, 3, 5 for κ2). 10 simulations were run for each combination, and an example simulation is shown for each specified pair of values (κ1, κ2). (C) Varying a-factor diffusion rates in the presence of noise. Simulations performed as in (A) except in the presence of noise (κ1 = 5, κ2 = 3). All simulations produced mating except Da = 0.1.
Fig 3.
Computer simulations of mating efficiency.
(A) Schematic of determining mating efficiency. In the simulation on the left, the tips marked by gray and black dots (polarisomes) of the two projections fall within a distance threshold (see Methods) so that the mating is considered successful. In the simulation on the right, the tips do not pass close enough to one another by the end of the simulation, and so the mating is deemed unsuccessful. (B) Faster and slower boundary velocities yielded similar mating trajectories. We ran simulations at two different boundary velocities (Vamp = 0.0001 and Vamp = 0.0002 μm/s). A plot of the distance between polarisomes of mating partners as a function of time is shown for a sample simulation. The plots are similar except the slower velocity took approximately twice as long to mate. (C) Direction plots for different boundary velocities and shorter cell-to-cell distance. In this plot each data circle represents one mating simulation. The average direction of each projection is plotted on the x-axis for the α-cell, and y-axis for the a-cell. The projections are toward one another when the data point lies along the diagonal line (i.e. top right and bottom left quadrants). We show the direction plots for the default simulation parameters (V = 0.0002 μm/s, left), slow boundary simulation (V = 0.0001 μm/s, middle), and close-cell positions (cell-to-cell distance = 2.5 μm instead of 4 μm, right). The mating efficiencies were similar for all three simulations. (D) Average mating time of successful matings under different simulation conditions same as in (C). Each bar represents the average time (± standard deviation) for successful mating. We performed 20 simulations for each condition, and the numbers of successful matings for default, slow and close parameters are 15, 17 and 16 respectively.
Fig 4.
Mating efficiency of isotropic versus polarized pheromone source.
(A) Schematic diagram of isotropic versus polarized (non-isotropic) pheromone source. Top row indicates in black shading the spatial distribution of the pheromone source function. The bottom row depicts the a-factor diffusion profile shown as a concentration contour plot for the isotropic source (left) and the polarized source (right). (B) Polarization plots of u2 showing mating cells at end of simulation. Four sample simulations each from the isotropic source group and from the polarized source group are shown. The normalized level of u2 is color coded on the surface of the cell according to the colormap on right. The polarisome is denoted by the black or gray dot at the projection tip. The polarized source produces higher mating efficiencies; the 1 or 0 indicates a successful or unsuccessful mating. The polarization plots, distance plots, and direction plots are color coded (blue, red, green, brown) for a particular simulation. (C) Distance plots for each of the four simulations. These plots show the distance between polarisomes of the mating partners as a function of time. With the isotropic source, the distances do not converge to 0 for some of the simulations. The green isotropic source simulation was terminated early because it did not meet the distance/direction threshold. (D) Direction plots for polarized source and isotropic source simulations. Each data point represents the averaged direction of the projection from each cell during mating. Axes are described in the legend to Fig 3C. Mating is more likely if the projections are in the same direction i.e. along the diagonal in the top right or bottom left quadrants. The average distance from the diagonal is 0.26 radians for the isotropic source compared to 0.12 for the polarized source matings. Colored filled circles correspond to simulations shown in (B) and (C). (E) Average mating time of successful matings with isotropic and polarized sources. Each bar represents the average time (± standard deviation) for successful matings. We performed 20 simulations for both conditions, and the numbers of successful matings for isotropic and polarized sources are 6 and 15 respectively.
Fig 5.
Reduced mating efficiency for supersensitive cells.
(A) Polarization plots of u2 showing four pairs of supersensitive mating cells at the end time point. The spatial distribution of u2 is represented according to the normalized color map on the right. The 0’s indicate that none of the matings were successful. Both cells had β2 = 2.5. (B) Distance plot showing trajectories from four sample supersensitive mating simulations. The distance between polarisomes was plotted as a function of time. The distances did not steadily decrease as was observed in the normal sensitivity simulations. The four plots are color-coded to match with the polarization plots. (C) Direction plot for supersensitive cell mating simulations. Many of the data points lie far off the diagonal indicating that the cells are not pointing toward each other; the average distance from the diagonal is 0.68 radians compared to 0.12 for the normal sensitivity matings.
Table 1.
Mating efficiency: Bar1+ versus bar1Δ simulations.
Fig 6.
(A) Bar1 helps a-cell distinguish closer α-cell. Two α-cells and one a-cell were positioned approximately at the vertices of a triangle with one of the two α-cells slightly closer to the a-cell than the other. We tested whether a Bar1+ or a bar1Δ a-cell could distinguish between the two α-cells in simulations performed in the absence of noise. The Bar1+ cell projected toward the closer α-cell, whereas the bar1Δ cell projected toward the middle between the two α-cells. (B) Mating competition simulations in which two a-cells compete for a single α-cell. In these three-cell simulations, one a-cell is Bar1+ and the other is bar1Δ. In 20/20 simulations, the Bar1+ cell mated with the α-cell, and two sample simulations are shown. At the top are snapshots with the projections in contact. In the middle are the α-factor profiles from the two simulations, which show how the high concentration of α-factor in the absence of Bar1 precludes gradient detection. At the bottom is the α-factor distribution along the cross-section between the α-cell and a-cell. In both cases, the steeper gradient is observed with the Bar1+ a-cell.
Fig 7.
Modeling mating discrimination.
(A) Three-cell mating discrimination simulations. One a-cell and two α-cells were arranged so that the a-cell was equidistant from the α-cells. One α-cell makes α-factor (α-factor producer, green) and the other α-cell does not (α-factor non-producer, blue). 20 simulations were run to determine the ratio at which the a-cell would mate with the α-factor producer versus the non-producer. Two sample simulations are presented. The left panel shows an a-cell with wild-type sensitivity, and the right panel shows a supersensitive a-cell. ME indicates mating efficiency; MD indicates mating discrimination. (B) Five-cell mating discrimination simulations. Four α-cells are arranged in a square with one bar1Δ a-cell in the center. One α-cell makes α-factor (α-factor producer, green) and the other three cells α-cell do not (α-factor non-producers, blue). 20 simulations were run to determine mating discrimination, and two sample simulations are presented. The left panel shows an a-cell with wild-type sensitivity, and the right panel shows a supersensitive a-cell. (C) Mating location plots for a-cells possessing normal sensitivity (WT, green) or supersensitivity (SS, red) in five-cell mating discrimination simulations. Each dot (correct MD) or cross (incorrect MD) symbol represents the polarisome location of the a-cell at the time of mating. The α-cell producing α-factor was in the top-right quadrant. The cells possessing normal sensitivity showed significantly better mating discrimination (MD) than the supersensitive cells (p < 0.0001, Fisher’s Exact Test).
Fig 8.
Role of Bar1 in mating discrimination with background α-factor.
(A) Five-cell mating discrimination simulations with background α-factor in the presence and absence of Bar1. Four α-cells are arranged in a square with one a-cell in the center. One α-cell makes α-factor (α-factor producer, top right corner) and the other three cells do not. Background α-factor source was set to C = 50. There are two sample simulations for bar1Δ a-cells (left), and two sample simulations for Bar1+ a-cells (right). ME is mating efficiency, and MD is mating discrimination. Bar1 was secreted in a polarized fashion. The second row shows the α-factor profiles for one sample (left) simulation from each group. The third row shows the α-factor profiles along the top-right to bottom-left diagonal for one example (yellow dotted line). There is an early (T = 50s) and late (T = 570s) time point for each simulation with α-factor concentration indicated by the shading (color bar). Pheromone profiles show a steeper gradient in Bar1+ a-cell simulations; troughs represent the cell body which excludes α-factor. (B) Mating location plots for Bar1+ a-cells (green) or bar1Δ (red) in five-cell mating discrimination simulations. Each circle (correct MD) or cross (incorrect MD) symbol represents the polarisome location of the a-cell at the time of mating. The α-cell producing α-factor was in the top-right quadrant. The Bar1+ cells showed significantly better mating discrimination (MD) than the bar1Δ cells (p < 0.05, Fisher’s Exact Test).
Fig 9.
Estimating the diffusion constant of a-factor.
(A) Projection lengths in bar1Δ versus Bar1+ a-cells. In the presence of Bar1, we only observed short-range matings in which both a-cells and α-cells possessed short projections. In the absence of Bar1 (bar1Δ matings), we observed longer projections made by the bar1Δ a-cells, whereas the α-cell projections remained short. The top two panels are fluorescent images of Spa2-GFP (a-cell) and Spa2-mCherry (α-cell) showing the adjacent/overlapping polarisomes indicating a successful mating. The bottom two panels are DIC images that depict the projection morphologies of the mating cells. Scale bars = 5 μm. (B) The relative projection lengths of α-cells versus a-cells in simulations compared to experiments. In the top bar graph, the α-cell projection length is presented as the fraction of the sum of the two projection lengths (n = 25 matings for Exp.); the average and standard deviation (error bars) are shown. The two-cell simulations with noise were performed as described in Fig 2 for varying α-factor diffusion values: Da = 0.1, 1, 10, and 100 μm2/s. The average and standard deviation of the normalized α-cell projection length from 10 simulations are shown. In the bottom bar graph, the corresponding unnormalized a-cell and α-cell projection lengths (mean ± SD in μm) are shown. The a-cells in both experiments and simulations are bar1Δ. (C) Concentration profiles of a-factor for different diffusion constants. The a-factor distribution is color-coded using gray scale at T = 830s in one example simulation for different diffusion rates. With a diffusion constant of 0.1 μm2/s, a-factor is highly localized to its source and does not reach the mating partner. With the diffusion constant of 100 μm2/s, a-factor spreads widely and is almost homogeneous distributed.