Browsing by Subject "reaction-diffusion"

How do single cells—like neutrophils, amoebae, neurons, yeast, etc.—grow or move in a directed fashion in response to spatial chemical gradients? To address this question, we used the mating response in the budding yeast, Saccharomyces cerevisiae, as a biological model. To mate, pairs of yeast cells orient their cell fronts toward each other and fuse. Each cell relies on a pheromone gradient established by its partner to orient correctly. The ability for cells to resolve gradients is striking, because each cell is only ~5 μm wide and is thought to be operating in complex and noisy environments. Interestingly, mating pairs of cells often start out not facing each other. When this happens, the front of each cell—defined by a patch of cortical polarity proteins—undergoes a series of erratic and random movements along the cell cortex till it ‘finds’ the mating partner’s patch. We sought to understand how polarity patches in misaligned cells find each other. To this end, we first characterized patch movement in cells by the distribution of their step-lengths and turning angles and analyzed a bottom-up model of the polarity patch’s dynamics. The final version of our model combines 11 reaction-diffusion equations representing polarity protein dynamics with a stochastic module representing vesicle trafficking on a plane with periodic boundary conditions. We found that the model could not quantitatively reproduce step-length and turning angle distributions, which suggested that some mechanisms driving patch movement may not be present in the model. Incorpo-rating biologically inspired features into the model—such as focused vesicle delivery, sudden fluctuations in vesicle delivery rates, and the presence of polarity inhibitors on vesicles—allowed us to quantitatively match the in vivo polarity patch’s behavior. We then introduced a pathway, which connects pheromone sensing to polarity, to see how the model behaved when exposed to pheromone gradients. Concurrently, we analyzed the behavior of fluores-cently labeled polarity patches in mating pairs of cells. We discovered that the ~1 μm wide patch could (remarkably) sense and bias its movement up pheromone gradients, a result corroborated by our model. Further analysis of the model revealed that while the polarity patch tends to bias the location of a cluster of pheromone-sensing-receptors, the receptors can transform an external pheromone distribution into a peaked non-linear “polarity-activation” profile that “pulls” the patch. Stochastic perturbations cause the patch to “ping-pong” around the activation-profile. In a gradient of pheromone, this ping-ponging be-comes biased, leading to net patch movement up the gradient. We speculate that such a mechanism could be used by single cells with mobile fronts to track chemical gradients.