Browsing by Subject "Chemotaxis"

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.

Budding yeast decode pheromone gradients to locate mating partners, providing a model of chemotropism in fungi. How yeast polarize toward a single partner in crowded environments is unclear. Initially, cells often polarize in unproductive directions, but then they relocate the polarity site until two partners’ polarity sites align, whereupon the cells “commit” to each other by stabilizing polarity to promote fusion. Using live-cell fluorescence microscopy, computational modeling, and quantitative autocorrelation analyses, I address the role of the early mobile polarity sites, finding that commitment by either partner failed if just one partner was defective in generating, orienting, or stabilizing its mobile polarity sites. Mobile polarity sites were enriched for pheromone receptors and G proteins, suggesting that such sites engage in an exploratory search of the local pheromone landscape, stabilizing only when they detect elevated pheromone levels. Mobile polarity sites were also enriched for pheromone secretion factors, and simulations suggest that only focal secretion at polarity sites would produce high pheromone concentrations at the partner’s polarity site, triggering commitment.

Many cells are remarkably proficient at tracking even shallow chemical gradients, despite tiny differences in receptor occupancy across the cell. Stochastic receptor-ligand interactions introduce considerable noise in instantaneous receptor occupancy, so it is thought that spatial information must be integrated over time to allow noise filtering. The mechanism of temporal integration is unknown. We used the mating response of the budding yeast, Saccharomyces cerevisiae, as a model to study eukaryotic gradient tracking.

During mating, yeast cells polarize and grow up a gradient of pheromone to find and fuse with opposite-sex partners. Exposure to pheromone causes polarity regulators to cluster into a tight "patch" at the cortex, directing growth toward that site. Timelapse microscopy of fluorescently-labeled polarity proteins revealed that the patch wandered around the cortex during gradient tracking. Mathematical modeling and genetic analysis suggested that fusion of vesicles near the polarization site could perturb the polarity patch and promote wandering. Wandering is decreased due to global effects from pheromone signaling as well as interactions between receptor-activated Gβ and the exchange factor for the polarity regulator Cdc42. We found that artificially stabilizing patch wandering impaired accurate gradient tracking.

We suggest that ongoing polarized vesicle traffic causes patch wandering, which is locally reduced by pheromone-bound receptors. Thus, over time, spatial information from the pheromone gradient biases the random wandering of the polarity patch so that growth occurs predominantly up-gradient. Such temporal integration may enable sorting the low signal from stochastic noise when tracking shallow gradients.

This dissertation focuses on applications of partial differential equations with an emphasis on chemotaxis. Chemotaxis is a response of motile cells or organisms in which the direction of movement is affected by the gradient of a diffusible substance. In multicellular organisms, chemotaxis is critical to development as well as normal function. We also include a specific application that utilizes differential equations and stochastic simulation to model placental transmission of Cytomegalovirus (CMV) with experimental data.Our methods include regularity estimates, maximal and comparison principles, probabilistic techniques, and stochastic processes. This work resulted in several conclusions: We prove quantitatively chemotaxis enhances reaction in 1D setting: the upper bound for reaction time with chemotaxis is smaller than the lower bound for reaction time without chemotaxis.

We have also analyzed a random searcher in shear flow and chemotaxis; on the rigorous level, we are able to establish that the very large shear rates are a dimension reduction mechanism: the expected search time converges to the one of the corresponding one-dimensional problem. Numerically, we see fast decrease of the expected hitting time for shear and chemotactic coupling; we discover there is an optimal shear rate range where the searching time is minimal.

We also explore a model aiming to describe the origin of chemotactic ability of cells, in particular proving global regularity.

We present an end-to-end model of placental CMV transmission that allow us to study different type of infections, the timing of inoculation, the effect of immune suppression on the risk of placental transmission, and the effect of treatment.