Testing the limits of gradient sensing

Abstract

The ability to detect a chemical gradient is fundamental to many cellular processes. In multicellular organisms gradient sensing plays an important role in many physiological processes such as wound healing and development. Unicellular organisms use gradient sensing to move (chemotaxis) or grow (chemotropism) towards a favorable environment. Some cells are capable of detecting extremely shallow gradients, even in the presence of significant molecular-level noise. For example, yeast have been reported to detect pheromone gradients as shallow as 0.1 nM/μm. Noise reduction mechanisms, such as time-averaging and the internalization of pheromone molecules, have been proposed to explain how yeast cells filter fluctuations and detect shallow gradients. Here, we use a Particle-Based Reaction-Diffusion model of ligand-receptor dynamics to test the effectiveness of these mechanisms and to determine the limits of gradient sensing. In particular, we develop novel simulation methods for establishing chemical gradients that not only allow us to study gradient sensing under steady-state conditions, but also take into account transient effects as the gradient forms. Based on reported measurements of reaction rates, our results indicate neither time-averaging nor receptor endocytosis significantly improves the cell’s accuracy in detecting gradients over time scales associated with the initiation of polarized growth. Additionally, our results demonstrate the physical barrier of the cell membrane sharpens chemical gradients across the cell. While our studies are motivated by the mating response of yeast, we believe our results and simulation methods will find applications in many different contexts.

Mating yeast cells use an intrinsic polarity site to assemble a pheromone-gradient tracking machine

“…It has been estimated that a 1% difference in receptor occupancy across the 5-µm diameter of a yeast cell is sufficient to elicit robust orientation (Segall, 1993). Moreover, computational modeling suggests that noise at the level of the receptor is greater than the spatial signal in physiological gradients (Lakhani and Elston, 2017). And yet, in mating mixtures, yeast cells invariably select a single partner, even when surrounded by competing suitors.…”

Particle-based simulations of polarity establishment reveal stochastic promotion of Turing pattern formation

“…The cytoplasmic reservoir was treated implicitly: we only tracked the number of molecules in the reservoir, instead of the dynamics of individual particles. To simulate stochastic exchange between the explicitly-modeled and implicitly-modeled regions of the cytoplasm, we took a similar approach as described in [ 44 ], using diffusional probability distributions to determine the number of molecules injected into ( n inj ) and ejected from ( n ejc ) the explicitly-modeled cytoplasm at each time step. Diffusional probability densities were integrated to obtain P inj and P ejc , which correspond to the probability that a single molecule at a depth z diffuses the distance required to enter ( z impl — z ) or exit ( z – z impl ) the explicit simulation region (see Appendix D in S1 Text for derivation).…”

“…Symmetry breaking in many contexts involves guiding cues not considered here, such as a pheromone gradients or bud scars in yeast [ 1 ]. However, these cues can be surprisingly weak: a computational study of yeast pheromone receptors in a pheromone gradient predicted differences in receptor occupancy as small as 45±50 molecules between the front (towards with the gradient) and the back [ 44 ]. Future work may focus on examining how weak cues may allow robust polarization along shallow gradients.…”

Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows

“…We compute here in the first part the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a an infinite domain. Computing the fluxes of Brownian particles moving inside a bounded domain to small absorbing windows located on a boundary falls into the narrow escape problems [19,13,15,16,7,21] and has also been studied numerically [20]. However, the mean passage time to a small hole becomes infinite in an unbounded domain due to long excursions to infinity of Brownian trajectories.…”