Gradient sensing by a bistable regulatory motif enhances signal amplification but decreases accuracy in individual cells.

Many vital eukaryotic cellular functions require the cell to respond to a directional gradient of a signaling molecule. The first two steps in any eukaryotic chemotactic/chemotropic pathway are gradient detection and cell polarization. Like many processes, such chemotactic and chemotropic decisions are made using a relatively small number of molecules and are thus susceptible to internal and external fluctuations during signal transduction. Large cell-to-cell variations in the magnitude and direction of a response are therefore possible and do, in fact, occur in natural systems. In this work we use three-dimensional probabilistic modeling of a simple gradient sensing pathway to study the capacity for individual cells to accurately determine the direction of a gradient, despite fluctuations. We include a stochastic external gradient in our simulations using a novel gradient boundary condition modeling a point emitter a short distance away. We compare and contrast three different variants of the pathway, one monostable and two bistable. The simulation data show that an architecture combining bistability with spatial positive feedback permits the cell to both accurately detect and internally amplify an external gradient. We observe strong polarization in all individual cells, but in a distribution of directions centered on the gradient. Polarization accuracy in our study was strongly dependent upon a spatial positive feedback term that allows the pathway to trade accuracy for polarization strength. Finally, we show that additional feedback links providing information about the gradient to multiple levels in the pathway can help the cell to refine initial inaccuracy in the polarization direction.