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Open Access Research article

Noise filtering tradeoffs in spatial gradient sensing and cell polarization response

Ching-Shan Chou1, Lee Bardwell3, Qing Nie2 and Tau-Mu Yi34*

  • * Corresponding author: Tau-Mu Yi

  • † Equal contributors

Author Affiliations

1 Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA

2 Center for Mathematical and Computational Biology Center for Complex Biological Systems Department of Mathematics University of California, Irvine Irvine, CA 92697, USA

3 Center for Complex Biological Systems Department of Developmental and Cell Biology University of California, Irvine Irvine, CA 92697, USA

4 Tau-Mu Yi Assistant Professor of Developmental and Cell Biology 2011 Biological Sciences III University of California, Irvine Irvine, CA 92697, USA

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BMC Systems Biology 2011, 5:196  doi:10.1186/1752-0509-5-196

Published: 13 December 2011



Cells sense chemical spatial gradients and respond by polarizing internal components. This process can be disrupted by gradient noise caused by fluctuations in chemical concentration.


We investigated how external gradient noise affects spatial sensing and response focusing on noise-filtering and the resultant tradeoffs. First, using a coarse-grained mathematical model of gradient-sensing and cell polarity, we characterized three negative consequences of noise: Inhibition of the extent of polarization, degradation of directional accuracy, and production of a noisy output polarization. Next, we explored filtering strategies and discovered that a combination of positive feedback, multiple signaling stages, and time-averaging produced good results. There was an important tradeoff, however, because filtering resulted in slower polarization. Simulations demonstrated that a two-stage filter-amplifier resulted in a balanced outcome. Then, we analyzed the effect of noise on a mechanistic model of yeast cell polarization in response to gradients of mating pheromone. This analysis showed that yeast cells likely also combine the above three filtering mechanisms into a filter-amplifier structure to achieve impressive spatial-noise tolerance, but with the consequence of a slow response time. Further investigation of the amplifier architecture revealed two positive feedback loops, a fast inner and a slow outer, both of which contributed to noise-tolerant polarization. This model also made specific predictions about how orientation performance depended upon the ratio between the gradient slope (signal) and the noise variance. To test these predictions, we performed microfluidics experiments measuring the ability of yeast cells to orient to shallow gradients of mating pheromone. The results of these experiments agreed well with the modeling predictions, demonstrating that yeast cells can sense gradients shallower than 0.1% μm-1, approximately a single receptor-ligand molecule difference between front and back, on par with motile eukaryotic cells.


Spatial noise impedes the extent, accuracy, and smoothness of cell polarization. A combined filtering strategy implemented by a filter-amplifier architecture with slow dynamics was effective. Modeling and experimental data suggest that yeast cells employ these elaborate mechanisms to filter gradient noise resulting in a slow but relatively accurate polarization response.

Noise/gradient-sensing/G-protein/cell; polarity/yeast mating