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An Information-Theoretic Characterization of the Optimal Gradient Sensing Response of Cells

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  • Burton W Andrews
  • Pablo A Iglesias

Abstract

Many cellular systems rely on the ability to interpret spatial heterogeneities in chemoattractant concentration to direct cell migration. The accuracy of this process is limited by stochastic fluctuations in the concentration of the external signal and in the internal signaling components. Here we use information theory to determine the optimal scheme to detect the location of an external chemoattractant source in the presence of noise. We compute the minimum amount of mutual information needed between the chemoattractant gradient and the internal signal to achieve a prespecified chemotactic accuracy. We show that more accurate chemotaxis requires greater mutual information. We also demonstrate that a priori information can improve chemotaxis efficiency. We compare the optimal signaling schemes with existing experimental measurements and models of eukaryotic gradient sensing. Remarkably, there is good quantitative agreement between the optimal response when no a priori assumption is made about the location of the existing source, and the observed experimental response of unpolarized Dictyostelium discoideum cells. In contrast, the measured response of polarized D. discoideum cells matches closely the optimal scheme, assuming prior knowledge of the external gradient—for example, through prolonged chemotaxis in a given direction. Our results demonstrate that different observed classes of responses in cells (polarized and unpolarized) are optimal under varying information assumptions.: For many cell types, the direction of migration is determined in response to spatial differences in the concentration of chemoattractant, a process known as chemotaxis. Precise chemotaxis—that is, motility with low directional distortion—requires that cells make accurate decisions based on the stochastic fluctuations inherent in cell-surface receptor occupancy. Here, we use rate distortion theory, a branch of information theory, to determine chemotaxis strategies for cells based on this imperfect information about their environment. In engineering, rate distortion theory provides the information processing capabilities required to achieve a desired accuracy. We demonstrate that more accurate chemotaxis requires greater information. We also show that a priori information can improve chemotaxis efficiency. We compare the optimal signaling schemes to existing experimental measurements and models of eukaryotic gradient sensing and demonstrate that different observed types of cellular responses (polarized and unpolarized) are optimal under varying information assumptions. Our results also highlight the constraints that noise places on the performance of cellular systems.

Suggested Citation

  • Burton W Andrews & Pablo A Iglesias, 2007. "An Information-Theoretic Characterization of the Optimal Gradient Sensing Response of Cells," PLOS Computational Biology, Public Library of Science, vol. 3(8), pages 1-9, August.
  • Handle: RePEc:plo:pcbi00:0030153
    DOI: 10.1371/journal.pcbi.0030153
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    References listed on IDEAS

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    1. William J. Blake & Mads KÆrn & Charles R. Cantor & J. J. Collins, 2003. "Noise in eukaryotic gene expression," Nature, Nature, vol. 422(6932), pages 633-637, April.
    2. Markus Kollmann & Linda Løvdok & Kilian Bartholomé & Jens Timmer & Victor Sourjik, 2005. "Design principles of a bacterial signalling network," Nature, Nature, vol. 438(7067), pages 504-507, November.
    3. Christopher V. Rao & Denise M. Wolf & Adam P. Arkin, 2002. "Control, exploitation and tolerance of intracellular noise," Nature, Nature, vol. 420(6912), pages 231-237, November.
    4. Alejandro Colman-Lerner & Andrew Gordon & Eduard Serra & Tina Chin & Orna Resnekov & Drew Endy & C. Gustavo Pesce & Roger Brent, 2005. "Regulated cell-to-cell variation in a cell-fate decision system," Nature, Nature, vol. 437(7059), pages 699-706, September.
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    1. Can Guven & Erin Rericha & Edward Ott & Wolfgang Losert, 2013. "Modeling and Measuring Signal Relay in Noisy Directed Migration of Cell Groups," PLOS Computational Biology, Public Library of Science, vol. 9(5), pages 1-13, May.
    2. Chopra, Abha & Nanjundiah, Vidyanand, 2013. "The precision with which single cells of Dictyostelium discoideum can locate a source of cyclic AMP," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 3-12.

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