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

Andrews, Burton W.; Iglesias, Pablo A.

doi:10.1371/journal.pcbi.0030153

Cited by 89 publications

(87 citation statements)

References 39 publications

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“…To quantify the fluctuations originating from the external binding process we first computed the mutual information (22) between the external chemoattractant gradient direction θ s and the resulting spatial distributions of bound receptors Y. This mutual information is a measure of how much the uncertainty in Y is reduced by the knowledge of θ s .…”

Section: Resultsmentioning

confidence: 99%

External and internal constraints on eukaryotic chemotaxis

Fuller¹,

Chen²,

Adler³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

129

168

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Chemotaxis, the chemically guided movement of cells, plays an important role in several biological processes including cancer, wound healing, and embryogenesis. Chemotacting cells are able to sense shallow chemical gradients where the concentration of chemoattractant differs by only a few percent from one side of the cell to the other, over a wide range of local concentrations. Exactly what limits the chemotactic ability of these cells is presently unclear. Here we determine the chemotactic response of Dictyostelium cells to exponential gradients of varying steepness and local concentration of the chemoattractant cAMP. We find that the cells are sensitive to the steepness of the gradient as well as to the local concentration. Using information theory techniques, we derive a formula for the mutual information between the input gradient and the spatial distribution of bound receptors and also compute the mutual information between the input gradient and the motility direction in the experiments. A comparison between these quantities reveals that for shallow gradients, in which the concentration difference between the back and the front of a 10-μm-diameter cell is <5%, and for small local concentrations (<10 nM) the intracellular information loss is insignificant. Thus, external fluctuations due to the finite number of receptors dominate and limit the chemotactic response. For steeper gradients and higher local concentrations, the intracellular information processing is suboptimal and results in a smaller mutual information between the input gradient and the motility direction than would have been predicted from the ligand-receptor binding process.mutual information | noise limits | Dictyostelium | microfluidics C hemotaxis, the motion of cells guided by chemical gradients, plays an important role in a variety of biological processes, including wound healing, embryogenesis, and cancer metastasis. The chemical gradients required for efficient chemotaxis can be very shallow for eukaryotic cells. For example, the rapidly crawling neutrophils of the mammalian immune system and the social amoebae, Dictyostelium discoideum (1-8), are able to sense shallow chemical gradients where the concentration of chemoattractant differs by only a few percent from one side of the cell to the other, over a wide range of local concentrations (9-11).The chemotactic response of these cells can be considered as the outcome from two distinct steps: establishment of spatial differences in the distribution of receptors with bound chemoattractant on the cell's surface (12) and the response to these differences by the signal transduction pathways leading to directed motility (13). The first step is subject to the external fluctuations in chemoattractant binding to the surface receptor. This external noise can be precisely characterized, either through direct numerical simulations (14, 15) or through approximate analytical calculations (16-18). The second step involves a number of pathways that are subject to internal background noise generated ...

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Section: Resultsmentioning

confidence: 99%

External and internal constraints on eukaryotic chemotaxis

Fuller¹,

Chen²,

Adler³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

129

168

View full text Add to dashboard Cite

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“…A number of other studies have also recognized the importance of noise in directional sensing (20)(21)(22)(23)(24). Several of these attempt to estimate the SNR of the input signal, taken to be the difference between the number of bound receptors at the front and at the back of the cell (20,23).…”

Section: Discussionmentioning

confidence: 99%

“…Several recent studies have investigated this issue, by using different approaches, including information theoretical ones (21), general considerations (20,22,23) and 1D caricatures of the cell (24). What has been lacking to date, however, is a treatment of the directional sensing problem that (i) exactly quantifies the fluctuations in the number of bound receptors taking into account the spatial extent of the cell and (ii) couples this noisy signal to a downstream intracellular directional sensing pathway.…”

Section: Uring Eukaryotic Chemotaxis Chemical Gradients Determinementioning

confidence: 99%

Receptor noise limitations on chemotactic sensing

Rappel

Levine

2008

Proc. Natl. Acad. Sci. U.S.A.

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Chemotactic eukaryotic cells are able to detect chemoattractant gradients that are both shallow and have a low background concentration. Under these conditions, the noise in the number of bound receptors can be significant and needs to be taken into account in determining the directional sensing process. Here, we quantify numerically the number of bound receptors on the membrane of a disk-shaped cell by using a numerical Monte Carlo tool. The obtained time traces of the receptor occupancy can be used as inputs for any directional sensing model. We investigate the response of the local excitation global inhibition model and a recently developed balanced inactivation model. We determine a measure for the motility of the cell for each model, based on the relevant output variable, as a function of experimental parameters, resulting in several experimentally testable predictions. Furthermore, we show that these two models behave in a qualitatively different fashion when the background concentration is varied. Thus, to properly characterize the sensitivity of cells to receptor occupancy, it is not sufficient to examine the input signal. Rather, one needs to take into account the response of the second messenger pathway.chemotaxis | motility D uring eukaryotic chemotaxis, chemical gradients determine and guide the crawling motion of cells. Chemotaxis plays a fundamental role in development and in immune responses and is implicated in the spreading of cancer (1-3). The external gradient of the chemoattractant results in an asymmetric distribution of bound receptors on the cell's membrane and the directional sensing process translates this receptor asymmetry into directed cell motion. A number of biochemical components of the directional sensing pathway of several model systems have been determined (4-7) and an array of different mechanisms have been proposed, including Turing-type instability mechanisms (8), phase separation mechanisms (9), bistable mechanisms (10), depletion mechanisms (11, 12), and communication through diffusible inhibitors (13)(14)(15)(16). Despite the recent experimental progress and theoretical efforts, however, the precise mechanisms underlying chemotaxis, in general, and directional sensing, in particular, are poorly understood (17,18).Further complicating the directional sensing problem is the potential role of stochasticity. It has been shown that cells are able to chemotax in very shallow gradients with a large range of background concentrations (19,20). For these shallow gradients the difference in the number of bound receptors at the front and the back of the cell can be as little as 20. Comparing this with the total number of bound receptors, which is of the order of several hundred, leads to the question of noise in directional sensing.Several recent studies have investigated this issue, by using different approaches, including information theoretical ones (21), general considerations (20,22,23) and 1D caricatures of the cell (24). What has been lacking to date, however, is a treatment of...

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“…In fact, at threshold the difference in the number of bound receptors at the front and the back can be estimated to be on the order of 20 while the total number of bound receptors is only a few hundred. This immediately raises the question of the effect of noise on chemotaxis, a topic that has been studied previously using a variety of approximative techniques [3][4][5][6]. What has been lacking, however, is a formalism that simulates quantitatively the receptor noise and its correlations and uses this as input for an intracellular chemotactic model.…”

Section: Introductionmentioning

confidence: 99%

Receptor Noise and Directional Sensing in Eukaryotic Chemotaxis

Rappel

Levine

2008

Phys. Rev. Lett.

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Chemotacting eukaryotic cells are able to detect very small chemical gradients (~1%) for a large range of background concentrations. For these chemical environments, fluctuations in the number of bound ligands will become important. Here, we investigate the effect of receptor noise in a simplified one-dimensional geometry. The auto-and cross-correlations of the noise sources at the front and the back of the cell are explicitly computed using an effective Monte Carlo simulation tool. The resulting stochastic equations for the investigated directional sensing model can be solved analytically in Fourier space. We determine the chemotactic efficiency, a measure of motility for the cell, as a function of several experimental parameters, leading to explicit experimental predictions.Chemotaxis, the directed movement of cells in response to external chemical gradients, plays an important role in a wide variety of biological processes including wound healing, fetal development, and cancer metastasis [1]. The externally diffusing chemoattractant molecules (ligands) bind to cell membrane receptors which activate second messenger signaling pathways. In the case of eukaryotic cells, the subject of this Letter, these pathways eventually leads to cell motion in the form of crawling up the gradient.Surprisingly, eukaryotic cells have been found to chemotax in gradients that are only 1%-2% across the cell body. Furthermore, Dictyostelium discoideum cells, a social amoeba, were found to be able to direct their motion even when the average external chemoattractant concentration was well below the dissociation constant K d (the value for which half the receptors are bound in equilibrium) [2]. In fact, at threshold the difference in the number of bound receptors at the front and the back can be estimated to be on the order of 20 while the total number of bound receptors is only a few hundred. This immediately raises the question of the effect of noise on chemotaxis, a topic that has been studied previously using a variety of approximative techniques [3][4][5][6]. What has been lacking, however, is a formalism that simulates quantitatively the receptor noise and its correlations and uses this as input for an intracellular chemotactic model.In this Letter, we will address the role of receptor noise in directional sensing, the first step in chemotaxis during which cells determine the direction of the gradient. We will use a simplified one-dimensional geometry, schematically shown in Fig. 1, which allows us to obtain analytical expressions for the diffusive part of the directional sensing model. Our 1D cell contains a front and a back, both considers to be points, connected by a line, representing the interior, or cytosol, of the cell. The input S at the front and back of the cell represents the number of bound receptors arising from the simple ligand-receptor interaction L + R 0 ⇌ R 1 . The forward rate k + [L], where [L] represents the ligand concentration, and backward rate k − determine the transitions between the unoccupie...

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

Cited by 89 publications

References 39 publications

External and internal constraints on eukaryotic chemotaxis

External and internal constraints on eukaryotic chemotaxis

Receptor noise limitations on chemotactic sensing

Receptor Noise and Directional Sensing in Eukaryotic Chemotaxis

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