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. 2025 Sep 30;20(9):e0333522.
doi: 10.1371/journal.pone.0333522. eCollection 2025.

Information bounds on the accuracy of cell polarization

Tau-Mu Yi  1
Affiliations

Information bounds on the accuracy of cell polarization

Tau-Mu Yi. PLoS One. .

Abstract

Here we characterized an information measure for cell polarity that applies to non-motile cells responding to a chemical gradient. The central idea is that polarization represents information about the direction of the gradient. We applied a theory of optimal gradient sensing and response in the presence of external noise based on the information capacity of a Gaussian channel. First, we formulated an information framework that describes spatial gradient sensing and polarization response. As part of this section, we modeled ligand diffusion and receptor-binding dynamics as a mixed Poisson distribution, confirming the single receptor accuracy limits derived by ten Wolde and colleagues. Second, we performed numerical calculations of stochastic ligand levels at the cell surface to estimate the information provided about the directional component of the gradient vector, which was close to the Gaussian channel bound for low signal-to-noise ratios. Third, we used the information framework to evaluate the noise-robustness of three generic models of cell polarity, demonstrating that a filter-amplifier architecture and time integration can attenuate the detrimental impact of noise on polarity so that the model can approach the theoretical limits. Fourth, we compared the theory to published experimental data on yeast mating projection growth in a pheromone gradient, identifying the ligand association rate and integration time as two key parameters affecting directional accuracy. By varying these parameters, we showed that for certain ranges the theory is roughly in agreement with the data, and that the slow binding rate constant is a key limiting factor. We concluded that temporal averaging can help overcome the slow binding rate to achieve greater accuracy, but with the drawback of a slow mating response.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Schematic diagrams of gradient-directed cell polarization.
A: Circular cell with the surface membrane evenly divided into bins. The background shading and arrow underneath depict the gradient direction. A cellular species on the surface localizes to the front of the cell over a time interval resulting in polarization. B: Gradient sensing by receptors on the cell surface. Each cell surface compartment contains a single receptor (Y-shape). The receptor senses the gradient chemical concentration ci at bin i. C: The receptor measures the local concentration (ci) of ligand (red circle) by binding ligand molecules over a time interval Δt. This monitoring process is subject to noise from the stochastic nature of diffusion (ligand molecules diffusing into and out of the receptor local neighborhood) and receptor-ligand binding.
Fig 2
Fig 2. Relationships between different measures of polarization on 2D disk.
A: Relationship between polarization information and full width at half maximum (FWHM). Gaussian polarization profiles were constructed for a range of standard deviation values, and then polarization information (bits) and FWHM (degrees) were calculated for each and plotted (nb = 512). B: Relationship between total information and signal-to-noise ratio. Total information was computed using the Gaussian channel approximation for nb = 64 bins/receptors (solid). In addition, total information was approximated by the expression loge4g2r2nbN (dashed) in which g is the gradient slope, r is the disk radius, and N is the noise variance. Also shown is the polarization information (0.8×Itot, dotted). The signal-to-noise ratio is expressed as gN. C: Relationship between projection directional accuracy (cos(θ)) and signal-to-noise ratio (gN). The Blahut-Arimoto algorithm was used to convert the polarization information values from 2B into directional accuracy as measured by the cosine of the angle θ between projection and gradient directions. The dotted line indicates cos(θ)=1.
Fig 3
Fig 3. Estimating the directional component of total information from gradient.
A: Numerical calculation of polarization information (Ip) compared to theoretical calculation of total information (Itot). The directional component of total information was computed for a circular cell containing nb = 32 bins subjected to a gradient of slope g corrupted by noise N for a range of signal-to-noise ratios (gN). It was compared to the total information, which was determined using the Gaussian channel approximation summed over 32 bins. B: The data from 3A were replotted as the ratio of polarization information to total information (IpItot). Standard deviations are provided in S1 Table and are within the size of the data points on the plot. The dotted line is the ratio 0.8. C: The ratio of polarization information to total information as a function of the number of bins (nb) for gN=0.01.
Fig 4
Fig 4. Comparing polarization information of simulations to theory.
A: Polarization profiles at different noise standard deviation values (N) for three models (from left to right): cooperative (Coop), positive feedback (PF), and filter-amplifier (FA). The polarization profiles on a 2D disk (polarized species in each bin marked in radians) represent the average peak polarization over 100 simulations for the following values of N: 0.001, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5. The gradient slope g=0.01μm−1 B: Polarization information (Ip) as a function of N for each of the three models. The simulation Ip was computed from the average peak polarization profiles (solid black). There were three trials (each of 100 simulations); standard deviations are provided in S2 Table and are within the size of the data points on the plot. The theory Ip was obtained from the convolution of 0-noise simulation with the numerically determined polarization profile (e.g. Fig 3) for each noise value (red dashed).
Fig 5
Fig 5. Comparing theory with yeast gradient sensing experiments.
Polarization directional accuracy measured as cos(θ) is plotted versus gradient slope (μm−1). A: The theory curves represent the maximum polarization information calculated using Eq 3 (multiplied by 0.8) converted to cos(θ) values. The noise value N was estimated using default parameter values (S3 Table) in Eq 4 with the exception of the integration time: Tlo = 1000s (dashed) and Thi = 10000s (solid). The experimental data are from reference [36]. B: The theory curves were generated over a ten thousand-fold range of ka (from 2×103 to 2×107 M−1s−1 as shown in the figure legend), and using the integration time Thi = 10000s and the default values for the other parameters. C: The theory curves were generated using the lowest experimentally observed association rate constant ka from reference [43], 4×103 M−1s−1, and either Tlo = 1000s (dashed) or Thi = 10000s (solid).
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