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Optimal Distributions of Receptors on Arbitrarily Shaped Cell Surfaces

Daoning Wu (吴道宁)1,*, Sayun Mao (毛飒韵)1,2,*, and Jie Lin (林杰)3,4,†

  • 1Yuanpei College, Peking University, Beijing, China
  • 2Department of Computational Medicine, UCLA, Los Angeles, California 90095-1766, USA
  • 3Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China
  • 4Peking-Tsinghua Center for Life Sciences, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing, China

  • *These authors contributed equally to this work.
  • †Contact author: linjie@pku.edu.cn
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Phys. Rev. Lett. 135, 208401 – Published 10 November, 2025

DOI: https://doi.org/10.1103/xklg-qy2t

Abstract

Efficient absorption of molecules through receptors on cell surfaces is crucial for various biological processes. While ubiquitous patterns of receptor distributions, including polar localization in rod-shaped cells, have been widely observed, the underlying evolutionary advantage of these patterns is unclear. In this Letter, we investigate how the spatial distribution of receptors on the cell surface affects the total flux entering the cell. We develop a numerical method that allows for the calculation of fluxes through all receptors using linear equations. Our calculations show that the flux through each receptor is spatially dependent for uniformly distributed receptors: the fluxes are highest near the poles in rod-shaped cells and near the invagination in defective spherical cells. Surprisingly, we show that the optimal receptor distribution on an arbitrarily shaped cell, which maximizes the total flux, is precisely the charge density distribution on an ideal conductor of the same shape, in agreement with numerical simulations. Our Letter unveils the evolutionary origin of receptor localizations.

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Phys. Rev. Lett. 135, 208401– Published 10 November, 2025
  • Received 24 March 2025
  • Accepted 3 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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