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Modulation of antigen discrimination by duration of immune contacts in a kinetic proofreading model of T cell activation with extreme statistics.

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Updated: May 28, 2025

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Kinetic Monte Carlo methods for three-dimensional diffusive capture problems in exterior domains.

Andrew J Bernoff1, Alan E Lindsay2

  • 1Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA.

Royal Society Open Science
|February 13, 2025
PubMed
Summary

A new kinetic Monte Carlo method accurately simulates how signaling molecules reach cell surfaces. This computational tool aids in understanding cellular decisions influenced by molecular diffusion and capture dynamics.

Keywords:
Brownian motionMonte Carlo methodsasymptotic analysisdirectional sensingfirst passage times

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Area of Science:

  • Computational biology
  • Biophysics
  • Mathematical modeling

Background:

  • Cellular processes rely on signaling molecule diffusion and capture.
  • Modeling these diffusive capture problems is computationally intensive due to complex geometries and boundary conditions.

Purpose of the Study:

  • To develop a rapid and accurate particle-based kinetic Monte Carlo (KMC) method for simulating molecular arrival statistics.
  • To address the computational challenges in diffusive capture problems relevant to cellular signaling.

Main Methods:

  • A particle-based kinetic Monte Carlo (KMC) method was employed.
  • Simulations were performed for a half-space with absorbing traps and the exterior of a convex cell with traps.
  • The method was validated against classical results and theoretical expansions.

Main Results:

  • The KMC method provides rapid and accurate simulation of arrival statistics.
  • Validation confirmed the method's efficacy for both simple and complex geometries.
  • A novel 'shielding effect' was identified in non-spherical domains, influencing source directionality estimates.

Conclusions:

  • The developed KMC method offers an efficient approach to studying cellular signaling dynamics.
  • The findings enhance the understanding of molecular diffusion, capture, and their impact on cellular decision-making.
  • The identified shielding effect provides new insights into geometric influences on cellular signaling.