Reaction kinetics of membrane receptors: a spatial modeling approach

TL;DR

This paper presents a spatial modeling approach to analyze membrane receptor reaction kinetics, revealing that traditional well-mixed models often overestimate reaction rates by neglecting spatial effects.

Contribution

It introduces a homogenized spatial model and analytical solutions for receptor kinetics, improving upon classical reaction rate theories by incorporating spatial heterogeneity.

Findings

Naive well-mixed models overestimate reaction rates in certain regimes

Analytical expressions derived for four prototypical interaction scenarios

Spatial effects are crucial for accurate reaction rate predictions

Abstract

The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and describing the evolution of both molecular diffusion and molecule-receptor interactions. By analyzing a resulting partial differential equation coupled to ordinary differential equations, we derive analytical expressions for the steady-state molecular influx rate in four prototypical interaction scenarios: Michaelis-Menten kinetics, Substrate Competition, Competitive Inhibition, and Uncompetitive Inhibition. For each scenario, we show how to modify the classical well-mixed reaction rate theory to resolve spatial features inherent to receptors bound to cell membranes. We find that naive well-mixed calculations significantly overestimate reaction rates in certain biophysical parameter regimes.