2025/01/23 by Cengiz, Anil, Lawley, Sean D
#92C05 #92C37 #92C40 #Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Physical sciences #Quantitative Methods (q-bio.QM)
paper · doi:10.48550/arxiv.2501.13837
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.