Self-consistent theory of reversible ligand binding to a spherical cell

Understanding ligand-receptor interactions is essential for modeling cellular responses to external signals. Prior research has shown that ligand binding to receptors initiates many signaling pathways. Established models often assume uniform ligand distribution and constant binding rates. However, these assumptions may not hold in spatially heterogeneous environments. The Berg-Purcell model is widely used to estimate receptor-ligand association rates. This model assumes a constant effective on-rate based on receptor density and ligand diffusion. No prior work had resolved how rebinding affects the observed dissociation rate. That uncertainty drove the need for a more detailed kinetic framework. This paper introduces a self-consistent stochastic theory to address these limitations.

The aim of this research is to develop a comprehensive model of ligand-receptor binding on a spherical cell surface. The specific problem addressed is the lack of a unified framework that accounts for rebinding and spatial distribution effects. The motivation comes from the limitations of existing models, which neglect the dynamic nature of ligand concentration near the cell. This study seeks to clarify how binding and dissociation rates evolve over time. The researchers propose to incorporate diffusion, binding, and rebinding into a single theoretical framework. Their goal is to derive the time evolution of bound receptor fractions. They also aim to test the validity of the Berg-Purcell scaling in different time regimes. The findings may help refine experimental interpretations of binding dynamics.

The researchers employed a spherical geometry to model the cell surface and surrounding solution. They used a self-consistent stochastic approach to track ligand binding and unbinding events. The model included diffusion of ligands in the extracellular space and rebinding to receptors. Time-dependent ligand concentration was calculated using a self-consistent field approximation. The theory accounted for spatial gradients in ligand concentration near the cell. The researchers derived analytical expressions for the bound receptor fraction p(t). They tested the model in different time regimes: early, intermediate, and late. The results were compared to the predictions of the Berg-Purcell model.

The study found that the effective on-rate changes non-monotonically with time. At early and late times, the on-rate equals the intrinsic rate. In intermediate times, it approximates the Berg-Purcell value. The dissociation rate is strongly modified by rebinding events. The effective dissociation rate matches the Berg-Purcell value at intermediate times. At late times, the decay becomes algebraic rather than exponential. The ligand concentration in equilibrium equals its spatial mean. This ensures no local depletion near the cell surface. The results suggest that rebinding significantly affects observed dissociation rates. The model provides a more accurate description of binding kinetics than previous approaches.

The authors propose that the effective on-rate is time-dependent and deviates from the Berg-Purcell scaling at certain times. They suggest that rebinding events strongly influence the observed dissociation rate. The results indicate that the Berg-Purcell model applies only in intermediate time regimes. The ligand concentration remains uniform in equilibrium, contradicting earlier assumptions. These findings may improve the interpretation of binding experiments. The researchers propose that numerical simulations should incorporate time-dependent on-rates. They suggest that the model can be extended to more complex geometries. The study provides a framework for analyzing ligand-receptor systems with spatial heterogeneity.