Revising Berg-Purcell for finite receptor kinetics

Area of Science:

• Cell Biology
• Biophysics
• Mathematical Modeling

Background:

• Cellular processes like nutrient uptake and signaling rely on molecules binding to membrane receptors.
• Mathematical models often simplify receptor behavior by assuming infinite kinetic rates, neglecting real-world limitations.
• The Berg and Purcell formula, a key model, is limited to scenarios where receptor binding is much faster than molecule arrival.

Purpose of the Study:

• To develop a robust mathematical framework for modeling diffusion-coupled surface receptors with finite kinetic rates.
• To derive an accurate formula for cellular uptake rate considering receptor kinetics.
• To assess the impact of finite receptor kinetics on molecular uptake estimations.

Main Methods:

• Developed a modeling framework coupling bulk diffusion with surface receptors using boundary homogenization.
• Coupled the diffusion equation to nonlinear ordinary differential equations on the boundary.
• Employed many-particle stochastic system simulations for validation.

Main Results:

• Derived an explicit formula for cellular uptake rate that incorporates finite receptor kinetic rates.
• Demonstrated that the Berg and Purcell analysis can significantly overestimate molecular uptake in typical biophysical conditions.
• Numerical simulations confirmed the developed model's predictions.

Conclusions:

• Finite receptor kinetic rates are crucial for accurately modeling molecular uptake and cellular signaling.
• The developed framework provides a more realistic approach to understanding diffusion-receptor interactions.
• This work refines existing models and offers insights into the limitations of previous approximations.