Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium

Area of Science:

• Biophysics
• Cellular Biophysics
• Physical Chemistry

Background:

• Protein motion in living cells often displays transient anomalous diffusion (subdiffusion).
• This anomalous diffusion converges to Brownian motion with a reduced diffusion coefficient at longer timescales.
• Cellular membranes are heterogeneous, potentially causing localized slowdowns in Brownian motion.

Purpose of the Study:

• To investigate if transient anomalous diffusion and space-dependent slowed Brownian motion yield similar outcomes for reversible ligand-binding reactions in 2D.
• To compare the equilibrium properties of ligand binding under different diffusion models.

Main Methods:

• Theoretical analysis of diffusion models.
• Monte Carlo simulations of ligand-binding reactions in 2D.
• Comparison of continuous-time random walks (CTRW) with space-dependent Brownian motion.

Main Results:

• Continuous-time random walks decrease the apparent binding affinity.
• Locally slowed Brownian motion and obstacle hindrance both increase apparent binding affinity.
• Maximal affinity with slowed Brownian motion occurs when the slowdown is spatially restricted.

Conclusions:

• Different diffusion regimes (CTRW vs. slowed Brownian motion) have distinct, irreconcilable effects on ligand-binding affinity, even at equilibrium.
• The spatial distribution of reduced mobility significantly impacts reaction dynamics and apparent affinity.
• Understanding these diffusion-binding relationships is crucial for cellular processes.