Diffusion-controlled reaction rates for two active sites on a sphere.

Area of Science:

• Biophysical chemistry
• Biochemistry
• Chemical kinetics

Background:

• Generalizes diffusion-limited reaction rates for uniform spheres to anisotropic reactivity.
• Highlights limitations of the uniform sphere protein model in certain scenarios.
• Investigates the competitive binding of ligands to two active sites on spherical enzymes or cells.

Purpose of the Study:

• To analytically study the competition of ligands binding to two active sites on a spherical enzyme or cell.
• To generalize diffusion-limited reaction rates to anisotropic reactivity.
• To compare the reaction rate of two opposing sites with twice the rate of a single site.

Main Methods:

• Analytical treatment of ligand binding competition.
• Mathematical modeling of reaction kinetics on spherical surfaces.
• Comparison of reaction rates between single and dual active site models.

Main Results:

• Derived the reaction rate constant for two sites located at opposite ends of a spherical species.
• Observed that site competition reduces the reaction rate compared to individual site rates.
• Quantified that competition becomes apparent when the site half-angle exceeds 30 degrees.

Conclusions:

• Ligand competition is negligible for small active sites.
• The competitive effect intensifies as the active site size (theta) increases.
• The maximum competitive effect is observed when the site half-angle reaches pi/2 (90 degrees).