Theory of Diffusion-Influenced Reaction Networks

Area of Science:

• Chemical Kinetics
• Physical Chemistry
• Reaction Dynamics

Background:

• Diffusion significantly impacts reaction kinetics, especially for reversible association-dissociation reactions.
• Existing theories struggle to incorporate diffusion's influence on reaction schemes and rate equations.
• Conformational changes can further complicate reactivity, necessitating a more robust theoretical framework.

Purpose of the Study:

• To develop a general formalism describing diffusion's effect on coupled reversible reactions with conformational changes.
• To provide a concise and elegant method for analyzing diffusion in complex chemical kinetic networks.
• To elucidate the role of diffusion in introducing new reaction channels and modifying existing ones.

Main Methods:

• Development of non-Markovian rate equations incorporating stoichiometric matrices and net reaction rates.
• Introduction of a time-dependent pair association flux matrix to couple reaction rates.
• Analysis of the Markovian limit using committors (splitting/capture probabilities).

Main Results:

• A novel formalism accurately describes diffusion-influenced kinetics, coupling reaction rates via a physically interpretable flux matrix.
• In the Markovian limit, committors quantify the probability of association versus diffusion.
• Application to three reaction schemes reveals new reaction channels, direct coupling between bound states, and exchange-type bimolecular reactions, with some diffusion-modified rate constants becoming negative, indicating memory effects.

Conclusions:

• The developed formalism offers a powerful tool for studying diffusion-influenced reaction networks of arbitrary complexity.
• Diffusion can fundamentally alter kinetic schemes by introducing new pathways and coupling mechanisms.
• Memory effects are crucial in diffusion-modified reactions, as evidenced by negative rate constants in the Markovian limit.