A method for defining steady-state unidirectional fluxes through branched chemical, osmotic and chemiosmotic reactions

Area of Science:

• Chemical Kinetics
• Mathematical Modeling
• Physical Chemistry

Background:

• Analyzing complex chemical reaction systems requires robust mathematical techniques.
• Previous methods for flux calculation can be limited in scope or require distinctions between labeled and unlabeled species.
• Understanding steady-state unidirectional fluxes is crucial for various chemical and biological processes.

Purpose of the Study:

• To present a general mathematical technique for deriving analytical and numerical solutions for steady-state unidirectional fluxes.
• To provide an alternative method for calculating isotopic exchange velocities in complex reaction systems.
• To demonstrate the technique's applicability to systems with branched and overlapping elementary processes.

Main Methods:

• Application of Markov process theory with conditional probabilities for chemical state transitions.
• Evaluation of an infinite power series using matrix Taylor series expansion.
• Derivation of analytical expressions and numerical solutions for reaction fluxes.

Main Results:

• The technique provides a general method for calculating steady-state unidirectional fluxes in complex reaction networks.
• It offers a distinct alternative to existing methods for isotopic exchange velocity equations.
• The method is applicable to systems where labeled and unlabeled species are not distinguished.

Conclusions:

• The described mathematical technique offers a versatile approach to analyzing chemical reaction dynamics.
• It simplifies the derivation of flux equations for complex systems, including those with intermediate states.
• The method's applicability is demonstrated through a second-order carrier-mediated transport mechanism.