Modeling of active transport systems

Nonisothermal reaction-diffusion systems control the behavior of many transport and rate processes in physical, chemical, and biological systems, such as pattern formation and molecular pumps. Considerable work has been published on mathematically coupled nonlinear differential equations by neglecting thermodynamic coupling between a chemical reaction and transport processes of mass and heat. The thermodynamic coupling refers that a flow occurs without or against its primary thermodynamic driving force, which may be a gradient of temperature, or chemical potential, or reaction affinity. Energy coupling in the membranes of living cells plays major role in the respiratory electron transport chain leading to synthesizing adenosine triphosphate (ATP). The ATP synthesis in turn, is matched and synchronized to cellular ATP utilization. Consequently, the hydrolysis of ATP is thermodynamically coupled to the transport of substrates. This study presents the modeling of thermodynamically coupled system of a simple elementary chemical reaction with molecular heat and mass transport. The modeling is based on the linear nonequilibrium thermodynamics (LNET) approach by assuming that the system is in the vicinity of global equilibrium. Experimental investigations revealed that LNET is capable of describing thermodynamically coupled processes of oxidative phosphorylation, mitochondrial H⁺ pumps, and (Na⁺ and K⁺)- ATPase. Moreover, the LNET formulation does not require the detailed mechanism of the coupling. The modeling equations lead to unique definitions of cross coefficients between a chemical reaction and heat and mass flows in terms of kinetic parameters, transport coefficients, and degrees of coupling, which are measurable. These newly derived cross coefficients need to be determined to describe some coupled reaction-transport systems. Some methodologies are suggested for the determination of the cross coefficients and some representative numerical solutions for coupled reaction-transport systems are presented. Such modeling may improve our understanding of active transport by molecular pumps.