Membrane transport system modeled by network thermodynamics

Abstract

This paper outlines a model of the membrane transport system in which the process of membrane transport is carried out in two steps. In the first step, using the bond-graph method of network thermodynamics, resistive and capacitive modules express subsystems as integrated circuits. The resistive module represents the irreversible dissipative process in the system. In the bond-graph representation of the resistive membrane module, the coupled dissipative process of a two-power system is simplified into a bond graph of the elemental circuit consisting of a transducer and two resistors. The Kedem and Katchalsky equation is interpreted by this elemental circuit. It is shown that a combination of elemental circuits becomes a resistive membrane module which includes several transport processes and an active transport mechanism. A paired capacitive module is also described which represents the reversible free-energy change process in both solution compartments across the membrane. In the bond-graph representation of the paired capacitive solutions module, a new two-port chemical element is introduced which provides for the relation of the solute flow, the volume flow and the concentration change. As the concentration of a solute is a two-valued function of solute and volume, the two-port capacitor represents the changes of both the chemical potential and osmotic pressure of a solute due to solute and volume changes in the solution compartment. Using the differences in the chemical potentials and osmotic pressures across the membrane as force variables, a model of a paired capacitive solution module representing the process of the total free-energy change in the single membrane transport system is made from one- and two-port capacitors and transducers. p]In the second step, the membrane transport system is designed from a combination of the resistive module and the paired capacitive module as subsystems. Using the model which encorepasses the design of both modules, simulation of the cell membrane behavior was attempted and the results are outlined in this paper. It is predicted that the electroosmosis and the volume changes within the compartments are critical factors in the mechanism of cell membrane transport.