Amino acid/K+ symport (cotransport) across a model epithelium, the lepidopteran midgut, is energized by an electrogenic H+ V-ATPase (H+ pump) in parallel with an electrophoretic K+/H+ antiporter (exchanger). Attempts to analyze this process using well-known equilibrium thermodynamic equations (Nernst, Gibbs), diffusion equations (Nernst, Planck, Einstein, Goldman, Hodgkin, Katz) and equations based on Ohm's law (Hodgkin, Huxley) have all encountered major difficulties. Although they are useful for analyzing nerve/muscle action potentials, these state equations assume that brief perturbations in membrane conductance, gm, and membrane voltage, Vm, occur so rapidly that no other parameters are significantly disturbed. However, transport studies often extend for minutes, even for hours. Perturbation of one parameter in complex transport systems invariably results in a state change as all of the other elements adjust to the prolonged stress. The development of a comprehensive mathematical treatment for transport systems that contain pumps and porters (transporters) has been hampered by the empirical nature of the concept of membrane permeability and conductance. The empirical definition of permeability was developed before pumps and porters were known. Thus, 'permeability' is a gross parameter that, in practice if not in theory, could describe all transport pathways including pumps, porters and channels. To surmount these difficulties, we have applied ionic circuit analysis to vesicular systems containing insect midgut transport proteins. In this analysis, pumps, porters and channels, as well as ionic concentration gradients and membrane capacitance, are components of ionic circuits that function to transform metabolic energy (e.g. from ATP hydrolysis) into useful metabolic work (e.g. amino acid uptake). Computer-generated by an H+ V-ATPase to K+/2H+ antiport and amino acid/K+ symport in the lepidopteran midgut.

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