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# TranspMM.2sol2sided.Comp2

Model number: 0023

A two compartment two-sided Michaelis-Menten transporter with two solutes.

## Detailed Description

A facilitated transporter kinetic model assuming instantaneous solute binding to transporter of Michaelis-Menten type, single site available from both sides of the membrane. This model contains two solutes in two compartments, giving concentrations A1, A2, B1, and B2. Permeability-Surface Area product (PS) is determined by the concentration of A1 and B2. PSmax is max PS at 0% saturation. There is Gulosity in V2. In V2, A is consumed, forming B. B is also consumed.

## Relevant Equations

$\large { PS(t) = \frac {PS_{\text{\small{max}}}}{1 + \frac {A1 + A2}{K_{\text{\small{mA}}}} + \frac {B1 + B2}{K_{\text{\small{mB}}}}}$

$\large { V1 \frac {d}{dt}A1(t) = -PS(A1-A2)$

$\large { V2 \frac {d}{dt}A2(t) = PS(A1-A2) - G_{\text{\small{A2}}} A2$

$\large { V1 \frac {d}{dt}B1(t) = -PS(B1-B2)$

$\large { V2 \frac {d}{dt}B2(t) = PS(B1-B2) + G_{\text{\small{A2}}} A2 - G_{\text{\small{B2}}} B2$

KmA and KmB are the equilibrium dissociation constants for each solute on both sides.

## Run JSim Model

Press the "Run Applet" button to bring up the model in a separate window.

## References

Klingenberg M. Membrane protein oligomeric structure and transport function. Nature 290: 449-454, 1981.

Stein WD. The Movement of Molecules across Cell Membranes. New York: Academic Press, 1967.

Stein WD. Transport and Diffusion across Cell Membranes. Orlando, Florida: Academic Press Inc., 1986.

Wilbrandt W and Rosenberg T. The concept of carrier transport and its corollaries in pharmacology. Pharmacol Rev 13: 109-183, 1961.

Schwartz LM, Bukowski TR, Ploger JD, and Bassingthwaighte JB. Endothelial adenosin transporter characterization in perfused guinea pig hearts. Am J Physiol Heart Circ Physiol 279: H1502-H1511, 2000.

Foster DM and Jacquez JA. An analysis of the adequacy of the asymmetric carrier model for sugar transport. Biochim Biophys Acta 436: 210-221, 1976.

## Key Terms

Gulosity, Michaelis-Menten, two sided, two compartment, two solutes, Permeability Surface, Equilibrium Dissociation Constant, tutorial

## JSim Tutorial

Click here to go to a JSim tutorial webpage, with an introduction to the JSim GUI, detailed usage instructions, and an accompaying video.