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# TranspMM.2sol2sided.Comp2F

Model number: 0024

A two compartment two-sided Michaelis-Menten transporter, with flow.

## 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. There is Flow into the first compartment, with concentration Ain. The outflow, Aout, equals A1(t). 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

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

$\large { V1 \frac {d}{dt}A1(t) = -PS(A1-A2) + Flow(A_{\text{\small{in}}} - A1)$

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

$\large { V1 \frac {d}{dt}B1(t) = -PS(B1-B2) + Flow(B_{\text{\small{in}}} - B1)$

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

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

## Run JSim Model

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## 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, Flow

## JSim Tutorial

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