TranspMM.sided.Comp2F Notes 19nov08
Parameter Set Conct
t.min = 0
t.max = 1E3
t.delta = .01
V1 = 1
V2 = 1
Flow = .1
Vmax = .01
G2 = .02
Km = .01
A1init = 0
A2init = 0
B1init = 0
B2init = 0
Ain = fgen_1
Flow and fgen for Ain set to about the same results as were
set up for TranspMM.2sol2sided.Comp2. The difference is that in this program the input into A1 and B1 is provided by the inflow instead of the initial conditions, just a detail really, but illustrates a different and practical type of experiment that could not be achieved in a biological setting where initial conditions cannot be set.
Program Version for solute A: Solute A only binds to transporter.
The only influence of concn on the PS is by A1 from side 1 (cis side).
The problems are that trans side binding is not accounted for, nor is there
capacitance in the membrane to account for any binding of A to transporter..
Conclusion: A simple MM tranpsorter cannot be correct, because:
1. Cis and trans sides not treated identically.
2. No capacitance in membrane, and thus no Barrer time lag.
3. No oppportunity for sidedness due to coupling with energy source..
Running the program:
1. ParSet MM.par
. View the results on PlotPage "Conc_t". Initially A1 decreases linearly with time, as does B1.
Put A1(t) on a new plot page and make the axes semilog to check whether or not it is exactly exponential. What is the rate constant for the exponential? What should the rate constant be? How close is it to G2/(V1+V2)?
The PS2/(Vmax/Km) for solute B is (1 + B1/Km +B2/Km).instead of that used for A, (1+ A1/Km),. The rates of decline from the initial values appears to be identical in spite of the different PSs. Why should this be so?
2. Observing the PS's: ParSet FacMM.par.
View Plot "PS.vs.Conc" where PS/PSmax is plotted versus the concentration sum normalized re the KmA and KmB.
JSim v1.1
/*
MODEL NUMBER: 0024
MODEL NAME: TranspMM.2sol2sided.Comp2F
SHORT DESCRIPTION: A two compartment two-sided Michaelis-Menten transporter, with flow.
*/
import nsrunit; unit uM = 1e-6 M; unit conversion on;
math TranspMM_2sided_Comp2F { realDomain t sec; t.min = 0; t.max = 1000; t.delta = 0.01;
//PARAMETERS
real V1 = 1 ml/g, // Volume 1
V2 = 1 ml/g, // Volume 2
Flow= 1 ml/(g*s), // Flow through V1
PSmax = 1 ml/(g*s), // PSmax is max conductance at Zero % saturation.
GA2 = 2 ml/(g*s), // Gulosity, first order consumption in V2
GB2 = 0.1 ml/(g*s), // Gulosity, first order consumption in V2
KmA = 1 mM, // Equilib dissoc const fir A on each side
KmB = 1 mM, // Equilib dissoc const fir A on each side
A1init = 1 mM, A2init = 0 mM, // Initial concns in V1 and V2
B1init = 2 mM, B2init = 0 mM; // Solute B uses same transporter
// State variables
real A1(t) mM, A2(t) mM, // Solute A conc side 1, side 2
B1(t) mM, B2(t) mM, // Solute B conc side 1, side 2
PS(t) ml/(g*s);
extern real Ain(t) mM, Bin(t);
// initial conditions
when(t=t.min) {A1 = A1init; A2 = A2init; B1 = B1init; B2 = B2init; }
// ODEs:FOR ONE-SIDED VERSION
PS = PSmax/(1 + (A1+A2)/KmA + (B1+B2)/KmB); // PS calc
V1*A1:t = - PS* (A1-A2) + Flow* (Ain - A1);
V2*A2:t = PS* (A1-A2) - GA2* A2;
V1*B1:t = - PS* (B1-B2) + Flow* (Bin - B1);
V2*B2:t = PS* (B1-B2) + GA2* A2- GB2* B2;
real NormConc(t) dimensionless;
NormConc = (A1+A2)/KmA +(B1+B2)/KmB; //Used for X-axis for PS/PSmax
}
/*
DIAGRAM:
__________________
Flow |V1 A1(t),B1(t) |--------->Aout
------->| |
Ain | ^ PS | PS = PSmax /
--------|--------| (1 + A1/KmA + A2/KmA
| v | + B1/KmB + B2/KmB)
| A2(t),B2(t) |
|V2 |
-----------------|
DETAILED DESCRIPTION:
Facilitated transporter kinetic model assuming instantaneous
solute binding to transporter of Michaelis Menten type, single site available from
either side of membrane. Two versions are included in this program:
1. Cis side driven: concn A1 determines the fractional saturation, PS/PSmax.
2. Cis-trans driven: governing concn is average of A1 and A2.
Stirred tank model for facilitated exchange between instantly
mixed chambers.
An external input function, Ain, flows into the plasma supplying solute A.
A in V1 permeates the membrane to A2 via a facilitating saturable Michaelis-
Menten typs transporter with rapid binding and release of A.
Reaction of solute A --> solute B (and the reverse reaction) occurs in ISF.
B can re-enter plasma by a similar separate transporter, non-competing.
SHORTCOMINGS/GENERAL COMMENTS:
- Specific inadequacies or next level steps
KEY WORDS: Gulosity, Michaelis-Menten, two sided, two compartment, two solutes, Permeability Surface,
Equilibrium Dissociation Constant, Flow, tutorial
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.
REVISION HISTORY:
Original Author : JBB Date: Nov/08
Revised by : BEJ Date: 16/Dec/09
Revision: 1) Update format of comments
2) Change units of V, Vmax, G
COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE:
Copyright (C) 1999-2009 University of Washington. From the National Simulation Resource,
Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Academic use is unrestricted. Software may be copied so long as this copyright notice is included.
This software was developed with support from NIH grant HL073598.
Please cite this grant in any publication for which this software is used and send an email
with the citation and, if possible, a PDF file of the paper to: staff@bioeng.washington.edu.
*/