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TransComp2

Two compartment master transporter model with choices:
Flow: yes or no,
Solutes: A only, A and B;
Conversion A to B: none, linear, Michaelis-Menten (MM);
Transporters: Passive, MM A1 1-sided, MM A1,A2 two 1-sided,MM A1,A2 one 2-sided, MM A,B 2-sided, and T1&T2 (facilitated).

Looping on parameters flow, solutes, convert, and transporter (all lower case) allows comparisons to be made between different model formulations.

Model number: 0304

Figure

The choices producing this diagram include no flow, two solutes. a linear conversion of A to B in the second compartment, and T1T2 facilitated transport. Solute A is initialized to 1 mM in the first compartment (A1(0) = 1 mM). A is transported from V1 to V2 by a transporter that can bind to either A or B. The transporter can flip from side to side in the unbound form T, or in the bound forms, TA and TB. In V2, A is converted to B by a linear reaction process.

Note that B in compartment one (B1) is greater than B in compartment 2 (B2) where B is produced. B has been transported against a gradient, from low concentration to high concentration.

Description

    TransComp2 is a general model for transporter between two compartments. The
model has five basic choice options:

FLOW
    (1) YES: The model has a flow in compartment 1.
    (2) NO:  The model has no flow.
SOLUTES
    (1) A only:  The model has only one solute, A.
    (2) A and B: The model has  two solutes, A and B.
CONVERT
    (1) None:        There is no conversion of A2 into B2.
    (2) G2aTOb:      If there are two solutes, the loss from A2
                     and gain to B2 is a linear process given
                     by G2aTOb/V2*A2.
    (3) GmaxA2,KmA2: If there are two solutes, the loss from A2
                     and gain to B2 is a Michaelis-Menten process
                     given by
                               GmaxA2*A2/(V2*(1+A2/KmA2)).
TRANSPORTER
    (1) PSa,PSb, Passive: The transport is by a passive process. 
                          A1 change = PSa/V1*(A2-A1).
                          A2 change = PSa/V2*(A1-A2).
                          B1 change = PSb/V1*(B2-B1).
                          B2 change = PSb/V2*(B1-B2).
    (2) PSmaxA1, TKmA1 MM A1 1-SIDED: The transport of A1 and A2 is a
           Michaelis-Menten process governed by only the A1 concentration.
                          A1 change = (PSmaxA1/V1)/(1 + A1/TKmA1)*(A2-A1).
                          A2 change = (PSmaxA1/V2)/(1 + A1/TKmA1)*(A1-A2).
    (3) PSmaxA2, TKmA2 MM A1 A2 2 1-SIDED: The transport of A1 and A2 are
           Michaelis-Menten processes where each side has a 1-sided transporter
           for A1 and A2. 
                          A1 change = (PSmaxA2/V1)/(1 + A2/TKmA2)*(A2   )+
                                      (PSmaxA1/V1)/(1 + A1/TKmA1)*(  -A1).
                          A2 change = (PSmaxA2/V2)/(1 + A2/TKmA2)*(  -A2)+
                                      (PSmaxA1/V2)/(1 + A1/TKmA1)*(A1   ).
    (4) PSmaxA, TKmA MM A1 A2 2-SIDED: The transport of A1 and A2 is a
          Michaelis-Menten process where the transporter is 2-sided:
                          A1 change = (PSmaxA/V1)/(1 + (A1+A2)/TKmA)*(A2-A1).
                          A2 change = (PSmaxA/V2)/(1 + (A1+A2)/TKmA)*(A1-A2).
    (5) PSmaxAB, TKmAB MM A&B 2-SIDED: The transport of A and B is  governed
          by a single Michaelis-Menten process where the transporter is dependent
          on all four species:
                          A1 change = (PSmaxAB/V1)/(1 + (A1+A2+B1+B2)/TKmAB)*(A2-A1).
                          A2 change = (PSmaxAB/V2)/(1 + (A1+A2+B1+B2)/TKmAB)*(A1-A2).
                          B1 change = (PSmaxAB/V1)/(1 + (A1+A2+B1+B2)/TKmAB)*(B2-B1).
                          B2 change = (PSmaxAB/V2)/(1 + (A1+A2+B1+B2)/TKmAB)*(B1-B2).
    (6) T1&T2, facilitated: A free transporter T flips between side 1 and side 2. (T1<->T2)
        For solute = A only, the change in concentrations are
                          A1 change = SoV1*(koffA1*TA1 - konA1*A1*T1).
                          A2 change = SoV2*(koffA2*TA2 - konA2*A2*T2).
                          T1 change = (koffA1*TA1-konA1*A1*T1)  - kT12*T1   + kT21*T2;
                          TA1 change= (konA1*A1*T1 - koffA1*TA1 - kTA12*TA1 + kTA21*TA2) ;
                          TA2 change=(konA2*A2*T2 - koffA2*TA2 + kTA12*TA1 - kTA21*TA2) ;
                          T2  change = Ttot - TA1 - TA2  - T1.
        For solute = A and B, The equations for A1, A2, TA1, and TA2 are unchanged. The
        equations for T1 and T2 are changed and equations for B1, B2, TB1, and TB2 are added:
                          T1 change = (koffA1*TA1-konA1*A1*T1)  - kT12*T1   + kT21*T2
                                     +(koffB1*Tb1-konB1*B1*T1);
                          T2 change = Ttot - TA1 - TA2 - TB1 -TB2 - T1.

                          B1 change = SoV1*(koffB1*TB1 - konB1*B1*T1).
                          B2 change = SoV2*(koffB2*TB2 - konB2*B2*T2).
                          TB1 change= (konB1*B1*T1 - koffB1*TB1 - kTB12*TB1 + kTB21*TB2) ;
                          TB2 change= (konB2*B2*T2 - koffB2*TB2 + kTB12*TB1 - kTB21*TB2) ;
STAT_FlowYes: STATISTICS: FLOW must be YES for this calculation to be performed.
    (1) A only            Cin = Ain, Cout = Aout.
    (2) B only            Cin = Bin, Cout = Bout.
    (3) A and B           Cin = Ain+Bin, Cout = Aout+Bout;
    The area, mean transit time and relative dispersion are calculated for Cin and Cout.
    In addition, the system transit time and relative dispersion are calculated.

   WARNING: An additional thermodynamic constraint is not included in the model.  
   For a passive transporter, the transport rate constants should satisfy
   the following constraints:
  
   kTA12*kT21*konA1*koffA2
   ------------------------ = 1    (1)  see TestA
   kTA21*kT12*koffA1*konA2
  
   kTB12*kT21*konB1*koffB2
   ------------------------ = 1    (2)  see TestB
   kTB21*kT12*koffB1*konB2
  
   These constraints ensure that the model runs to equlibrium at steady-state.
   If these ratios deviate from 1, the model will run to a steady-state
   net concentration gradient.  This would be the case if the transporter
   is coupled to a energy source, which is not explicitly modeled here.
     

Equations

Not displayed here.

 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.