Facilitating Transporter for 2 competing solutes including binding steps. Shows countertransport facilitation/inhibition Enymatic conversion in V2.
Model number: 0010
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This model is a six state transporter model for 2 solutes in competition. Two solute species compete for the transporter site on either side of a membrane between two mixing chambers. In chamber 2 A is reacted to form B in an enzymatic reaction approximated by a Michaelis Menten expression, and without any accounting for binding of substrate or product to the enzyme. When the rates of conformational state change for transmembrane flipping of TA and TB are high compared to that for uncomplexed transporter T, then the model behaves much like an obligatory countertransporter, exchanging B for A across the membrane; MODEL VERIFICATION: Total Mass is conserved: Substrate in solution is totalled as SubstrateV, and substrate bound to transporter as SubstrateM, for membrane bound. Total transporter conservation is forced through the equation for T2. 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.
Ordinary Differential Equations
Ordinary Differential Equations
Transporter Mass Conservation
Substrate Mass Conservation Check
WARNING: Thermodynamic constraint are not included in the model. For a passive transporter, the transport rate constants should satisfy the following constraints:
The equations for this model may also be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.
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.
- TransComp2: 2 compartments, flow/no flow, 1 or 2 solutes, 2 types of reactions, 6 types of transporters
- Comp2Exchange: 2 compartments, no flow, 1 solute, 2 sided passive transporter
- Comp2FlowExchange: 2 compartments, with flow, 1 solute, 2 sided passive transporter
- Comp2ExchangeReaction: 2 compartments, no flow, 2 solutes, 2 sided passive transporter
- Comp2FlowExchangeReaction: 2 compartments, with flow, 2 solutes, 2 sided passive transporter
- Comp2FlowMMExchangeReaction: 2 compartments, with flow, 2 solutes, 4 single 1 sided Michaelis-Menten transporters
- BTEX20: 2 distributed regions (PDE), with flow, 1 solute, 2 sided passive transporter
- CTEX20: 2 distributed regions (serially connected ODEs), with flow, 1 solute, 2 sided passive transporter
- CTEX20b: 2 distributed regions (serially connected ODEs), with flow, 1 solute, 2 sided passive and 1 sided Michaelis-Menten transporter
- No Flow
- TranspMM1sidedComp2: 2 compartments, no flow, 1 solute, 1 sided MM transporter
- TranspMM.2sided.Comp2: 2 compartments, no flow, 1 solute, both 1 sided and 2 sided MM transporters
- With Flow
- 1 solute
- Transp1sol.Comp2: 2 compartments, no flow, 1 solute, T1-T2 transporter
- Transp1sol.Comp2F: 2 compartments, with flow, 1 solute, T1-T2 transporter
- Two solutes
- Transp2sol.Comp2: 2 compartments, no flow, 2 solutes, competitive T1-T2 transporter
- Transp2sol.Comp2: 2 compartments, with flow, 2 solutes, competitive T1-T2 transporter
- Transp2sol.Distrib2F: 2 regions with flow, 2 solutes, both T1-T2 and passive transporters, Michaelis-Menten enzymatic reaction, Counter-Transport Faciliation
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[This page was last modified 02Nov16, 3:07 pm.]
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