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A kinetic study of a ternary cycle between adenine nucleotides
Edelmira Valero1, Ramo ́ n Varo ́ n1 and Francisco Garcı ́a-Carmona2
1 Departamento de Qu ́ımica-F ́ısica, Escuela Polite ́cnica Superior de Albacete, Universidad de Castilla-La Mancha, Albacete, Spain 2 Departamento de Bioqu ́ımica y Biolog ́ıa Molecular A, Facultad de Biolog ́ıa, Universidad de Murcia, Spain
In the present paper, a kinetic study is made of the behavior of a moiety- conserved ternary cycle between the adenine nucleotides. The system con- tains the enzymes S-acetyl coenzyme A synthetase, adenylate kinase and pyruvate kinase, and converts ATP into AMP, then into ADP and finally back to ATP. l-Lactate dehydrogenase is added to the system to enable continuous monitoring of the progress of the reaction. The cycle cannot work when the only recycling substrate in the reaction medium is AMP. A mathematical model is proposed whose kinetic behavior has been analyzed both numerically by integration of the nonlinear differential equations describing the kinetics of the reactions involved, and analytically under steady-state conditions, with good agreement with the experimental results being obtained. The data obtained showed that there is a threshold value of the S-acetyl coenzyme A synthetase⁄adenylate kinase ratio, above which the cycle stops because all the recycling substrate has been accumulated as AMP, never reaching the steady state. In addition, the concept of adenylate energy charge has been applied to the system, obtaining the enabled values of the rate constants for a fixed adenylate energy charge value and vice versa.
FEBS Journal 273 (2006) 3598–3613
Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.
| Name | Definition | |
|---|---|---|
| — | 1e-06 mole | |
| — | 1.0 second | |
| — | 1.0 litre | |
| — | 1e-06 mole litre^(-1.0) |
| Id | Name | Spatial dimensions | Size | |
|---|---|---|---|---|
| default_compartment | — | 3.0 | 1.0 L |
| Id | Name | Initial quantity | Compartment | Fixed | |
|---|---|---|---|---|---|
| ADP | — | 0.0 umol/L | default_compartment | ✘ | |
| AMP | — | 0.0 umol/L | default_compartment | ✘ | |
| ATP | — | 16.3 umol/L | default_compartment | ✘ | |
| Lac | — | 0.0 umol/L | default_compartment | ✔ | |
| NADH | NADH | 1.0 umol/L | default_compartment | ✘ | |
| Pyr | — | 0.0 umol/L | default_compartment | ✘ |
Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.
| Definition |
|---|
| Id | Name | Objective coefficient | Reaction Equation and Kinetic Law | Flux bounds | |
|---|---|---|---|---|---|
| v_1 | — | ATP = AMP Vmapp1*ATP/(Kmapp1 + ATP) | |||
| v_2 | — | ATP + AMP = {2.0}ADP Vm2*ATP*AMP/(K + Km2ATP*AMP + Km2AMP*ATP + ATP*AMP) | |||
| v_3 | — | ADP = ATP + Pyr Vmapp3*ADP/(Kmapp3 + ADP) | |||
| v_4 | — | Pyr + NADH = Lac k4*Pyr |
| Id | Value | |
|---|---|---|
| K | 71000.0 | |
| Km2AMP | 110.0 | |
| Km2ATP | 25.0 | |
| Kmapp1 | 700.0 | |
| Kmapp3 | 260.0 | |
| Vm2 | 170.0 | |
| Vmapp1 | 2.3 | |
| Vmapp3 | 65.0 | |
| k4 | 5.0 |
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