ataullahkhanov1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000054) Biomodels notes: The model reproduces ion and adenylate pool concentration corresponding to line 2 of Fig 3 of the publication. This model was tested successfully on Jarnac JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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A possible role of adenylate metabolism in human erythrocytes: simple mathematical model.

  • Fazoil I Ataullakhanov
  • Svetlana V Komarova
  • VM Vitvitsky
J. Theor. Biol. 1996; 179 (1): 75
Abstract
A simplified mathematical model of cell metabolism describing ion pump, glycolysis and adenylate metabolism was developed and investigated in order to clarify the functional role of the adenylate metabolism system in human erythrocytes. The adenylate metabolism system was shown to be able to function as a specific regulatory system stabilizing intracellular ion concentration and, hence, erythrocyte volume under changes in the permeability of cell membrane. This stabilization is provided via an increase in adenylate pool in association with ATPases rate elevation. Proper regulation of adenylate pool size might be achieved even in the case when AMP synthesis rate remains constant and only AMP degradation rate varies. The best stabilization of intracellular ion concentration in the model is attained when the rate of AMP destruction is directly proportional to ATP concentration and is inversely proportional to AMP concentration. An optimal rate of adenylate metabolism in erythrocytes ranges from several tenths of a percent to several percent of the glycolytic flux. An increase in this rate results in deterioration of cell metabolism stability. Decrease in the rate of adenylate metabolism makes the functioning of this metabolic system inefficient, because the time necessary to achieve stabilization of intracellular ion concentration becomes comparable with erythrocyte life span.

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
0.001 mole
3600.0 second
Id Name Spatial dimensions Size
cell Erythrocyte 3.0 1.0
Id Name Initial quantity Compartment Fixed
A Adenylate pool 1.11 cell (Erythrocyte)
E Energy pool 2.1 cell (Erythrocyte)
I Ions 10.0 cell (Erythrocyte)

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
U1 Passive ion influx ∅ > I

cell * P * J
U2 ATP consumption by ion pump {3.0}I + E > ∅

cell * W2 * I * T
U3 ATP from glycolysis ∅ > E

cell * W3 * pow(T, 0.52) * pow(M, 0.41)
U6_plus_3U7 AMP synthesis de novo E > ∅

cell * 2 * U
U6_plus_U7_minus_U8 Adenylate pool ∅ > A

cell * U * (1 - W * pow(T, n) * pow(M, k))

Global parameters

Id Value
J 100.0
M 0.01
P 0.121
T 1.0
U 0.02
W 0.01
W2 0.2
W3 13.48
k -1.0
n 1.2

Local parameters

Id Value Reaction

Assignment rules

Definition
T = (A + 3.0 * E - pow(6.0 * A * E - 3.0 * pow(E, 2.0) + pow(A, 2.0), 0.5)) / 6.0
M = (7.0 * A - 3.0 * E - pow(6.0 * A * E - 3.0 * pow(E, 2.0) + pow(A, 2.0), 0.5)) / 6.0

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments