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A mathematical model quantifying GnRH-induced LH secretion from gonadotropes.

  • JJ Blum
  • Michael C Reed
  • JA Janovick
  • PM Conn
Am. J. Physiol. Endocrinol. Metab. 2000; 278 (2):
Abstract
A mathematical model is developed to investigate the rate of release of luteinizing hormone (LH) from pituitary gonadotropes in response to short pulses of gonadotropin-releasing hormone (GnRH). The model includes binding of the hormone to its receptor, dimerization, interaction with a G protein, production of inositol 1,4, 5-trisphosphate, release of Ca(2+) from the endoplasmic reticulum, entrance of Ca(2+) into the cytosol via voltage-gated membrane channels, pumping of Ca(2+) out of the cytosol via membrane and endoplasmic reticulum pumps, and release of LH. Cytosolic Ca(2+) dynamics are simplified (i.e., oscillations are not included in the model), and it is assumed that there is only one pool of releasable LH. Despite these and other simplifications, the model explains the qualitative features of LH release in response to GnRH pulses of various durations and different concentrations in the presence and absence of external Ca(2+).

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
60.0 second
1e-09 mole
0.016666666666666666 second^(-1.0)
Id Name Spatial dimensions Size
cell cell 3.0 1.0
Id Name Initial quantity Compartment Fixed
CHO CHO 0.0 cell (cell)
E E 0.0 cell (cell)
GQ GQ 0.1 cell (cell)
H H 1.0 cell (cell)
HR HR 0.0 cell (cell)
HRRH HRRH 0.0 cell (cell)
IP3 IP3 0.0 cell (cell)
R R 0.01 cell (cell)

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
reaction_0 H binding to R H + R = HR

cell * (k1 * H * R - k2 * HR)
reaction_1 HR forming HRRH {2.0}HR = HRRH

cell * (k1 * pow(HR, 2) - k2 * HRRH)
reaction_2 G protein react with dimer producing E HRRH + GQ = E

cell * (k1 * HRRH * GQ - k2 * E)
reaction_3 IP3 converted into inactive metabolites IP3 > ∅

cell * k1 * IP3
reaction_4 Production of IP3 ∅ > IP3

cell * k * E

Global parameters

Id Value
alpha 2.0 substance
beta 4.0

Local parameters

Id Value Reaction
k1 2.5 reaction_0 (H binding to R)
k2 5.0 reaction_0 (H binding to R)
k1 2500.0 reaction_1 (HR forming HRRH)
k2 5.0 reaction_1 (HR forming HRRH)
k1 4000.0 reaction_2 (G protein react with dimer producing E)
k2 200.0 reaction_2 (G protein react with dimer producing E)
k1 10.0 reaction_3 (IP3 converted into inactive metabolites)
k 20000000.0 reaction_4 (Production of IP3)

Assignment rules

Definition
CHO = 0.001 * alpha * IP3 * (0.3 + 0.3 * beta * time * exp(1.0 - beta * time)) / (1.0 + 0.001 * alpha * IP3)

Rate rules

Definition

Algebraic rules

Definition
Definition
Trigger Assignments
gt(time, 5) H = 0