A mathematical model for LH release in response to continuous and pulsatile exposure of gonadotrophs to GnRH

Abstract

In a previous study, a model was developed to investigate the release of luteinizing hormone (LH) from pituitary cells in response to a short pulse of gonadotropin-releasing hormone (GnRH). The model included: binding of GnRH to its receptor (R), dimerization and internalization of the hormone receptor complex, interaction with a G protein, production of inositol 1,4,5-trisphosphate (IP3), release of calcium from the endoplasmic reticulum (ER), entrance of calcium into the cytosol via voltage gated membrane channels, pumping of calcium out of the cytosol via membrane and ER pumps, and release of LH. The extended model, presented in this paper, also includes the following physiologically important phenomena: desensitization of calcium channels; internalization of the dimerized receptors and recycling of some of the internalized receptors; an increase in Gq concentration near the plasma membrane in response to receptor dimerization; and basal rates of synthesis and degradation of the receptors. With suitable choices of the parameters, good agreement with a variety of experimental data of the LH release pattern in response to pulses of various durations, repetition rates, and concentrations of GnRH were obtained. The mathematical model allows us to assess the effects of internalization and desensitization on the shapes and time courses of LH response curves.

Figure 1

Amount of LH released in five minute intervals in response to constant exposure to 5 nM GnRH. The solid circles show the results of the present model while the open circles show the results of the original model [1]. The decay of LH release to zero is in accord with experimental results (see discussion in text); thus, new mechanisms included in the present model allow one to match this data (and other data, see other figures) from several laboratories for medium-term GnRH exposure experiments.

Figure 4

Experimental data of Hawes et al.[21]. Gonadotrophs were treated continuously with lO nM GnRH (Panel A), with 5 minute pulses every 30 minutes (Panel B), or every 15 minutes (Panel C).

Figure 2

Panel A shows the total amount of LH released as a function of time during continuous exposure to 5 nM GnRH, while Panel B shows the instantaneous rate of LH release at each moment of time. Panels C and D show the calcium concentration in the cytosol and the endoplasmic reticulum, respectively. Panels E and F show the fraction of open calcium channels in the outer membrane and the endoplasmic reticulum, respectively. The solid lines show the results of the present model while the dashed lines show the results of the earlier model [1].

Figure 3

Panels A, C, and D show the concentrations of free, bound, and dimerized receptors, respectively, while Panel B shows the total amount of receptors in the membrane. Panel E shows the concentration of IP3. Panel F shows the GQ concentration at the membrane as a function of time during the continuous exposure to 5 nM GnRH. The solid lines show the results of the current model and the dashed lines show the results of the earlier model in [1].

Figure 5

Experimental data of Baird et al.[22]. Panels A and B show the response of pubertal rat and hamster anterior pituitary cells, respectively, to six minute pulses of 10 nM GnRH.

Figure 6

Amount of LH released as a function of time during a series of 5 minute pulses of 5 nM GnRH every 15 minutes. Open circles are the original model results and solid circles are the current model results.

Figure 7

Model responses to a series of 5 minute pulses of 5 nM GnRH every 15 minutes.

Figure 8

Model responses to a series of 5 minute pulses of 5 nM GnRH every 15 minutes.

Figure 9

Dependence of desensitization on GnRH concentration and pulse frequency. Panels A, B, and C show model LH outputs in response to 5 minutes pulses of GnRH at pulse periods of 15 (Panel A), 30 (Panel B), and 60(Panel C) minutes. Each panel shows responses to 10 nM(*), 1 nM(+), and O.1 nM(○) GnRH.

Figure 10

LH released during 2 minute pulses of GnRH administered every 30 minutes at the indicated increasing concentrations of GnRH.

Figure 11

Total LH released after a 1 hour (open circles) and 2 hour (closed circles) continuous exposure to the concentrations of GnRH shown on the abscissa.

Figure 12

LH released in the model in response to 20 minute pulses of 100 nM GnRH administered every hour.

Figure 13

LH released during constant exposure (Panel A) and to 5 minute pulses every 15 minutes (Panel B) to 5 nM GnRH. Open circles indicate the model with no desensiti-zation of calcium channels in outer membrane (v₁ = 0 and v₂ = 0); solid circles indicate the model with calcium channel desensitization but with no internalization of receptors (k₁₁ = 0); open squares indicate the full model.

Figure 14

Panel A shows the results of an experiment of Stojilkovic et al.[19] in which rat pituitary cells were exposed to two 30 minute pulses of 100 nM GnRH at one hour intervals. Panel B shows the response of the present model to the same pulses. If, how-ever, the rate of recovery of the calcium channels in the outer membrane is increased from v₂ = 0.002 min^-1 to v₂ = 0.02 min^-1 and the rate internalization of receptors is decreased from k₁₁ = 0.08/n nM^-1·min^-1 to k₁₁ = 0.04/n nM^-1·min^-1, then the present model gives responses (Panel C) similar to the exerperimental results in Panel A. The ordinate units for Panels B and C are ng.

Figure 15

Panel A shows the results of an experiment of Stojilkovic et al. [6] in which rat pituitary cells were exposed to two 30 minute pulses of 100 nM endothelin at one hour intervals. Note that the response to Endothelin is markedly different than the response to GnRH in Panel A of Figure 14. If we change the present model by increasing in internalization of receptors (k₁₁ = 0.8/n nM^-1·min^-1) and a decreasing the return of internalized receptors (from 60% to 10%), then the model (Panel B) closely approximates the experimental results. The ordinate units for Panels B are ng.

Figure 16

Model responses to six minutes pulses of 10 nM GnRH every 30 minutes with the standard parameters (crosses), with v₁ changed from 0.02/min to 0.005/min (stars) or to 0.05/min (open circles). The weak desensitization (stars) is similar to that of the rat in the experiments of Baird et al.[22](our Figure 5A) and the strong desensitization (open circles) is similar to that seen in the hamster (our Figure 5B).