A mathematical model of luteinizing hormone release from ovine pituitary cells in perifusion

A mathematical model of luteinizing hormone release from ovine pituitary cells in perifusion

Model Structure

One of the quintessential characteristics of reproductive hormones is their pulsatile nature. Semi-regular pulses of gonadotropin releasing hormone (GnRH) are secreted from the hypothalamus at varying frequencies, usually about once an hour, and the hormone travels through the portal circulation to the pituitary where it stimulates the release of luteinizing hormone (LH). LH secretion is also often semi-regular and pulsatile, although the presence of high-frequency or continuous GnRH the GnRH-LH relationship is disrupted and LH synthesis is reduced in a process called desensitisation. In turn, reduced concentrations of LH delay follicular development, steroid production and ovulation.

The complexity of the GnRH-LH relationship lends itself to mathematical modelling, with the hope that a theoretical approach can further support experimental results. In the paper described here, Heinze et al. present a mathematical model of luteinizing hormone release from ovine pituitary cells in perifusion. The model consists of a system of nonlinear differential equations and incorporates two different possible mechanisms to account for the observed disruption of the GnRH-LH relationship in the presence of continuous GnRH exposure.

The original publication contains three different mathematical models:

  • The first represents the core model which describes the basic dynamics of GnRH-receptor binding in the pituitary and the subsequent release of LH. It includes two different possible mechanisms to account for the observed disruption of the GnRH-LH relationship in the presence of continuous GnRH exposure:

  • a) a desensitised receptor, and

  • b) a limited, yet replenishable, pool of releasable LH

  • In the second model the constant addition of LH to the releasable pool is removed such that it becomes exhaustable.

  • Finally, in the third model the desensitised receptor is removed.

There was good agreement between experimental data and simulation results for all three models. Consideration of the latter two models revealed the desensitised receptor (model 2) had a significant effect on the LH levels. Furthermore, the LH replenishment mechanism also had a significant effect in three of the four scenarios tested.

Schematic diagram of the components and reactions involved in the first model of luteinizing hormone (LH) release. kfb, kdf, and kbd are kinetic constants, F, B, and D represent the free, bound, and desensitised states of the gonadotropin-releasing hormone (GnRH) receptor, while R represents releasable LH and B is bound LH. s is the rate of the reaction, a1 determines the rate of basal LH secretion and a2 is the rate of LH secretion in the presence of bound receptor.

The complete original paper reference is cited below:

A mathematical model of luteinizing hormone release from ovine pituitary cells in perifusion, K. Heinze, R. W. Keener, and A. R. Midgley, Jr., 1998, American Journal of Physiology , 275, E1061-E1071. (Full text and PDF versions of the article are available to journal subscribers on the American Journal of Physiology website.) PubMed ID: 9843750

The CellML model presented here represents the first model. The other two models have also been coded in CellML and can be downloaded as version 1 variants 1 and 2 of the model.