An acute response of LH to a stimulatory pulse of GnRH is modelled as a result of a pathway (Pathway I) that consists of two compartments including a single (rate limiting) intermediate. In addition, a second pathway (Pathway II) was added, consisting of an intermediate transcription factor and subsequently a synthesised protein. Pathway II had a delayed effect on LH release due to the time taken to produce the intermediate protein. The model included synergism between these two pathways, which yielded an augmented response. The model accounts for a number of observations, including GnRH self-priming and the biphasic pattern of LH response. The same model was used to fit the data of the LH response when gonadotrophs responded to the addition of oxytocin in the response with a shoulder on the profile. Pathway I is able to be conceptualised as the basic Ca2+-mediated pathway. Pathway II contains features characteristic of the cAMP-mediated pathway. Thus, we have provided an explanation for details of the nature of the profile of LH secretion and additionally enabled incorporation of cAMP in an integrating model. The study investigated the possibility of two interacting pathways being at the basis of both the shoulder on the LH surges and self-priming, and the model illustrates that this appears to be highly likely.
The release of luteinising hormone (LH) from gonadotrophs is central to reproductive function. LH exhibits an episodic pattern, which is a result of gonadotropin-releasing hormone (GnRH) being transported from the hypothalamus to the pituitary in pulses. Following GnRH occupation of its cognate receptor on gonadotrophs, its stimulatory signal is transduced to the cell utilising associated intracellular pathways [
We produced a set of detailed data of the response in vitro, and for the model, we took note of the characteristics of the response: (i) a shoulder is present in the declining phase, (ii) enhancement occurs in a primed pulse, (iii) the enhancement is delayed; that is, by definition it did not occur at the initial pulse. We developed a model in which there are two pathways, Pathway I, which elicits a rapid LH response, and Pathway II, which has an effect that is delayed. The model required that the pathways interact and synergise.
We conceptualised a biological mechanism that was consistent with the model. The Ca2+-mediated pathway may be considered to be represented by Pathway I in our model. Our model is also consistent with additional effects being mediated by cyclic AMP, in whuch cAMP-mediated processes were noted to have characteristics of Pathway II. We then conceptualised the process of self-priming as being due to crosstalk between the Ca2+-mediated pathway and the cAMP/PKA pathway.
We produced a distilled model which can be interpreted as incorporating parallel effects of GnRH on LH release (Ca2+-stimulated exocytosis) and protein synthesis (cAMP transcription/translation). Oxytocin enhances the LH response to GnRH [
To take into account the dynamic nature of the LH response, our model is based primarily on data from perifusion studies [
A schematic diagram of our model is shown in Figure
The elements of the interaction model. GnRH activates two pathways in this model, which synergize to produce an augmented LH response.
Only those salient parameters that are essential and consistent with the model’s ability to describe the experimental results are included. The introduction of more intermediates and thence parameters would make no difference to the model.
The release of LH by Pathway I is described by two compartments. The first comprises the processes from GnRH stimulation to formation of an intermediate, and the second compartment results in the release of LH. An instantaneous impulsive input of GnRH is assumed; it is straightforward to account for a finite duration of input of GnRH. The rate of production of LH can be assumed to depend on a rate limiting step that produces the intermediate,
The time parameter
The LH response to two pulses of GnRH by halved hemipituitaries illustrating GnRH self-priming. The black bar shows the onset and duration of the GnRH pulse. (a) LH response to two GnRH pulses. (b) LH response to two GnRH pulses and continuous presence of oxytocin.
In practice as the concentration of GnRH increases, there is a maximum level of response that the LH secretory process can attain, which may be called saturation of the response. Therefore, the response of LH to GnRH is in general nonlinear. A saturation nonlinearity for the response to the GnRH input may then be incorporated into the model. However, it appears that nonlinearity does not substantially affect the basic shape of the intermediate response to GnRH [
The model for Pathway I may also be extended to contain three or more compartments with the inclusion of additional intermediates. However, for the purposes of this study, a two-compartment model is satisfactory as we examine the longer term behaviour of the response to GnRH rather than the short-to-medium term responses considered by other authors [
The kinetics of this pathway, once initiated, is assumed to be similar to that of Pathway I. Pathway II will involve steps that cause a delay at which LH is available, in particular, the transfer of the signal through transcription factors and protein synthesis. This means that effectively (for purposes of the model) it takes longer to initiate a detectable LH response, so a time lag,
The intermediate
We note the model for Pathway I does not account for the presence of a shoulder in LH concentrations seen in the perifusion data. This is also the case when there is a nonlinearity in the response to GnRH or alternatively an additional compartment is incorporated in the model. Therefore, we modelled an interaction between Pathway I and the second pathway, Pathway II, that will produce both the effects of the shoulder and priming; this is done in Section
To simulate the experimental results, it is necessary to achieve a model that combines the pathways. To provide the priming and synergistic effects seen in the experiments, it is appropriate for the slow pathway to augment the fast pathway for the first intermediate. A combined model is formulated for one LH surge by augmenting the response of the intermediate on Pathway I at a level proportional to the concentration of the intermediate protein of Pathway II. The combined pathway model is then
When multiple GnRH surges occur, say
The model was extended further to include the effect of exposure to oxytocin. To model the effect of oxytocin, a new parameter (OT) was added to the model, representing both the concentration of oxytocin (present from
The raw data [
The mathematical model described in Methods is discussed in Section
Firstly, numerical integration of (
The optimal solution to the interaction model, (
To illustrate that the model would fit the two surge data better, the model was adapted to allow for both surges to be considered. This was done by optimising the parameters from equation (10) from the data for both surges, with the second surge to occur at time
A new initial value of LH concentration
The optimal solution to the interaction model, (
We next illustrate how well the model could fit the two surge data when the oxytocin data was used to optimise over all parameters; then
Taking the optimal parameter values obtained across the data sets for GnRH only and GnRH plus oxytocin produces
To test the validity of the optimal values found from our computer programme pseudo-random Gaussian noise was added to the simulated LH points predicted by the model with these optimal parameter values, using the Monte Carlo method. By repeating this 10 times, 10 new datasets were obtained and for each, the model was optimised to obtain 10 new sets of parameters. For GnRH only, the parameter values converged to the true values as the hypothetical experimental error was reduced. 96 per cent of the 95% confidence intervals contained the true value. This result supports the validity of the optimal parameter values obtained. For GnRH plus oxytocin 92 percent of the 95% confidence intervals contained the true value. This again supports the validity of the optimal parameter values obtained.
To test the possibility that nonindependent variation of parameters occurred in the experimental data, parameters for each of the six individual experimental datasets were optimised and average and SDs of the values were determined. The mean parameter values obtained from optimal values for individual datasets were compared to the optimal parameter values obtained from the mean of the data. All of the 95% confidence intervals around these mean parameter values included the optimal value. When the set of parameters for GnRH only was compared to that for GnRH plus oxytocin, the only significant difference was associated with the presence of oxytocin. Thus, the results of the model reflected the proposed biological mechanisms.
It is also possible to examine the input of constant GnRH over an extended period in the model. Indeed a biphasic response similar to that inherent in our model is observed in experiments [
We can conceptualise Pathway I representing a rapid Ca2+ pathway and Pathway II being a pathway involving cAMP. Processes involving the cAMP pathway have been observed to have a progressive development over time. The delay in the effect of cAMP in inducing a visible change in LH secretion is consistent with the model as a result of the time taken for additional processes required for development of the response. The sequence of events in the cAMP-mediated pathway includes activation of PKA, its translocation to the nucleus, induction of a transcription factor such as cAMP response element binding protein (CREB) [
The model was used to see how it provided predictive capability and it was found that when the model was fitted to the first LH surge only, it was able to predict the second surge with good accuracy (see Figure
The effect of oxytocin was such that the same model was able to be used and the mechanism predicted an increase in the value of parameter
With oxytocin exposure, there was an increase in the value of
To further illustrate the predictive ability of our model, we show in Figure
Multiple GnRH pulses simulation using the optimal parameters of Figure
Multiple GnRH pulses with pulses after the first spaced 60 minutes apart
Multiple GnRH pulses with pulses after the first spaced 60 minutes apart
Multiple GnRH pulses with pulses after the first spaced 60 minutes apart. In this case the term
Finally, in Figure
Such observations as those in the previous section suggest further potential to investigate other peptides that also interact with GnRH and which enhance GnRH-stimulated LH secretion, for example, pituitary adenylate cyclase-activating polypeptide (PACAP). PACAP stimulates cAMP expression with a time course in which the cAMP peaks at approximately 30 min [
It would be possible to also apply the model to the LH profile resulting from the response to two pulses of GnRH produced in the presence of gonadotrophin surge attenuating/inhibiting factor (GnSAF) [
Our modelling has provided a system that explains a number of diverse aspects of the LH response: (1) GnRH self-priming; (2) a delayed effect following exposure to GnRH; (3) a shoulder on the declining phase of the response [
In the presence of oxytocin, it was shown that there was an increase in the value of
The model presented here that incorporates two pathways, designated Pathways I and II, which when conceptualised as an interaction between the Ca2+ and the cAMP/PKA pathways, neatly explains the augmentation of the LH response resulting from the activation of cAMP and enables the coherent interpretation of investigations into the role of cAMP in the LH response to GnRH. Extra understanding of interactions between cAMP and other systems is expected to further the model analysis. Recent molecular studies have concluded that interaction between Ca2+ and cAMP may be important [
In early investigations of the mechanism(s) of the LH response to GnRH, cAMP was investigated as an obvious candidate. Many of the attempts which sought to establish its role resulted in negative conclusions [
The self-priming response to GnRH, but not the initial response, involved protein synthesis [
Hence, it is consistent that controversy regarding the role of cAMP in modulation of LH secretion can be considered to be
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by grants from the NZ Lottery Health Committee, Canterbury Medical Research Foundation, and NZ Health Research Council. The authors thank Dr. T. J. Connolly for the helpful assistance in developing the model.