Hindawi Publishing Corporation International Journal of Endocrinology Volume 2013, Article ID 410348, 10 pages http://dx.doi.org/10.1155/2013/410348 Research Article A Two-Pathway Mathematical Model of the LH Response to GnRH that Predicts Self-Priming J. J. Evans, 1,2,3 T. M. Wilkinson, 3,4 and D. J. N. Wall 4,5 1 Centre for Neuroendocrinology, University of Otago, Christchurch, New Zealand 2 MacDiarmid Institute for Advanced Materials and Nanoengineering, University of Otago, Christchurch, New Zealand 3 Department of Obstetrics and Gynaecology, University of Otago, Christchurch, New Zealand 4 Biomathematics Research Centre, University of Canterbury, Christchurch, New Zealand 5 Department of Mathematics, University of Canterbury, Christchurch, New Zealand Correspondence should be addressed to J. J. Evans; john.evans@otago.ac.nz Received 22 August 2013; Accepted 2 October 2013 Academic Editor: Stanko S. Stojilkovic Copyright © 2013 J. J. Evans et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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 efect on LH release due to the time taken to produce the intermediate protein. Te model included synergism between these two pathways, which yielded an augmented response. Te model accounts for a number of observations, including GnRH self-priming and the biphasic pattern of LH response. Te same model was used to ft the data of the LH response when gonadotrophs responded to the addition of oxytocin in the response with a shoulder on the profle. Pathway I is able to be conceptualised as the basic Ca 2+ -mediated pathway. Pathway II contains features characteristic of the cAMP-mediated pathway. Tus, we have provided an explanation for details of the nature of the profle of LH secretion and additionally enabled incorporation of cAMP in an integrating model. Te 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. 1. Introduction Te 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 trans- duced to the cell utilising associated intracellular pathways [1] and secretion of luteinising hormone (LH) occurs. In an oestrogenised environment, a process called GnRH self- priming occurs, whereby an initial pulse of GnRH primes the gonadotrophs in readiness for a subsequent pulse of GnRH. Te complexity is such that it is impossible to establish the detailed components of a stimulatory pulse of GnRH with simple reductionist concepts. Some laboratories have begun to construct mathematical models of the processes that are involved. We document here a model that applies to the female gonadotrophs in the preovulatory, oestrogenised state. 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 defnition 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 efect that is delayed. Te model required that the pathways interact and synergise. We conceptualised a biological mechanism that was consistent with the model. Te Ca 2+ -mediated pathway may be considered to be represented by Pathway I in our model. Our model is also consistent with additional efects being mediated by cyclic AMP, in whuch cAMP-mediated processes were noted to have characteristics of Pathway II. We then