A mathematical model of pregnancy recognition in mammals

In this paper we develop a mathematical model of the luteal phase of the reproductive cycle in mammals with the aim to generate a systems understanding of pregnancy recognition. Pregnancy recognition is initiated by the production of interferon tau (IFNτ) by the growing conceptus. This ensures that the maternal corpus luteum (CL) remains viable to secrete progesterone, which is critical for providing a uterine microenvironment suitable for embryonic growth. Our mathematical model describes the interactions among the CL, the reproductive hormones and the hormone receptors in the uterus. It also characterises the complex interactions amongst the uterine oestrogen, progesterone and oxytocin receptors that control the sensitivity of the uterus to oestrogen, progesterone and oxytocin, respectively. The model is represented by a dynamical system and exhibits qualitative features consistent with the known experimental results in sheep. A key factor identified was a time-dependent threshold for the IFNτ signal below which the presence of the embryo might not be recognised and thus pregnancy would likely fail. Furthermore, the model indicated that if the IFNτ signal is later than around day 13 of the cycle, then pregnancy will not be recognised irrespective of the IFNτ concentration. The thresholds in the concentration and time of the IFNτ signal is a screening mechanism whereby only embryos of sufficient quality are able to prevent luteolysis (i.e. regression of the CL). The effect of progesterone secretion rate from the CL on pregnancy recognition was investigated. The model suggests that if the secretion rate is low then the initiation of the IFNτ signal is delayed, which in turn compromises the likelihood of a pregnancy being recognised by the CL. Furthermore, pregnancy recognition does not occur below a critical threshold in the progesterone secretion rate. In summary, the model can be used to identify the most favourable conditions for pregnancy recognition.