Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis

Reduced model for female endocrine dynamics: Validation and functional variations

A normally functioning menstrual cycle requires significant crosstalk between hormones originating in ovarian and brain tissues. Reproductive hormone dysregulation may cause abnormal function and sometimes infertility. The inherent complexity in this endocrine system is a challenge to identifying mechanisms of cycle disruption, particularly given the large number of unknown parameters in existing mathematical models. We develop a new endocrine model to limit model complexity and use simulated distributions of unknown parameters for model analysis. By employing a comprehensive model evaluation, we identify a collection of mechanisms that differentiate normal and abnormal phenotypes. We also discover an intermediate phenotype-displaying relatively normal hormone levels and cycle dynamics-that is grouped statistically with the irregular phenotype. Results provide insight into how clinical symptoms associated with ovulatory disruption may not be detected through hormone measurements alone.

Integrating theoretical and empirical approaches for a robust understanding of endocrine flexibility

There is growing interest in studying hormones beyond single 'snapshot' measurements, as recognition that individual variation in the endocrine response to environmental change may underlie many rapid, coordinated phenotypic changes. Repeated measures of hormone levels in individuals provide additional insight into individual variation in endocrine flexibility - that is, how individuals modulate hormone levels in response to the environment. The ability to quickly and appropriately modify phenotype is predicted to be favored by selection, especially in unpredictable environments. The need for repeated samples from individuals can make empirical studies of endocrine flexibility logistically challenging, but methods based in mathematical modeling can provide insights that circumvent these challenges. Our Review introduces and defines endocrine flexibility, reviews existing studies, makes suggestions for future empirical work, and recommends mathematical modeling approaches to complement empirical work and significantly advance our understanding. Mathematical modeling is not yet widely employed in endocrinology, but can be used to identify innovative areas for future research and generate novel predictions for empirical testing.

Mathematical modeling approaches of cellular endocrinology within the hypothalamo-pituitary-gonadal axis

The reproductive neuroendocrine axis, or hypothalamo-pituitary-gonadal (HPG) axis, is a paragon of complex biological system involving numerous cell types, spread over several anatomical levels communicating through entangled endocrine feedback loops. The HPG axis exhibits remarkable dynamic behaviors on multiple time and space scales, which are an inexhaustible source of studies for mathematical and computational biology. In this review, we will describe a variety of modeling approaches of the HPG axis from a cellular endocrinology viewpoint. We will in particular investigate the questions raised by some of the most striking features of the HPG axis: (i) the pulsatile secretion of hypothalamic and pituitary hormones, and its counterpart, the cell signaling induced by frequency-encoded hormonal signals, and (ii) the dual, gametogenic and glandular function of the gonads, which relies on the tight control of the somatic cell populations ensuring the proper maturation and timely release of the germ cells.

An integrate-and-fire model for pulsatility in the neuroendocrine system

A model for pulsatility in neuroendocrine regulation is proposed which combines Goodwin-type feedback control with impulsive input from neurons located in the hypothalamus. The impulsive neural input is modeled using an integrate-and-fire mechanism; namely, inputs are generated only when the membrane potential crosses a threshold, after which it is reset to baseline. The resultant model takes the form of a functional-differential equation with continuous and impulsive components. Despite the impulsive nature of the inputs, realistic hormone profiles are generated, including ultradian and circadian rhythms, pulsatile secretory patterns, and even chaotic dynamics.

Managing the Oocyte Meiotic Arrest-Lessons from Frogs and Jellyfish

During oocyte development, meiosis arrests in prophase of the first division for a remarkably prolonged period firstly during oocyte growth, and then when awaiting the appropriate hormonal signals for egg release. This prophase arrest is finally unlocked when locally produced maturation initiation hormones (MIHs) trigger entry into M-phase. Here, we assess the current knowledge of the successive cellular and molecular mechanisms responsible for keeping meiotic progression on hold. We focus on two model organisms, the amphibian Xenopus laevis, and the hydrozoan jellyfish Clytia hemisphaerica. Conserved mechanisms govern the initial meiotic programme of the oocyte prior to oocyte growth and also, much later, the onset of mitotic divisions, via activation of two key kinase systems: Cdk1-Cyclin B/Gwl (MPF) for M-phase activation and Mos-MAPkinase to orchestrate polar body formation and cytostatic (CSF) arrest. In contrast, maintenance of the prophase state of the fully-grown oocyte is assured by highly specific mechanisms, reflecting enormous variation between species in MIHs, MIH receptors and their immediate downstream signalling response. Convergence of multiple signalling pathway components to promote MPF activation in some oocytes, including Xenopus, is likely a heritage of the complex evolutionary history of spawning regulation, but also helps ensure a robust and reliable mechanism for gamete production.

Bridging the Data Gap From in vitro Toxicity Testing to Chemical Safety Assessment Through Computational Modeling

Chemical toxicity testing is moving steadily toward a human cell and organoid-based in vitro approach for reasons including scientific relevancy, efficiency, cost, and ethical rightfulness. Inferring human health risk from chemical exposure based on in vitro testing data is a challenging task, facing various data gaps along the way. This review identifies these gaps and makes a case for the in silico approach of computational dose-response and extrapolation modeling to address many of the challenges. Mathematical models that can mechanistically describe chemical toxicokinetics (TK) and toxicodynamics (TD), for both in vitro and in vivo conditions, are the founding pieces in this regard. Identifying toxicity pathways and in vitro point of departure (PoD) associated with adverse health outcomes requires an understanding of the molecular key events in the interacting transcriptome, proteome, and metabolome. Such an understanding will in turn help determine the sets of sensitive biomarkers to be measured in vitro and the scope of toxicity pathways to be modeled in silico. In vitro data reporting both pathway perturbation and chemical biokinetics in the culture medium serve to calibrate the toxicity pathway and virtual tissue models, which can then help predict PoDs in response to chemical dosimetry experienced by cells in vivo. Two types of in vitro to in vivo extrapolation (IVIVE) are needed. (1) For toxic effects involving systemic regulations, such as endocrine disruption, organism-level adverse outcome pathway (AOP) models are needed to extrapolate in vitro toxicity pathway perturbation to in vivo PoD. (2) Physiologically-based toxicokinetic (PBTK) modeling is needed to extrapolate in vitro PoD dose metrics into external doses for expected exposure scenarios. Linked PBTK and TD models can explore the parameter space to recapitulate human population variability in response to chemical insults. While challenges remain for applying these modeling tools to support in vitro toxicity testing, they open the door toward population-stratified and personalized risk assessment.

Coupling a reproductive function model to a productive function model to simulate lifetime performance in dairy cows

Reproductive success is a key component of lifetime performance in dairy cows but is difficult to predict due to interactions with productive function. Accordingly, this study introduces a dynamic model to simulate the productive and reproductive performance of a cow during her lifetime. The cow model consists of an existing productive function model (GARUNS) which is coupled to a new reproductive function model (RFM). The GARUNS model simulates the individual productive performance of a dairy cow throughout her lifespan. It provides, with a daily time step, changes in BW and composition, fetal growth, milk yield and composition and food intake. Genetic-scaling parameters are incorporated to scale individual performance and simulate differences within and between breeds. GARUNS responds to the discrete event signals 'conception' and 'death' (of embryo or fetus) generated by RFM. In turn, RFM responds to the GARUNS outputs concerning the cow's energetic status: the daily total processed metabolizable energy per kg BW (TPEW) and the net energy balance (EB). Reproductive function model models the reproductive system as a compartmental system transitioning between nine competence stages: prepubertal (PRPB), anestrous (ANST), anovulatory (ANOV), pre-ovulating (PREO), ovulating (OVUL), post-ovulating (PSTO), luteinizing (LUTZ), luteal (LUTL) and gestating (GEST). The transition from PRPB to ANST represents the start of reproductive activity at puberty. The cyclic path through ANST, PREO, OVUL, PSTO, LUTZ and LUTL forms the regime of ovulatory cycles, whereas ANOV and GEST are transient stages that interrupt this regime. Anovulatory refers explicitly to a stage in which ovulation cannot occur (i.e. interrupted cyclicity), whereas ANST is a pivotal stage within ovulatory cycles. Reproductive function model generates estradiol and progesterone hormonal profiles consistent with reference profiles derived from literature. Cyclicity is impacted by the GARUNS output EB and clearance of estradiol is impacted by TPEW. A farming system model was designed to describe different farm protocols of heat detection, insemination, feeding (amount and energy density), drying-off and culling. Results of model simulation (10 000 simulations of individual cows over 5000 days lifetime period, with randomly drawn genetic-scaling parameters and standard diet) are consistent with literature for reproductive performance. This model allows simulation of deviations in reproductive trajectories along physiological stages of the cow reproductive cycle. It thus provides the basis for evaluation of the relative importance of different factors affecting fertility at individual cow and herd levels across different breeds and management environments.