Mathematical model of FSH-induced cAMP production in ovarian follicles

A Mechanism for Ovulation Number Control

Every menstrual cycle, many follicles begin to develop but only a specific number ovulate. This ovulation number determines how many offspring are produced per litter, and differs between species. The physiological mechanism that controls ovulation number is unknown; a class of mathematical models can explain it, but these models have no physiological basis. Here, we suggest a physiological mechanism for ovulation number control, which enables selection of a specific number of follicles out of many, and analyze it in a mathematical model of follicular growth. The mechanism is based on a signal, intra-follicular androgen concentration, that measures follicle size relative to the other follicles. This signal has a biphasic effect, suppressing follicles that are too large or too small compared to others. The ovulation number is determined by the androgen inhibitory thresholds. The model has a scaling symmetry that explains why the dominant follicles grow linearly with time, as observed in human ultrasound data. This approach also explains how chronic hyperandrogenism disrupts ovulation in polycystic ovary syndrome (PCOS), a leading cause of infertility. We propose specific experiments for testing the proposed mechanism.

FSH Receptor Signaling: Complexity of Interactions and Signal Diversity

FSH is synthesized in the pituitary by gonadotrope cells. By binding to and interacting with its cognate receptor [FSH receptor (FSHR)] in the gonads, this gonadotropin plays a key role in the control of gonadal function and reproduction. Upon activation, the FSHR undergoes conformational changes leading to transduction of intracellular signals, including dissociation of G protein complexes into components and activation of several associated interacting partners, which concertedly regulate downstream effectors. The canonical Gs/cAMP/protein kinase A pathway, considered for a long time as the sole effector of FSHR-mediated signaling, is now viewed as one of several mechanisms employed by this receptor to transduce intracellular signals in response to the FSH stimulus. This complex network of signaling pathways allows for a fine-tuning regulation of the gonadotropic stimulus, where activation/inhibition of its multiple components vary depending on the cell context, cell developmental stage, and concentration of associated receptors and corresponding ligands. Activation of these multiple signaling modules eventually converge to the hormone-integrated biological response, including survival, proliferation and differentiation of target cells, synthesis and secretion of paracrine/autocrine regulators, and, at the molecular level, functional selectivity and differential gene expression. In this mini-review, we discuss the complexity of FSHR-mediated intracellular signals activated in response to ligand stimulation. A better understanding of the signaling pathways involved in FSH action might potentially influence the development of new therapeutic strategies for reproductive disorders.

Mathematical modeling of the female reproductive system: from oocyte to delivery

From ovulation to delivery, and through the menstrual cycle, the female reproductive system undergoes many dynamic changes to provide an optimal environment for the embryo to implant, and to develop successfully. It is difficult ethically and practically to observe the system over the timescales involved in growth and development (often hours to days). Even in carefully monitored conditions clinicians and biologists can only see snapshots of the development process. Mathematical models are emerging as a key means to supplement our knowledge of the reproductive process, and to tease apart complexity in the reproductive system. These models have been used successfully to test existing hypotheses regarding the mechanisms of female infertility and pathological fetal development, and also to provide new experimentally testable hypotheses regarding the process of development. This new knowledge has allowed for improvements in assisted reproductive technologies and is moving toward translation to clinical practice via multiscale assessments of the dynamics of ovulation, development in pregnancy, and the timing and mechanics of delivery. WIREs Syst Biol Med 2017, 9:e1353. doi: 10.1002/wsbm.1353 For further resources related to this article, please visit the WIREs website.

LAPS-FSH: a new and effective long-acting follicle-stimulating hormone analogue for the treatment of infertility

Although several long-acting follicle-stimulating hormone (FSH) therapies have been developed to enhance the ovarian response, a disadvantage of FSH therapy is its relatively short half-life, which requires women to receive one to two injections per day for almost 2 weeks. In the present study, we developed a novel FSH analogue by conjugating recombinant human FSH (rhFSH) and the constant region of the human immunoglobulin G4 fragment via non-peptidyl linkers. The efficacy of the FSH analogue was evaluated in vitro by cAMP level assessments, pharmacokinetic studies and a determination of ovarian weight and by comparing these findings with the results from other FSH analogues. In addition, the total number of antral and Graafian follicles was determined after 7 days of treatment with control, 6µgkg(-1) follitropin β, 6, 12 or 42µgkg(-1) corifollitropin α or 3, 6 or 12µgkg(-1) long acting protein/peptide discovery-follicle-stimulating hormone (LAPS-FSH). As a result, the animals treated with 12µgkg(-1) LAPS-FSH produced additional and larger healthy follicles. These data demonstrate that LAPS-FSH promotes growth and inhibits atresia of the ovarian follicle compared with other available drugs, suggesting that our new drug enhances the efficacy and duration of treatment. It is expected that our new FSH analogue will result in a higher chance of pregnancy in patients who are unresponsive to other drugs.

Bioengineering the ovarian follicle microenvironment

Chemo- and radiation therapies used to treat cancer can have the unintended effect of making patients infertile. Clinically established fertility preservation methods, such as egg and embryo cryopreservation, are not applicable to all patients, which has motivated the development of strategies that involve ovarian tissue removal and cryopreservation before the first sterilizing treatment. To restore fertility at a later date, the early-stage follicles present in the tissue must be matured to produce functional oocytes, a process that is not possible using existing cell culture technologies. This review describes the application of tissue engineering principles to promote ovarian follicle maturation and produce mature oocytes through either in vitro culture or transplantation. The design principles for these engineered systems are presented, along with identification of emerging opportunities in reproductive biology.

Estrous behavior in dairy cows: identification of underlying mechanisms and gene functions

Selection in dairy cattle for a higher milk yield has coincided with declined fertility. One of the factors is reduced expression of estrous behavior. Changes in systems that regulate the estrous behavior could be manifested by altered gene expression. This literature review describes the current knowledge on mechanisms and genes involved in the regulation of estrous behavior. The endocrinological regulation of the estrous cycle in dairy cows is well described. Estradiol (E2) is assumed to be the key regulator that synchronizes endocrine and behavioral events. Other pivotal hormones are, for example, progesterone, gonadotropin releasing hormone and insulin-like growth factor-1. Interactions between the latter and E2 may play a role in the unfavorable effects of milk yield-related metabolic stress on fertility in high milk-producing dairy cows. However, a clear understanding of how endocrine mechanisms are tied to estrous behavior in cows is only starting to emerge. Recent studies on gene expression and signaling pathways in rodents and other animals contribute to our understanding of genes and mechanisms involved in estrous behavior. Studies in rodents, for example, show that estrogen-induced gene expression in specific brain areas such as the hypothalamus play an important role. Through these estrogen-induced gene expressions, E2 alters the functioning of neuronal networks that underlie estrous behavior, by affecting dendritic connections between cells, receptor populations and neurotransmitter releases. To improve the understanding of complex biological networks, like estrus regulation, and to deal with the increasing amount of genomic information that becomes available, mathematical models can be helpful. Systems biology combines physiological and genomic data with mathematical modeling. Possible applications of systems biology approaches in the field of female fertility and estrous behavior are discussed.

Autocatalytic loop, amplification and diffusion: a mathematical and computational model of cell polarization in neural chemotaxis

The chemotactic response of cells to graded fields of chemical cues is a complex process that requires the coordination of several intracellular activities. Fundamental steps to obtain a front vs. back differentiation in the cell are the localized distribution of internal molecules and the amplification of the external signal. The goal of this work is to develop a mathematical and computational model for the quantitative study of such phenomena in the context of axon chemotactic pathfinding in neural development. In order to perform turning decisions, axons develop front-back polarization in their distal structure, the growth cone. Starting from the recent experimental findings of the biased redistribution of receptors on the growth cone membrane, driven by the interaction with the cytoskeleton, we propose a model to investigate the significance of this process. Our main contribution is to quantitatively demonstrate that the autocatalytic loop involving receptors, cytoplasmic species and cytoskeleton is adequate to give rise to the chemotactic behavior of neural cells. We assess the fact that spatial bias in receptors is a precursory key event for chemotactic response, establishing the necessity of a tight link between upstream gradient sensing and downstream cytoskeleton dynamics. We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor. The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization. Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response.

Modelling of the activation of G-protein coupled receptors: drug free constitutive receptor activity

G-protein coupled receptors (GPCRs) form a crucial component of approximately 80% of hormone pathways. In this paper, the most popular mechanism for activation of GPCRs-the shuttling mechanism-is modelled mathematically. An asymptotic analysis of this model clarifies the dynamics of the system in the absence of drug, in particular which reactions dominate during the different timescales. Equilibrium analysis of the model demonstrates the model's ability to predict constitutive receptor activity.

A complex mathematical model of the human menstrual cycle

Despite the fact that more than 100 million women worldwide use birth control pills and that half of the world's population is concerned, the menstrual cycle has so far received comparatively little attention in the field of mathematical modeling. The term menstrual cycle comprises the processes of the control system in the female body that, under healthy circumstances, lead to ovulation at regular intervals, thus making reproduction possible. If this is not the case or ovulation is not desired, the question arises how this control system can be influenced, for example, by hormonal treatments. In order to be able to cover a vast range of external manipulations, the mathematical model must comprise the main components where the processes belonging to the menstrual cycle occur, as well as their interrelations. A system of differential equations serves as the mathematical model, describing the dynamics of hormones, enzymes, receptors, and follicular phases. Since the processes take place in different parts of the body and influence each other with a certain delay, passing over to delay differential equations is deemed a reasonable step. The pulsatile release of the gonadotropin-releasing hormone (GnRH) is controlled by a complex neural network. We choose to model the pulse time points of this GnRH pulse generator by a stochastic process. Focus in this paper is on the model development. This rather elaborate mathematical model is the basis for a detailed analysis and could be helpful for possible drug design.

Resonant waveguide grating biosensor for living cell sensing

This article presents theoretical analysis and experimental data for the use of resonant waveguide grating (RWG) biosensors to characterize stimulation-mediated cell responses including signaling. The biosensor is capable of detecting redistribution of cellular contents in both directions that are perpendicular and parallel to the sensor surface. This capability relies on online monitoring cell responses with multiple optical output parameters, including the changes in incident angle and the shape of the resonant peaks. Although the changes in peak shape are mainly contributed to stimulation-modulated inhomogeneous redistribution of cellular contents parallel to the sensor surface, the shift in incident angle primarily reflects the stimulation-triggered dynamic mass redistribution (DMR) perpendicular to the sensor surface. The optical signatures are obtained and used to characterize several cellular processes including cell adhesion and spreading, detachment and signaling by trypsinization, and signaling through either epidermal growth factor receptor or bradykinin B2 receptor. A mathematical model is developed to link the bradykinin-mediated DMR signals to the dynamic relocation of intracellular proteins and the receptor internalization during B2 receptor signaling cycle. This model takes the form of a set of nonlinear, ordinary differential equations that describe the changes in four different states of B2 receptors, diffusion of proteins and receptor-protein complexes, and the DMR responses. Classical analysis shows that the system converges to a unique optical signature, whose dynamics (amplitudes, transition time, and kinetics) is dependent on the bradykinin signal input, and consistent with those observed using the RWG biosensors. This study provides fundamentals for probing living cells with the RWG biosensors, in general, optical biosensors.

Multi-scale modeling of the follicle selection process in the ovary

The biological meaning of follicular development is to free fertilizable oocytes at the time of ovulation. The ovulation rate results from an FSH-dependent follicle selection process. In this paper, we designed a multi-scale model of follicular development, where selection arises from the endocrine feedback between the ovaries and pituitary gland and appeals to control theory concepts. Each ovarian follicle is described through a 2D density function giving an age and maturity-structured description of its cell population. The control intervenes in the velocity, gain and loss terms of the conservation law ruling the changes in the density. The model accounts for the changes in the total cell number, growth fraction and global maturity of both ovulatory and degenerating follicles for various intensities of the selection rate. The different selection process outputs (mono- or poly-ovulation, anovulation) predicted by the model are consistent with physiological knowledge regarding vascularization, pituitary sensitivity to ovarian feedback and treatment with exogenous FSH.

Contribution of a mathematical modelling approach to the understanding of the ovarian function

The biological meaning of folliculogenesis is to free fertilisable oocytes at the time of ovulation. We approached the study of the control of follicular development at the level of follicular granulosa cells, on the experimental as well as mathematical modelling grounds. We built a mathematical model allowing for the processes of proliferation, differentiation and apoptosis. State variables correspond to the numbers of cells undergoing these different processes, while control variables correspond to the cellular transition rates. The model results raised the notion of proliferative resources, which leads to consider the optimal management of these resources and has motivated the settling of an experiment investigating the changes in the growth fraction within the granulosa throughout terminal development. We are now investigating the way gonadotrophins, and especially FSH, operate on granulosa cells, in order to account for the hormonal control of the divergent commitment of granulosa cells towards either proliferation, differentiation or apoptosis. We are thus focusing on the dynamics of cAMP production, which appears to be a keypoint in FSH signal transduction.