Mathematical modeling of gonadotropin-releasing hormone signaling

Gonadotropin-releasing hormone (GnRH) acts via G-protein coupled receptors on pituitary gonadotropes to control reproduction. These are Gq-coupled receptors that mediate acute effects of GnRH on the exocytotic secretion of luteinizing hormone (LH) and follicle-stimulating hormone (FSH), as well as the chronic regulation of their synthesis. GnRH is secreted in short pulses and GnRH effects on its target cells are dependent upon the dynamics of these pulses. Here we overview GnRH receptors and their signaling network, placing emphasis on pulsatile signaling, and how mechanistic mathematical models and an information theoretic approach have helped further this field

Steady state running rate sets the speed and accuracy of accumulation of swimming bacteria

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system, where the steady-state rate of the switching changes in different environments. Understanding chemotaxis quantitatively requires that one links the measured steady-state switching rates of the rotary system, as well as the directional changes of individual swimming bacteria in a gradient of chemoattractant/repellant, to the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model, parametrized with our experimental data, and show that the response of a population to the gradient is complex. We find the changes to the steady-state switching rate in the absence of gradients affect the average speed of the swimming bacterial population response as well as the width of the distribution. Both must be taken into account when optimizing the overall response of the population in complex environments

Statement by Eric Mehnert and Rhonda Decontie collected by Rachel George on December 5, 2014

This is the author accepted manuscript. The final version is available from the Society for Neuroscience via the DOI in this recordFertility critically depends on the gonadotropin-releasing hormone (GnRH) pulse generator, a neural construct comprised of hypothalamic neurons co-expressing kisspeptin, neurokoinin-B and dynorphin. Here, using mathematical modelling and in-vivo optogenetics we reveal for the first time how this neural construct initiates and sustains the appropriate ultradian frequency essential for reproduction. Prompted by mathematical modelling, we show experimentally using female estrous mice that robust pulsatile release of luteinizing hormone, a proxy for GnRH, emerges abruptly as we increase the basal activity of the neuronal network using continuous low frequency optogenetic stimulation. Further increase in basal activity markedly increases pulse frequency and eventually leads to pulse termination. Additional model predictions that pulsatile dynamics emerge from non-linear positive and negative feedback interactions mediated through neurokinin-B and dynorphin signaling respectively are confirmed neuropharmacologically. Our results shed light on the long-elusive GnRH pulse generator offering new horizons for reproductive health and wellbeing.SIGNIFICANCE STATEMENTThe gonadotropin-releasing hormone (GnRH) pulse generator controls the pulsatile secretion of the gonadotropic hormones LH and FSH and is critical for fertility. The hypothalamic arcuate kisspeptin neurons are thought to represent the GnRH pulse generator, since their oscillatory activity is coincident with LH pulses in the blood; a proxy for GnRH pulses. However, the mechanisms underlying GnRH pulse generation remain elusive. We developed a mathematical model of the kisspeptin neuronal network and confirmed its predictions experimentally, showing how LH secretion is frequency-modulated as we increase the basal activity of the arcuate kisspeptin neurons in-vivo using continuous optogenetic stimulation. Our model provides a quantitative framework for understanding the reproductive neuroendocrine system and opens new horizons for fertility regulation.Engineering and Physical Sciences Research Council (EPSRC)Medical Research Council (MRC)Biotechnology and Biological Sciences Research Council (BBSRC

Gonadotropin-releasing hormone signaling:An information theoretic approach

Gonadotropin-releasing hormone (GnRH) is a peptide hormone that mediates central control of reproduction, acting via G-protein coupled receptors that are primarily Gq coupled and mediate GnRH effects on the synthesis and secretion of luteinizing hormone and follicle-stimulating hormone. A great deal is known about the GnRH receptor signaling network but GnRH is secreted in short pulses and much less is known about how gonadotropes decode this pulsatile signal. Similarly, single cell measures reveal considerable cell-cell heterogeneity in responses to GnRH but the impact of this variability on signaling is largely unknown. Ordinary differential equation-based mathematical models have been used to explore the decoding of pulse dynamics and information theory-derived statistical measures are increasingly used to address the influence of cell-cell variability on the amount of information transferred by signaling pathways. Here, we describe both approaches for GnRH signaling, with emphasis on novel insights gained from the information theoretic approach and on the fundamental question of why GnRH is secreted in pulses

Information Transfer in Gonadotropin-Releasing Hormone (GnRH) Signaling:Extracellular Signal-Regulated Kinase (ERK)-Mediated Feedback Loops Control Hormone Sensing

Cell signaling pathways are noisy communication channels, and statistical measures derived from information theory can be used to quantify the information they transfer. Here we use single cell signaling measures to calculate mutual information as a measure of information transfer via gonadotropin-releasing hormone (GnRH) receptors (GnRHR) to extracellular signal-regulated kinase (ERK) or nuclear factor of activated T-cells (NFAT). This revealed mutual information values <1 bit, implying that individual GnRH-responsive cells cannot unambiguously differentiate even two equally probable input concentrations. Addressing possible mechanisms for mitigation of information loss, we focused on the ERK pathway and developed a stochastic activation model incorporating negative feedback and constitutive activity. Model simulations revealed interplay between fast (min) and slow (min-h) negative feedback loops with maximal information transfer at intermediate feedback levels. Consistent with this, experiments revealed that reducing negative feedback (by expressing catalytically inactive ERK2) and increasing negative feedback (by Egr1-driven expression of dual-specificity phosphatase 5 (DUSP5)) both reduced information transfer from GnRHR to ERK. It was also reduced by blocking protein synthesis (to prevent GnRH from increasing DUSP expression) but did not differ for different GnRHRs that do or do not undergo rapid homologous desensitization. Thus, the first statistical measures of information transfer via these receptors reveals that individual cells are unreliable sensors of GnRH concentration and that this reliability is maximal at intermediate levels of ERK-mediated negative feedback but is not influenced by receptor desensitization

The fidelity of dynamic signaling by noisy biomolecular networks

This is the final version of the article. Available from Public Library of Science via the DOI in this record.Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the system's fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments.We acknowledge support from a Medical Research Council and Engineering and Physical Sciences Council funded Fellowship in Biomedical Informatics (CGB) and a Scottish Universities Life Sciences Alliance chair in Systems Biology (PSS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Measuring luteinising hormone pulsatility with a robotic aptamer-enabled electrochemical reader

Assessment of luteinising hormone pulsatility is important in the diagnosis of reproductive disorders. Here the authors develop a DNA aptamer-based electrochemical analysis integrated into a robotic platform for high-throughput and sensitive analysis