A model for the control of testosterone secretion

We produce here a model to explain the control of testosterone secretion. In this model the hypothalamic secretion of the hormone LHRH (luteinizing hormone releasing hormone) is controlled by a combination of local testosterone concentration and of the local concentration of the pituitary hormone LH (luteinizing hormone). Since LHRH stimulates the release of LH, and LH in turn stimulates the release of testosterone, the three hormones constitute a three-component "feedback" network. We show how this model is able to account for the pulsatility of the release of these three hormones. Furthermore, the model is consistent with results obtained from a wide range of experimental manipulations of the system. For example, it accounts for the changes observed in hormone release patterns after castration. In particular, it follows that no "neural clock", or "neural pulse-generator", is required to force the system into pulsatile behaviour.     

Electrical signaling in the olfactory bulb

The olfactory bulb employs lateral and feedback inhibitory pathways to distribute odor information across parallel assemblies of mitral and granule cells. The pathways involve dendritic action potentials that can interact with a variety of voltage-dependent conductances and synaptic transmission to produce complex and dynamic patterns of activity. Electrical coupling also helps to ensure proper coordination and synchronization of these patterns. These mechanisms provide numerous options for dynamic modulation and control of signaling in the olfactory bulb.     

Firing responses of bursting neurons with delayed feedback

Thalamic neurons, which play important roles in the genesis of rhythmic activities of the brain, show various bursting behaviors, particularly modulated by complex thalamocortical feedback via cortical neurons. As a first step to explore this complex neural system and focus on the effects of the feedback on the bursting behavior, a simple loop structure delayed in time and scaled by a coupling strength is added to a recent mean-field model of bursting neurons. Depending on the coupling strength and delay time, the modeled neurons show two distinct response patterns: one entrained to the unperturbed bursting frequency of the neurons and one entrained to the resonant frequency of the loop structure. Transitions between these two patterns are explored in the model’s parameter space via extensive numerical simulations. It is found that at a fixed loop delay, there is a critical coupling strength at which the dominant response frequency switches from the unperturbed bursting frequency to the loop-induced one. Furthermore, alternating occurrence of these two response frequencies is observed when the delay varies at fixed coupling strength. The results demonstrate that bursting is coupled with feedback to yield new dynamics, which will provide insights into such effects in more complex neural systems.     

Hormonal control of invertebrate behavior

Invertebrates show a wide variety of behaviors that are influenced by hormones. In insects the involvement of hormones at a particular life stage is directly correlated with the complexity of the behavioral repertoire at that stage. In larval stages, the steroid hormone, ecdysone, when present with juvenile hormone, apparently causes the behaviors observed during the periodic molts. At the end of larval life, ecdysone in the absence of juvenile hormone triggers the onset of premetamorphic behaviors such as wandering behavior and cocoon-spinning behavior. In insects having complete metamorphosis, the emergence (eclosion) of the adult from the pupal case is accomplished by a stereotyped program of movements that are triggered by a peptide hormone. In moths, injection of this “eclosion hormone” into competent recipients will cause the release of the eclosion program. Also this program can be elicited by the hormone from the isolated abdominal central nervous system (CNS). The onset of reproductive behavior in females of various species requires juvenile hormone. In addition, certain peptides are then involved in the transition from virgin to mated behaviors. Also, pupatitive peptide factors trigger specific stereotyped behaviors such as those involved in mate attraction and in oviposition. In males, the control is simpler. Juvenile hormone is required for the maturation of sexual behavior in only a few species. But in at least one insect group, the cockroaches, a neurosecretory hormone serves to release directly copulatory behavior. Social behavior and migratory behavior in certain insects are also under hormonal influence. Hormones play a prominent role in regulating the behavior of gastropod mollusks. The best studied examples involve the hormonal stimulation of egg-laying behavior by CNS peptides. Also, peptide hormones cause stereotyped changes in specific identified neurons in the CNS of various gastropods. In at least some cases, these latter changes are related to arousal from aestivation.With their simple nervous systems, invertebrates are especially suited for studies on the mode of action of hormones on the nervous system. In most cases the behavioral effects of these hormones appear to be due to their direct action on the CNS. Indeed, the isolated moth CNS will respond to the eclosion hormone by generating the motor program that gives rise to the emergence behavior, and various isolated molluscan preparations will respond to hormones with stereotyped neural responses. By the direct application of hormone to the surface of identified nerve cells in mollusks it has been possible to localize target cells for specific hormones. Little is known of the mode of action of ecdysone or juvenile hormone in altering behavior. Peptide hormones appear to have effects which long outlast the actual presence of the hormone. In at least two cases, cyclic AMP has been implicated as a mediator of the hormonal response.     

Metabolic feedback in mammalian endocrine systems.

Information processing through feedback loops is an integral part of most endocrine systems, and ranges from simple negative loops to complex combinations of negative and positive loops. Moreover, feedback may occur at local (paracrine) or long-distance sites, and with multiple time-domains. Traditionally, feedback is visualized as one hormone stimulating release of a second hormone, which then circulates in the blood to carry out various biological activities, one of which is to inhibit further secretion of the first hormone. This represents a fail-safe mechanism to protect the organism against the potentially damaging effects of uncontrolled secretion of many of the common hormones, some of which are highly catabolic or anabolic. However, it is becoming increasingly apparent that the products of catabolism and anabolism may themselves participate in the feedback process in either a feed-forward or feedback manner. For example, free fatty acids are liberated by the action of growth hormone, and in turn are potent inhibitors of growth hormone secretion (feedback). On the other hand, stress activates adrenal cortical and medullary secretion, which also promotes lipolysis, but in this case the liberated free fatty acids may actually stimulate the system further (feed-forward). Similarly, glucose has been shown to directly inhibit the activity of several different endocrine pathways, and must now be considered an integral part of the overall regulatory mechanism involved in fine-tuning secretion and possibly production of hormones. By constructing models of feedback of increasing complexity, it is possible to make predictions about previously unrecognized relationships between hormones and products of metabolism.     

Modeling of the vertebrate visual system. II. Application to the turtle cone retina

The model of the vertebrate cone retina was adapted to the turtle retina with its red cone- and L-channel-dominances. The model consists of an ordering of four spatial organizations of unit hexagons, weighted inputs for all cones in the receptive fields, and linear polarization factors based on data from literature on turtle retina. Data generated by the model for spatial and chromatic patterns of receptive fields, intensity-response curves, dynamic ranges for cones, horizontal and bipolar cells proved remarkably consistent with literature. The model also generates observed phenomena such as near-field enhancement of cones due to stray light effects and electrical coupling of like-cones and far-field decrease in responses due to negative feedback from L-type horizontal cells to cones. Annular stimuli were shown to be more effective than spot stimuli for horizontal cells. The formal approach of the model demonstrates factors which play roles in various observed phenomena and all aspects of model can be displayed and tested both qualitatively and quantitatively.     

Modelling the transition from simple to complex Ca2+oscillations in pancreatic acinar cells

A mathematical model is proposed which systematically investigates complex calcium oscillations in pancreatic acinar cells. This model is based on calcium-induced calcium release via inositol trisphosphate receptors (IPR) and ryanodine receptors (RyR) and includes calcium modulation of inositol (1,4,5) trisphosphate (IP₃) levels through feedback regulation of degradation and production. In our model, the apical and the basal regions are separated by a region containing mitochondria, which is capable of restricting Ca²⁺ responses to the apical region. We were able to reproduce the observed oscillatory patterns, from baseline spikes to sinusoidal oscillations. The model predicts that calcium-dependent production and degradation of IP₃ is a key mechanism for complex calcium oscillations in pancreatic acinar cells. A partial bifurcation analysis is performed which explores the dynamic behaviour of the model in both apical and basal regions.     

The interrelationships between nonapeptide and steroid hormones secretion by bovine granulosa cells in vitro.

The effects of adding oxytocin (OT) and arginine-vasopressin (AVP) on progesterone and estradiol-17 beta secretion by bovine granulosa cells in culture were studied. The influence of these steroids on OT and AVP release was also evaluated. OT (1, 10, 100 or 1000 mIU/ml) stimulates both progesterone and estradiol output. Small doses (10 pM/ml) of exogenous progesterone or estradiol stimulated a surge in OT, while the intermediate doses (100 or 1000 pM/ml) had no influence, and large doses (10,000 pM/ml) inhibited OT secretion by granulosa cells. Thus, a potential regulatory loop between OT and steroid hormone release by granulosa cells was demonstrated. Stimulation of a surge in steroids by OT, activation of OT release by small doses of steroids and inhibition of OT secretion by excess steroids may suggest the existence of a feedback mechanism regulating these hormones production. Addition of AVP (1, 10, 100 or 1000 pM/ml) inhibited progesterone and stimulated a surge in estradiol, while steroid hormones did not induce AVP release. These data suggest the regulation of ovarian steroidogenesis by AVP, feedback influences are less likely.     

Insect tissue culture systems: models for study of hormonal control of development

Summary The regulation of growth and development of insects is under endocrine control and involves both juvenile hormones and ecdysteroids. Neuropeptides are master regulators which control the secretion of these hormones. Most experiments in insect endocrinology have been conducted in vivo, but tissue culture methodology is playing an increasing role due to the great interest in simpler model systems for the study of complex processes that occur in vivo. The availability of appropriate media has allowed the culture of a variety of insect organs and cell lines of defined origin which have kept certain properties of the parent tissues. Tissue culture approaches have been useful for studying hormonal control of morphogenetic processes. Cell lines are particularly suited to the study of hormonally regulated mechanisms of macromolecular biosynthesis and gene expression. Thus, the value of in vitro analysis in studies of regulation of hormone production is now recognized. Results obtained from tissue culture allow more precise definition of the hormonal requirements of insect cells and tissues for growth and differentiation and might make possible the discovery of new growth regulators.     

Steroid induction of a peptide hormone gene leads to orchestration of a defined behavioral sequence.

At the end of each molt, insects shed the old cuticle by performing preecdysis and ecdysis behaviors. Regulation of these centrally patterned movements involves peptide signaling between endocrine Inka cells and the CNS. In Inka cells, we have identified the cDNA and gene encoding preecdysis-triggering hormone (PETH) and ecdysis-triggering hormone (ETH), which activate these behaviors. Prior to behavioral onset, rising ecdysteroid levels induce expression of the ecdysone receptor (EcR) and ETH gene in Inka cells and evoke CNS sensitivity to PETH and ETH. Subsequent ecdysteroid decline is required for peptide release, which initiates three motor patterns in specific order: PETH triggers preecdysis I, while ETH activates preecdysis II and ecdysis. The Inka cell provides a model for linking steroid regulation of peptide hormone expression and release with activation of a defined behavioral sequence.     

Regulation of gut hormone secretion. Studies using isolated perfused intestines

The incretin hormones glucagon-like peptide 1 (GLP-1) and glucose-dependent insulinotropic polypeptide (GIP) are secreted from enteroendocrine cells in the intestine along with other gut hormones (PYY, CCK and neurotensin) shown to affect metabolism and/or appetite. The secretion of many gut hormones is highly increased after gastric bypass operations, which have turned out to be an effective therapy of not only obesity but also type 2 diabetes. These effects are likely to be due, at least in part, to increases in the secretion of these gut hormones (except GIP). Therefore, stimulation of the endogenous hormone represents an appealing therapeutic strategy, which has spurred an interest in understanding the regulation of gut hormone secretion and a search for particularly GLP-1 and PYY secretagogues.The secretion of the gut hormones is stimulated by oral intake of nutrients often including carbohydrate, protein and lipid. This review focuses on stimulators of gut hormone secretion, the mechanisms involved, and in particular models used to investigate secretion. A major break-through in this field was the development of methods to identify and isolate specific hormone producing cells, which allow detailed mapping of the expression profiles of these cells, whereas they are less suitable for physiological studies of secretion. Isolated perfused preparations of mouse and rat intestines have proven to be reliable models for dynamic hormone secretion and should be able to bridge the gap between the molecular details derived from the single cells to the integrated patterns observed in the intact animals.     

Discrete models of autocrine cell communication in epithelial layers

Pattern formation in epithelial layers heavily relies on cell communication by secreted ligands. Whereas the experimentally observed signaling patterns can be visualized at single-cell resolution, a biophysical framework for their interpretation is currently lacking. To this end, we develop a family of discrete models of cell communication in epithelial layers. The models are based on the introduction of cell-to-cell coupling coefficients that characterize the spatial range of intercellular signaling by diffusing ligands. We derive the coupling coefficients as functions of geometric, cellular, and molecular parameters of the ligand transport problem. Using these coupling coefficients, we analyze a nonlinear model of positive feedback between ligand release and binding. In particular, we study criteria of existence of the patterns consisting of clusters of a few signaling cells, as well as the onset of signal propagation. We use our model to interpret recent experimental studies of the EGFR/Rhomboid/Spitz module in Drosophila development.     

Isolated mouse islets respond to glucose with an initial peak of glucagon release followed by pulses of insulin and somatostatin in antisynchrony with glucagon

Recent studies of isolated human islets have shown that glucose induces hormone release with repetitive pulses of insulin and somatostatin in antisynchrony with those of glucagon. Since the mouse is the most important animal model we studied the temporal relation between hormones released from mouse islets. Batches of 5-10 islets were perifused and the hormones measured with radioimmunoassay in 30s fractions. At 3mM glucose, hormone secretion was stable with no detectable pulses of glucagon, insulin or somatostatin. Increase of glucose to 20mM resulted in an early secretory phase with a glucagon peak followed by peaks of insulin and somatostatin. Subsequent hormone secretion was pulsatile with a periodicity of 5min. Cross-correlation analyses showed that the glucagon pulses were antisynchronous to those of insulin and somatostatin. In contrast to the marked stimulation of insulin and somatostatin secretion, the pulsatility resulted in inhibition of overall glucagon release. The cytoarchitecture of mouse islets differs from that of human islets, which may affect the interactions between the hormone-producing cells. Although indicating that paracrine regulation is important for the characteristic patterns of pulsatile hormone secretion, the mouse data mimic those of human islets with more than 20-fold variations of the insulin/glucagon ratio. The data indicate that the mouse serves as an appropriate animal model for studying the temporal relation between the islet hormones controlling glucose production in the liver.     

Continuum limits of pattern formation in hexagonal-cell monolayers

Intercellular signalling is key in determining cell fate. In closely packed tissues such as epithelia, juxtacrine signalling is thought to be a mechanism for the generation of fine-grained spatial patterns in cell differentiation commonly observed in early development. Theoretical studies of such signalling processes have shown that negative feedback between receptor activation and ligand production is a robust mechanism for fine-grained pattern generation and that cell shape is an important factor in the resulting pattern type. It has previously been assumed that such patterns can be analysed only with discrete models since significant variation occurs over a lengthscale concomitant with an individual cell; however, considering a generic juxtacrine signalling model in square cells, in O’Dea and King (Math Biosci 231(2):172–185 2011), a systematic method for the derivation of a continuum model capturing such phenomena due to variations in a model parameter associated with signalling feedback strength was presented. Here, we extend this work to derive continuum models of the more complex fine-grained patterning in hexagonal cells, constructing individual models for the generation of patterns from the homogeneous state and for the transition between patterning modes. In addition, by considering patterning behaviour under the influence of simultaneous variation of feedback parameters, we construct a more general continuum representation, capturing the emergence of the patterning bifurcation structure. Comparison with the steady-state and dynamic behaviour of the underlying discrete system is made; in particular, we consider pattern-generating travelling waves and the competition between various stable patterning modes, through which we highlight an important deficiency in the ability of continuum representations to accommodate certain dynamics associated with discrete systems.     

Dynamics of thyroid diseases and thyroid‐axis gland masses

Thyroid disorders are common and often require lifelong hormone replacement. Treating thyroid disorders involves a fascinating and troublesome delay, in which it takes many weeks for serum thyroid‐stimulating hormone (TSH) concentration to normalize after thyroid hormones return to normal. This delay challenges attempts to stabilize thyroid hormones in millions of patients. Despite its importance, the physiological mechanism for the delay is unclear. Here, we present data on hormone delays from Israeli medical records spanning 46 million life‐years and develop a mathematical model for dynamic compensation in the thyroid axis, which explains the delays. The delays are due to a feedback mechanism in which peripheral thyroid hormones and TSH control the growth of the thyroid and pituitary glands; enlarged or atrophied glands take many weeks to recover upon treatment due to the slow turnover of the tissues. The model explains why thyroid disorders such as Hashimoto''s thyroiditis and Graves'' disease have both subclinical and clinical states and explains the complex inverse relation between TSH and thyroid hormones. The present model may guide approaches to dynamically adjust the treatment of thyroid disorders.