Modelling and analysis of cAMP-induced mixed-mode oscillations in cortical neurons: Critical roles of HCN and M-type potassium channels.

Cyclic AMP controls neuronal ion channel activity. For example hyperpolarization-activated cyclic nucleotide-gated (HCN) and M-type K+ channels are activated by cAMP. These effects have been suggested to be involved in astrocyte control of neuronal activity, for example, by controlling the action potential firing frequency. In cortical neurons, cAMP can induce mixed-mode oscillations (MMOs) consisting of small-amplitude, subthreshold oscillations separating complete action potentials, which lowers the firing frequency greatly. We extend a model of neuronal activity by including HCN and M channels, and show that it can reproduce a series of experimental results under various conditions involving and inferring with cAMP-induced activation of HCN and M channels. In particular, we find that the model can exhibit MMOs as found experimentally, and argue that both HCN and M channels are crucial for reproducing these patterns. To understand how M and HCN channels contribute to produce MMOs, we exploit the fact that the model is a three-time scale dynamical system with one fast, two slow, and two super-slow variables. We show that the MMO mechanism does not rely on the super-slow dynamics of HCN and M channel gating variables, since the model is able to produce MMOs even when HCN and M channel activity is kept constant. In other words, the cAMP-induced increase in the average activity of HCN and M channels allows MMOs to be produced by the slow-fast subsystem alone. We show that the slow-fast subsystem MMOs are due to a folded node singularity, a geometrical structure well known to be involved in the generation of MMOs in slow-fast systems. Besides raising new mathematical questions for multiple-timescale systems, our work is a starting point for future research on how cAMP signalling, for example resulting from interactions between neurons and glial cells, affects neuronal activity via HCN and M channels.

Modeling Doxorubicin Pharmacokinetics in Multiple Myeloma Suggests Mechanism of Drug Resistance.

OBJECTIVE: Multiple myeloma (MM) is a plasma cell malignancy often treated with chemotherapy drugs. Among these, doxorubicin (DOXO) is commonly employed, sometimes in combined-drug therapies, but it has to be optimally administered in order to maximize its efficacy and reduce possible side effects. To support DOXO studies and treatment optimization, here we propose an experimental/modeling approach to establish a model describing DOXO pharmacokinetics (PK) in MM cells. METHODS: A series of in vitro experiments were performed in MM1R and MOLP-2 cells. DOXO was administered at two dosages (200 nM, 450 nM) at [Formula: see text] = 0 and removed at [Formula: see text] = 3 hrs. Intracellular DOXO concentration was measured via fluorescence microscopy during both drug uptake ([Formula: see text] = 0-3 hrs) and release phases ([Formula: see text] = 3-8 hrs). Four PK candidate models were identified, and were compared and selected based on their ability to describe DOXO data and numerical parameter identification. RESULTS: The most parsimonious model consists of three compartments describing DOXO distribution between the extracellular space, the cell cytoplasm and the nucleus, and defines the intracellular DOXO efflux rate through a Hill function, simulating a threshold/saturation drug resistance mechanism. This model predicted DOXO data well in all the experiments and provided precise parameter estimates (mean ± standard deviation coefficient of variation: 15.8 ± 12.2%). CONCLUSIONS: A reliable PK model describing DOXO uptake and release in MM cells has been successfully developed. SIGNIFICANCE: The proposed PK model, once integrated with DOXO pharmacodynamics, has the potential of allowing the study and the optimization of DOXO treatment strategies in MM.

Machine learning provides insight into models of heterogeneous electrical activity in human beta-cells.

Understanding how heterogeneous cellular responses emerge from cell-to-cell variations in expression and function of subcellular components is of general interest. Here, we focus on human insulin-secreting beta-cells, which are believed to constitute a population in which heterogeneity is of physiological importance. We exploit recent single-cell electrophysiological data that allow biologically realistic population modeling of human beta-cells that accounts for cellular heterogeneity and correlation between ion channel parameters. To investigate how ion channels influence the dynamics of our updated mathematical model of human pancreatic beta-cells, we explore several machine learning techniques to determine which model parameters are important for determining the qualitative patterns of electrical activity of the model cells. As expected, K＋ channels promote absence of activity, but once a cell is active, they increase the likelihood of having action potential firing. HERG channels were of great importance for determining cell behavior in most of the investigated scenarios. Fast bursting is influenced by the time scales of ion channel activation and, interestingly, by the type of Ca2＋ channels coupled to BK channels in BK-CaV complexes. Slow, metabolically driven oscillations are promoted mostly by K(ATP) channels. In summary, combining population modeling with machine learning analysis provides insight into the model and generates new hypotheses to be investigated both experimentally, via simulations and through mathematical analysis.

Calcium Signaling in the Photodamaged Skin: In Vivo Experiments and Mathematical Modeling.

The epidermis forms an essential barrier against a variety of insults. The overall goal of this study was to shed light not only on the effects of accidental epidermal injury, but also on the mechanisms that support laser skin resurfacing with intra-epidermal focal laser-induced photodamage, a widespread medical practice used to treat a range of skin conditions. To this end, we selectively photodamaged a single keratinocyte with intense, focused and pulsed laser radiation, triggering Ca2+ waves in the epidermis of live anesthetized mice with ubiquitous expression of a genetically encoded Ca2+ indicator. Waves expanded radially and rapidly, reaching up to eight orders of bystander cells that remained activated for tens of minutes, without displaying oscillations of the cytosolic free Ca2+ concentration ([Formula: see text]). By combining in vivo pharmacological dissection with mathematical modeling, we demonstrate that Ca2+ wave propagation depended primarily on the release of ATP, a prime damage-associated molecular patterns (DAMPs), from the hit cell. Increments of the [Formula: see text] in bystander cells were chiefly due to Ca2+ release from the endoplasmic reticulum (ER), downstream of ATP binding to P2Y purinoceptors. ATP-dependent ATP release though connexin hemichannels (HCs) affected wave propagation at larger distances, where the extracellular ATP concentration was reduced by the combined effect of passive diffusion and hydrolysis due to the action of ectonucleotidases, whereas pannexin channels had no role. Bifurcation analysis suggests basal keratinocytes have too few P2Y receptors (P2YRs) and/or phospholipase C (PLC) to transduce elevated extracellular ATP levels into inositol trisphosphate (IP3) production rates sufficiently large to sustain [Formula: see text] oscillations.

Amplitude-modulated spiking as a novel route to bursting: Coupling-induced mixed-mode oscillations by symmetry breaking.

Mixed-mode oscillations consisting of alternating small- and large-amplitude oscillations are increasingly well understood and are often caused by folded singularities, canard orbits, or singular Hopf bifurcations. We show that coupling between identical nonlinear oscillators can cause mixed-mode oscillations because of symmetry breaking. This behavior is illustrated for diffusively coupled FitzHugh-Nagumo oscillators with negative coupling constant, and we show that it is caused by a singular Hopf bifurcation related to a folded saddle-node (FSN) singularity. Inspired by earlier work on models of pancreatic beta-cells [Sherman, Bull. Math. Biol. 56, 811 (1994)], we then identify a new type of bursting dynamics due to diffusive coupling of cells firing action potentials when isolated. In the presence of coupling, small-amplitude oscillations in the action potential height precede transitions to square-wave bursting. Confirming the hypothesis from the earlier work that this behavior is related to a pitchfork-of-limit-cycles bifurcation in the fast subsystem, we find that it is caused by symmetry breaking. Moreover, we show that it is organized by a FSN in the averaged system, which causes a singular Hopf bifurcation. Such behavior is related to the recently studied dynamics caused by the so-called torus canards.

Modeling Pharmacokinetics of Doxorubicin in Multiple Myeloma Cells.

Doxorubicin (DOXO) is a well-established chemotherapy drug for treatment of different tumors, ranging from breast cancer, melanoma to multiple myeloma (MM). Here, we present a coupled experimental/modeling approach to study DOXO pharmacokinetics in MM cells, investigate its distribution among the extracellular and intracellular compartments during time. Three model candidates are considered and identified. Model selection is performed based on its ability to describe the data both qualitatively and in terms of quantitative indexes. The most parsimonious model consists of a nonlinear structure with a saturation-threshold control of intracellular DOXO efflux by the DOXO bound to the cellular DNA. This structure could explain the hypothesis that MM cells are drug-resistant, likely due to the involvement of P-glycoproteins.The proposed model is able to predict the intracellular (free and bound) DOXO and suggests the presence of a saturation-threshold drug-resistant mechanism.Clinical Relevance- The model can be used to properly understand and guide further experimental setup, e.g., to investigate multiple myeloma cell variability among different cell lines.

Data-driven estimation of change points reveals correlation between face mask use and accelerated curtailing of the first wave of the COVID-19 epidemic in Italy.

BACKGROUND: Italy was the first Western country to be seriously affected by COVID-19, and the first to implement drastic measures, which successfully curtailed the first wave of the epidemic. METHODS: To understand which containment measures altered disease dynamics, we estimated change points in COVID-19 dynamics from official Italian data. RESULTS: We found an excellent correlation between nationwide lockdown and the epidemic peak in late March 2020. Surprisingly, we found a change point in mid-April, which did not correspond to national measures, but may be explained by regional interventions. Change points in regional COVID-19 dynamics correlated well with local distribution of free face masks and regional orders requiring their mandatory use. Regions with no specific interventions showed no change point during April. CONCLUSIONS: Our findings of the observed correlation between face mask use and disease dynamics lend further support to the importance of face masks in addition to lockdowns and other restrictions for the control of COVID-19.

Surging critical care capacity for COVID-19: Key now and in the future.

The COVID-19 pandemic has shocked health systems worldwide, with visible impacts on intensive care units and emergency departments. The concept of "surge capacity" should be analyzed within this context as this crisis could be seen as an opportunity to improve the knowledge base of intensive care units and emergency departments. We reflected, based on our experience from work at the frontlines, on health service planning and with epidemiological data, about the importance of surging critical care capacity for COVID, now and as lessons for the future. We summarize and relate virus clinical characteristics, epidemiological patterns and critical care surge capacity as important factors to consider for effective health systems response. Some practical aspects are described, but also the role that mathematical models can play to improve intensive care units surge capacity by considering its importance as a predictor of needs according to epidemiological patterns. Also, in the transitional phase, we consider the importance of coexisting COVID-19 and non-covid-19 health care services, and the importance of a new surge capacity for postponed activities. In this new transitional phase, also emergency departments will have to adapt their surge capacity for a rebound effect due to delayed visits from non-COVID-19 health conditions during the pandemic. Health systems and society must remain vigilant for potential resurgence of cases as measures are relaxed to restart the economy and a new normal. Emergency departments and intensive care units have to develop surge strategies to deal together with COVID-19 and non-COVID-19 flow of patients.

Calcium signaling and secretory granule pool dynamics underlie biphasic insulin secretion and its amplification by glucose: experiments and modeling.

Glucose-stimulated insulin secretion from pancreatic ß-cells is controlled by a triggering pathway that culminates in calcium influx and regulated exocytosis of secretory granules, and by a less understood amplifying pathway that augments calcium-induced exocytosis. In response to an abrupt increase in glucose concentration, insulin secretion exhibits a first peak followed by a lower sustained second phase. This biphasic secretion pattern is disturbed in diabetes. It has been attributed to depletion and subsequent refilling of a readily releasable pool of granules or to the phasic cytosolic calcium dynamics induced by glucose. Here, we apply mathematical modeling to experimental data from mouse islets to investigate how calcium and granule pool dynamics interact to control dynamic insulin secretion. Experimental calcium traces are used as inputs in three increasingly complex models of pool dynamics, which are fitted to insulin secretory patterns obtained using a set of protocols of glucose and tolbutamide stimulation. New calcium and secretion data for so-called staircase protocols, in which the glucose concentration is progressively increased, are presented. These data can be reproduced without assuming any heterogeneity in the model, in contrast to previous modeling, because of nontrivial calcium dynamics. We find that amplification by glucose can be explained by increased mobilization and priming of granules. Overall, our results indicate that calcium dynamics contribute substantially to shaping insulin secretion kinetics, which implies that better insight into the events creating phasic calcium changes in human ß-cells is needed to understand the cellular mechanisms that disturb biphasic insulin secretion in diabetes.

Gap-junction coupling can prolong beta-cell burst period by an order of magnitude via phantom bursting.

Pancreatic ß-cells show multiple intrinsic modes of oscillation with bursting electrical activity playing a crucial role. Bursting is seen both in experimentally isolated ß-cells as well as in electrically coupled cells in the pancreatic islets, but the burst period is typically an order of magnitude greater in coupled cells. This difference has previously been attributed to noisier dynamics, or perturbed electrophysiological properties, in isolated ß-cells. Here, we show that diffusive coupling alone can extend the period more than ten-fold in bursting oscillators modeled with a so-called phantom burster model and analyze this result with slow-fast bifurcation analysis of an electrically coupled pair of cells. Our results should be applicable to other scenarios where coupling of bursting units, e.g., neurons, may increase the oscillation period drastically.

Explicit Theoretical Analysis of How the Rate of Exocytosis Depends on Local Control by Ca2+ Channels.

Hormones and neurotransmitters are released from cells by calcium-regulated exocytosis, and local coupling between Ca2+ channels (CaVs) and secretory granules is a key factor determining the exocytosis rate. Here, we devise a methodology based on Markov chain models that allows us to obtain analytic results for the expected rate. First, we analyze the property of the secretory complex obtained by coupling a single granule with one CaV. Then, we extend our results to a more general case where the granule is coupled with n CaVs. We investigate how the exocytosis rate is affected by varying the location of granules and CaVs. Moreover, we assume that the single granule can form complexes with inactivating or non-inactivating CaVs. We find that increasing the number of CaVs coupled with the granule determines a much higher rise of the exocytosis rate that, in case of inactivating CaVs, is more pronounced when the granule is close to CaVs, while, surprisingly, in case of non-inactivating CaVs, the highest relative increase in rate is obtained when the granule is far from the CaVs. Finally, we exploit the devised model to investigate the relation between exocytosis and calcium influx. We find that the quantities are typically linearly related, as observed experimentally. For the case of inactivating CaVs, our simulations show a change of the linear relation due to near-complete inactivation of CaVs.

Concise Whole-Cell Modeling of BKCa-CaV Activity Controlled by Local Coupling and Stoichiometry.

Large-conductance Ca2+-dependent K+ (BKCa) channels are important regulators of electrical activity. These channels colocalize and form ion channel complexes with voltage-dependent Ca2+ (CaV) channels. Recent stochastic simulations of the BKCa-CaV complex with 1:1 stoichiometry have given important insight into the local control of BKCa channels by fluctuating nanodomains of Ca2+. However, such Monte Carlo simulations are computationally expensive, and are therefore not suitable for large-scale simulations of cellular electrical activity. In this work we extend the stochastic model to more realistic BKCa-CaV complexes with 1:n stoichiometry, and analyze the single-complex model with Markov chain theory. From the description of a single BKCa-CaV complex, using arguments based on timescale analysis, we derive a concise model of whole-cell BKCa currents, which can readily be analyzed and inserted into models of cellular electrical activity. We illustrate the usefulness of our results by inserting our BKCa description into previously published whole-cell models, and perform simulations of electrical activity in various cell types, which show that BKCa-CaV stoichiometry can affect whole-cell behavior substantially. Our work provides a simple formulation for the whole-cell BKCa current that respects local interactions in BKCa-CaV complexes, and indicates how local-global coupling of ion channels may affect cell behavior.

CFTR is involved in the regulation of glucagon secretion in human and rodent alpha cells.

Glucagon is the main counterregulatory hormone in the body. Still, the mechanism involved in the regulation of glucagon secretion from pancreatic alpha cells remains elusive. Dysregulated glucagon secretion is common in patients with Cystic Fibrosis (CF) that develop CF related diabetes (CFRD). CF is caused by a mutation in the Cl- channel Cystic fibrosis transmembrane conductance regulator (CFTR), but whether CFTR is present in human alpha cells and regulate glucagon secretion has not been investigated in detail. Here, both human and mouse alpha cells showed CFTR protein expression, whereas CFTR was absent in somatostatin secreting delta cells. CFTR-current activity induced by cAMP was measured in single alpha cells. Glucagon secretion at different glucose levels and in the presence of forskolin was increased by CFTR-inhibition in human islets, whereas depolarization-induced glucagon secretion was unaffected. CFTR is suggested to mainly regulate the membrane potential through an intrinsic alpha cell effect, as supported by a mathematical model of alpha cell electrophysiology. In conclusion, CFTR channels are present in alpha cells and act as important negative regulators of cAMP-enhanced glucagon secretion through effects on alpha cell membrane potential. Our data support that loss-of-function mutations in CFTR contributes to dysregulated glucagon secretion in CFRD.

Spatiotemporal Modeling of Triggering and Amplifying Pathways in GLP-1 Secreting Intestinal L Cells.

Glucagon-like peptide 1 (GLP-1) is secreted by intestinal L-cells, and augments glucose-induced insulin secretion, thus playing an important role in glucose control. The stimulus-secretion pathway in L-cells is still incompletely understood and a topic of debate. It is known that GLP-1 secreting cells can sense glucose to promote electrical activity either by the electrogenic sodium-glucose cotransporter SGLT1, or by closure of ATP-sensitive potassium channels after glucose metabolism. Glucose also has an effect on GLP-1 secretion downstream of electrical activity. An important aspect to take into account is the spatial organization of the cell. Indeed, the glucose transporter GLUT2 is located at the basolateral, vascular side, while SGLT1 is exposed to luminal glucose at the apical side of the cell, suggesting that the two types of transporters play different roles in glucose sensing. Here, we extend our recent model of electrical activity in primary L-cells to include spatiotemporal glucose and Ca2+ dynamics, and GLP-1 secretion. The model confirmed that glucose transportation into the cell through SGLT1 cotransporters can induce Ca2+ influx and release of GLP-1 as a result of electrical activity, while glucose metabolism alone is insufficient to depolarize the cell and evoke GLP-1 secretion in the model, suggesting a crucial role for SGLT1 in triggering GLP-1 release in agreement with experimental studies. We suggest a secondary, but participating, role of GLUT2 and glucose metabolism for GLP-1 secretion via an amplifying pathway that increases the secretion rate at a given Ca2+ level.

Recent advances in mathematical modeling and statistical analysis of exocytosis in endocrine cells.

Most endocrine cells secrete hormones as a result of Ca2+-regulated exocytosis, i.e., fusion of the membranes of hormone-containing secretory granules with the cell membrane, which allows the hormone molecules to escape to the extracellular space. As in neurons, electrical activity and cell depolarization open voltage-sensitive Ca2+ channels, and the resulting Ca2+ influx elevate the intracellular Ca2+ concentration, which in turn causes exocytosis. Whereas the main molecular components involved in exocytosis are increasingly well understood, quantitative understanding of the dynamical aspects of exocytosis is still lacking. Due to the nontrivial spatiotemporal Ca2+ dynamics, which depends on the particular pattern of electrical activity as well as Ca2+ channel kinetics, exocytosis is dependent on the spatial arrangement of Ca2+ channels and secretory granules. For example, the creation of local Ca2+ microdomains, where the Ca2+ concentration reaches tens of µM, are believed to be important for triggering exocytosis. Spatiotemporal simulations of buffered Ca2+ diffusion have provided important insight into the interplay between electrical activity, Ca2+ channel kinetics, and the location of granules and Ca2+ channels. By confronting simulations with statistical time-to-event (or survival) regression analysis of single granule exocytosis monitored with TIRF microscopy, a direct connection between location and rate of exocytosis can be obtained at the local, single-granule level. To get insight into whole-cell secretion, simplifications of the full spatiotemporal dynamics have shown to be highly helpful. Here, we provide an overview of recent approaches and results for quantitative analysis of Ca2+ regulated exocytosis of hormone-containing granules.

Statistical Frailty Modeling for Quantitative Analysis of Exocytotic Events Recorded by Live Cell Imaging: Rapid Release of Insulin-Containing Granules Is Impaired in Human Diabetic ß-cells.

Hormones and neurotransmitters are released when secretory granules or synaptic vesicles fuse with the cell membrane, a process denoted exocytosis. Modern imaging techniques, in particular total internal reflection fluorescence (TIRF) microscopy, allow the investigator to monitor secretory granules at the plasma membrane before and when they undergo exocytosis. However, rigorous statistical approaches for temporal analysis of such exocytosis data are still lacking. We propose here that statistical methods from time-to-event (also known as survival) analysis are well suited for the problem. These methods are typically used in clinical settings when individuals are followed over time to the occurrence of an event such as death, remission or conception. We model the rate of exocytosis in response to pulses of stimuli in insulin-secreting pancreatic ß-cell from healthy and diabetic human donors using piecewise-constant hazard modeling. To study heterogeneity in the granule population we exploit frailty modeling, which describe unobserved differences in the propensity to exocytosis. In particular, we insert a discrete frailty in our statistical model to account for the higher rate of exocytosis in an immediately releasable pool (IRP) of insulin-containing granules. Estimates of parameters are obtained from maximum-likelihood methods. Since granules within the same cell are correlated, i.e., the data are clustered, a modified likelihood function is used for log-likelihood ratio tests in order to perform valid inference. Our approach allows us for example to estimate the size of the IRP in the cells, and we find that the IRP is deficient in diabetic cells. This novel application of time-to-event analysis and frailty modeling should be useful also for the study of other well-defined temporal events at the cellular level.

Dapagliflozin stimulates glucagon secretion at high glucose: experiments and mathematical simulations of human A-cells.

Glucagon is one of the main regulators of blood glucose levels and dysfunctional stimulus secretion coupling in pancreatic A-cells is believed to be an important factor during development of diabetes. However, regulation of glucagon secretion is poorly understood. Recently it has been shown that Na(+)/glucose co-transporter (SGLT) inhibitors used for the treatment of diabetes increase glucagon levels in man. Here, we show experimentally that the SGLT2 inhibitor dapagliflozin increases glucagon secretion at high glucose levels both in human and mouse islets, but has little effect at low glucose concentrations. Because glucagon secretion is regulated by electrical activity we developed a mathematical model of A-cell electrical activity based on published data from human A-cells. With operating SGLT2, simulated glucose application leads to cell depolarization and inactivation of the voltage-gated ion channels carrying the action potential, and hence to reduce action potential height. According to our model, inhibition of SGLT2 reduces glucose-induced depolarization via electrical mechanisms. We suggest that blocking SGLTs partly relieves glucose suppression of glucagon secretion by allowing full-scale action potentials to develop. Based on our simulations we propose that SGLT2 is a glucose sensor and actively contributes to regulation of glucagon levels in humans which has clinical implications.

Heterogeneity and nearest-neighbor coupling can explain small-worldness and wave properties in pancreatic islets.

Many multicellular systems consist of coupled cells that work as a syncytium. The pancreatic islet of Langerhans is a well-studied example of such a microorgan. The islets are responsible for secretion of glucose-regulating hormones, mainly glucagon and insulin, which are released in distinct pulses. In order to observe pulsatile insulin secretion from the ß-cells within the islets, the cellular responses must be synchronized. It is now well established that gap junctions provide the electrical nearest-neighbor coupling that allows excitation waves to spread across islets to synchronize the ß-cell population. Surprisingly, functional coupling analysis of calcium responses in ß-cells shows small-world properties, i.e., a high degree of local coupling with a few long-range "short-cut" connections that reduce the average path-length greatly. Here, we investigate how such long-range functional coupling can appear as a result of heterogeneity, nearest-neighbor coupling, and wave propagation. Heterogeneity is also able to explain a set of experimentally observed synchronization and wave properties without introducing all-or-none cell coupling and percolation theory. Our theoretical results highlight how local biological coupling can give rise to functional small-world properties via heterogeneity and wave propagation.

Is bursting more effective than spiking in evoking pituitary hormone secretion? A spatiotemporal simulation study of calcium and granule dynamics.

Endocrine cells of the pituitary gland secrete a number of hormones, and the amount of hormone released by a cell is controlled in large part by the cell's electrical activity and subsequent Ca(2+) influx. Typical electrical behaviors of pituitary cells include continuous spiking and so-called pseudo-plateau bursting. It has been shown that the amplitude of Ca(2+) fluctuations is greater in bursting cells, leading to the hypothesis that bursting cells release more hormone than spiking cells. In this work, we apply computer simulations to test this hypothesis. We use experimental recordings of electrical activity as input to mathematical models of Ca(2+) channel activity, buffered Ca(2+) diffusion, and Ca(2+)-driven exocytosis. To compare the efficacy of spiking and bursting on the same cell, we pharmacologically block the large-conductance potassium (BK) current from a bursting cell or add a BK current to a spiking cell via dynamic clamp. We find that bursting is generally at least as effective as spiking at evoking hormone release and is often considerably more effective, even when normalizing to Ca(2+) influx. Our hybrid experimental/modeling approach confirms that adding a BK-type K(+) current, which is typically associated with decreased cell activity and reduced secretion, can actually produce an increase in hormone secretion, as suggested earlier.