Bayesian deconvolution analysis of pulsatile hormone concentration profiles

Many hormones are secreted into the circulatory system in a pulsatile manner and are cleared exponentially. The most common method of analyzing these systems is to deconvolve the hormone concentration into a secretion function and a clearance function. Accurate estimation of the model parameters depends on the number and location of the secretion pulses. To date, deconvolution analysis assumes the number and approximate location of these pulses are known a priori. In this article, we present a novel Bayesian approach to deconvolution that jointly models the number of pulses along with all other model parameters. Our method stochastically searches for the secretion pulses. This is accomplished by viewing the set of parameters that define the pulses as a point process. Pulses are determined by a birth-death process which is embedded in Markov chain Monte Carlo algorithm. This idea originated with Stephens (2000, Annals of Statistics 28, 40-74) in the context of finite mixture model density estimation, where the number of mixture components is unknown. There are several advantages that our model enjoys over the traditional frequentist approaches. These advantages are highlighted with four datasets consisting of serum concentration levels of luteinizing hormone obtained from ovariectomized ewes.     

Modeling of hormone secretion-generating mechanisms with splines: a pseudo-likelihood approach

A flexible and robust approach is proposed for the investigation of underlying hormone secretion-generating mechanisms. Characterizing hormone time series is a difficult task as most hormones are secreted in a pulsatile manner and pulses are often masked by slow decay. We model hormone concentration as a filtered counting process where the intensity function of the counting process is modeled nonparametrically using periodic splines. The intensity function and parameters are estimated using a combination of weighted least squares and pseudo-likelihood based on the first two moments. Our method uses concentration measurements directly, which avoids the difficult task of estimating pulse numbers and locations. Both simulations and applications suggest that our method performs well for estimating the intensity function of the pulse-generating counting processes.     

Analysis of pulsatile hormone concentration profiles with nonconstant Basal concentration: a bayesian approach

Many challenges arise in the analysis of pulsatile, or episodic, hormone concentration time series data. Among these challenges is the determination of the number and location of pulsatile events and the discrimination of events from noise. Analyses of these data are typically performed in two stages. In the first stage, the number and approximate location of the pulses are determined. In the second stage, a model (typically a deconvolution model) is fit to the data conditional on the number of pulses. Any error made in the first stage is carried over to the second stage. Furthermore, current methods, except two, assume that the underlying basal concentration is constant. We present a fully Bayesian deconvolution model that simultaneously estimates the number of secretion episodes, as well as their locations, and a nonconstant basal concentration. This model obviates the need to determine the number of events a priori. Furthermore, we estimate probabilities for all "candidate" event locations. We demonstrate our method on a real data set.     

Deconvolution of Serum Cortisol Levels by Using Compressed Sensing

The pulsatile release of cortisol from the adrenal glands is controlled by a hierarchical system that involves corticotropin releasing hormone (CRH) from the hypothalamus, adrenocorticotropin hormone (ACTH) from the pituitary, and cortisol from the adrenal glands. Determining the number, timing, and amplitude of the cortisol secretory events and recovering the infusion and clearance rates from serial measurements of serum cortisol levels is a challenging problem. Despite many years of work on this problem, a complete satisfactory solution has been elusive. We formulate this question as a non-convex optimization problem, and solve it using a coordinate descent algorithm that has a principled combination of (i) compressed sensing for recovering the amplitude and timing of the secretory events, and (ii) generalized cross validation for choosing the regularization parameter. Using only the observed serum cortisol levels, we model cortisol secretion from the adrenal glands using a second-order linear differential equation with pulsatile inputs that represent cortisol pulses released in response to pulses of ACTH. Using our algorithm and the assumption that the number of pulses is between 15 to 22 pulses over 24 hours, we successfully deconvolve both simulated datasets and actual 24-hr serum cortisol datasets sampled every 10 minutes from 10 healthy women. Assuming a one-minute resolution for the secretory events, we obtain physiologically plausible timings and amplitudes of each cortisol secretory event with R ² above 0.92. Identification of the amplitude and timing of pulsatile hormone release allows (i) quantifying of normal and abnormal secretion patterns towards the goal of understanding pathological neuroendocrine states, and (ii) potentially designing optimal approaches for treating hormonal disorders.     

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.     

Detecting pulsatile hormone secretions using nonlinear mixed effects partial spline models

Neuroendocrine ensembles communicate with their remote and proximal target cells via an intermittent pattern of chemical signaling. The identification of episodic releases of hormonal pulse signals constitutes a major emphasis of endocrine investigation. Estimating the number, temporal locations, secretion rate, and elimination rate from hormone concentration measurements is of critical importance in endocrinology. In this article, we propose a new flexible statistical method for pulse detection based on nonlinear mixed effects partial spline models. We model pulsatile secretions using biophysical models and investigate biological variation between pulses using random effects. Pooling information from different pulses provides more efficient and stable estimation for parameters of interest. We combine all nuisance parameters including a nonconstant basal secretion rate and biological variations into a baseline function that is modeled nonparametrically using smoothing splines. We develop model selection and parameter estimation methods for the general nonlinear mixed effects partial spline models and an R package for pulse detection and estimation. We evaluate performance and the benefit of shrinkage by simulations and apply our methods to data from a medical experiment.     

Detecting regulatory mechanisms in endocrine time series measurements

The regulatory mechanisms underlying pulsatile secretion are complex, especially as it is partly controlled by other hormones and the combined action of multiple agents. Regulatory relations between hormones are not directly observable but may be deduced from time series measurements of plasma hormone concentrations. Variation in plasma hormone levels are the resultant of secretion and clearance from the circulation. A strategy is proposed to extract inhibition, activation, thresholds and circadian synchronicity from concentration data, using particular association methods. Time delayed associations between hormone concentrations and/or extracted secretion pulse profiles reveal the information on regulatory mechanisms. The above mentioned regulatory mechanisms are illustrated with simulated data. Additionally, data from a lean cohort of healthy control subjects is used to illustrate activation (ACTH and cortisol) and circadian synchronicity (ACTH and TSH) in real data. The simulation and the real data both consist of 145 equidistant samples per individual, matching a 24-hr time span with 10 minute intervals. The results of the simulation and the real data are in concordance.     

Pulsatile patterns of gonadotropins and ovarian steroids during estrus and pseudopregnancy in the rabbit

Consecutive daily plasma levels of luteinizing hormone (LH), follicle-stimulating hormone (FSH), estradiol-17 beta (E2), progesterone (P4) and 20 alpha-hydroxypregn-4-en-3-one (20 alpha-OHP) were monitored in estrous rabbits and in these same doses during pseudopregnancy (PSP); these daily hormone levels, as well as the immediate post-coital changes in gonadotropin secretion, were similar to those in previous reports. To examine the pulsatile patterns of the gonadotropins and ovarian steroids, sequential, 10-min plasma samples were collected for 6 h from estrous does and on Days 3, 10, and 17 of PSP. All five hormones were measured in the serial samples from estrous and PSP Day 10 does; LH and FSH only were assayed in the remaining sequential samples. The amplitude and frequency of FSH pulses did not differ between any of these stages. In marked contrast, LH pulse amplitudes, and even pulse frequencies in Day 17 does, were profoundly increased during PSP above those in estrous does. Progestin secretions, both P4 and 20 alpha-OHP, also were sharply elevated in PSP Day 10 does as compared with those in estrous rabbits; the pulse amplitudes of both progestins were severalfold higher during PSP. P4 pulse frequencies were also increased at this time. Conversely, the parameters of E2 secretion did not differ between estrous and PSP Day 10 animals. In PSP Day 10 does, high amplitude pulses of both P4 and 20 alpha-OHP occurred simultaneously with high amplitude LH pulses. Simultaneous E2 and P4 pulses were evident in these same sequential plasma samples, and this E2-P4 pulse association was greater than that of 20 alpha-OHP pulses with E2 pulses. Our findings failed to identify conclusively the trophic stimulus for the progestin pulse patterns, but the mechanism may involve the coordinated action of LH and E2. The results do demonstrate that each gonadotropin and ovarian steroid is secreted in a pulsatile manner in both estrous and pseudopregnant rabbits. There are altered profiles in LH and progestin pulses, without major changes in FSH and E2 patterns, between the stages of estrus and PSP. The causes and consequences of these divergent endocrine shifts cannot be deduced from these data.     

Evidence for an inherent rhythm in pulsatile LH release in ovariectomized cows

Luteinizing hormone levels were measured in blood samples collected at 5 minute (min) intervals for 3 hours (hr) during the a.m. and p.m. of 3 consecutive days from long-term ovariectomized cows. Levels of LH fluctuated in a pulsatile manner in all animals. During the pulses, LH levels increased rapidly (2.5 to 6.0 ng/ml). Following the rapid increase, a more gradual exponential decline was observed. The interval between pulses was consistent both within and between days of blood sample collection within cows. From the results we suggest that each cow may have an inherent consistent rhythmic pattern of LH release in the absence of an ovarian source of hormones.     

Interpreting Frequency Responses to Dose-Conserved Pulsatile Input Signals in Simple Cell Signaling Motifs

Many hormones are released in pulsatile patterns. This pattern can be modified, for instance by changing pulse frequency, to encode relevant physiological information. Often other properties of the pulse pattern will also change with frequency. How do signaling pathways of cells targeted by these hormones respond to different input patterns? In this study, we examine how a given dose of hormone can induce different outputs from the target system, depending on how this dose is distributed in time. We use simple mathematical models of feedforward signaling motifs to understand how the properties of the target system give rise to preferences in input pulse pattern. We frame these problems in terms of frequency responses to pulsatile inputs, where the amplitude or duration of the pulses is varied along with frequency to conserve input dose. We find that the form of the nonlinearity in the steady state input-output function of the system predicts the optimal input pattern. It does so by selecting an optimal input signal amplitude. Our results predict the behavior of common signaling motifs such as receptor binding with dimerization, and protein phosphorylation. The findings have implications for experiments aimed at studying the frequency response to pulsatile inputs, as well as for understanding how pulsatile patterns drive biological responses via feedforward signaling pathways.     

Frequency specificity in intercellular communication. Influence of patterns of periodic signaling on target cell responsiveness.

Cells often communicate by means of periodic signals, as exemplified by a large number of hormones and by the aggregation of Dictyostelium discoideum amebas in response to periodic pulses of cyclic AMP. Periodic signaling allows bypassing the phenomenon of desensitization brought about by constant stimuli. To gain further insight into the efficiency of pulsatile signaling, we analyze the effect of periodic stimulation on the dynamic behavior of a receptor system capable of desensitization toward its ligand. We first show that the receptor system adapts to square-wave stimuli, i.e., the response eventually reaches a steady, periodic pattern after a transient phase. By analyzing the dependence of the response on the characteristics of the square-wave stimulation, we show that there exist a waveform and a period of that signal that result in maximum responsiveness of the target system. Similar results are obtained when the signal takes the more realistic form of a periodically repeated stimulation followed by exponential decay of the ligand. The results are discussed with respect to the role of pulsatile secretion of gonadotropin-releasing hormone (GnRH) by the hypothalamus and of periodic signaling by cyclic AMP pulses in Dictyostelium. The analysis accounts for the existence, in both cases, of an optimal frequency and waveform of the periodic stimulus that correspond to maximum target cell responsiveness.     

Hormone multifunctionalities: a theory of endocrine signaling, command and control

A theory is presented outlining how organisms can function and benefit from multifunctionality of hormones in order to enhance greatly the information-carrying potential of endocrine signaling. Hormones are produced continuously as micropulses, and intermittently as larger pulses. It is generally believed that micropulses generate fluctuating basal hormone concentrations, which may consistently elicit particular responses among diverse variables. Evidence is discussed suggesting that in contrast to the hormone micropulses, the larger endogenous hormone pulses may elicit responses which may differ from one pulse to another and may therefore serve different physiological functions. In this paper we postulate that an endogenous hormone pulse is a specific form of a multisignal message that serves a certain physiological function. Different pulses of a hormone may be signals of diverse multisignal messages that serve different functions. A multisignal message may elicit congruous responses by selectively enhancing some actions and suppressing other actions of the component signals. Various roles of signals of multisignal messages are discussed, as well as processes that may be involved in the diversity and selectivity of actions of different pulses of a hormone. Hormones also are converted into other hormones; we analyze how precursor and derived hormones may function independently of each other, and how precursor hormones may give rise to permissive effects. Mechanisms involved in therapeutic and adverse effects of hormone administrations are analyzed, and a strategy is suggested for developing more selective hormonal therapies.     

Age-specific changes in the regulation of LH-dependent testosterone secretion: assessing responsiveness to varying endogenous gonadotropin output in normal men

Pulsatile and thus total testosterone (Te) secretion declines in older men, albeit for unknown reasons. Analytical models forecast that aging may reduce the capability of endogenous luteinizing hormone (LH) pulses to stimulate Leydig cell steroidogenesis. This notion has been difficult to test experimentally. The present study used graded doses of a selective gonadotropin releasing hormone (GnRH)-receptor antagonist to yield four distinct strata of pulsatile LH release in each of 18 healthy men ages 23-72 yr. Deconvolution analysis was applied to frequently sampled LH and Te concentration time series to quantitate pulsatile Te secretion over a 16-h interval. Log-linear regression was used to relate pulsatile LH secretion to attendant pulsatile Te secretion (LH-Te drive) across the four stepwise interventions in each subject. Linear regression of the 18 individual estimates of LH-Te feedforward dose-response slopes on age disclosed a strongly negative relationship (r = -0.721, P < 0.001). Accordingly, the present data support the thesis that aging in healthy men attenuates amplitude-dependent LH drive of burst-like Te secretion. The experimental strategy of graded suppression of neuroglandular outflow may have utility in estimating dose-response adaptations in other endocrine systems.     

Effects of food restriction and restoration on gonadotropin and growth hormone secretion in immature male rats

This experiment concerned the changing patterns in secretion of luteinizing hormone (LH), follicle-stimulating hormone (FSH), and growth hormone (GH) under conditions of food restriction and subsequent catch-up growth. Weanling male rats were given either restricted (4 g food/day) or unrestricted access to food until 60 days of age. At this age, food-restricted rats weighed only 25% as much as rats fed ad libitum. Food restriction resulted in a dramatic decrease in the frequency of LH and GH pulses, and in the amplitude of GH pulses. It also slightly but significantly decreased mean blood levels of FSH (which was not secreted in a pulsatile manner in 60-day-old controls fed ad libitum). When restricted rats were given unrestricted access to food, frequency of LH and GH pulses and mean levels of FSH increased significantly and simultaneously within 2 days in half of the animals. Only an additional 8-10% of their body weight decrement was recovered at this time. After 10 days of food restoration, when restricted rats still weighed 50% less than controls, their secretory patterns of all three hormones were not significantly different from those of controls. Thus, recovery of gonadotropin and GH secretion was relatively rapid. Except for the quantitatively lesser impact of food restriction on FSH secretion, there was no evidence of any priorities in the secretion of the three hormones. Under conditions of rapid catch-up growth, the secretory patterns of LH, FSH, and GH appeared to develop simultaneously.     

Median eminence lesions reveal separate hypothalamic control of pulsatile follicle-stimulating hormone and luteinizing hormone release

The effects of hypothalamic lesions designed to destroy either the anterior median eminence (ME) or the posterior and mid-ME on pulsatile release of follicle-stimulating hormone (FSH) and luteinizing hormone (LH) were determined in castrated male rats. In sham-operated animals, mean plasma FSH concentrations rose to peak at 10 min after the onset of sampling, whereas LH declined to a nadir during this time. In the final sample at 120 min, the mean FSH concentrations peaked as LH decreased to its minimal value. In rats with anterior ME lesions, there was suppression of LH pulses with continuing FSH pulses in 12 of 21 rats. On the other hand, in animals with posterior to mid-ME lesions, 3 out of 21 rats had elimination of FSH pulses, whereas LH pulses were maintained. Fifteen of 42 operated rats had complete ME lesions, and pulses of both hormones were abolished. The remaining 12 rats had partial ME lesions that produced a partial block of the release of both hormones. The results support the concept of separate hypothalamic control of FSH and LH release with the axons of the putative FSH-releasing factor (FSHRF) neuronal system terminating primarily in the mid- to caudal ME, whereas those of the LHRH neuronal system terminate in the anterior and mid-median eminence. We hypothesize that pulses of FSH alone are mediated by release of the FSHRF into the hypophyseal portal vessels, whereas those of LH alone are mediated by LHRH. Pulses of both gonadotropins simultaneously may be mediated by pulses of both releasing hormones simultaneously. Alternatively, relatively large pulses of LHRH alone may account for simultaneous pulses of both gonadotropins since LHRH has intrinsic FSH-releasing activity.     

Dynamic testosterone responses to near-physiological LH pulses are determined by the time pattern of prior intravenous LH infusion

The long-lived glycoprotein hormone, human chorionic gonadotropin (hCG), downregulates testosterone (T) biosynthesis in vitro and in vivo in animals and humans. The degree to which short-lived pulses of pituitary luteinizing hormone (LH) do so, particularly at physiological concentrations, is not known. We test the hypothesis that continuous LH infusion compared with bolus injections of LH every 1 h or every 2 h overnight downregulates T secretory responses to a subsequent fixed template of three consecutive intravenous pulses of a physiological amount of recombinant human (rh) LH (triple stimulus). Nineteen healthy men ages 18-49 yr each underwent four separate randomly ordered overnight gonadotropin-releasing hormone-receptor antagonist treatments with superimposed intravenous infusions of saline or rhLH (1-h pulses, 2-h pulses, or continuously). Each 12-h infusion protocol was followed by the triple rhLH-pulse stimulus the next morning. During the triple stimulus, basal (nonpulsatile) as well as total (basal plus pulsatile) T secretion was higher after overnight 2- and 1-h rhLH pulses than after continuous rhLH or saline delivery. Approximate entropy, a probabilistic measure of feedforward-induced irregularity of T concentration time series, was higher after 1-h rhLH pulses than after continuous rhLH. Analytical estimation of pulsatile rhLH-T dose-response measures revealed higher T secretory sensitivity and greater rhLH potency (lower EC(50)) after exposure to 1-h than 2-h rhLH pulses. Collectively, these data indicate that in vivo dynamics of LH-stimulated T secretion under standardized conditions in men depend on the prior time mode of LH delivery in the bloodstream.