Differential coding of humoral stimuli by timing and amplitude of intracellular calcium spike trains.

The ubiquitous Ca2(+)-phosphoinositide pathway transduces extracellular signals to cellular effectors. Using a mathematical model, we simulated intracellular Ca2+ fluctuations in hepatocytes upon humoral stimulation. We estimated the information encoded about random humoral stimuli in these Ca2+ spike trains using an information-theoretic approach based on stimulus estimation methods. We demonstrate accurate transfer of information about random humoral signals with low temporal cutoff frequencies. In contrast, our results suggest that high-frequency stimuli are poorly transduced by the transmembrane machinery. We found that humoral signals are encoded in both the timing and amplitude of intracellular Ca2+ spikes. The information transmitted per spike is similar to that of sensory neuronal systems, in spite of several orders of magnitude difference in firing rate.

Precision of intracellular calcium spike timing in primary rat hepatocytes.

Extracellular stimuli are often encoded in the frequency, amplitude and duration of spikes in the intracellular concentration of calcium ([Ca2+]i). However, the timing of individual [Ca2+]i-spikes in relation to the dynamics of an extracellular stimulus is still an open question. To address this question, we use a systems biology approach combining experimental and theoretical methods. Using computer simulations, we predict that more naturalistic pulsed stimuli generate precisely-timed [Ca2+]i-spikes in contrast to the application of constant stimuli of the same dose. These computational results are confirmed experimentally in single primary rat hepatocytes upon alpha1-adrenergic stimulation. Hormonal signalling in analogy to neuronal signalling thus has the potential to make use of temporal coding on the level of single cells. The [Ca2+]i-signalling cascade provides a first example for increasing the information capacity of an intracellular regulatory signal beyond the known coding mechanisms of amplitude (AM) and frequency modulation (FM).

Humoral coding and decoding.

Humoral communication systems are dynamically regulated. Most hormones are released in a pulsatile or burst-like manner into the bloodstream. It is well known that information coded in the frequency and amplitude of secretory pulses allows for the differential regulation of specific target cell function and structure. However, despite intensive study of transmembrane signalling relatively little is known about how the temporal dynamics of extracellular humoral stimuli specifically regulates the temporal pattern of intracellular signalling pathways, such as Ca2+-dependent signalling. Repetitive spikes of Ca2+ encode this information in their amplitude, duration and frequency, and are in turn decoded into the pattern of gene expression and phosphorylation of target proteins. Using a mathematical model for G protein-coupled Ca2+ signalling and information-theoretic approaches to stimulus reconstruction we have systematically quantified the amount of information coded in the Ca2+-signal about the dynamics of the stimulus, which allows us to explore the temporal bandwidth of transmembrane signalling. These in silico approaches permit us to differentiate the amount of information coded in the frequency, temporal precision, amplitude and the complete Ca2+-signal. This may open an avenue to the quantification of information flow and processing in the intra- and intercellular coding and decoding machinery.

Noise enhanced hormonal signal transduction through intracellular calcium oscillations.

In a wide range of non-linear dynamical systems, noise may enhance the detection of weak deterministic input signals. Here, we demonstrate this phenomenon for transmembrane signaling in a hormonal model system of intracellular Ca(2+) oscillations. Adding Gaussian noise to a subthreshold extracellular pulsatile stimulus increased the sensitivity in the dose-response relation of the Ca(2+) oscillations compared to the same noise signal added as a constant mean level. These findings may have important physiological consequences for the operation of hormonal and other physiological signal transduction systems close to the threshold level.

Prediction and significance of the temporal pattern of hormone secretion in disease states.

Comparison of the temporal pattern of hormone secretion in health and disease reveals distinct differences in many systems. Analysis of these visually apparent differences conventionally rests on computer-assisted programs based on either model assumptions, or estimations of hormonal decay rates or threshold values, all of which may not accurately reflect physiological and/or pathophysiological states. Only recently have new methods evolved which are independent of preexisting knowledge of the system under study. Apart from the widely used approximate entropy statistic (ApEn), a measure for the regularity of a time-series, artificial neural networks are able to capture temporal structures in endocrine rhythms without any previous assumptions. In particular, non-linear dynamical systems may be delineated and separated from random behaviour. This is achieved by mapping complex input data to a given complex output by propagating data from the input layer to the output layer through a larger number of interconnections, so-called hidden layers. The networks are capable to extract relevant features from training samples and store this information in the distributed structure of interconnections. Using this approach on growth hormone (GH) rhythms of healthy controls, fasted healthy subjects, untreated acromegalic patients and acromegalics under octreotide suppressive therapy we were recently able to demonstrate the power of this approach to differentiate the temporal pattern of GH secretion following normalization of the data for absolute amplitudes. In a second approach we were able to significantly reduce the number of data points required to characterize the temporal structure of these rhythms. This latter quality of the networks may help to transfer analysis of changes in the temporal pattern of hormone secretion on a more routine basis.

Coding efficiency and information rates in transmembrane signaling.

A variety of cell types responds to hormonal stimuli by repetitive spikes in the intracellular concentration of calcium ([Ca(2+)](i)) which have been demonstrated to encode information in their frequency, amplitude, and duration. These [Ca(2+)](i)-spike trains are able to specifically regulate distinct cellular functions. Using a mathematical model for receptor-controlled [Ca(2+)](i) oscillations in hepatocytes we investigate the encoding of fluctuating hormonal signals in [Ca(2+)](i)-spike trains. The transmembrane information transfer is quantified by using an information-theoretic reverse-engineering approach which allows to reconstruct the dynamic hormonal stimulus from the [Ca(2+)](i)-spike trains. This approach allows to estimate the accuracy of coding as well as the rate of transmembrane information transfer. We found that up to 87% of the dynamic stimulus information can be encoded in the [Ca(2+)](i)-spike train at a maximum information transfer rate of 1.1 bit per [Ca(2+)](i)-spike. These numerical results for humoral information transfer are in the same order as in a number of sensory neuronal systems despite several orders of magnitude different time scales of operation suggesting a universal principle of information processing in both biological systems.

Ca2+/calmodulin inhibition and phospholipase C-linked Ca2+ Signaling in clonal beta-cells.

Neurotransmitters and hormones, such as arginine vasopressin (AVP) and bombesin, evoke frequency-modulated repetitive Ca2+ transients in insulin-secreting HIT-T15 cells by binding to receptors linked to phospholipase C (PLC). The role of calmodulin (CaM)-dependent mechanisms in the generation of PLC-linked Ca2+ transients was investigated by use of the naphthalenesulfonamide CaM antagonists W-7 and W-13 and their dechlorinated control analogs W-5 and W-12. W-7 (10-30 microM) and W-13 (30-100 microM), but not W-5 (100 microM) and W-12 (300 microM), reversibly inhibited the AVP- and bombesin-induced Ca2+ transients. As the generation of PLC-linked Ca2+ transients requires mobilization of internal Ca2+ and Ca2+ influx through voltage-sensitive (VSCC) and -insensitive (VICC) Ca2+ channels, the effects of the W compounds on these processes were further investigated. First, W-7 dose dependently diminished K+ (45 mM)-induced Ca2+ signals (IC50, approximately 25 microM), and W-13 (100 microM) reduced the K+ (45 mM)-induced [Ca2+]i rise by about 40-60%, whereas W-5 (100 microM) and W-12 (300 microM) had no effect. In addition, W-7 (100 microM) inhibited whole cell Ca2+ currents in mouse beta-cells by about 60%. Second, pretreatment of cells (5 min) with W-7 (30 microM), but not W-5 (30 microM), inhibited agonist-induced internal Ca2+ mobilization by about 75% in Ca2+-free medium. Neither W-7 (30 microM) nor W-5 (30 microM) affected AVP (100 nM)-stimulated formation of IP3. Third, capacitative Ca2+ influx through VICC activated by thapsigargin (2 microM) in the presence of verapamil (50 microM) was inhibited by W-7 (30 microM) but not by W-5 (30 microM). As all of the W compound effects corresponded well to their reported anticalmodulin activity, a specific anticalmodulin action can be assumed. Thus, Ca2+ via activation of CaM-dependent processes could provide positive feedback on the generation of PLC-linked Ca2+ transients in HIT-T15 cells. This appears to involve CaM-dependent regulation of both mobilization of internal Ca2+ and Ca2+ influx through VSCC and VICC.

Coding of time-varying hormonal signals in intracellular calcium spike trains.

In a variety of cell types extracellular hormonal stimuli varying in time are transfered across the cell membrane into repetitive spikes of the intracellular calcium concentration ([Ca2+]i). Distinct temporal patterns of [Ca2+]i spikes are capable of regulating the function and structure of target cells. Here, we investigate the ability of transmembrane signaling to encode time-varying hormonal stimulations (bandlimited Gaussian white noise) in a model of receptor-controlled [Ca2+]i oscillations. The encoding of hormonal signals in [Ca2+]i spike trains is quantified by using an information-theoretic approach allowing to estimate the hormonal stimulus from [Ca2+]i spike trains. Our results suggest that intracellular [Ca2+]i spike trains convey faithful information on temporal variations of extracellular hormonal concentrations at scales of 30-200 sec, corresponding to cut-off frequencies between 5 and 30 mHz of the random hormonal stimulation.

Coarse-grained entropy rates quantify fast Ca2+ dynamics modulated by pharmacological stimulation.

Calcium (Ca2+) is an ubiquitous intracellular messenger which regulates cellular processes, such as secretion, contraction, and cell proliferation. A variety of cell types respond to hormonal stimuli with periodic oscillations of the intracellular free Ca2+ concentration ([Ca2+]i) which can be modulated in their frequency in a dose-dependent manner. The period of these well-studied oscillations varies normally between 30 sec and a couple of minutes. Here we study [Ca2+]i oscillations in clonal beta cells (hamster insulin secreting cells, HIT) under pharmacological stimulation. Besides the well-known high-amplitude low frequency oscillations we try to analyze for the first time low-amplitude high frequency oscillations of [Ca2+]i under pharmacological stimulation which have not been explored in experimental approaches to date. Using coarse-grained entropy rates computed from information-theoretic functionals we demonstrate differences in temporal complexity of the fast low-amplitude [Ca2+]i dynamics corresponding to different phases of pharmacological stimulation which are additional to the well-known dose-dependent pattern of low-frequency high amplitude [Ca2+]i dynamics.

Predictive neural networks for learning the time course of blood glucose levels from the complex interaction of counterregulatory hormones.

Diabetes mellitus is a widespread disease associated with an impaired hormonal regulation of normal blood glucose levels. Patients with insulin-dependent diabetes mellitus (IDDM) who practice conventional insulin therapy are at risk of developing hypoglycemia (low levels of blood glucose), which can lead to severe dysfunction of the central nervous system. In large retrospective studies, up to approximately 4% of deaths of patients with IDDM have been attributed to hypoglycemia (Cryer, Fisher, & Shamoon, 1994; Tunbridge, 1981; Deckert, Poulson, & Larsen, 1978). Thus, a better understanding of the complex hormonal interaction preventing hypoglycemia is crucial for treatment. Experimental data from a study on insulin-induced hypoglycemia in healthy subjects are used to demonstrate that feedforward neural networks are capable of predicting the time course of blood glucose levels from the complex interaction of glucose counterregulatory (glucose-raising) hormones and insulin. By simulating the deficiency of single hormonal factors in this regulatory network, we found that the predictive impact of glucagon, epinephrine, and growth hormone secretion, but not of cortisol and norepinephrine, were dominant in restoring normal levels of blood glucose following hypoglycemia.

Central nervous system control of thyrotropin secretion during sleep and wakefulness.

Thyrotropin (TSH) is a pulsatile secreted hormone with a pronounced circadian rhythmicity and a characteristic nightly surge based on an augmentation of pulsatile release. A number of physiological factors influence TSH secretion via an alteration in the amount of pulsatile released hormone. An increase in somatostatinergic tone during fasting appears to decrease TSH pulse amplitude and sequentially mean TSH serum levels. In contrast, blockade of dopaminergic tone by metoclopramide infusion when circulating TSH levels are low during the afternoon hours increase TSH pulse amplitude to levels comparable to the nightly TSH surge suggesting a physiological dampening of TSH pulse amplitude by dopamine during the daytime.

Neural networks in the analysis of episodic growth hormone release.

Pulsatile secretion of growth hormone (GH) has been observed in healthy controls as well as acromegalic patients. In healthy adults, highly regulated secretory pulses of GH occur 4-8 times within 24 h. This episodic pattern of secretion seems to be related to the optimal induction of physiological effects at the peripheral level. In contrast to normal subjects, acromegalic patients demonstrate an irregular pattern of excessive GH release. This pattern of secretion is responsible for many systemic effects, such as the stimulation of connective tissue growth, cardiovascular and cerebrovascular disease, diabetes mellitus and arthritis. Standard methods for the analysis of pulsatile patterns of hormone secretion did not consistently separate the temporal dynamics of GH release in healthy controls and acromegalic patients under various study conditions. Using the cutting edge technology of artificial neural networks for time series prediction, we were able to achieve significant separation of both groups under various conditions by means of the predictability of their GH secretory dynamics. Improving the predictive results by using a more refined system of multiple neural networks acting in parallel (adaptive mixtures of local experts), we found that this system performed a self-organized segmentation of hormone pulsatility. It separated phases of secretory bursts and quiescence without any prior knowledge of the form of a GH pulse or a model of secretion. Comparing the predictive results for the GH dynamics with those for computer-stimulated stochastic processes, we were able to define the irregular pattern of GH secretion in acromegaly as a random autonomous process. The introduction of neural networks to the analysis of dynamic endocrine systems might help to expand the existing analytical approaches beyond counting frequency and amplitude of hormone pulses.

Algorithmic complexity of growth hormone release in humans.

Most hormones are secreted in an pulsatile rather than in a constant manner. This temporal pattern of pulsatile hormone release plays an important role in the regulation of cellular function and structure. In healthy humans growth hormone (GH) secretion is characterized by distinct pulses whereas patients bearing a GH producing tumor accompanied with excessive secretion (acromegaly) exhibit a highly irregular pattern of GH release. It has been hypothesized that this highly disorderly pattern of GH release in acromegaly arises from random events in the GH-producing tumor under decreased normal control of GH secretion. Using a context-free grammar complexity measure (algorithmic complexity) in conjunction with random surrogate data sets we demonstrate that the temporal pattern of GH release in acromegaly is not significantly different from a variety of stochastic processes. In contrast, normal subjects clearly exhibit deterministic structure in their temporal patterns of GH secretion. Our results support the hypothesis that GH release in acromegaly is due to random events in the GH-producing tumorous cells which might become independent from hypothalamic regulation.

Twenty-four-hour rhythms of plasma catecholamines and their relation to cardiovascular parameters in healthy young men.

Diurnal and ultradian rhythms of plasma norepinephrine and epinephrine and their role in the regulation of cardiovascular parameters were investigated over 24 h of recumbency in a group of five men. Catecholamines were measured at 10 min intervals, and blood pressure and heart rate were recorded continuously. Norepinephrine and epinephrine rapidly fluctuated in each subject, with no obvious diurnal rhythm. Spectral analysis suggested two ultradian rhythms with periods of around 12 h and 50-100 min for both catecholamines. The pulse detection programs PULSAR and CLUSTER revealed 20-30 pulses/24 h for norepinephrine and epinephrine, with a significant correlation between the two rhythms (r = 0.63-0.80, P < 0.001). Neither the frequency nor the amplitude of these rapid fluctuations differed between day and night. Arousal in the morning caused a small increase in plasma catecholamines and getting out of bed a large increase. Thus changes in posture and activity are the main influences on the diurnal variations of plasma catecholamines reported previously, while the ultradian rhythms of sympathoadrenomedullary activity appear to be of intrinsic origin. Blood pressure and heart rate exhibited a diurnal rhythm with a nightly decrease. Arousal and rising from bed increased blood pressure and heart rate significantly. Although the amplitude of the rapid fluctuations of plasma catecholamines at times exceeded those caused by postural changes in the morning, when both plasma norepinephrine and epinephrine levels correlated highly with all cardiovascular parameters, correlations were not significant during recumbency. Thus the intrinsic ultradian fluctuations of plasma catecholamines appear not to be involved in the control of cardiovascular parameters during recumbency, and the increase in blood pressure and heart rate in the morning appears to be controlled by direct sympathetic neural input to the heart and vasculature in response to changes in activity and posture rather than by an endogenous surge of plasma catecholamines.

Self-organized segmentation of time series: separating growth hormone secretion in acromegaly from normal controls.

The pulsatile pattern of growth hormone (GH) secretion was assessed by sampling blood every 10 min over 24 h in healthy subjects (n = 10) under normal food intake and under fasting conditions (n = 6) and in patients with a GH-producing tumor (acromegaly, n = 6), before and after treatment with the somatostatin analog octreotide. Using autocorrelation, we found no consistent separation in the temporal dynamics of GH secretion in healthy controls and acromegalic patients. Time series prediction based on a single neural network has recently been demonstrated to separate the secretory dynamics of parathyroid hormone in healthy controls from osteoporotic patients. To better distinguish the differences in GH dynamics in healthy subjects and patients, we tested time series predictions based on a single neural network and a more refined system of multiple neural networks acting in parallel (adaptive mixtures of local experts). Both approaches significantly separated GH dynamics under the various conditions. By performing a self-organized segmentation of the alternating phases of secretory bursts and quiescence of GH, we significantly improved the performance of the multiple network system over that of the single network. It thus may represent a potential tool for characterizing alterations of the dynamic regulation associated with diseased states.

Time series prediction of plasma hormone concentration. Evidence for differences in predictability of parathyroid hormone secretion between osteoporotic patients and normal controls.

Recent evidence links osteoporosis, a disease of bone remodeling, to changes in the dynamics of parathyroid hormone secretion. We use nonlinear and linear time series prediction to characterize the secretory dynamics of parathyroid hormone in both healthy human subjects and patients with osteoporosis. Osteoporotic patients appear to lack the periods of high predictability found in normal humans. Our results may provide an explanation for why an intermittent administration of parathyroid hormone is effective in restoring bone mass in osteoporotic patients.

Pulsatile hormone secretion: Analysis and biological significance.

Pulsatile hormone release is a general phenomenon that can be observed in numerous endocrine systems. The analysis and biological significance of pulsatile hormone release were discussed at a Ferring satellite symposium of the Third European Congress of Endocrinology, held on July 23 and 24, 1994, in Hannover, Germany.

[Pulsatile hormone secretion for control of target organs]. / Die Bedeutung pulsatiler Hormonsekretion für die Steuerung von Zielorganen.

Pulsatile secretion of hormones are observed in many endocrine systems. Here we discuss the significance of pulsatile patterns of hormone secretion for the regulation of endocrine target tissues in physiology and pathophysiology. New approaches to analyze endocrine rhythms are introduced that may enable to better define the temporal patterns of secretion relevant for the regulation of distinct processes in complex in vivo systems. This may lead to improved diagnostic and therapeutic strategies of endocrine diseases.

Is there low-dimensional chaos in pulsatile secretion of parathyroid hormone in normal human subjects?

In many biological systems information is transferred by hormonal ligands, and it is assumed that these hormonal signals encode developmental and regulatory programs in mammalian organisms. The specificity of the biological response on activation by a hormone has so far been located within the interaction of a specific conformation of the ligand with the corresponding receptor structure. According to these classical explanations, the constant circulating hormonal pool described by the rate of its production and metabolic clearance is a major determinant of this interaction. Recently it has become apparent that hormone pulses contribute to this hormonal pool. Phase-space analysis of dynamic parathyroid hormone (PTH) secretion allowed the definition (in comparison to normal subjects) of a relatively quiet "low dynamic" secretory pattern in osteoporosis, and a "high dynamic" state in hyperparathyroidism. We now investigate whether this pulsatile secretion of PTH in healthy humans exhibits characteristics of low-dimensional deterministic chaos. Our findings suggest that this indeed appears to be the case. PTH secretion thus seems to be a first example of a chaotic hormonal rhythm in human physiology.