Mechanism of receptor-oriented intercellular calcium wave propagation in hepatocytes

Pacing intracellular Ca2+ signals in exocrine acinar cells

An increase in intracellular [Ca2+ ] in exocrine acinar cells resident in the salivary glands or pancreas is a fundamental event that drives fluid secretion and exocytosis of proteins. Stimulation with secretagogues initiates Ca2+ signals with precise spatiotemporal properties thought to be important for driving physiological output. Both in vitro, in acutely isolated acini, and in vivo, in animals expressing genetically encoded indicators, individual cells appear specialized to initiate Ca2+ signals upon stimulation. Furthermore, these signals appear to spread to neighbouring cells. These properties are present in the absence of a conventional pacemaker mechanism dependent on the cyclical activation of Ca2+ -dependent or Ca2+ -conducting plasma membrane ion channels. In this article, we propose a model for 'pacing' intracellular Ca2+ signals in acinar cells based on the enhanced sensitivity of a subpopulation of individual cells and the intercellular diffusion through gap junctions of inositol 1,4,5-trisphosphate and Ca2+ to neighbouring cells.

Numerical simulation of calcium dynamics dependent ATP degradation, IP3 and NADH production due to obesity in a hepatocyte cell

Calcium (Ca[Formula: see text]) signals have a crucial role in regulating various processes of almost every cell to maintain its structure and function. Calcium dynamics has been studied in various cells including hepatocytes by many researchers, but the mechanisms of calcium signals involved in regulation and dysregulation of various processes like ATP degradation rate, IP[Formula: see text] and NADH production rate respectively in normal and obese cells are still poorly understood. In this paper, a reaction diffusion equation of calcium is employed to propose a model of calcium dynamics by coupling ATP degradation rate, IP[Formula: see text] and NADH production rate in hepatocyte cells under normal and obese conditions. The processes like source influx, buffer, endoplasmic reticulum (ER), mitochondrial calcium uniporters (MCU) and Na[Formula: see text]/Ca[Formula: see text] exchanger (NCX) have been incorporated in the model. Linear finite element method is used along spatial dimension, and Crank-Nicolson method is used along temporal dimension for numerical simulation. The results have been obtained for the normal hepatocyte cells and for cells due to obesity. The comparative study of these results reveal significant difference caused due to obesity in Ca[Formula: see text] dynamics as well as in ATP degradation rate, IP[Formula: see text] and NADH production rate.

A Tale of two receptors

Calcium (Ca²⁺) oscillations in hepatocytes have a wide dynamic range. In particular, recent experimental evidence shows that agonist stimulation of the P2Y family of receptors leads to qualitatively diverse Ca²⁺ oscillations. We present a new model of Ca²⁺ oscillations in hepatocytes based on these experiments to investigate the mechanisms controlling P2Y-activated Ca²⁺ oscillations. The model accounts for Ca²⁺ regulation of the IP₃ receptor (IP₃R), the positive feedback from Ca²⁺ on phospholipase C (PLC) and the P2Y receptor phosphorylation by protein kinase C (PKC). Furthermore, PKC is shown to control multiple cellular substrates. Utilising the model, we suggest the activity and intensity of PLC and PKC necessary to explain the qualitatively diverse Ca²⁺ oscillations in response to P2Y receptor activation.

Gap junctions coordinate the propagation of glycogenolysis induced by norepinephrine in the pineal gland

Chemical and electrical synapses are the two major communication systems that permit cell-to-cell communication within the nervous system. Although most studies are focused on chemical synapses (glutamate, γ-aminobutyric acid, and other neurotransmitters), clearly both types of synapses interact and cooperate to allow the coordination of several cell functions within the nervous system. The pineal gland has limited independent axonal innervation and not every cell has access to nerve terminals. Thus, additional communication systems, such as gap junctions, have been postulated to coordinate metabolism and signaling. Using acutely isolated glands and dissociated cells, we found that gap junctions spread glycogenolytic signals from cells containing adrenoreceptors to the entire gland lacking these receptors. Our data using glycogen and lactate quantification, electrical stimulation, and high-performance liquid chromatography with electrochemical detection, demonstrate that gap junctional communication between cells of the rat pineal gland allows cell-to-cell propagation of norepinephrine-induced signal that promotes glycogenolysis throughout the entire gland. Thus, the interplay of both synapses is essential for coordinating glycogen metabolism and lactate production in the pineal gland.

The Effect of Gap Junctional Coupling on the Spatiotemporal Patterns of Ca2+ Signals and the Harmonization of Ca2+-Related Cellular Responses

Calcium ions (Ca²⁺) are important mediators of a great variety of cellular activities e.g. in response to an agonist activation of a receptor. The magnitude of a cellular response is often encoded by frequency modulation of Ca²⁺ oscillations and correlated with the stimulation intensity. The stimulation intensity highly depends on the sensitivity of a cell to a certain agonist. In some cases, it is essential that neighboring cells produce a similar and synchronized response to an agonist despite their different sensitivity. In order to decipher the presumed function of Ca²⁺ waves spreading among connecting cells, a mathematical model was developed. This model allows to numerically modifying the connectivity probability between neighboring cells, the permeability of gap junctions and the individual sensitivity of cells to an agonist. Here, we show numerically that strong gap junctional coupling between neighbors ensures an equilibrated response to agonist stimulation via formation of Ca²⁺ phase waves, i.e. a less sensitive neighbor will produce the same or similar Ca²⁺ signal as its highly sensitive neighbor. The most sensitive cells within an ensemble are the wave initiator cells. The Ca²⁺ wave in the cytoplasm is driven by a sensitization wave front in the endoplasmic reticulum. The wave velocity is proportional to the cellular sensitivity and to the strength of the coupling. The waves can form different patterns including circular rings and spirals. The observed pattern depends on the strength of noise, gap junctional permeability and the connectivity probability between neighboring cells. Our simulations reveal that one highly sensitive region gradually takes the lead within the entire noisy system by generating directed circular phase waves originating from this region.

The calcium ion (Ca²⁺), a universal signaling molecule, is widely recognized to play a fundamental role in the regulation of various biological processes. Agonist–evoked Ca²⁺ signals often manifest as rhythmic changes in the cytosolic free Ca²⁺ concentration (c_cyt) called Ca²⁺ oscillations. Stimuli intensity was found to be proportional to the oscillation frequency and the evoked down-steam cellular response. Stochastic receptor expression in individual cells in a cell population inevitably leads to individually different oscillation frequencies and individually different Ca²⁺-related cellular responses. However, in many organs, the neighboring cells have to overcome their individually different sensitivity and produce a synchronized response. Gap junctions are integral membrane structures that enable the direct cytoplasmic exchange of Ca²⁺ ions and InsP₃ molecules between neighboring cells. By simulations, we were able to demonstrate how the strength of intercellular gap junctional coupling in relation to stimulus intensity can modify the spatiotemporal patterns of Ca²⁺ signals and harmonize the Ca²⁺-related cellular responses via synchronization of oscillation frequency. We demonstrate that the most sensitive cells are the wave initiator cells and that a highly sensitive region plays an important role in the determination of the Ca²⁺ phase wave direction. This sensitive region will then also progressively determine the global behavior of the entire system.

Calcium-dependent regulation of glucose homeostasis in the liver

A major role of the liver is to integrate multiple signals to maintain normal blood glucose levels. The balance between glucose storage and mobilization is primarily regulated by the counteracting effects of insulin and glucagon. However, numerous signals converge in the liver to ensure energy demand matches the physiological status of the organism. Many circulating hormones regulate glycogenolysis, gluconeogenesis and mitochondrial metabolism by calcium-dependent signaling mechanisms that manifest as cytosolic Ca(2+) oscillations. Stimulus-strength is encoded in the Ca(2+) oscillation frequency, and also by the range of intercellular Ca(2+) wave propagation in the intact liver. In this article, we describe how Ca(2+) oscillations and waves can regulate glucose output and oxidative metabolism in the intact liver; how multiple stimuli are decoded though Ca(2+) signaling at the organ level, and the implications of Ca(2+) signal dysregulation in diseases such as metabolic syndrome and non-alcoholic fatty liver disease.

Gap junctions

Gap junctions are essential to the function of multicellular animals, which require a high degree of coordination between cells. In vertebrates, gap junctions comprise connexins and currently 21 connexins are known in humans. The functions of gap junctions are highly diverse and include exchange of metabolites and electrical signals between cells, as well as functions, which are apparently unrelated to intercellular communication. Given the diversity of gap junction physiology, regulation of gap junction activity is complex. The structure of the various connexins is known to some extent; and structural rearrangements and intramolecular interactions are important for regulation of channel function. Intercellular coupling is further regulated by the number and activity of channels present in gap junctional plaques. The number of connexins in cell-cell channels is regulated by controlling transcription, translation, trafficking, and degradation; and all of these processes are under strict control. Once in the membrane, channel activity is determined by the conductive properties of the connexin involved, which can be regulated by voltage and chemical gating, as well as a large number of posttranslational modifications. The aim of the present article is to review our current knowledge on the structure, regulation, function, and pharmacology of gap junctions. This will be supported by examples of how different connexins and their regulation act in concert to achieve appropriate physiological control, and how disturbances of connexin function can lead to disease.

Intercellular Ca(2+) waves: mechanisms and function

Intercellular calcium (Ca(2+)) waves (ICWs) represent the propagation of increases in intracellular Ca(2+) through a syncytium of cells and appear to be a fundamental mechanism for coordinating multicellular responses. ICWs occur in a wide diversity of cells and have been extensively studied in vitro. More recent studies focus on ICWs in vivo. ICWs are triggered by a variety of stimuli and involve the release of Ca(2+) from internal stores. The propagation of ICWs predominately involves cell communication with internal messengers moving via gap junctions or extracellular messengers mediating paracrine signaling. ICWs appear to be important in both normal physiology as well as pathophysiological processes in a variety of organs and tissues including brain, liver, retina, cochlea, and vascular tissue. We review here the mechanisms of initiation and propagation of ICWs, the key intra- and extracellular messengers (inositol 1,4,5-trisphosphate and ATP) mediating ICWs, and the proposed physiological functions of ICWs.

Systems biology of cellular rhythms

Rhythms abound in biological systems, particularly at the cellular level where they originate from the feedback loops present in regulatory networks. Cellular rhythms can be investigated both by experimental and modeling approaches, and thus represent a prototypic field of research for systems biology. They have also become a major topic in synthetic biology. We review advances in the study of cellular rhythms of biochemical rather than electrical origin by considering a variety of oscillatory processes such as Ca++ oscillations, circadian rhythms, the segmentation clock, oscillations in p53 and NF-κB, synthetic oscillators, and the oscillatory dynamics of cyclin-dependent kinases driving the cell cycle. Finally we discuss the coupling between cellular rhythms and their robustness with respect to molecular noise.

Calcium signalling and liver regeneration

After partial hepatectomy (PH) the initial mass of the organ is restored through a complex network of cellular interactions that orchestrate both proliferative and hepatoprotective signalling cascades. Among agonists involved in this network many of them drive Ca(2+) movements. During liver regeneration in the rat, hepatocyte cytosolic Ca(2+) signalling has been shown on the one hand to be deeply remodelled and on the other hand to enhance progression of hepatocytes through the cell cycle. Mechanisms through which cytosolic Ca(2+) signals impact on hepatocyte cell cycle early after PH are not completely understood, but at least they include regulation of immediate early gene transcription and ERK and CREB phosphorylation. In addition to cytosolic Ca(2+), there is also evidence that mitochondrial Ca(2+) and also nuclear Ca(2+) may be critical for the regulation of liver regeneration. Finally, Ca(2+) movements in hepatocytes, and possibly in other liver cells, not only impact hepatocyte progression in the cell cycle but more generally may regulate cellular homeostasis after PH.

[Experimental and computational approach of calcium signaling]

In many cell types, specific and robust signalling relies on a high level of spatiotemporal organization of Ca(2+) dynamics. In response to external stimulation, Ca(2+) signals ranging from a small increase of a few tens of nanomolar concentrations at the mouth of an inositol 1, 4, 5-trisphosphate receptor to the periodic propagation of waves invading an organ or a tissue, can be observed. Here, we review our combined experimental and computational approach of Ca(2+) dynamics, which has been mainly carried out on liver hepatocytes. We focus in particular on the understanding of the relationship between elementary Ca(2+) increases, Ca(2+) oscillations and intra- or intercellular Ca(2+) waves. The physiological impact of such signalling on liver function is also discussed.

Intercellular calcium waves in glial cells with bistable dynamics

A two-dimensional model is proposed for intercellular calcium (Ca(2 +)) waves with Ca(2 +)-induced IP(3) regeneration and the diffusion of IP(3) through gap junctions. Many experimental observations in glial cells, i.e. responding to local mechanical stimulation, glutamate application, mechanical stimulation followed by ACh application, and glutamate followed by mechanical stimulation, are reproduced and classified by the model. We show that a glial cell model with bistable dynamics, i.e. a Ca(2 +) oscillation state coexisting with a fixed point, can cause a prolonged plateau of Ca(2 +) signals in the cells nearby the stimulated cell when the cell network responds to the local mechanical stimulation.

Calcium oscillations

Calcium signaling results from a complex interplay between activation and inactivation of intracellular and extracellular calcium permeable channels. This complexity is obvious from the pattern of calcium signals observed with modest, physiological concentrations of calcium-mobilizing agonists, which typically present as sequential regenerative discharges of stored calcium, a process referred to as calcium oscillations. In this review, we discuss recent advances in understanding the underlying mechanism of calcium oscillations through the power of mathematical modeling. We also summarize recent findings on the role of calcium entry through store-operated channels in sustaining calcium oscillations and in the mechanism by which calcium oscillations couple to downstream effectors.

What can we learn from the irregularity of Ca2+ oscillations?

In most cells, Ca(2+) increases in response to external stimulation are organized in the form of oscillations and waves that sometimes propagate from one cell to another. Numerous experimental and theoretical studies reveal that this spatiotemporal organization contains a non-negligible level of stochasticity. In this study, we extend the previous work based on a statistical analysis of experimental Ca(2+) traces in isolated, hormone-stimulated hepatocytes and on stochastic simulations of Ca(2+) oscillations based on the Gillespie's algorithm. Comparison of the coefficients of variation in the periods of experimental and simulated Ca(2+) spikes provides information about the clustering and the specific subtypes of the Ca(2+) channels. In hepatocytes coupled by gap junctions, the global perfusion with a hormone leads to successive Ca(2+) responses, giving the appearance of an intercellular wave. Statistical analysis of experimental Ca(2+) oscillations in coupled hepatocytes confirms that this coordinated Ca(2+) spiking corresponds to a phase wave but suggests the existence of an additional coupling mechanism.

Hepatic denervation impairs the assembly and secretion of VLDL-TAG

VLDL secretion is a regulated process that depends on the availability of lipids, apoB and MTP. Our aim was to investigate the effect of liver denervation upon the secretion of VLDL and the expression of proteins involved in this process. Denervation was achieved by applying a 85% phenol solution onto the portal tract, while control animals were treated with 9% NaCl. VLDL secretion was evaluated by the Tyloxapol method. The hepatic concentration of TAG and cholesterol, and the plasma concentration of TAG, cholesterol, VLDL-TAG, VLDL-cholesterol and HDL-cholesterol were measured, as well as mRNA expression of proteins involved in the process of VLDL assembly. Hepatic acinar distribution of MTP and apoB was evaluated by immunohistochemistry. Denervation increased plasma concentration of cholesterol (125.3 +/- 10.1 vs. 67.1 +/- 4.9 mg dL(-1)) and VLDL-cholesterol (61.6 +/- 5.6 vs. 29.4 +/- 3.3 mg dL(-1)), but HDL-cholesterol was unchanged (45.5 +/- 6.1 vs. 36.9 +/- 3.9 mg dL(-1)). Secretion of VLDL-TAG (47.5 +/- 23.8 vs. 148.5 +/- 27.4 mg dL h(-1)) and mRNA expression of CPT I and apoB were reduced (p < 0.01) in the denervated animals. MTP and apoB acinar distribution was not altered in the denervated animals, but the intensity of the reaction was reduced in relation to controls.

Long-range interaction effects on calcium-wave propagation

In this paper, numerical simulation of calcium waves in a network of cells coupled together by a paracrine signaling is investigated. The model takes into account the long-range interaction between cells due to the action of extracellular messengers, which provide links between first-neighbor cells, but also on cells located far away from the excited cell. When considering bidirectional coupling, the long-range interaction influences neither the frequency nor the amplitude of oscillations, contrary to one-directional coupling. The long-range interaction influences the speed of propagation of Ca2+ waves in the network and induces enlargement of the transition zone before the steady regime of propagation is attained. We also investigate the long-range effects on the colonization of a given niche by a pathogenic microorganism signal on calcium wave propagation in the network.

Coupling and internal noise sustain synchronized oscillation in calcium system

In this work, the effects of coupling on two calcium subsystems were investigated, the cooperation between coupling and internal noise was also considered. When two non-identical subsystems are in steady state, coupling can induce oscillations, and distinctly enlarge the oscillatory region in bifurcation diagram. Besides, coupling can make the two non-identical oscillators synchronized. With the increment of the coupling strength, the cross-correlation time of the two oscillators firstly increases and then decreases to be constant, showing the synchronization without tuning coupling strength. When internal noise is considered, similar phenomena can also be obtained under the cooperation between coupling and internal noise.

Connexin channel permeability to cytoplasmic molecules

Connexin channels are known to be permeable to a variety of cytoplasmic molecules. The first observation of second messenger junctional permeability, made approximately 30 years ago, sparked broad interest in gap junction channels as mediators of intercellular molecular signaling. Since then, much has been learned about the diversity of connexin channels with regard to isoform diversity, tissue and developmental distribution, modes of channel regulation, assembly, expression, biochemical modification and permeability, all of which appear to be dynamically regulated. This information has expanded the potential roles of connexin channels in development, physiology and disease, and made their elucidation much more complex--30 years ago such an orchestra of junctional dynamics was unanticipated. Only recently, however, have investigators been able to directly address, in this more complex framework, the key issue: what specific biological molecules, second messengers and others, are able to permeate the various types of connexin channels, and how well? An important related issue, given the ever-growing list of connexin-related pathologies, is how these permeabilities are altered by disease-causing connexin mutations. Together, many studies show that a variety of cytoplasmic molecules can permeate the different types of connexin channels. A few studies reveal differences in permeation by different molecules through a particular type of connexin channel, and differences in permeation by a particular molecule through different types of connexin channels. This article describes and evaluates the various methods used to obtain these data, presents an annotated compilation of the results, and discusses the findings in the context of what can be inferred about mechanism of selectivity and potential relevance to signaling. The data strongly suggest that highly specific interactions take place between connexin pores and specific biological molecular permeants, and that those interactions determine which cytoplasmic molecules can permeate and how well. At this time, the nature of those interactions is unclear. One hopes that with more detailed permeability and structural information, the specific molecular mechanisms of the selectivity can be elucidated.

Mean-field coupling of calcium oscillations in a multicellular system of rat hepatocytes

In a multicellular system of rat hepatocytes and even in an intact liver, cytoplasmic calcium oscillations are synchronized and highly coordinated. In this paper, the mean-field coupling term has been introduced to describe the coupling flux, which is more efficient than gap junctional coupling terms. An optimal coupling strength and an optimal stimulation level for the synchronization of the coupled system have been observed in this paper. Moreover, it has been proved that these results are independent of the cells number. Interestingly, it has been observed that the intracellular noise and the extracellular noise have different effects on the synchronization of the coupled system.

Calcium Dynamics: Spatio‐Temporal Organization from the Subcellular to the Organ Level

Many essential physiological processes are controlled by calcium. To ensure reliability and specificity, calcium signals are highly organized in time and space in the form of oscillations and waves. Interesting findings have been obtained at various scales, ranging from the stochastic opening of a single calcium channel to the intercellular calcium wave spreading through an entire organ. A detailed understanding of calcium dynamics thus requires a link between observations at different scales. It appears that some regulations such as calcium-induced calcium release or PLC activation by calcium, as well as the weak diffusibility of calcium ions play a role at all levels of organization in most cell types. To comprehend how calcium waves spread from one cell to another, specific gap-junctional coupling and paracrine signaling must also be taken into account. On the basis of a pluridisciplinar approach ranging from physics to physiology, a unified description of calcium dynamics is emerging, which could help understanding how such a small ion can mediate so many vital functions in living systems.

A mesoscopic stochastic mechanism of cytosolic calcium oscillations

Based on a model of intracellular calcium (Ca(2+)) oscillation with self-modulation of inositol 1,4,5-trisphosphate signal, the mesoscopic stochastic differential equations for the intracellular Ca(2+) oscillations are theoretically derived by using the chemical Langevin equation method. The effects of the finite biochemical reaction molecule number on both simple and complex cytosolic Ca(2+) oscillations are numerically studied. In the case of simple intracellular Ca(2+) oscillation, it is found that, with the increase of molecule number, the coherence resonance or autonomous resonance phenomena can occur for some external stimulation parameter values. In the cases of complex cytosolic Ca(2+) oscillations, each extremum of concentration of cytosolic Ca(2+) oscillations corresponds to a peak in the histogram of Ca(2+) concentration, and the most probability appeared during the bursting plateau level for bursting, but at the largest minimum of Ca(2+) concentration for chaos. For quasi-periodicity, however, there are only two peaks in the histogram of Ca(2+) concentration, and the most probability is located at low concentration state.

Intercellular waves propagation in an array of cells coupled through paracrine signaling: a computer simulation study

A linear chain of cells is considered in which calcium (Ca2+) fluctuations within a cell are described by a simple minimal model. Cells are coupled together by bidirectional paracrine signaling via calcium oscillations. Two typical zones of propagation are observed: a transition zone and a regular zone. The transition zone exhibits the same phenomena that can be observed in single cells, pairs or triplets of cells. Within the regular zone, simple periodic oscillations of calcium propagate and the Ca2+ signal is similar from one cell to another (same amplitude and same frequency). But, the signals are separated by a slight phase shift characterizing the propagation of Ca2+ waves due to the type of coupling used. We also consider the colonization of the lattice by the abnormal oscillations of sick cells.

Is there a specific role for the plasma membrane Ca2+ -ATPase in the hepatocyte?

The plasma membrane Ca2+ -ATPase (PMCA) is responsible for the fine, long-term regulation of the cytoplasmic calcium concentration by extrusion of this cation from the cell. Although the general kinetic mechanisms for the action of both, well coordinated hydrolytic activity and calcium transport are reasonably understood in the majority of cell types, due to the complex physiologic and biochemical characteristics shown by the hepatocyte, the study of this enzyme in this cell type has become a real challenge. Here, we review the various molecular aspects known to date to be associated with liver PMCA activity, and outline the strategies to follow for establishing the role of this enzyme in the overall physiology of the hepatocyte. In this way, we first concentrate on the basic biochemical aspects of liver cell PMCA, and place an important emphasis on expression of its molecular forms to finally focus on the critical hormonal regulation of the enzyme. Although these complex aspects have been studied mainly under normal conditions, the significance of PMCA in the calcium homeostasis of an abnormal liver cell is also reviewed.

A stochastic two-dimensional model of intercellular Ca2+ wave spread in glia

We describe a two-dimensional stochastic model of intercellular Ca(2+) wave (ICW) spread in glia that includes contributions of external stimuli, ionotropic and metabotropic P2 receptors, exo- and ecto-nucleotidases, second messengers, and gap junctions. In this model, an initial stimulus evokes ATP and UTP release from a single cell. Agonists diffuse and are degraded both in bulk solution and at cell surfaces. Ca(2+) elevation in individual cells is determined by bound agonist concentrations s and by number and features of P2 receptors summed with that generated by IP(3) diffusing through gap junction channels. Variability of ICWs is provided by randomly distributing a predetermined density of cells in a rectangular grid and by randomly selecting within intervals values characterizing the extracellular compartment, individual cells, and interconnections with neighboring cells. Variability intervals were obtained from experiments on astrocytoma cells transfected to express individual P2 receptors and/or the gap junction protein connexin43. The simulation program (available as Supplementary Material) permits individual alteration of ICW components, allowing comparison of simulations with data from cells expressing connexin43 and/or various P2 receptor subtypes. Such modeling is expected to be useful for testing phenomenological hypotheses and in understanding consequences of alteration of system components under experimental or pathological conditions.

Effects of gap junction to Ca(2+) and to IP(3) on the synchronization of intercellular calcium oscillations in hepatocytes

The frequency of free cytosolic calcium concentration ([Ca(2+)]) oscillations elicited by a given agonist concentration differs between individual hepatocytes. However, in multicellular systems of rat hepatocytes and even in the intact liver, [Ca(2+)] oscillations are synchronized and highly coordinated. In this paper, we have investigated theoretically the gap junction permeable to calcium and to IP(3) on intercellular synchronization by means of a mathematical model, respectively. It is shown that gap junction permeable to calcium and to IP(3) are effective on synchronizing calcium oscillations in coupled hepatocytes. Our theoretical results are similar either for the case of Ca(2+) acting as coordinating messenger or for the case of IP(3) as coordinating messenger. There exists an optimal coupling strength for a pair of connected hepatocytes. Appropriate coupling strength and IP(3) level can induce various harmonic locking of intercellular [Ca(2+)] oscillations. Furthermore, a phase diagram in two-dimensional parameter space of the coupling strength and IP(3) level (or the velocity of IP(3) synthesis) has been predicted, in which the synchronization region is similar to Arnol'd tongue.

Role of voltage-dependent modulation of store Ca2+ release in synchronization of Ca2+ oscillations

Slow waves are rhythmic depolarizations that underlie mechanical activity of many smooth muscles. Slow waves result through rhythmic Ca(2+) release from intracellular Ca(2+) stores through inositol 1,4,5-trisphosphate (IP(3)) sensitive receptors and Ca(2+)-induced Ca(2+) release. Ca(2+) oscillations are transformed into membrane depolarizations by generation of a Ca(2+)-activated inward current. Importantly, the store Ca(2+) oscillations that underlie slow waves are entrained across many cells over large distances. It has been shown that IP(3) receptor-mediated Ca(2+) release is enhanced by membrane depolarization. Previous studies have implicated diffusion of Ca(2+) or the second messenger IP(3) across gap junctions in synchronization of Ca(2+) oscillations. In this study, a novel mechanism of Ca(2+) store entrainment through depolarization-induced IP(3) receptor-mediated Ca(2+) release is investigated. This mechanism is significantly different from chemical coupling-based mechanisms, as membrane potential has a coupling effect over distances several orders of magnitude greater than either diffusion of Ca(2+) or IP(3) through gap junctions. It is shown that electrical coupling acting through voltage-dependent modulation of store Ca(2+) release is able to synchronize oscillations of cells even when cells are widely separated and have different intrinsic frequencies of oscillation.

Phase synchronization and coherence resonance of stochastic calcium oscillations in coupled hepatocytes

The frequency of free cytosolic calcium concentration ([Ca(2+)]) oscillations elicited by a given agonist concentration differs between individual hepatocytes. However, in multicellular systems of rat hepatocytes and even in the intact liver, [Ca(2+)] oscillations are synchronized and highly coordinated. In this paper, we have investigated theoretically the effects of gap junction permeable to calcium and of the total Ca(2+) channel number located on endoplasmic reticulum on intercellular synchronization. Figures of ratio between mean oscillating frequency of coupled cells describe visually the process of phase-locking. By virtue of a set of phase analysis, we can observe a gradual transition from synchronous behavior to nonsynchronous behavior. Furthermore, a signal-to-noise ratio in two dimensional parameter space (coupling strength-total Ca(2+) channel number) has suggested that, coherence resonance will occur for appropriate noise and coupling.

Calcium oscillations in a triplet of pancreatic acinar cells

We use a mathematical model of calcium dynamics in pancreatic acinar cells to investigate calcium oscillations in a ring of three coupled cells. A connected group of cells is modeled in two different ways: 1), as coupled point oscillators, each oscillator being described by a spatially homogeneous model; and 2), as spatially distributed cells coupled along their common boundaries by gap-junctional diffusion of inositol trisphosphate and/or calcium. We show that, although the point-oscillator model gives a reasonably accurate general picture, the behavior of the spatially distributed cells cannot always be predicted from the simpler analysis; spatially distributed diffusion and cell geometry both play important roles in determining behavior. In particular, oscillations in which two cells are in synchrony, with the third phase-locked but not synchronous, appears to be more dominant in the spatially distributed model than in the point-oscillator model. In both types of model, intercellular coupling leads to a variety of synchronous, phase-locked, or asynchronous behaviors. For some parameter values there are multiple, simultaneous stable types of oscillation. We predict 1), that intercellular calcium diffusion is necessary and sufficient to coordinate the responses in neighboring cells; 2), that the function of intercellular inositol trisphosphate diffusion is to smooth out any concentration differences between the cells, thus making it easier for the diffusion of calcium to synchronize the oscillations; 3), that groups of coupled cells will tend to respond in a clumped manner, with groups of synchronized cells, rather than with regular phase-locked periodic intercellular waves; and 4), that enzyme secretion is maximized by the presence of a pacemaker cell in each cluster which drives the other cells at a frequency greater than their intrinsic frequency.

Local dissipation and coupling properties of cellular oscillators: a case study on calcium oscillations

Synchronised signal transduction between cells is crucial, since it assures fast and immutable information processing, which is vital for flawless functioning of living organisms. The question arises how to recognise the ability of a cell to be easily coupled with other cells. In the present paper, we investigate the system properties that determine best coupling abilities and assure the most efficient signal transduction between cells. A case study is done for intercellular calcium oscillations. For a particular diffusion-like coupled system of cellular oscillators, we determined the minimal gap-junctional permeability that is necessary for synchronisation of initially asynchronous oscillators. Our results show that dissipation is a crucial system property that determines the coupling ability of cellular oscillators. We found that low dissipation assures synchronisation of coupled cells already at very low gap-junctional permeability, whereas highly dissipative oscillators require much higher gap-junctional permeability in order to synchronise. The results are discussed in the sense of their biological importance for systems where the synchronous responses of cells were recognised to be indispensable for appropriate physiological functioning of the tissue.

Simulation of calcium waves in ascidian eggs: insights into the origin of the pacemaker sites and the possible nature of the sperm factor

Fertilization triggers repetitive waves of cytosolic Ca2+ in the egg of many species. The mechanism involved in the generation of Ca2+ waves has been studied in much detail in mature ascidian eggs, by raising artificially the level of inositol 1,4,5-trisphosphate [Ins(1,4,5)P3] or of its poorly metabolizable analogue, glycero-myo-phosphatidylinositol 4,5-bisphosphate [gPtdIns(4,5)P2]. Here, we use this strategy and the experimental results it provides to develop a realistic theoretical model for repetitive Ca2+ wave generation and propagation in mature eggs. The model takes into account the heterogeneous spatial distribution of the endoplasmic reticulum. Our results corroborate the hypothesis that Ca2+ wave pacemakers are associated with cortical accumulations of endoplasmic reticulum. The model is first tested and validated by the adequate match between its theoretical predictions and the observed effects of localized injections of massive amounts of Ins(1,4,5)P3 analogues. In a second step, we use the model to make some propositions about the possible characteristics of the sperm factor. We find that to account for the spatial characteristics of the first series of Ca2+ waves seen at fertilization in ascidian eggs, it has to be assumed that, if the sperm factor is a phospholipase C, it is Ca2+-sensitive and highly diffusible. Although the actual state of knowledge does not allow us to explain the observed relocalization of the Ca2+ wave pacemaker site, the model corroborates the assumption that PtdIns(4,5)P2, the substrate for phospholipase C is distributed over the entire egg. We also predict that the dose of sperm factor injected into the egg should modulate the temporal characteristics of the first, long-lasting fertilization wave.

Intercellular calcium signalling in cultured renal epithelia: a theoretical study of synchronization mode and pacemaker activity

We investigate a two-dimensional lattice model representation of intercellular Ca2+ signalling in a population of epithelial cells coupled by gap junctions. The model is based on and compared with Ca2+ imaging data from globally bradykinin-stimulated MDCK-I (Madin-Darby canine kidney)-I cell layers. We study large-scale synchronization of relevance to our laboratory experiments. The system is found to express a wealth of dynamics, including quasiperiodic, chaotic and multiply-periodic behaviour for intermediate couplings. We take a particular interest in understanding the role of "pacemaker cells" in the synchronization process. It has been hypothesized that a few highly hormone-sensitive cells control the collective frequency of oscillation, which is close to the natural frequencies (without coupling) of these cells. The model behaviour is consistent with the conjectures of the pacemaker cell hypothesis near the critical coupling where the cells lock onto a single frequency. However, the simulations predict that the frequency in globally connected systems decreases with increasing coupling. It is found that a pacemaker is not defined by its natural frequency alone, but that other intrinsic or local factors must be considered. Inclusion of partly sensitized cells that do not oscillate autonomously in the cell layer increases the coupling necessary for global synchronization. For not excessively high coupling, these cells oscillate irregularly and with distinctive lower frequencies. In summary, the present study shows that the frequency of synchronized oscillations is not dictated by one or few fast-responding cells. The collective frequency is the result of a two-way communication between the phase-advanced pacemaker and its environment.

Plasma membrane channels formed by connexins: their regulation and functions

Members of the connexin gene family are integral membrane proteins that form hexamers called connexons. Most cells express two or more connexins. Open connexons found at the nonjunctional plasma membrane connect the cell interior with the extracellular milieu. They have been implicated in physiological functions including paracrine intercellular signaling and in induction of cell death under pathological conditions. Gap junction channels are formed by docking of two connexons and are found at cell-cell appositions. Gap junction channels are responsible for direct intercellular transfer of ions and small molecules including propagation of inositol trisphosphate-dependent calcium waves. They are involved in coordinating the electrical and metabolic responses of heterogeneous cells. New approaches have expanded our knowledge of channel structure and connexin biochemistry (e.g., protein trafficking/assembly, phosphorylation, and interactions with other connexins or other proteins). The physiological role of gap junctions in several tissues has been elucidated by the discovery of mutant connexins associated with genetic diseases and by the generation of mice with targeted ablation of specific connexin genes. The observed phenotypes range from specific tissue dysfunction to embryonic lethality.

Under what conditions signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations

Sensitivity and flexibility are typical properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. In particular, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization is not significantly different in regular and chaotic Ca2+ oscillations. However, both types of oscillation are highly flexible in regimes with weak dissipation. Therefore, we conclude that dissipation of free energy is a suitable index characterizing flexibility. For biological systems this appears to be of special importance since for thermodynamic reasons, notably in view of low free energy consumption, dissipation should be minimized.

Hormone receptor gradients supporting directional Ca2+ signals: direct evidence in rat hepatocytes

BACKGROUND/AIMS

In the liver, InsP(3)-dependent agonists such as vasopressin and noradrenaline induce tightly coordinated sequences of intracellular Ca(2+) increases, leading to apparent unidirectional Ca(2+) waves. In previous works, we have postulated that cell-to-cell differences in hormone receptor density create a cellular sensitivity gradient that determines which cell initiates the intercellular Ca(2+) wave and the direction of propagation of the Ca(2+) signal. The aim of this study was to test directly this hypothesis.

METHODS

Lobular distribution of V1a vasopressin receptors and alpha1 adrenergic receptors were observed by autoradiography in rat liver sections. Cell-to-cell differences in the number of these receptors were evaluated on hepatocyte multiplets using specific fluorescent probes.

RESULTS

The relative amount of fluorescence associated with the V1a receptor differed significantly between cells within multiplets. The 'cell-after-cell' Ca(2+) increase induced by vasopressin was correlated with the number of V1a receptors. These observations may be more general, as autoradiography revealed similar lobular distributions of V1a receptors and alpha1 adrenergic receptors; the amounts of both were greatest in hepatocytes surrounding central veins.

CONCLUSIONS

These data confirm that a fine gradient along liver cell plates contributes to the molecular basis of the unidirectional hormone-induced Ca(2+) signalling observed in the liver lobule.

Intercellular calcium waves mediate preferential cell growth toward the wound edge in polarized hepatic cells

During liver regeneration, hepatocytes sense the damage and initiate proliferation of the quiescent cells through poorly understood mechanisms. Here, we have used cultured hepatic cells to study the roles played by intercellular calcium in mediating wound-healing processes. Well-differentiated and polarized Hep-G2 cells repaired an experimentally induced wound by induction of cell divisions. The resulting cellular growth did not occur evenly across the healing cell lawn; instead, proliferations were three times more active within 150-200 microm from the wound edge than further away; this periwound preferential cell growth was not observed in the poorly differentiated and/or nonpolarized cells. We have provided experimental evidence demonstrating that the wounding procedure itself could elicit a propagating calcium wave, and interestingly, blocking this injury-associated intercellular calcium communication could effectively inhibit the biased cell growth along the margin of the wound. A photolithography-based patterned cell culture system was employed to help delineate the mechanisms underlying this type of calcium signaling. In conclusion, our results suggested that intercellular communications via propagating calcium waves coordinate regenerative cell proliferations in response to hepatic tissue losses.

Intercellular communication via intracellular calcium oscillations

In this letter, we present the results of a simple model for intercellular communication via calcium oscillations, motivated in part by a recent experimental study. The model describes two cells (a "donor" and "sensor") whose intracellular dynamics involve a calcium-induced, calcium release process. The cells are coupled by assuming that the input of the sensor cell is proportional to the output of the donor cell. As one varies the frequency of calcium oscillations of the donor cell, the sensor cell passes through a sequence of N : M phase-locked regimes and exhibits a "Devil's staircase" behavior. Such a phase-locked response has been seen experimentally in pulsatile stimulation of single cells. We also study a stochastic version of the coupled two-cell model. We find that phase locking holds for realistic choices for the cell volume.

Ca2+ phase waves: a basis for cellular pacemaking and long-range synchronicity in the guinea-pig gastric pylorus

Ca2+ imaging and multiple microelectrode recording procedures were used to investigate a slow wave-like electrical rhythmicity in single bundle strips from the circular muscle layer of the guinea-pig gastric pylorus. The 'slow waves' (SWs) consisted of a pacemaker and regenerative component, with both potentials composed of more elementary events variously termed spontaneous transient depolarizations (STDs) or unitary potentials. STDs and SW pacemaker and regenerative potentials exhibited associated local and distributed Ca2+ transients, respectively. Ca2+ transients were often larger in cellular regions that exhibited higher basal Ca2+ indicator-associated fluorescence, typical of regions likely to contain intramuscular interstitial cells of Cajal (ICCIM). The emergence of rhythmicity arose through entrainment of STDs resulting in pacemaker Ca2+ transients and potentials, events that exhibited considerable spatial synchronicity. Application of ACh to strips exhibiting weak rhythmicity caused marked enhancement of SW synchronicity. SWs and underlying Ca2+ increases exhibited very high 'apparent conduction velocities' ('CVs') orders of magnitude greater than for sequentially conducting Ca2+ waves. Central interruption of either intercellular connectivity or inositol 1,4,5-trisphosphate receptor (IP3R)-mediated store Ca2+ release in strips caused SWs at the two ends to run independently of each other, consistent with a coupled oscillator-based mechanism. Central inhibition of stores required much wider regions of blockade than inhibition of connectivity indicating that stores were voltage-coupled. Simulations, made using a conventional store array model but now including depolarization coupled to IP3R-mediated Ca2+ release, predicted the experimental findings. The linkage between membrane voltage and Ca2+ release provides a means for stores to interact as strongly coupled oscillators, resulting in the emergence of Ca2+ phase waves and associated pacemaker potentials. This distributed pacemaker triggers regenerative Ca2+ release and resultant SWs.

Ca2+ oscillations in hepatocytes do not require the modulation of InsP3 3-kinase activity by Ca2+

Receptor-mediated production of inositol 1,4,5-trisphosphate (InsP(3)) initiates Ca(2+) release and is responsible for cytosolic Ca(2+) oscillations. InsP(3) oscillations have also been observed in some cells. One of the enzymes controlling InsP(3) catabolism, the InsP(3) 3-kinase, is stimulated by Ca(2+); this regulation is presumably part of the reason for InsP(3) oscillations that have been observed in some cells. Here, we investigate the possible role of Ca(2+)-activated InsP(3) catabolism on the characteristics of the InsP(3)-induced Ca(2+) oscillations. Numerical simulations show that if it is assumed that the Ca(2+)-independent InsP(3) catabolism is predominant, Ca(2+) oscillations remain qualitatively unchanged although the relative amplitude of the oscillations in InsP(3) concentrations becomes minimal. We tested this prediction in hepatocytes by masking the Ca(2+)-dependent InsP(3) catabolism by 3-kinase through the injection of massive amounts of InsP(3) 5-phosphatase, which is not stimulated by Ca(2+). We find that in such injected hepatocytes, Ca(2+) oscillations generated by modest agonist levels are suppressed, presumably because of the decreased dose in InsP(3), but that at higher doses of agonist, oscillations reappear, with characteristics similar to those of untreated cells at low agonist doses. Altogether, these results suggest that oscillations in InsP(3) concentration due to Ca(2+)-stimulated InsP(3) catabolism do not play a major role for the oscillations in Ca(2+) concentration.

Computational approaches to cellular rhythms

Oscillations arise in genetic and metabolic networks as a result of various modes of cellular regulation. In view of the large number of variables involved and of the complexity of feedback processes that generate oscillations, mathematical models and numerical simulations are needed to fully grasp the molecular mechanisms and functions of biological rhythms. Models are also necessary to comprehend the transition from simple to complex oscillatory behaviour and to delineate the conditions under which they arise. Examples ranging from calcium oscillations to pulsatile intercellular communication and circadian rhythms illustrate how computational biology contributes to clarify the molecular and dynamical bases of cellular rhythms.

Expression and regulation of gap junctions in rat cholangiocytes

Hepatocytes and other digestive epithelia exchange second messengers and coordinate their functions by communicating through gap junctions. However, little is known about intercellular communication in cholangiocytes. The aim of this study was to examine expression and regulation of gap junctions in cholangiocytes. Connexin expression was determined by confocal immunofluorescence in rat bile ducts and in normal rat cholangiocyte (NRC) cells, a polarized cholangiocyte cell line. Intercellular Ca(2+) signaling was monitored by fluorescent microscopy. Microinjection studies assessed regulation of gap junction permeability in NRC cells and in SKHep1 cells, a liver-derived cell line engineered to express connexin 43. Immunochemistry showed that cholangiocytes from normal rat liver as well as the NRC cells express connexin 43. Localization of apical, basolateral, and tight junction proteins confirmed that NRC cells are well polarized. Apical exposure to ATP induced Ca(2+) oscillations that were coordinated among neighboring NRC cells, and inhibition of gap junction conductance desynchronized the Ca(2+) oscillations. NRC cells transfected with a connexin 43 antisense were significantly less coupled. Transcellular dye spreading was inhibited by activation of protein kinase A or protein kinase C. The same was observed in transfected SKHep1 cells, which expressed only connexin 43. Rat cholangiocytes and NRC cells express connexin 43, which permits synchronization of Ca(2+) signals among cells. Permeability of connexin 43-gap junctions is negatively regulated by protein kinases A and C. In conclusion, cholangiocytes have the capacity for intercellular communication of second messenger signals via gap junctions in a fashion that is under hormonal control.

Control and plasticity of intercellular calcium waves in astrocytes: a modeling approach

Intercellular Ca2+ waves in astrocytes are thought to serve as a pathway of long-range signaling. The waves can propagate by the diffusion of molecules through gap junctions and across the extracellular space. In rat striatal astrocytes, the gap-junctional route was shown to be dominant. To analyze the interplay of the processes involved in wave propagation, a mathematical model of this system has been developed. The kinetic description of Ca2+ signaling within a single cell accounts for inositol 1,4,5-trisphosphate (IP3) generation, including its activation by cytoplasmic Ca2+, IP3-induced Ca2+ liberation from intracellular stores and various other Ca2+ transports, and cytoplasmic diffusion of IP3 and Ca2+. When cells are coupled by gap junction channels in a two-dimensional array, IP3 generation in one cell triggers Ca2+ waves propagating across some tens of cells. The spatial range of wave propagation is limited, yet depends sensitively on the Ca2+-mediated regeneration of the IP3 signal. Accordingly, the term "limited regenerative signaling" is proposed. The gap-junctional permeability for IP3 is the crucial permissive factor for wave propagation, and heterogeneity of gap-junctional coupling yields preferential pathways of wave propagation. Processes involved in both signal initiation (activation of IP3 production caused by receptor agonist) and regeneration (activation of IP3 production by Ca2+, loading of the Ca2+ stores) are found to exert the main control on the wave range. The refractory period of signaling strongly depends on the refilling kinetics of the Ca2+ stores. Thus the model identifies multiple steps that may be involved in the regulation of this intercellular signaling pathway.

Polarized calcium and calmodulin signaling in secretory epithelia

This review examines polarized calcium and calmodulin signaling in exocrine epithelial cells. The calcium ion is a simple, evolutionarily ancient, and universal second messenger. In exocrine epithelial cells, it regulates essential functions such as exocytosis, fluid secretion, and gene expression. Exocrine cells are structurally polarized, with the apical region usually dedicated to secretion. Recent advances in technology, in particular the development of videoimaging and confocal microscopy, have led to the discovery of polarized, subcellular calcium signals in these cell types. The properties of a rich variety of local and global calcium signals have now been described in secretory epithelial cells. Secretagogues stimulate apical-to-basal waves of calcium in many exocrine cell types, but there are some interesting exceptions to this rule. The shapes of intracellular calcium signals are determined by the distribution of calcium-releasing channels and mechanisms that limit calcium elevation. Polarized distribution of calcium-handling mechanisms also leads to transcellular calcium transport in exocrine epithelial cells. This transport can deliver considerable amounts of calcium into secreted fluids. Multicellular polarized calcium signals can coordinate the activity of many individual cells in epithelial secretory tissue. Certain particularly sensitive cells serve as pacemakers for initiation of intercellular calcium waves. Many calcium signaling pathways involve activation of calmodulin. This ubiquitous protein regulates secretion in exocrine cells and also activates interesting feedback interactions with calcium channels and transporters. Very recently it became possible to directly study polarized calcium-calmodulin reactions and to visualize the process of hormone-induced redistribution of calmodulin in live cells. The structural and functional polarity of secretory epithelia alongside the polarity of its calcium and calmodulin signaling present an interesting lesson in tissue organization.