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Immune responses are tightly regulated by a diverse set of interacting immune cell populations. Alongside decision-making processes such as differentiation into specific effector cell types, immune cells initiate proliferation at the beginning of an inflammation, forming two layers of complexity. Here, we developed a general mathematical framework for the data-driven analysis of collective immune-cell dynamics. We identified qualitative and quantitative properties of generic network motifs, and we specified differentiation dynamics by analysis of kinetic transcriptome data. Further, we derived a specific, data-driven mathematical model for Th1 vs. Tfh cell fate-decision dynamics in acute and chronic LCMV infections in mice. The model recapitulates important dynamical properties without model fitting, and solely by employing measured response-time distributions. Model simulations predict different windows of opportunity for perturbation in acute and chronic infection scenarios, with potential implications for optimization of targeted immunotherapy.

Selective differentiation of CD4+ T helper (Th) cells into specialized subsets such as Th1 and Th2 cells is a key element of the adaptive immune system driving appropriate immune responses. Besides those canonical Th cell lineages, hybrid phenotypes such as Th1/2 cells arise in vivo, and their generation could be reproduced in vitro. While master-regulator transcription factors like T-bet for Th1 and GATA-3 for Th2 cells drive and maintain differentiation into the canonical lineages, the transcriptional architecture of hybrid phenotypes is less well understood. In particular, it has remained unclear whether a hybrid phenotype implies a mixture of the effects of several canonical lineages for each gene, or rather a bimodal behavior across genes. Th cell differentiation is a dynamic process in which the regulatory factors are modulated over time, but longitudinal studies of Th cell differentiation are sparse. Here, we present a dynamic transcriptome analysis following Th cell differentiation into Th1, Th2 and Th1/2 hybrid cells. We identified an early bifurcation point in gene expression programs, and we found that only a minority of ∼20% of Th cell-specific genes showed mixed effects from both Th1 and Th2 cells on Th1/2 hybrid cells. While most genes followed either Th1 or Th2 cell gene expression, another fraction of ∼20% of genes followed a Th1 and Th2 cell-independent transcriptional program under control of the transcription factors STAT1 and STAT4. Overall, our results emphasize the key role of high-resolution longitudinal data for the characterization of cellular phenotypes.

Cytokines are diffusible mediators of cell-cell communication among immune cells with critical regulatory functions for cell differentiation and proliferation. Previous studies have revealed considerable spatial inhomogeneities in the distribution of cytokine molecules in tissues, potentially shaping the efficacy and range of paracrine cytokine signals. How such cytokine gradients emerge and are controlled within cell populations is incompletely understood. In this work, we employed a spatial reaction-diffusion model to systematically investigate the formation and influence of spatial cytokine gradients. We found the fraction of cytokine secreting cells to be the main source of spatial inhomogeneity and subsequent activation. Positive feedback from local cytokine levels upon cytokine receptor expression leads to further increased spatial cytokine inhomogeneities. By exploring the effect of co-clustering cytokine secreting cells and cells with large amounts of receptor expression, as in the presence of regulatory T cells in the vicinity of antigen-presenting cells, we found that such constrained tissue architecture can have profound effects on the range of paracrine cytokine signals.

Resident memory T lymphocytes (T

While it is generally accepted that tissue-resident memory T lymphocytes protect host tissues from secondary immune challenges, it is unclear whether, and if so, how they contribute to systemic secondary immune responses. Here we show that in human individuals with an established immune memory to measles, mumps and rubella viruses, when challenged with the measles-mumps-rubella (MMR) vaccine again, tissue-resident memory CD4+ T cells are mobilized into the blood within 16 to 48 hours after vaccination. These cells then leave the blood again, and apparently contribute to the systemic secondary immune reaction, as is evident from the representation of mobilized T cell receptor Vβ clonotypes among newly generated circulating memory T lymphocytes, from day 7 onwards. Mobilization of the tissue-resident memory T cells is cognate, in that memory T lymphocytes recognizing other antigens, e.g. tetanus toxin, are not mobilized, unless they cross-react with the vaccine. These data originally demonstrate the essential contribution of tissue-resident memory T cells to secondary systemic immune responses, confirming that immunological memories to systemic pathogens are maintained (also) by tissue-resident memory T cells. In practical terms, the present work defines day 1 to 2 after antigenic challenge as a time window to assess the entire immunological T cell memory for a certain pathogen, including mobilized tissue-resident memory T cells, and its correlates of effectivity.Capsule summaryThe study demonstrates the rapid and cognate mobilization of tissue-resident memory CD4+ T cells into the blood upon antigenic rechallenge, and their contribution to secondary systemic immune responses.

Natural killer (NK) cells are innate lymphocytes that lack antigen-specific rearranged receptors, a hallmark of adaptive lymphocytes. In some people infected with human cytomegalovirus (HCMV), an NK cell subset expressing the activating receptor NKG2C undergoes clonal-like expansion that partially resembles anti-viral adaptive responses. However, the viral ligand that drives the activation and differentiation of adaptive NKG2C+ NK cells has remained unclear. Here we found that adaptive NKG2C+ NK cells differentially recognized distinct HCMV strains encoding variable UL40 peptides that, in combination with pro-inflammatory signals, controlled the population expansion and differentiation of adaptive NKG2C+ NK cells. Thus, we propose that polymorphic HCMV peptides contribute to shaping of the heterogeneity of adaptive NKG2C+ NK cell populations among HCMV-seropositive people.

SUMMARY Cell-to-cell communication networks have critical roles in coordinating diverse organismal processes, such as tissue development or immune cell response. However, compared with intracellular signal transduction networks, the function and engineering principles of cell-to-cell communication networks are far less understood. Major complications include: cells are themselves regulated by complex intracellular signaling networks; individual cells are heterogeneous; and output of any one cell can recursively become an additional input signal to other cells. Here, we make use of a framework that treats intracellular signal transduction networks as “black boxes” with characterized input-to-output response relationships. We study simple cell-to-cell communication circuit motifs and find conditions that generate bimodal responses in time, as well as mechanisms for independently controlling synchronization and delay of cell-population responses. We apply our modeling approach to explain otherwise puzzling data on cytokine secretion onset times in T cells. Our approach can be used to predict communication network structure using experimentally accessible input-to-output measurements and without detailed knowledge of intermediate steps., In Brief Interacting cellular communities have critical roles in biological functions such as tissue development or immune responses. Cell-to-cell communication networks comprise both intra- and intercellular processes, making detailed mathematical models intractable. Here, we develop a scalable framework for modeling extra-cellular communication networks that treats intracellular signal transduction networks as “black boxes” with characterized input-to-output response relationships. We discover that a range of dynamic cell-population behaviors, including cellular synchronization, delays, and bimodal responses, can emerge from simple cell-to-cell communication networks.

Cell-to-cell communication networks have critical roles in diverse organismal processes, such as coordinating tissue development or immune cell response. However, compared to intracellular signal transduction networks, the function and engineering principles of cell-to-cell communication networks are far less understood. Here, we study cell-to-cell communication networks using a framework that models the input-to-output relationship of intracellular signal transduction networks with a single function—the response-time distribution. We identify a prototypic response-time distribution—the gamma distribution—arising in both experimental data sets and mathematical models of signal-transduction pathways. We find that simple cell-to-cell communication circuits can generate bimodal response-time distributions, and can control synchronization and delay of cell-population responses independently. We apply our modeling approach to explain otherwise puzzling data on cytokine secretion onset times in T cells. Our approach can be used to predict communication network structure using experimentally accessible input-to-output measurements and without detailed knowledge of intermediate steps.

Circadian rhythms govern multiple aspects of animal metabolism. Transcriptome-, proteome- and metabolome-wide measurements have revealed widespread circadian rhythms in metabolism governed by a cellular genetic oscillator, the circadian core clock. However, it remains unclear if and under which conditions transcriptional rhythms cause rhythms in particular metabolites and metabolic fluxes. Here, we analyzed the circadian orchestration of metabolic pathways by direct measurement of enzyme activities, analysis of transcriptome data, and developing a theoretical method called circadian response analysis. Contrary to a common assumption, we found that pronounced rhythms in metabolic pathways are often favored by separation rather than alignment in the times of peak activity of key enzymes. This property holds true for a set of metabolic pathway motifs (e.g., linear chains and branching points) and also under the conditions of fast kinetics typical for metabolic reactions. By circadian response analysis of pathway motifs, we determined exact timing separation constraints on rhythmic enzyme activities that allow for substantial rhythms in pathway flux and metabolite concentrations. Direct measurements of circadian enzyme activities in mouse skeletal muscle confirmed that such timing separation occurs in vivo.

For efficient polarity and migration, cells need to regulate the magnitude and spatial distribution of actin assembly. This process is coordinated by reciprocal interactions between the actin cytoskeleton and mechanical forces. Actin polymerization-based protrusion increases tension in the plasma membrane, which in turn acts as a long-range inhibitor of actin assembly. These interactions form a negative feedback circuit that limits the magnitude of membrane tension in neutrophils and prevents expansion of the existing front and the formation of secondary fronts. It has been suggested that the plasma membrane directly inhibits actin assembly by serving as a physical barrier that opposes protrusion. Here we show that efficient control of actin polymerization-based protrusion requires an additional mechanosensory feedback cascade that indirectly links membrane tension with actin assembly. Specifically, elevated membrane tension acts through phospholipase D2 (PLD2) and the mammalian target of rapamycin complex 2 (mTORC2) to limit actin nucleation. In the absence of this pathway, neutrophils exhibit larger leading edges, higher membrane tension, and profoundly defective chemotaxis. Mathematical modeling suggests roles for both the direct (mechanical) and indirect (biochemical via PLD2 and mTORC2) feedback loops in organizing cell polarity and motility—the indirect loop is better suited to enable competition between fronts, whereas the direct loop helps spatially organize actin nucleation for efficient leading edge formation and cell movement. This circuit is essential for polarity, motility, and the control of membrane tension., A mechanosensory biochemical cascade involving phospholipase D2 and mTORC2 coordinates physical forces and cytoskeletal rearrangements to allow efficient polarization and migration of neutrophils., Author Summary How cells regulate the size and number of their protrusions for efficient polarity and motility is a fundamental question in cell biology. We recently found that immune cells known as neutrophils use physical forces to regulate this process. Actin polymerization-based protrusion stretches the plasma membrane, and this increased membrane tension acts as a long-range inhibitor of actin-based protrusions elsewhere in the cell. Here we investigate how membrane tension limits protrusion. We demonstrate that the magnitude of actin network assembly in neutrophils is determined by a mechanosensory biochemical cascade that converts increases in membrane tension into decreases in protrusion. Specifically, we show that increasing plasma membrane tension acts through a pathway containing the phospholipase D2 (PLD2) and the mammalian target of rapamycin complex 2 (mTORC2) to limit actin network assembly. Without this negative feedback pathway, neutrophils exhibit larger leading edges, higher membrane tension, and profoundly defective chemotaxis. Mathematical modeling indicates that this feedback circuit is a favorable topology to enable competition between protrusions during neutrophil polarization. Our work shows how biochemical signals, physical forces, and the cytoskeleton can collaborate to generate large-scale cellular organization.

Cancer therapy has traditionally focused on eliminating fast-growing populations of cells. Yet, an increasing body of evidence suggests that small subpopulations of cancer cells can evade strong selective drug pressure by entering a ‘persister' state of negligible growth. This drug-tolerant state has been hypothesized to be part of an initial strategy towards eventual acquisition of bona fide drug-resistance mechanisms. However, the diversity of drug-resistance mechanisms that can expand from a persister bottleneck is unknown. Here we compare persister-derived, erlotinib-resistant colonies that arose from a single, EGFR-addicted lung cancer cell. We find, using a combination of large-scale drug screening and whole-exome sequencing, that our erlotinib-resistant colonies acquired diverse resistance mechanisms, including the most commonly observed clinical resistance mechanisms. Thus, the drug-tolerant persister state does not limit—and may even provide a latent reservoir of cells for—the emergence of heterogeneous drug-resistance mechanisms., Cancer cells that survive initial drug treatment can persist in the presence of drugs. Here, the authors generate persister cells that are resistant to the EGFR tyrosine kinase inhibitor erlotinib and show by single cell analysis that multiple mechanism give rise to the drug-resistant persister state.

Ca 2+ is a universal second messenger in eukaryotic cells transmitting information through sequences of concentration spikes. A prominent mechanism to generate these spikes involves Ca 2+ release from the endoplasmic reticulum Ca 2+ store via inositol 1,4,5-trisphosphate (IP 3 )-sensitive channels. Puffs are elemental events of IP 3 -induced Ca 2+ release through single clusters of channels. Intracellular Ca 2+ dynamics are a stochastic system, but a complete stochastic theory has not been developed yet. We formulate the theory in terms of interpuff interval and puff duration distributions because, unlike the properties of individual channels, they can be measured in vivo. Our theory reproduces the typical spectrum of Ca 2+ signals like puffs, spiking, and bursting in analytically treatable test cases as well as in more realistic simulations. We find conditions for spiking and calculate interspike interval (ISI) distributions. Signal form, average ISI and ISI distributions depend sensitively on the details of cluster properties and their spatial arrangement. In contrast to that, the relation between the average and the standard deviation of ISIs does not depend on cluster properties and cluster arrangement and is robust with respect to cell variability. It is controlled by the global feedback processes in the Ca 2+ signaling pathway (e.g., via IP 3 -3-kinase or endoplasmic reticulum depletion). That relation is essential for pathway function because it ensures frequency encoding despite the randomness of ISIs and determines the maximal spike train information content. Hence, we find a division of tasks between global feedbacks and local cluster properties that guarantees robustness of function while maintaining sensitivity of control of the average ISI.

Cytokines are pleiotropic and readily diffusible messenger molecules, raising the question of how their action can be confined to specific target cells. The T cell cytokine interleukin-2 (IL-2) is essential for the homeostasis of regulatory T (Treg) cells that suppress (auto)immunity and stimulates immune responses mediated by conventional T cells. We combined mathematical modeling and experiments to dissect the dynamics of the IL-2 signaling network that links the prototypical IL-2 producers, conventional T helper (Th) cells, and Treg cells. We show how the IL-2-induced upregulation of high-affinity IL-2 receptors (IL-2R) establishes a positive feedback loop of IL-2 signaling. This feedback mediates a digital switch for the proliferation of Th cells and functions as an analog amplifier for the IL-2 uptake capacity of Treg cells. Unlike other positive feedbacks in cell signaling that augment signal propagation, the IL-2/IL-2R loop enhances the capture of the signal molecule and its degradation. Thus Treg and Th cells can compete for IL-2 and restrict its range of action through efficient cellular uptake. Depending on activation status and spatial localization of the cells, IL-2 may be consumed exclusively by Treg or Th cells, or be shared between them. In particular, a Treg cell can deprive a stimulated Th cell of its IL-2, but only when the cells are located in close proximity, within a few tens of micrometers. The present findings explain how IL-2 can play two disctinct roles in immune regulation and point to a hitherto largely unexplored spatiotemporal complexity of cytokine signaling.

Immune responses are regulated by diffusible mediators, the cytokines, which act at sub-nanomolar concentrations. The spatial range of cytokine communication is a crucial, yet poorly understood, functional property. Both containment of cytokine action in narrow junctions between immune cells (immunological synapses) and global signaling throughout entire lymph nodes have been proposed, but the conditions under which they might occur are not clear. Here we analyze spatially three-dimensional reaction-diffusion models for the dynamics of cytokine signaling at two successive scales: in immunological synapses and in dense multicellular environments. For realistic parameter values, we observe local spatial gradients, with the cytokine concentration around secreting cells decaying sharply across only a few cell diameters. Focusing on the well-characterized T-cell cytokine interleukin-2, we show how cytokine secretion and competitive uptake determine this signaling range. Uptake is shaped locally by the geometry of the immunological synapse. However, even for narrow synapses, which favor intrasynaptic cytokine consumption, escape fluxes into the extrasynaptic space are expected to be substantial (≥20% of secretion). Hence paracrine signaling will generally extend beyond the synapse but can be limited to cellular microenvironments through uptake by target cells or strong competitors, such as regulatory T cells. By contrast, long-range cytokine signaling requires a high density of cytokine producers or weak consumption (e.g., by sparsely distributed target cells). Thus in a physiological setting, cytokine gradients between cells, and not bulk-phase concentrations, are crucial for cell-to-cell communication, emphasizing the need for spatially resolved data on cytokine signaling., Author Summary The adaptive immune system fights pathogens through the activation of immune cell clones that specifically recognize a particular pathogen. Tight contacts, so-called immunological synapses, of immune cells with cells that present ‘digested’ pathogen molecules are pivotal for ensuring specificity. The discovery that immune responses are regulated by small diffusible proteins – the cytokines – has been surprising because cytokine diffusion to ‘bystander’ cells might compromise specificity. It has therefore been argued that cytokines are trapped in immunological synapses, whereas other authors have found that cytokines act on a larger scale through entire lymph nodes. Measurements of cytokine concentrations with fine spatial resolution have not been achieved. Here, we study the spatio-temporal dynamics of cytokines through mathematical analysis and three-dimensional numerical simulation and identify key parameters that control signaling range. We predict that even tight immunological synapses leak a substantial portion of the secreted cytokines. Nevertheless, rapid cellular uptake will render cytokine signals short-range and thus incidental activation of bystander cells can be limited. Long-range signals will only occur with multiple secreting cells or/and slow consumption by sparse target cells. Thus our study identifies key determinants of the spatial range of cytokine communication in realistic multicellular geometries.

Ca(2+) is a ubiquitous intracellular messenger that regulates diverse cellular activities. Extracellular stimuli often evoke sequences of intracellular Ca(2+) spikes, and spike frequency may encode stimulus intensity. However, the timing of spikes within a cell is random because each interspike interval has a large stochastic component. In human embryonic kidney (HEK) 293 cells and rat primary hepatocytes, we found that the average interspike interval also varied between individual cells. To evaluate how individual cells reliably encoded stimuli when Ca(2+) spikes exhibited such unpredictability, we combined Ca(2+) imaging of single cells with mathematical analyses of the Ca(2+) spikes evoked by receptors that stimulate formation of inositol 1,4,5-trisphosphate (IP3). This analysis revealed that signal-to-noise ratios were improved by slow recovery from feedback inhibition of Ca(2+) spiking operating at the whole-cell level and that they were robust against perturbations of the signaling pathway. Despite variability in the frequency of Ca(2+) spikes between cells, steps in stimulus intensity caused the stochastic period of the interspike interval to change by the same factor in all cells. These fold changes reliably encoded changes in stimulus intensity, and they resulted in an exponential dependence of average interspike interval on stimulation strength. We conclude that Ca(2+) spikes enable reliable signaling in a cell population despite randomness and cell-to-cell variability, because global feedback reduces noise, and changes in stimulus intensity are represented by fold changes in the stochastic period of the interspike interval.

The correct name of the third author is: Kevin Thurley The correct version of Figure 5 available here

Ca(2+) is not only one of the most versatile and ubiquitous second messengers but also a well-established representative example of cell signaling. The identification of most key elements involved in Ca(2+) signaling enables a mechanistic and quantitative understanding of this particular pathway. Cellular behavior relies in general on the orchestration of molecular behavior leading to reliable cellular responses that allow for regulation and adaptation. Ca(2+) signaling uses a hierarchical organization to transform single molecule behavior into cell wide signals. We have recently shown experimentally that this organization carries single channel signatures onto the whole cell level and renders Ca(2+) oscillations stochastic. Here, we briefly review the co-evolution of experimental and theoretical studies in Ca(2+) -signaling and show how dynamic bottom-up modeling can be used to address -biological questions and illuminate biological principles of cell signaling.

Ca(2+) is not only one of the most versatile and ubiquitous second messengers but also a well-established representative example of cell signaling. The identification of most key elements involved in Ca(2+) signaling enables a mechanistic and quantitative understanding of this particular pathway. Cellular behavior relies in general on the orchestration of molecular behavior leading to reliable cellular responses that allow for regulation and adaptation. Ca(2+) signaling uses a hierarchical organization to transform single molecule behavior into cell wide signals. We have recently shown experimentally that this organization carries single channel signatures onto the whole cell level and renders Ca(2+) oscillations stochastic. Here, we briefly review the co-evolution of experimental and theoretical studies in Ca(2+) -signaling and show how dynamic bottom-up modeling can be used to address -biological questions and illuminate biological principles of cell signaling.

Background Ca²⁺ is a ubiquitous and versatile second messenger that transmits information through changes of the cytosolic Ca²⁺ concentration. Recent investigations changed basic ideas on the dynamic character of Ca²⁺ signals and challenge traditional ideas on information transmission. Scope of review We present recent findings on key characteristics of the cytosolic Ca²⁺ dynamics and theoretical concepts that explain the wide range of experimentally observed Ca²⁺ signals. Further, we relate properties of the dynamical regulation of the cytosolic Ca²⁺ concentration to ideas about information transmission by stochastic signals. Major conclusions We demonstrate the importance of the hierarchal arrangement of Ca²⁺ release sites on the emergence of cellular Ca²⁺ spikes. Stochastic Ca²⁺ signals are functionally robust and adaptive to changing environmental conditions. Fluctuations of interspike intervals (ISIs) and the moment relation derived from ISI distributions contain information on the channel cluster open probability and on pathway properties. General significance Robust and reliable signal transduction pathways that entail Ca²⁺ dynamics are essential for eukaryotic organisms. Moreover, we expect that the design of a stochastic mechanism which provides robustness and adaptivity will be found also in other biological systems. Ca2 + dynamics demonstrate that the fluctuations of cellular signals contain information on molecular behavior. This article is part of a Special Issue entitled Biochemical, biophysical and genetic approaches to intracellular calcium signaling. Highlights ► We review recent findings on key characteristics of cytosolic Ca²⁺ dynamics. ► We demonstrate the importance of the hierarchal arrangement of Ca²⁺ release sites. ► New theoretical concepts exploit emergent behavior of cellular Ca²⁺ spikes. ► We relate the dynamical regulation of [Ca²⁺] to information transmission. ► Stochastic Ca²⁺ signals are functionally robust and adaptive to changing conditions.

International audience; Mitochondria play a central role in cellular energetic metabolism. The essential parts of this metabolism are the tricarboxylic acid (TCA) cycle, the respiratory chain and the adenosine triphosphate (ATP) synthesis machinery. Here a simplified model of these three metabolic components with a limited set of differential equations is presented. The existence of a steady state is demonstrated and results of numerical simulations are presented. The relevance of a simple model to represent actual in vivo behavior is discussed.

Ca2+ is a ubiquitous intracellular messenger. Extracellular stimuli often evoke sequences of Ca2+ spikes, and it is suggested that spike frequency may encode stimulus intensity. However, the timing of spikes is random because each interspike interval (ISI) has a large stochastic component. We also find that average ISI vary considerably between cells. Can individual cells reliably encode stimuli when Ca2+ spikes are so unpredictable? Analysis of Ca2+ spikes evoked by receptors that stimulate formation of inositol 1,4,5-trisphosphate (IP3) reveals that signal-to-noise ratios are improved by slow recovery from global feedback inhibition and that they are robust against perturbations of the signalling pathway. Despite variability in the frequency of Ca2+ spikes between cells, steps in stimulus intensity cause the stochastic period of the ISI to change by the same factor in all cells. These fold-changes reliably encode changes in stimulus intensity, and they entail an exponential dependence of average ISI on stimulation strength. We find the latter to apply to different cells, stimuli and stimulation intensities. We conclude that Ca2+ spikes allow reliable signalling in many cells despite randomness and cell-to-cell variability because global feedback robustly reduces noise, and stimulation steps are encoded by fold-changes in the stochastic period of the ISI.

We investigate the key characteristics of Ca(2+) puffs in deterministic and stochastic frameworks that all incorporate the cellular morphology of IP(3) receptor channel clusters. In the first step, we numerically study the Ca(2+) liberation in a three-dimensional representation of a cluster environment with reaction-diffusion dynamics in both the cytosol and the lumen. These simulations reveal that Ca(2+) concentrations at a releasing cluster range from 80 to 170 microM and equilibrate almost instantaneously on the time scale of the release duration. These highly elevated Ca(2+) concentrations eliminate Ca(2+) oscillations in a deterministic model of an IP(3)R channel cluster at physiological parameter values as revealed by a linear stability analysis. The reason lies in the saturation of all feedback processes in the IP(3)R gating dynamics, so that only fluctuations can restore experimentally observed Ca(2+) oscillations. In this spirit, we derive master equations that allow us to analytically quantify the onset of Ca(2+) puffs and hence the stochastic time scale of intracellular Ca(2+) dynamics. Moving up the spatial scale, we suggest to formulate cellular dynamics in terms of waiting time distribution functions. This approach prevents the state space explosion that is typical for the description of cellular dynamics based on channel states and still contains information on molecular fluctuations. We illustrate this method by studying global Ca(2+) oscillations.

The behavior of biological systems is determined by the properties of their component molecules, but the interactions are usually too complex to understand fully how molecular behavior generates cellular behavior. Ca(2+) signaling by inositol trisphosphate receptors (IP(3)R) offers an opportunity to understand this relationship because the cellular behavior is defined largely by Ca(2+)-mediated interactions between IP(3)R. Ca(2+) released by a cluster of IP(3)R (giving a local Ca(2+) puff) diffuses and ignites the behavior of neighboring clusters (to give repetitive global Ca(2+) spikes). We use total internal reflection fluorescence microscopy of two mammalian cell lines to define the temporal relationships between Ca(2+) puffs (interpuff intervals, IPI) and Ca(2+) spikes (interspike intervals) evoked by flash photolysis of caged IP(3). We find that IPI are much shorter than interspike intervals, that puff activity is stochastic with a recovery time that is much shorter than the refractory period of the cell, and that IPI are not periodic. We conclude that Ca(2+) spikes do not arise from oscillatory dynamics of IP(3)R clusters, but that repetitive Ca(2+) spiking with its longer timescales is an emergent property of the dynamics of the whole cluster array.

It has recently been shown that Ca(2+) spikes are stochastic and that the Ca(2+) concentration is subject to huge intracellular gradients. These findings underline the need for stochastic models taking single molecule state transitions into account (Master Equations are impossible due to the high number of states). We developed such a modeling concept based on the fact that for cellular concentration dynamics, it is only relevant whether channels are open or closed, but not in which open or closed state they are. That requires a non-Markovian formulation of the theory which we will present. This formulation permits direct integration of measurable quantities into the model, whereas detailed knowledge of physiologic parameters is not necessary. Therefore, input and output can be directly compared with experiments, if we consider observables like the probability that no spike happens or the average spike length. The model covers experimentally observed modes of system behavior like bursting, spiking or local events. Statistic properties of interspike intervals are in good accordance with experimental data. Since we have developed an analytic description as well as an efficient simulation algorithm, we are in a position to analyze a broad range of possible system configurations based on a solid theoretical background. In particular, we find that the spiking pattern can be predicted merely from two parameters, the cluster coupling and the average channel open time. The latter is probably constant and the former can be regulated by second messengers or by the number of active clusters, e. g. This implies that local dynamics emerges to a single control parameter determining global dynamics. Since we expect similar mechanisms to work in various fields of biology (e.g. cAMP dynamics and DNA replication), our theory should be widely applicable.