A Deterministic Model Predicts the Properties of Stochastic Calcium Oscillations in Airway Smooth Muscle Cells

The inositol trisphosphate receptor () is one of the most important cellular components responsible for oscillations in the cytoplasmic calcium concentration. Over the past decade, two major questions about the have arisen. Firstly, how best should the be modeled? In other words, what fundamental properties of the allow it to perform its function, and what are their quantitative properties? Secondly, although calcium oscillations are caused by the stochastic opening and closing of small numbers of , is it possible for a deterministic model to be a reliable predictor of calcium behavior? Here, we answer these two questions, using airway smooth muscle cells (ASMC) as a specific example. Firstly, we show that periodic calcium waves in ASMC, as well as the statistics of calcium puffs in other cell types, can be quantitatively reproduced by a two-state model of the , and thus the behavior of the is essentially determined by its modal structure. The structure within each mode is irrelevant for function. Secondly, we show that, although calcium waves in ASMC are generated by a stochastic mechanism, stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model.     

The inhibitory effects of dantrolene on action potential-induced calcium transients in cultured rat dorsal root ganglion neurons

We investigated the actions of dantrolene Ca(2+)-induced on Ca(2+)-release (CICR) evoked by action potentials in cultured rat sensory neurons. The effect of dantrolene on action potential after-depolarization and voltage-activated calcium currents was studied in cultured neonatal rat dorsal root ganglion cells (DRG) using the whole-cell patch-clamp technique. Depolarizing current injection evoked action potentials and depolarizing after-potentials, which are activated as a result of CICR following a single action potential in some cells. The type of after-potentials was determined by inducing action potentials from the resting membrane potential. Extracellular application of dantrolene (10 microM) abolished after-depolarizations without affecting action potential properties. Furthermore, dantrolene significantly reduced repetitive action potentials after depolarizing current injection into these neurons, but had no significant effect on the steady-state current voltage relationship of calcium currents in these neurons. We conclude that dantrolene inhibits the induction of action potential after depolarizations by inhibiting CICR in cultured rat sensory neurons.     

Modeling Secondary Messenger Pathways in Neurovascular Coupling

Neurovascular coupling is the well-documented link between neural stimulation and constriction or dilation of the surrounding vasculature. Glial cells mediate this response via their unique anatomy, which connects neurons to arterioles. It is believed that calcium transients and the release of secondary messengers by these cells influence the vascular response. We present a model of intracellular calcium dynamics in an astrocyte (glial cell) and show that stable oscillatory behaviour is possible under certain conditions. We then couple this to a novel model for the relationship between calcium concentration and the production of vasoactive secondary messengers through a fatty-acid intermediate. The two secondary messengers modelled are epoxyeicosatrienoic and 20-hydroxyeicosatetraenoic acids (EET and 20-HETE, respectively). These secondary messengers are produced on different time scales, and we show how this supports the observation that the vasculature dilates rapidly in response to neural stimulation, before returning to baseline levels on a slower time scale.     

Red blood cells of the lizards Ameiva ameiva (Squamata, Teiidae) display multiple mechanisms to control cytosolic calcium

We have previously reported that lizard red blood cells control their cytosolic calcium concentration by sequestering calcium ions in pools, which could be discharged by thapsigargin, by the Na+/H+ ionophore, monensin, by the K+/H+ ionophore, nigericin and by the proton pump inhibitor, bafilomycin A1 [1]. We have now demonstrated, with the aid of confocal microscopy, the presence in these cells of organelles, which accumulate the dye acridine orange and are thus by inference the sites of proton pools. We have found, moreover, that monensin, nigericin and bafilomycin all act to discharge these pools. We further show that calcium release ensues when the calcium ionophore, ionomycin, is added after thapsigargin and monensin; this implies the existence of a third pool, besides the acidic pool and the Endoplasmic Reticulum (ER), which participates in calcium homeostasis. The ER calcium pool can de discharged by the addition of the second messenger, IP3, and we present evidence, based on confocal microscopy, that the IP3 receptors are located in or close to the nucleus.     

Mathematical investigation of IP<Subscript>3</Subscript>-dependent calcium dynamics in astrocytes

We study evoked calcium dynamics in astrocytes, a major cell type in the mammalian brain. Experimental evidence has shown that such dynamics are highly variable between different trials, cells, and cell subcompartments. Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. Variation in the maximum flow in different calcium channels is also shown to determine the range of stable oscillations, as well as set the range of frequencies of the oscillations. Further, by conducting a randomized search through the parameter space and recording the resulting calcium responses, we create a database that can be used by experimentalists to help estimate the underlying channel distribution of their cells.     

Light modulated cnidocyte discharge predates the origins of eyes in Cnidaria

Complex biological traits often originate by integrating previously separate parts, but the organismal functions of these precursors are challenging to infer. If we can understand the ancestral functions of these precursors, it could help explain how they persisted and how they facilitated the origins of complex traits. Animal eyes are some of the best studied complex traits, and they include many parts, such as opsin‐based photoreceptor cells, pigment cells, and lens cells. Eye evolution is understood through conceptual models that argue these parts gradually came together to support increasingly sophisticated visual functions. Despite the well‐accepted logic of these conceptual models, explicit comparative studies to identify organismal functions of eye precursors are lacking. Here, we investigate how precursors functioned before they became part of eyes in Cnidaria, a group formed by sea anemones, corals, and jellyfish. Specifically, we test whether ancestral photoreceptor cells regulated the discharge of cnidocytes, the expensive single‐use cells with various functions including prey capture, locomotion, and protection. Similar to a previous study of Hydra, we show an additional four distantly related cnidarian groups discharge significantly more cnidocytes when exposed to dim blue light compared with bright blue light. Our comparative analyses support the hypothesis that the cnidarian ancestor was capable of modulating cnidocyte discharge with light, which we speculate uses an opsin‐based phototransduction pathway homologous to that previously described in Hydra. Although eye precursors might have had other functions like regulating timing of spawning, our findings are consistent with the hypothesis that photoreceptor cells which mediate cnidocyte discharge predated eyes, perhaps facilitating the prolific origination of eyes in Cnidaria.     

Tracking improves performance of biological collision avoidance models

Collision avoidance models derived from the study of insect brains do not perform universally well in practical collision scenarios, although the insects themselves may perform well in similar situations. In this article, we present a detailed simulation analysis of two well-known collision avoidance models and illustrate their limitations. In doing so, we present a novel continuous-time implementation of a neuronally based collision avoidance model. We then show that visual tracking can improve performance of these models by allowing an relative computation of the distance between the obstacle and the observer. We compare the results of simulations of the two models with and without tracking to show how tracking improves the ability of the model to detect an imminent collision. We present an implementation of one of these models processing imagery from a camera to show how it performs in real-world scenarios. These results suggest that insects may track looming objects with their gaze.     

Growth-dependent modulation of capacitative calcium entry in normal rat kidney fibroblasts

Normal rat kidney (NRK) fibroblasts have electrophysiological properties and intracellular calcium dynamics that are dependent upon their growth stage. In the present study we show that this differential behavior coincides with a differential calcium entry that can be either capacitative or non-capacitative. Confluent cells made quiescent by serum deprivation, which have a stable membrane potential near ? 70 mV and do not show spontaneous intracellular calcium oscillations, primarily exhibit the capacitative mechanism for calcium entry, also called store-operated calcium entry (SOCE). When the quiescent cells are grown to density-arrest in the presence of EGF as the sole polypeptide growth factor, these cells characteristically fire spontaneously repetitive calcium action potentials, which propagate throughout the whole monolayer and are accompanied by intracellular calcium transients. These density-arrested cells appear to exhibit in addition to SOCE also receptor-operated calcium entry (ROCE) as a mechanism for calcium entry. Furthermore we show that, in contrast to earlier studies, the employed SOCs and ROCs are permeable for both calcium and strontium ions. We examined the expression of the canonical transient receptor potential channels (Trpcs) that may be involved in SOCE and ROCE. We show that NRK fibroblasts express the genes encoding Trpc1, Trpc5 and Trpc6, and that the levels of their expression are dependent upon the growth stage of the cells. In addition we examined the growth stage dependent expression of the genes encoding Orai1 and Stim1, two proteins that have recently been shown to be involved in SOCE. Our results suggest that the differential expression of Trpc5, Trpc6, Orai1 and Stim1 in quiescent and density-arrested NRK fibroblasts is responsible for the difference in regulation of calcium entry between these cells. Finally, we show that inhibition or potentiation of SOCE and ROCE by pharmacological agents has profound effects on calcium dynamics in NRK fibroblasts.     

Copines-1, -2, -3, -6 and -7 show different calcium-dependent intracellular membrane translocation and targeting

The copines are a family of C2- and von Willebrand factor A-domain-containing proteins that have been proposed to respond to increases in intracellular calcium by translocating to the plasma membrane. The copines have been reported to interact with a range of cell signalling and cytoskeletal proteins, which may therefore be targeted to the membrane following increases in cellular calcium. However, neither the function of the copines, nor their actual movement to the plasma membrane, has been fully established in mammalian cells. Here, we show that copines-1, -2, -3, -6 and -7 respond differently to a methacholine-evoked intracellular increase in calcium in human embryonic kidney cell line-293 cells, and that their membrane association requires different levels of intracellular calcium. We demonstrate that two of these copines associate with different intracellular vesicles following calcium entry into cells, and identify a novel conserved amino acid sequence that is required for their membrane translocation in living cells. Our data show that the von Willebrand factor A-domain of the copines modulates their calcium sensitivity and intracellular targeting. Together, these findings suggest a different set of roles for the members of this protein family in mediating calcium-dependent processes in mammalian cells.     

Point process models of single-neuron discharges

In most neural systems, neurons communicate via sequences of action potentials. Contemporary models assume that the action potentials' times of occurrence rather than their waveforms convey information. The mathematical tool for describing sequences of events occurring in time and/or space is the theory of point processes. Using this theory, we show that neural discharge patterns convey time-varying information intermingled with the neuron's response characteristics. We review the basic techniques for analyzing single-neuron discharge patterns and describe what they reveal about the underlying point process model. By applying information theory and estimation theory to point processes, we describe the fundamental limits on how well information can be represented by and extracted from neural discharges. We illustrate applying these results by considering recordings from the lower auditory pathway.     

Synaptic mechanisms of spike generation in bursts by neurons of the carp tectum and olfactory bulb

Synaptic mechanisms of burst activity generation in certain neurons of the tectum opticum and mechanisms of generation of stimulation-induced group discharges by certain secondary neurons of the olfactory bulb were analyzed in carp (Cyprinus carpio L.). Spikes of the spontaneous discharge in neurons of the tectum were accompanied by depolarizing after-potentials, which caused the burst discharges of these cells. Evidence is given in support of the synaptic nature of the after-potential; it is suggested that it is generated by a recurrent collateral mechanism. Synaptic bombardment causing the appearance of a group discharge in olfactory bulb neurons and groups of spikes in their spontaneous activity was found to be intermittent in character. These features of unit activity in the olfactory bulb are shown to be connected with the presence of excitatory synaptic interaction between several neurons, probably dendro-dendritic in nature.M. V. Lomonosov Moscow State University. Translated from Neirofiziologiay, Vol. 14, No. 5, pp. 483–490, September–October, 1982.     

Cellular basis for response diversity in the olfactory periphery

An emerging idea in olfaction is that temporal coding of odor specificity can be intrinsic to the primary olfactory receptor neurons (ORNs). As a first step towards understanding whether lobster ORNs are capable of generating odor-specific temporal activity and what mechanisms underlie any such heterogeneity in discharge pattern, we characterized different patterns of activity in lobster ORNs individually and ensemble using patch-clamp recording and calcium imaging. We demonstrate that lobster ORNs show tonic excitation, tonic inhibition, phaso-tonic excitation, and bursting, and that these patterns are faithfully reflected in the calcium signal. We then demonstrate that the various dynamic patterns of response are inherent in the cells, and that this inherent heterogeneity is largely determined by heterogeneity in the underlying intrinsic conductances.     

A Kinetic Model of the Inositol Trisphosphate Receptor Based on Single-Channel Data

In many cell types, the inositol trisphosphate receptor is one of the important components controlling intracellular calcium dynamics, and an understanding of this receptor is necessary for an understanding of calcium oscillations and waves. Based on single-channel data from the type-I inositol trisphosphate receptor, and using a Markov chain Monte Carlo approach, we show that the most complex time-dependent model that can be unambiguously determined from steady-state data is one with three closed states and one open state, and we determine how the rate constants depend on calcium. Because the transitions between these states are complex functions of calcium concentration, each model state must correspond to a group of physical states. We fit two different topologies and find that both models predict that the main effect of [Ca²⁺] is to modulate the probability that the receptor is in a state that is able to open, rather than to modulate the transition rate to the open state.     

The unique antigen receptor signaling phenotype of B-1 cells is influenced by locale but induced by antigen

Normal animals contain an autoreactive B lymphocyte subset, the B-1 subset, which is controlled by undefined mechanisms to prevent autoimmunity. Using a V(H)11V(kappa)9 Ig transgenic mouse, with a specificity prototypic of the subset, we have explored conditions responsible for the previously reported Ag hyporesponsiveness of these cells. We report that peritoneal V(H)11V(kappa)9 B cells exhibit typical B-1 behavior with high basal intracellular free Ca(2+) and negligible receptor-mediated calcium mobilization. However, splenic B cells from this mouse, while phenotypically similar to their peritoneal counterparts, including expression of CD5, mount robust B-2-like responses to Ag as measured by calcium influx and altered tyrosine phosphorylation responses. When these splenic cells are adoptively transferred to the peritoneal cavity and encounter their cognate self-Ag, they acquire a B-1 signaling phenotype. The ensuing hyporesponsiveness is characterized by increases in both basal intracellular calcium and resting tyrosyl phosphorylation levels and is highlighted by a marked abrogation of B cell receptor-mediated calcium mobilization. Thus, we show that self-Ag recognition in specific microenvironments such as the peritoneum, and we would propose other privileged sites, confers a unique form of anergy on activated B cells. This may explain how autoreactive B-1 cells can exist while autoimmunity is avoided.     

Simulating the Real Origins of Communication

How communication systems emerge is a topic of relevance to several academic disciplines. Numerous existing models, both mathematical and computational, study this emergence. However, with few exceptions, these models all build some form of communication into their initial specification. Consequently, what these models study is how communication systems transition from one form to another, and not how communication itself emerges in the first place. Here we present a new computational model of the emergence of communication which, unlike previous models, does not pre-specify the existence of communication. We conduct two experiments using this model, in order to derive general statements about how communication systems emerge. The two main routes to communication that we identify correspond with findings from the empirical literature on the evolution of animal signals. We use this finding to explain when and why we should expect communication to emerge in nature. We also compare our model to experimental research on the origins of human communication systems, and hence show that humans are an important exception to the general trends we observe. We argue that this is because humans, and probably only humans, are able to ‘signal signalhood’, i.e. to express communicative intentions.     

Effects of low-amplitude pulsed magnetic fields on cellular ion transport

Pulsed magnetic fields (PMFs) are widely used to treat difficult fractures of bone and other disorders of connective tissue. It is not clear how they interact with tissue metabolism, although it has been proposed that induced currents or electric fields impinging on cell membranes may modify their ion transport function. This hypothesis was tested by treating in vitro models for ion transport processes with short-term exposure to PMFs. No change occurred in active transport of potassium or calcium in human red cells or in calcium transport through an epithelial membrane. We considered less direct action on red cell membranes, that their permeability might be modified after PMF treatment, and also that PMFs might alter the extracellular ionic activity within connective tissue by interacting with its Donnan potential. Each of these studies proved negative, and we conclude that the PMF waveforms used here do not exert a general short-term effect on cellular ion transport.     

A Study of Early Afterdepolarizations in a Model for Human Ventricular Tissue

Sudden cardiac death is often caused by cardiac arrhythmias. Recently, special attention has been given to a certain arrhythmogenic condition, the long-QT syndrome, which occurs as a result of genetic mutations or drug toxicity. The underlying mechanisms of arrhythmias, caused by the long-QT syndrome, are not fully understood. However, arrhythmias are often connected to special excitations of cardiac cells, called early afterdepolarizations (EADs), which are depolarizations during the repolarizing phase of the action potential. So far, EADs have been studied mainly in isolated cardiac cells. However, the question on how EADs at the single-cell level can result in fibrillation at the tissue level, especially in human cell models, has not been widely studied yet. In this paper, we study wave patterns that result from single-cell EAD dynamics in a mathematical model for human ventricular cardiac tissue. We induce EADs by modeling experimental conditions which have been shown to evoke EADs at a single-cell level: by an increase of L-type Ca currents and a decrease of the delayed rectifier potassium currents. We show that, at the tissue level and depending on these parameters, three types of abnormal wave patterns emerge. We classify them into two types of spiral fibrillation and one type of oscillatory dynamics. Moreover, we find that the emergent wave patterns can be driven by calcium or sodium currents and we find phase waves in the oscillatory excitation regime. From our simulations we predict that arrhythmias caused by EADs can occur during normal wave propagation and do not require tissue heterogeneities. Experimental verification of our results is possible for experiments at the cell-culture level, where EADs can be induced by an increase of the L-type calcium conductance and by the application of I blockers, and the properties of the emergent patterns can be studied by optical mapping of the voltage and calcium.     

Calcium oscillations in neocortical astrocytes under epileptiform conditions.

Morphological and functional alterations in astrocytic glia are often found in epileptic syndromes, although the exact role of astrocytes in epilepsy is poorly understood. During calcium imaging of epileptiform events in juvenile neocortical slices we previously discovered cells with spontaneous oscillations in their intracellular free calcium concentration ([Ca(2+)](i)). We have now characterized these oscillations using two in vitro models of epilepsy and find that they are produced by astrocytes. Astrocytic oscillations are widespread throughout the imaged territories, are remarkably regular and have long periods, averaging 100 s, which become shorter during development. Astrocytic oscillations are uncorrelated among themselves and with epileptiform events, are blocked by internal release antagonists and are stimulated by caffeine. Astrocytic calcium oscillations could mediate reactive astrogliosis, contribute to the pathogenesis of chronic epileptic syndromes, and be used as a diagnostic test for epileptic tissue.     

Solar Radiation Induces Non-Nuclear Perturbations and a False Start to Regulated Exocytosis in Cryptosporidium parvum

Stratospheric ozone depletion, climate warming and acidification of aquatic ecosystems have resulted in elevated levels of solar radiation reaching many aquatic environments with an increased deleterious impact on a wide range of living organisms. While detrimental effects on living organisms are thought to occur primarily through DNA damage, solar UV can also damage cellular proteins, lipids and signalling pathways. Cryptosporidium, a member of the eukaryotic phylum Apicomplexa, contain numerous vesicular secretory organelles and their discharge via regulated exocytosis is essential for the successful establishment of infection. Using flow cytometric techniques we demonstrate that solar UV rapidly induces sporozoite exocytosis resulting in a significant reduction in the ability of sporozoites to attach and invade host cells. We found that solar UV induced sporozoite membrane depolarization, resulting in reduced cellular ATP and increased cytosolic calcium. These changes were accompanied by a reduction in the internal granularity of sporozoites, indicative of apical organelle discharge, which was confirmed by analysis of sporozoites with an exocytosis-sensitive dye. The precise timing of apical organelle discharge in the presence of a compatible host cell is critical for sporozoite attachment and invasion. Our results demonstrate for the first time how solar UV radiation can interfere with exocytosis, a fundamental cellular process in all eukaryotic cells. We contend that not only may the forecast increases in solar radiation in both aquatic and terrestrial environments significantly affect members of the Apicomplexa, solar UV-induced membrane depolarizations resulting in cytosolic calcium perturbation may affect a wider range of eukaryotic organisms through antagonistic effects on a myriad of calcium dependant cellular functions.