Low mobility of the Ca2+ buffers in axons of cultured Aplysia neurons

Cross Talking Calcium, IP3 and Buffer Dynamics Alters ATP and NADH Level in Obese and Normal Hepatocyte Cell

The cross talk between calcium (Ca2+), IP3 and buffer dynamics regulate various mechanisms in hepatocyte cells. The study of independent systems of calcium, IP3, and buffer signaling provides limited information about cell dynamics. In the current study, coupled reaction-diffusion equations are used to design a cross-talk model for IP3, buffer, and calcium dynamics in a hepatocyte cell. The one-way feedback of calcium, buffer, and IP3 in ATP production, ATP degradation, and NADH production rate is incorporated into the model. Numerical simulation has been done using the Finite Element Method (FEM) along the spatial direction and the Crank-Nicolson (C-N) method along the temporal direction. The numerical results are analysed to determine the effects of alterations in processes of cross-talking dynamics of IP3, buffer, and calcium on ATP and NADH production and degradation rate of ATP in a hepatocyte cell under normal and obesity conditions. The comparative analysis of these findings unveils notable distinctions induced by obesity in calcium dynamics, ATP and NADH synthesis, and ATP degradation kinetics.

Physiology of intracellular calcium buffering

Calcium signaling underlies much of physiology. Almost all the Ca2+ in the cytoplasm is bound to buffers, with typically only ∼1% being freely ionized at resting levels in most cells. Physiological Ca2+ buffers include small molecules and proteins, and experimentally Ca2+ indicators will also buffer calcium. The chemistry of interactions between Ca2+ and buffers determines the extent and speed of Ca2+ binding. The physiological effects of Ca2+ buffers are determined by the kinetics with which they bind Ca2+ and their mobility within the cell. The degree of buffering depends on factors such as the affinity for Ca2+, the Ca2+ concentration, and whether Ca2+ ions bind cooperatively. Buffering affects both the amplitude and time course of cytoplasmic Ca2+ signals as well as changes of Ca2+ concentration in organelles. It can also facilitate Ca2+ diffusion inside the cell. Ca2+ buffering affects synaptic transmission, muscle contraction, Ca2+ transport across epithelia, and the killing of bacteria. Saturation of buffers leads to synaptic facilitation and tetanic contraction in skeletal muscle and may play a role in inotropy in the heart. This review focuses on the link between buffer chemistry and function and how Ca2+ buffering affects normal physiology and the consequences of changes in disease. As well as summarizing what is known, we point out the many areas where further work is required.

Spatio temporal interdependent calcium and buffer dynamics regulating DAG in a hepatocyte cell due to obesity

Calcium ions (Ca2+) serve as a crucial signaling mechanism in almost all cells. The buffers are proteins that bind free Ca2+ to reduce the cell's Ca2+ concentration. The most studies reported in the past on calcium signaling in various cells have considered the buffer concentration as constant in the cell. However, buffers also diffuse and their concentration varies dynamically in the cells. Almost no work has been reported on interdependent calcium and buffer dynamics in the cells. In the present study, a model is proposed for inter-dependent spatio-temporal dynamics of calcium and buffer by coupling reaction-diffusion equations of Ca2+ and buffer in a hepatocyte cell. Boundary and initial conditions are framed based on the physiological state of the cell. The effect of various parameters viz. inositol 1,4,5-triphosphate receptor (IP3R), diffusion coefficient, SERCA pump and ryanodine receptor (RyR) on spatio-temporal dynamics of calcium and buffer regulating diacylglycerol (DAG) in a normal and obese hepatocyte cell has been studied using finite element simulation. From the results, it is concluded that the dynamics of calcium and buffer impact each other significantly along the spatio-temporal dimensions, thereby affecting the regulation of all the processes including DAG in a hepatocyte cell. The proposed model is more realistic than the existing ones, as the interdependent system dynamics of calcium and buffer have different regulatory impacts as compared to the individual and independent dynamics of these signaling processes in a hepatocyte cell.

Microphysiological Modeling of the Structure and Function of Neuromuscular Transmitter Release Sites

The general mechanism of calcium-triggered chemical transmitter release from neuronal synapses has been intensely studied, is well-known, and highly conserved between species and synapses across the nervous system. However, the structural and functional details within each transmitter release site (or active zone) are difficult to study in living tissue using current experimental approaches owing to the small spatial compartment within the synapse where exocytosis occurs with a very rapid time course. Therefore, computer simulations offer the opportunity to explore these microphysiological environments of the synapse at nanometer spatial scales and on a sub-microsecond timescale. Because biological reactions and physiological processes at synapses occur under conditions where stochastic behavior is dominant, simulation approaches must be driven by such stochastic processes. MCell provides a powerful simulation approach that employs particle-based stochastic simulation tools to study presynaptic processes in realistic and complex (3D) geometries using optimized Monte Carlo algorithms to track finite numbers of molecules as they diffuse and interact in a complex cellular space with other molecules in solution and on surfaces (representing membranes, channels and binding sites). In this review we discuss MCell-based spatially realistic models of the mammalian and frog neuromuscular active zones that were developed to study presynaptic mechanisms that control transmitter release. In particular, these models focus on the role of presynaptic voltage-gated calcium channels, calcium sensors that control the probability of synaptic vesicle fusion, and the effects of action potential waveform shape on presynaptic calcium entry. With the development of these models, they can now be used in the future to predict disease-induced changes to the active zone, and the effects of candidate therapeutic approaches.

Cytosolic Ca2+ Buffers Are Inherently Ca2+ Signal Modulators

For precisely regulating intracellular Ca²⁺ signals in a time- and space-dependent manner, cells make use of various components of the "Ca²⁺ signaling toolkit," including Ca²⁺ entry and Ca²⁺ extrusion systems. A class of cytosolic Ca²⁺-binding proteins termed Ca²⁺ buffers serves as modulators of such, mostly short-lived Ca²⁺ signals. Prototypical Ca²⁺ buffers include parvalbumins (α and β isoforms), calbindin-D9k, calbindin-D28k, and calretinin. Although initially considered to function as pure Ca²⁺ buffers, that is, as intracellular Ca²⁺ signal modulators controlling the shape (amplitude, decay, spread) of Ca²⁺ signals, evidence has accumulated that calbindin-D28k and calretinin have additional Ca²⁺ sensor functions. These other functions are brought about by direct interactions with target proteins, thereby modulating their targets' function/activity. Dysregulation of Ca²⁺ buffer expression is associated with several neurologic/neurodevelopmental disorders including autism spectrum disorder (ASD) and schizophrenia. In some cases, the presence of these proteins is presumed to confer a neuroprotective effect, as evidenced in animal models of Parkinson's or Alzheimer's disease.

Cytoplasmic Calcium Buffering: An Integrative Crosstalk

Calcium (Ca²⁺) buffering is part of an integrative crosstalk between different mechanisms and elements involved in the control of free Ca²⁺ ions persistence in the cytoplasm and hence, in the Ca²⁺-dependence of many intracellular processes. Alterations of Ca²⁺ homeostasis and signaling from systemic to subcellular levels also play a pivotal role in the pathogenesis of many diseases.Compared with Ca²⁺ sequestration towards intracellular Ca²⁺ stores, Ca²⁺ buffering is a rapid process occurring in a subsecond scale. Any molecule (or binding site) with the ability to bind Ca²⁺ ions could be considered, at least in principle, as a buffer. However, the term Ca²⁺ buffer is applied only to a small subset of Ca²⁺ binding proteins containing acidic side-chain residues.Ca²⁺ buffering in the cytoplasm mainly relies on mobile and immobile or fixed buffers controlling the diffusion of free Ca²⁺ ions inside the cytosol both temporally and spatially. Mobility of buffers depends on their molecular weight, but other parameters as their concentration, affinity for Ca²⁺ or Ca²⁺ binding and dissociation kinetics next to their diffusional mobility also contribute to make Ca²⁺ signaling one of the most complex signaling activities of the cell.The crosstalk between all the elements involved in the intracellular Ca²⁺ dynamics is a process of extreme complexity due to the diversity of structural and molecular elements involved but permit a highly regulated spatiotemporal control of the signal mediated by Ca²⁺ ions. The basis of modeling tools to study Ca²⁺ dynamics are also presented.

The Low-Threshold Calcium Channel Cav3.2 Mediates Burst Firing of Mature Dentate Granule Cells

Mature granule cells are poorly excitable neurons that were recently shown to fire action potentials, preferentially in bursts. It is believed that the particularly pronounced short-term facilitation of mossy fiber synapses makes granule cell bursting a very effective means of properly transferring information to CA3. However, the mechanism underlying the unique bursting behavior of mature granule cells is currently unknown. Here, we show that Cav3.2 T-type channels at the axon initial segment are responsible for burst firing of mature granule cells in rats and mice. Accordingly, Cav3.2 knockout mice fire tonic spikes and exhibit impaired bursting, synaptic plasticity and dentate-to-CA3 communication. The data show that Cav3.2 channels are strong modulators of bursting and can be considered a critical molecular switch that enables effective information transfer from mature granule cells to the CA3 pyramids.

Geometric principles of second messenger dynamics in dendritic spines

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity.

Beyond Intracellular Signaling: The Ins and Outs of Second Messengers Microdomains

A typical characteristic of eukaryotic cells compared to prokaryotes is represented by the spatial heterogeneity of the different structural and functional components: for example, most of the genetic material is surrounded by a highly specific membrane structure (the nuclear membrane), continuous with, yet largely different from, the endoplasmic reticulum (ER); oxidative phosphorylation is carried out by organelles enclosed by a double membrane, the mitochondria; in addition, distinct domains, enriched in specific proteins, are present in the plasma membrane (PM) of most cells. Less obvious, but now generally accepted, is the notion that even the concentration of small molecules such as second messengers (Ca²⁺ and cAMP in particular) can be highly heterogeneous within cells. In the case of most organelles, the differences in the luminal levels of second messengers depend either on the existence on their membrane of proteins that allow the accumulation/release of the second messenger (e.g., in the case of Ca²⁺, pumps, exchangers or channels), or on the synthesis and degradation of the specific molecule within the lumen (the autonomous intramitochondrial cAMP system). It needs stressing that the existence of a surrounding membrane does not necessarily imply the existence of a gradient between the cytosol and the organelle lumen. For example, the nuclear membrane is highly permeable to both Ca²⁺ and cAMP (nuclear pores are permeable to solutes up to 50 kDa) and differences in [Ca²⁺] or [cAMP] between cytoplasm and nucleoplasm are not seen in steady state and only very transiently during cell activation. A similar situation has been observed, as far as Ca²⁺ is concerned, in peroxisomes.

Diffusion of Ca2+ from Small Boutons en Passant into the Axon Shapes AP-Evoked Ca2+ Transients

Not only the amplitude but also the time course of a presynaptic Ca²⁺ transient determine multiple aspects of synaptic transmission. In small bouton-type synapses, the mechanisms underlying the Ca²⁺ decay kinetics have not been fully investigated. Here, factors that shape an action-potential-evoked Ca²⁺ transient were quantitatively studied in synaptic boutons of neocortical layer 5 pyramidal neurons. Ca²⁺ transients were measured with different concentrations of fluorescent Ca²⁺ indicators and analyzed based on a single-compartment model. We found a small endogenous Ca²⁺-binding ratio (7 ± 2) and a high activity of Ca²⁺ transporters (0.64 ± 0.03 ms^-1), both of which enable rapid clearance of Ca²⁺ from the boutons. However, contrary to predictions of the single-compartment model, the decay time course of the measured Ca²⁺ transients was biexponential and became prolonged during repetitive stimulation. Measurements of [Ca²⁺]_i along the adjoining axon, together with an experimentally constrained model, showed that the initial fast decay of the Ca²⁺ transients predominantly arose from the diffusion of Ca²⁺ from the boutons into the axon. Therefore, for small boutons en passant, factors like terminal volume, axon diameter, and the concentration of mobile Ca²⁺-binding molecules are critical determinants of Ca²⁺ dynamics and thus Ca²⁺-dependent processes, including short-term synaptic plasticity.

Quantitative optical nanophysiology of Ca2+ signaling at inner hair cell active zones

Ca²⁺ influx triggers the release of synaptic vesicles at the presynaptic active zone (AZ). A quantitative characterization of presynaptic Ca²⁺ signaling is critical for understanding synaptic transmission. However, this has remained challenging to establish at the required resolution. Here, we employ confocal and stimulated emission depletion (STED) microscopy to quantify the number (20-330) and arrangement (mostly linear 70 nm × 100-600 nm clusters) of Ca²⁺ channels at AZs of mouse cochlear inner hair cells (IHCs). Establishing STED Ca²⁺ imaging, we analyze presynaptic Ca²⁺ signals at the nanometer scale and find confined elongated Ca²⁺ domains at normal IHC AZs, whereas Ca²⁺ domains are spatially spread out at the AZs of bassoon-deficient IHCs. Performing 2D-STED fluorescence lifetime analysis, we arrive at estimates of the Ca²⁺ concentrations at stimulated IHC AZs of on average 25 µM. We propose that IHCs form bassoon-dependent presynaptic Ca²⁺-channel clusters of similar density but scalable length, thereby varying the number of Ca²⁺ channels amongst individual AZs.

cAMP-dependent cell differentiation triggered by activated CRHR1 in hippocampal neuronal cells

Corticotropin-releasing hormone receptor 1 (CRHR1) activates the atypical soluble adenylyl cyclase (sAC) in addition to transmembrane adenylyl cyclases (tmACs). Both cAMP sources were shown to be required for the phosphorylation of ERK1/2 triggered by activated G protein coupled receptor (GPCR) CRHR1 in neuronal and neuroendocrine contexts. Here, we show that activated CRHR1 promotes growth arrest and neurite elongation in neuronal hippocampal cells (HT22-CRHR1 cells). By characterising CRHR1 signalling mechanisms involved in the neuritogenic effect, we demonstrate that neurite outgrowth in HT22-CRHR1 cells takes place by a sAC-dependent, ERK1/2-independent signalling cascade. Both tmACs and sAC are involved in corticotropin-releasing hormone (CRH)-mediated CREB phosphorylation and c-fos induction, but only sAC-generated cAMP pools are critical for the neuritogenic effect of CRH, further highlighting the engagement of two sources of cAMP downstream of the activation of a GPCR, and reinforcing the notion that restricted cAMP microdomains may regulate independent cellular processes.

NG2 glial cells integrate synaptic input in global and dendritic calcium signals

Synaptic signaling to NG2-expressing oligodendrocyte precursor cells (NG2 cells) could be key to rendering myelination of axons dependent on neuronal activity, but it has remained unclear whether NG2 glial cells integrate and respond to synaptic input. Here we show that NG2 cells perform linear integration of glutamatergic synaptic inputs and respond with increasing dendritic calcium elevations. Synaptic activity induces rapid Ca²⁺ signals mediated by low-voltage activated Ca²⁺ channels under strict inhibitory control of voltage-gated A-type K⁺ channels. Ca²⁺ signals can be global and originate throughout the cell. However, voltage-gated channels are also found in thin dendrites which act as compartmentalized processing units and generate local calcium transients. Taken together, the activity-dependent control of Ca²⁺ signals by A-type channels and the global versus local signaling domains make intracellular Ca²⁺ in NG2 cells a prime signaling molecule to transform neurotransmitter release into activity-dependent myelination.

DOI:http://dx.doi.org/10.7554/eLife.16262.001

Ca2+ removal by the plasma membrane Ca2+-ATPase influences the contribution of mitochondria to activity-dependent Ca2+ dynamics in Aplysia neuroendocrine cells

After Ca(2+) influx, mitochondria can sequester Ca(2+) and subsequently release it back into the cytosol. This form of Ca(2+)-induced Ca(2+) release (CICR) prolongs Ca(2+) signaling and can potentially mediate activity-dependent plasticity. As Ca(2+) is required for its subsequent release, Ca(2+) removal systems, like the plasma membrane Ca(2+)-ATPase (PMCA), could impact CICR. Here we examine such a role for the PMCA in the bag cell neurons of Aplysia californica CICR is triggered in these neurons during an afterdischarge and is implicated in sustaining membrane excitability and peptide secretion. Somatic Ca(2+) was measured from fura-PE3-loaded cultured bag cell neurons recorded under whole cell voltage clamp. Voltage-gated Ca(2+) influx was elicited with a 5-Hz, 1-min train, which mimics the fast phase of the afterdischarge. PMCA inhibition with carboxyeosin or extracellular alkalization augmented the effectiveness of Ca(2+) influx in eliciting mitochondrial CICR. A Ca(2+) compartment model recapitulated these findings and indicated that disrupting PMCA-dependent Ca(2+) removal increases CICR by enhancing mitochondrial Ca(2+) loading. Indeed, carboxyeosin augmented train-evoked mitochondrial Ca(2+) uptake. Consistent with their role on Ca(2+) dynamics, cell labeling revealed that the PMCA and mitochondria overlap with Ca(2+) entry sites. Finally, PMCA-dependent Ca(2+) extrusion did not impact endoplasmic reticulum-dependent Ca(2+) removal or release, despite the organelle residing near Ca(2+) entry sites. Our results demonstrate that Ca(2+) removal by the PMCA influences the propensity for stimulus-evoked CICR by adjusting the amount of Ca(2+) available for mitochondrial Ca(2+) uptake. This study highlights a mechanism by which the PMCA could impact activity-dependent plasticity in the bag cell neurons.

Reduced endogenous Ca2+ buffering speeds active zone Ca2+ signaling

Calcium influx during action potentials triggers neurotransmitter release at presynaptic active zones. Calcium buffers limit the spread of calcium and restrict neurotransmitter release to the vicinity of calcium channels. To sustain synchronous release during repetitive activity, rapid removal of calcium from the active zone is essential, but the underlying mechanisms are unclear. Therefore, we focused on cerebellar mossy fiber synapses, which are among the fastest synapses in the mammalian brain and found very weak presynaptic calcium buffering. One might assume that strong calcium buffering has the potential to efficiently remove calcium from active zones. In contrast, our results show that weak calcium buffering speeds active zone calcium clearance. Thus, the strength of presynaptic buffering limits the rate of synaptic transmission.

Fast synchronous neurotransmitter release at the presynaptic active zone is triggered by local Ca²⁺ signals, which are confined in their spatiotemporal extent by endogenous Ca²⁺ buffers. However, it remains elusive how rapid and reliable Ca²⁺ signaling can be sustained during repetitive release. Here, we established quantitative two-photon Ca²⁺ imaging in cerebellar mossy fiber boutons, which fire at exceptionally high rates. We show that endogenous fixed buffers have a surprisingly low Ca²⁺-binding ratio (∼15) and low affinity, whereas mobile buffers have high affinity. Experimentally constrained modeling revealed that the low endogenous buffering promotes fast clearance of Ca²⁺ from the active zone during repetitive firing. Measuring Ca²⁺ signals at different distances from active zones with ultra-high-resolution confirmed our model predictions. Our results lead to the concept that reduced Ca²⁺ buffering enables fast active zone Ca²⁺ signaling, suggesting that the strength of endogenous Ca²⁺ buffering limits the rate of synchronous synaptic transmission.

Buffer mobility and the regulation of neuronal calcium domains

The diffusion of calcium inside neurons is determined in part by the intracellular calcium binding species that rapidly bind to free calcium ions upon entry. It has long been known that some portion of a neuron's intracellular calcium binding capacity must be fixed or poorly mobile, as calcium diffusion is strongly slowed in the intracellular environment relative to diffusion in cytosolic extract. The working assumption was that these immobile calcium binding sites are provided by structural proteins bound to the cytoskeleton or intracellular membranes and may thereby be relatively similar in composition and capacity across different cell types. However, recent evidence suggests that the immobile buffering capacity can vary greatly between cell types and that some mobile calcium binding proteins may alter their mobility upon binding calcium, thus blurring the line between mobile and immobile. The ways in which immobile buffering capacity might be relevant to different calcium domains within neurons has been explored primarily through modeling. In certain regimes, the presence of immobile buffers and the interaction between mobile and immobile buffers have been shown to result in complex spatiotemporal patterns of free calcium. In total, these experimental and modeling findings call for a more nuanced consideration of the local intracellular calcium microenvironment. In this review we focus on the different amounts, affinities, and mobilities of immobile calcium binding species; propose a new conceptual category of physically diffusible but functionally immobile buffers; and discuss how these buffers might interact with mobile calcium binding partners to generate characteristic calcium domains.

A single-compartment model of calcium dynamics in nerve terminals and dendrites

This introduction describes a single-compartment model of calcium dynamics that has been applied to fluorescence measurements of intracellular free calcium concentration ([Ca(2+)]i) changes in neurons. The model describes intracellular calcium handling under simplified conditions, for which analytical expressions for the amplitude and the time constants of [Ca(2+)]i changes can be explicitly derived. In particular, it reveals the dependence of the measured [Ca(2+)]i changes on the calcium indicator concentration. Applied to experimental data from small cells or subcellular compartments, the model equations have been extremely useful for obtaining quantitative information about essential parameters of Ca(2+) influx, buffering, and clearance. We illustrate also several changes that occur when the basic assumptions do not hold (e.g., when calcium diffusion, dye saturation, or kinetic effects become significant). Finally, we discuss how the changes in calcium dynamics, which are explained by the model, have been exploited for measuring properties of calcium-driven reactions, such as those regulating short-term synaptic enhancement, vesicle recycling, and adaptation.

Estimation of presynaptic calcium currents and endogenous calcium buffers at the frog neuromuscular junction with two different calcium fluorescent dyes

At the frog neuromuscular junction, under physiological conditions, the direct measurement of calcium currents and of the concentration of intracellular calcium buffers—which determine the kinetics of calcium concentration and neurotransmitter release from the nerve terminal—has hitherto been technically impossible. With the aim of quantifying both Ca²⁺ currents and the intracellular calcium buffers, we measured fluorescence signals from nerve terminals loaded with the low-affinity calcium dye Magnesium Green or the high-affinity dye Oregon Green BAPTA-1, simultaneously with microelectrode recordings of nerve-action potentials and end-plate currents. The action-potential-induced fluorescence signals in the nerve terminals developed much more slowly than the postsynaptic response. To clarify the reasons for this observation and to define a spatiotemporal profile of intracellular calcium and of the concentration of mobile and fixed calcium buffers, mathematical modeling was employed. The best approximations of the experimental calcium transients for both calcium dyes were obtained when the calcium current had an amplitude of 1.6 ± 0.08 pA and a half-decay time of 1.2 ± 0.06 ms, and when the concentrations of mobile and fixed calcium buffers were 250 ± 13 μM and 8 ± 0.4 mM, respectively. High concentrations of endogenous buffers define the time course of calcium transients after an action potential in the axoplasm, and may modify synaptic plasticity.

Hydrodynamic enhancement of the diffusion rate in the region between two fluctuating membranes in close opposition: a theoretical and computational study

Periodic variation of the distance between two weakly adhering bodies gives rise to a huge tangential motions of the sandwiched solvent layer (squeezing flow). Oscillations either can be induced by an external applied field or can spontaneously arise from the coupling with the solvent heat bath. First we calculated by the Navier-Stokes equation the components of the fluid velocity near two oscillating juxtaposed plates. Then we evaluated the influence of plate oscillations on the transport properties of a trace diffusant dissolved at t = 0 in the outer medium for both deterministic and stochastic excitations. By employing both analytical (Fokker-Planck) and coarse-grained molecular dynamics (MD) simulations, we proved that the entry and migration rates of the diffusant sharply increases with the oscillation amplitudes. Enhancement was related to relevant parameters like oscillation frequency, fluid layer thickness, fluid viscosity, and temperature. An extension to the case of oscillating multistacked lamellae has been also made. Theoretical and MD results suggest a significant enhancement of the diffusant flux even in the worse situation of thermally excited small amplitude fluctuations. Excitation arising from other sources (e.g., microwave or ultrasound irradiation of solid-fluid layered systems) could have a dramatic effect on the transport phenomena. Possible implications to relevant biological problems have been discussed.

Anomalous viscosity effect in the early stages of the ion-assisted adhesion/fusion event between lipid bilayers: a theoretical and computational study

The effect of viscosity on the encounter rate of two interacting membranes was investigated by combining a non-equilibrium Fokker-Planck model together with extensive Molecular Dynamics (MD) calculations. The encounter probability and stabilization of transient contact points represent the preliminary steps toward short-range adhesion and fusion of lipid leaflets. To strengthen our analytical model, we used a Coarse Grained MD method to follow the behavior of two charged palmitoyl oleoyl phosphatidylglycerol membranes embedded in a electrolyte-containing box at different viscosity regimes. Solvent friction was modulated by varying the concentration of a neutral, water-soluble polymer, polyethylene glycol, while contact points were stabilized by divalent ions that form bridges among juxtaposed membranes. While a naïve picture foresees a monotonous decrease of the membranes encounter rate with solvent viscosity, both the analytical model and MD simulations show a complex behavior. Under particular conditions, the encounter rate could exhibit a maximum at a critical viscosity value or for a critical concentration of bridging ions. These results seem to be confirmed by experimental observations taken from the literature.

Inverse problems in neuronal calcium signaling

Calcium is the most important of the brain's second messengers. Thanks to engineered fluorescent indicators and caged compounds we have an excellent qualitative picture of its regulation and impact.With the advent of new scanning technology that permits one to observe the calcium signal throughout a highly branched neuron the potential exists for functional, single cell, quantitative calcium imaging. To help realize that potential we analyze a sequence of four inverse problems that infer the parameters of the cytosolic calcium buffers and plasma membrane calcium pumps and channels from the light shed by fluorescent indicators following specific stimulus protocols. Our analyses lead in each case to practical algorithms that we illustrate and test on synthetic data.

Tuning local calcium availability: cell-type-specific immobile calcium buffer capacity in hippocampal neurons

It has remained difficult to ascribe a specific functional role to immobile or fixed intracellular calcium buffers in central neurons because the amount of these buffers is unknown. Here, we explicitly isolated the fixed buffer fraction by prolonged whole-cell patch-clamp dialysis and quantified its buffering capacity in murine hippocampal slices using confocal calcium imaging and the "added-buffer" approach. In dentate granule cells, the calcium binding ratio (κ) after complete washout of calbindin D28k (Cb), κfixed, displayed a substantial value of ∼100. In contrast, in CA1 oriens lacunosum moleculare (OLM) interneurons, which do not contain any known calcium-binding protein(s), κfixed amounted to only ∼30. Based on these values, a theoretical analysis of dendritic spread of calcium after local entry showed that fixed buffers, in the absence of mobile species, decrease intracellular calcium mobility 100- and 30-fold in granule cells and OLM cells, respectively, and thereby strongly slow calcium signals. Although the large κfixed alone strongly delays the spread of calcium in granule cells, this value optimizes the benefits of additionally expressing the mobile calcium binding protein Cb. With such high κfixed, Cb effectively increases the propagation velocity to levels seen in OLM cells and, contrary to expectation, does not affect the peak calcium concentration close to the source but sharpens the spatial and temporal calcium gradients. The data suggest that the amount of fixed buffers determines the temporal availability of calcium for calcium-binding partners and plays a pivotal role in setting the repertoire of cellular calcium signaling regimens.

Quantitative aspects of calcium fluorimetry

Ca(2+) indicator dyes by necessity are Ca(2+) chelators, because it is the binding of Ca(2+) to dye molecules that induces the change in fluorescence on which the Ca(2+) signal is based. As chelators, once introduced into a cell, they contribute to cellular Ca(2+) buffering. It has been a question of much debate to what extent this added Ca(2+) buffer (exogenous Ca(2+) buffer) changes Ca(2+) homeostasis and the signals of interest. I discuss this problem here, emphasizing the distinction between the influence of the dyes on amplitudes (which may be not so severe) and on the dynamics of Ca(2+) signals (which may be drastic). Once the Ca(2+)-buffering action of dyes relative to intrinsic Ca(2+) buffers is understood for a given preparation, Ca(2+) dyes can be used as very versatile tools for studying both Ca(2+) concentrations and Ca(2+) fluxes. I describe in detail some of my own experiences in calibrating the indicator dye Fura-2. These refer exclusively to experiments in which the dye is loaded into the cell via a patch pipette because acetoxymethyl ester loading introduces problems that very often prohibit precise quantitative conclusions.

Evoked centripetal Ca(2+) mobilization in cardiac Purkinje cells: insight from a model of three Ca(2+) release regions

Despite strong suspicion that abnormal Ca(2+) handling in Purkinje cells (P-cells) is implicated in life-threatening forms of ventricular tachycardias, the mechanism underlying the Ca(2+) cycling of these cells under normal conditions is still unclear. There is mounting evidence that P-cells have a unique Ca(2+) handling system. Notably complex spontaneous Ca(2+) activity was previously recorded in canine P-cells and was explained by a mechanistic hypothesis involving a triple layered system of Ca(2+) release channels. Here we examined the validity of this hypothesis for the electrically evoked Ca(2+) transient which was shown, in the dog and rabbit, to occur progressively from the periphery to the interior of the cell. To do so, the hypothesis was incorporated in a model of intracellular Ca(2+) dynamics which was then used to reproduce numerically the Ca(2+) activity of P-cells under stimulated conditions. The modelling was thus performed through a 2D computational array that encompassed three distinct Ca(2+) release nodes arranged, respectively, into three consecutive adjacent regions. A system of partial differential equations (PDEs) expressed numerically the principal cellular functions that modulate the local cytosolic Ca(2+) concentration (Cai). The apparent node-to-node progression of elevated Cai was obtained by combining Ca(2+) diffusion and 'Ca(2+)-induced Ca(2+) release'. To provide the modelling with a reliable experimental reference, we first re-examined the Ca(2+) mobilization in swine stimulated P-cells by 2D confocal microscopy. As reported earlier for the dog and rabbit, a centripetal Ca(2+) transient was readily visible in 22 stimulated P-cells from six adult Yucatan swine hearts (pacing rate: 0.1 Hz; pulse duration: 25 ms, pulse amplitude: 10% above threshold; 1 mm Ca(2+); 35°C; pH 7.3). An accurate replication of the observed centripetal Ca(2+) propagation was generated by the model for four representative cell examples and confirmed by statistical comparisons of simulations against cell data. Selective inactivation of Ca(2+) release regions of the computational array showed that an intermediate layer of Ca(2+) release nodes with an ~30-40% lower Ca(2+) activation threshold was required to reproduce the phenomenon. Our computational analysis was therefore fully consistent with the activation of a triple layered system of Ca(2+) release channels as a mechanism of centripetal Ca(2+) signalling in P-cells. Moreover, the model clearly indicated that the intermediate Ca(2+) release layer with increased sensitivity for Ca(2+) plays an important role in the specific intracellular Ca(2+) mobilization of Purkinje fibres and could therefore be a relevant determinant of cardiac conduction.

Separate Ca2+ sources are buffered by distinct Ca2+ handling systems in aplysia neuroendocrine cells

Although the contribution of Ca(2+) buffering systems can vary between neuronal types and cellular compartments, it is unknown whether distinct Ca(2+) sources within a neuron have different buffers. As individual Ca(2+) sources can have separate functions, we propose that each is handled by unique systems. Using Aplysia californica bag cell neurons, which initiate reproduction through an afterdischarge involving multiple Ca(2+)-dependent processes, we investigated the role of endoplasmic reticulum (ER) and mitochondrial sequestration, as well as extrusion via the plasma membrane Ca(2+)-ATPase (PMCA) and Na(+)/Ca(2+) exchanger, to the clearance of voltage-gated Ca(2+) influx, Ca(2+)-induced Ca(2+)-release (CICR), and store-operated Ca(2+) influx. Cultured bag cell neurons were filled with the Ca(2+) indicator, fura-PE3, to image Ca(2+) under whole-cell voltage clamp. A 5 Hz, 1 min train of depolarizing voltage steps elicited voltage-gated Ca(2+) influx followed by EGTA-sensitive CICR from the mitochondria. A compartment model of Ca(2+) indicated the effect of EGTA on CICR was due to buffering of released mitochondrial Ca(2+) rather than uptake competition. Removal of voltage-gated Ca(2+) influx was dominated by the mitochondria and PMCA, with no contribution from the Na(+)/Ca(2+) exchanger or sarcoplasmic/endoplasmic Ca(2+)-ATPase (SERCA). In contrast, CICR recovery was slowed by eliminating the Na(+)/Ca(2+) exchanger and PMCA. Last, store-operated influx, evoked by ER depletion, was removed by the SERCA and depended on the mitochondrial membrane potential. Our results demonstrate that distinct buffering systems are dedicated to particular Ca(2+) sources. In general, this may represent a means to differentially regulate Ca(2+)-dependent processes, and for Aplysia, influence how reproductive behavior is triggered.

Monitoring and quantifying dynamic physiological processes in live neurons using fluorescence recovery after photobleaching

The direct visualization of subcellular dynamic processes is often hampered by limitations in the resolving power achievable with conventional microscopy techniques. Fluorescence recovery after photobleaching has emerged as a highly informative approach to address this challenge, permitting the quantitative measurement of the movement of small organelles and proteins in living functioning cells, and offering detailed insights into fundamental cellular phenomena of physiological importance. In recent years, its implementation has benefited from the increasing availability of confocal microscopy systems and of powerful labeling techniques based on genetically encoded fluorescent proteins or other chemical markers. In this review, we present fluorescence recovery after photobleaching and related techniques in the context of contemporary neurobiological research and discuss quantitative and semi-quantitative approaches to their interpretation.

Transients in global Ca2+ concentration induced by electrical activity in a giant nerve terminal

Giant nerve terminals offer a unique opportunity to learn about dynamic changes in intracellular global Ca(2+) concentration ([Ca(2+)]i) because this quantity can be measured precisely with indicator dyes and the composition of the intra-terminal ionic milieu can be controlled. We review here recent literature on [Ca(2+)]i signalling in the calyx of Held and discuss what these measurements can tell us about endogenous Ca(2+) buffers and Ca(2+) extrusion mechanisms. We conclude that in spite of the favourable experimental conditions, some unresolved questions still remain regarding absolute values for the Ca(2+)-binding ratio, the affinity of the basic fixed buffer and the Ca(2+) affinities of the major endogenous Ca(2+) binding proteins. Uncertainties about some of these presynaptic properties, including the roles of Mg(2+) and ATP (as a Mg(2+) buffer), however, extend to the point that mechanisms controlling the decay of [Ca(2+)]i signals in unperturbed terminals may have to be reconsidered.

Diffusion and extrusion shape standing calcium gradients during ongoing parallel fiber activity in dendrites of Purkinje neurons

Synaptically induced calcium transients in dendrites of Purkinje neurons (PNs) play a key role in the induction of plasticity in the cerebellar cortex (Ito, Physiol Rev 81:1143-1195, 2001). Long-term depression at parallel fiber-PN synapses can be induced by stimulation paradigms that are associated with long-lasting (>1 min) calcium signals. These signals remain strictly localized (Eilers et al., Learn Mem 3:159-168, 1997), an observation that was rather unexpected, given the high concentration of the mobile endogenous calcium-binding proteins parvalbumin and calbindin in PNs (Fierro and Llano, J Physiol (Lond) 496:617-625, 1996; Kosaka et al., Exp Brain Res 93:483-491, 1993). By combining two-photon calcium imaging experiments in acute slices with numerical computer simulations, we found that significant calcium diffusion out of active branches indeed takes places. It is outweighed, however, by rapid and powerful calcium extrusion along the dendritic shaft. The close interplay of diffusion and extrusion defines the spread of calcium between active and inactive dendritic branches, forming a steep gradient in calcium with drop ranges of ~13 μm (interquartile range, 10-18 μm).

Effects of calretinin on Ca2+ signals in cerebellar granule cells: implications of cooperative Ca2+ binding

Calretinin is thought to be the main endogenous calcium buffer in cerebellar granule cells (GrCs). However, little is known about the impact of cooperative Ca(2+) binding to calretinin on highly localized and more global (regional) Ca(2+) signals in these cells. Using numerical simulations, we show that an essential property of calretinin is a delayed equilibration with Ca(2+). Therefore, the amount of Ca(2+), which calretinin can accumulate with respect to equilibrium levels, depends on stimulus conditions. Based on our simulations of buffered Ca(2+) diffusion near a single Ca(2+) channel or a large cluster of Ca(2+) channels and previous experimental findings that 150 μM 1,2-bis(o-aminophenoxy) ethane-N, N, N', N'-tetraacetic acid (BAPTA) and endogenous calretinin have similar effects on GrC excitability, we estimated the concentration of mobile calretinin in GrCs in the range of 0.7-1.2 mM. Our results suggest that this estimate can provide a starting point for further analysis. We find that calretinin prominently reduces the action potential associated increase in cytosolic free Ca(2+) concentration ([Ca(2+)]( i )) even at a distance of 30 nm from a single Ca(2+) channel. In spite of a buildup of residual Ca(2+), it maintains almost constant maximal [Ca(2+)]( i ) levels during repetitive channel openings with a frequency less than 80 Hz. This occurs because of accelerated Ca(2+) binding as calretinin binds more Ca(2+). Unlike the buffering of high Ca(2+) levels within Ca(2+) nano/microdomains sensed by large conductance Ca(2+)-activated K(+) channels, the buffering of regional Ca(2+) signals by calretinin can never be mimicked by certain concentration of BAPTA under all different experimental conditions.

On-chip electroporation, membrane repair dynamics and transient in-cell recordings by arrays of gold mushroom-shaped microelectrodes

This study demonstrates the use of on-chip gold mushroom-shaped microelectrodes (gMμEs) to generate localized electropores in the plasma membrane of adhering cultured neurons and to electrophysiologically monitor the ensuing membrane repair dynamics. Delivery of an alternating voltage pulse (0.5-1 V, 100 Hz, 300 ms) through an extracellularly positioned micrometer-sized gMμE electroporates the patch of plasma membrane facing the microelectrode. The repair dynamics of the electropores were analyzed by continuous monitoring of the neuron transmembrane potential, input resistance (R(in)) and action potential (AP) amplitude with an intracellular microelectrode and a number of neighbouring extracellular gMμEs. Electroporation by a gMμE is associated with local elevation of the free intracellular calcium concentration ([Ca(2+)](i)) around the gMμE. The membrane repair kinetics proceeds as an exponential process interrupted by abrupt recovery steps. These abrupt events are consistent with the "membrane patch model" of membrane repair in which patches of intracellular membrane fuse with the plasma membrane at the site of injury. Membrane electroporation by a single gMμE generates a neuron-gMμE configuration that permits recordings of attenuated intracellular action potentials. We conclude that the use of on-chip cultured neurons via a gMμE configuration provides a unique neuroelectronic interface that enables the selection of individual cells for electroporation, generates a confined electroporated membrane patch, monitors membrane repair dynamics and records attenuated intracellular action potentials.

Mitochondrial Ca2+ uptake contributes to buffering cytoplasmic Ca2+ peaks in cardiomyocytes

Mitochondrial ability of shaping Ca(2+) signals has been demonstrated in a large number of cell types, but it is still debated in heart cells. Here, we take advantage of the molecular identification of the mitochondrial Ca(2+) uniporter (MCU) and of unique targeted Ca(2+) probes to directly address this issue. We demonstrate that, during spontaneous Ca(2+) pacing, Ca(2+) peaks on the outer mitochondrial membrane (OMM) are much greater than in the cytoplasm because of a large number of Ca(2+) hot spots generated on the OMM surface. Cytoplasmic Ca(2+) peaks are reduced or enhanced by MCU overexpression and siRNA silencing, respectively; the opposite occurs within the mitochondrial matrix. Accordingly, the extent of contraction is reduced by overexpression of MCU and augmented by its down-regulation. Modulation of MCU levels does not affect the ATP content of the cardiomyocytes. Thus, in neonatal cardiac myocytes, mitochondria significantly contribute to buffering the amplitude of systolic Ca(2+) rises.

Three functional facets of calbindin D-28k

Many neurons of the vertebrate central nervous system (CNS) express the Ca²⁺ binding protein calbindin D-28k (CB), including important projection neurons like cerebellar Purkinje cells but also neocortical interneurons. CB has moderate cytoplasmic mobility and comprises at least four EF-hands that function in Ca²⁺ binding with rapid to intermediate kinetics and affinity. Classically it was viewed as a pure Ca²⁺ buffer important for neuronal survival. This view was extended by showing that CB is a critical determinant in the control of synaptic Ca²⁺ dynamics, presumably with strong impact on plasticity and information processing. Already 30 years ago, in vitro studies suggested that CB could have an additional Ca²⁺ sensor function, like its prominent acquaintance calmodulin (CaM). More recent work substantiated this hypothesis, revealing direct CB interactions with several target proteins. Different from a classical sensor, however, CB appears to interact with its targets both, in its Ca²⁺-loaded and Ca²⁺-free forms. Finally, CB has been shown to be involved in buffered transport of Ca²⁺, in neurons but also in kidney. Thus, CB serves a threefold function as buffer, transporter and likely as a non-canonical sensor.

Combined computational and experimental approaches to understanding the Ca(2+) regulatory network in neurons

Ca(2+) is a ubiquitous signaling ion that regulates a variety of neuronal functions by binding to and altering the state of effector proteins. Spatial relationships and temporal dynamics of Ca(2+) elevations determine many cellular responses of neurons to chemical and electrical stimulation. There is a wealth of information regarding the properties and distribution of Ca(2+) channels, pumps, exchangers, and buffers that participate in Ca(2+) regulation. At the same time, new imaging techniques permit characterization of evoked Ca(2+) signals with increasing spatial and temporal resolution. However, understanding the mechanistic link between functional properties of Ca(2+) handling proteins and the stimulus-evoked Ca(2+) signals they orchestrate requires consideration of the way Ca(2+) handling mechanisms operate together as a system in native cells. A wide array of biophysical modeling approaches is available for studying this problem and can be used in a variety of ways. Models can be useful to explain the behavior of complex systems, to evaluate the role of individual Ca(2+) handling mechanisms, to extract valuable parameters, and to generate predictions that can be validated experimentally. In this review, we discuss recent advances in understanding the underlying mechanisms of Ca(2+) signaling in neurons via mathematical modeling. We emphasize the value of developing realistic models based on experimentally validated descriptions of Ca(2+) transport and buffering that can be tested and refined through new experiments to develop increasingly accurate biophysical descriptions of Ca(2+) signaling in neurons.

Barriers to diffusion in dendrites and estimation of calcium spread following synaptic inputs

The motion of ions, molecules or proteins in dendrites is restricted by cytoplasmic obstacles such as organelles, microtubules and actin network. To account for molecular crowding, we study the effect of diffusion barriers on local calcium spread in a dendrite. We first present a model based on a dimension reduction approach to approximate a three dimensional diffusion in a cylindrical dendrite by a one-dimensional effective diffusion process. By comparing uncaging experiments of an inert dye in a spiny dendrite and in a thin glass tube, we quantify the change in diffusion constants due to molecular crowding as D(cyto)/D(water) = 1/20. We validate our approach by reconstructing the uncaging experiments using Brownian simulations in a realistic 3D model dendrite. Finally, we construct a reduced reaction-diffusion equation to model calcium spread in a dendrite under the presence of additional buffers, pumps and synaptic input. We find that for moderate crowding, calcium dynamics is mainly regulated by the buffer concentration, but not by the cytoplasmic crowding, dendritic spines or synaptic inputs. Following high frequency stimulations, we predict that calcium spread in dendrites is limited to small microdomains of the order of a few microns (<5 μm).

The diffusional properties of dendrites depend on the density of dendritic spines

We combined computational modeling and experimental measurements to determine the influence of dendritic structure on the diffusion of intracellular chemical signals in mouse cerebellar Purkinje cells and hippocamal CA1 pyramidal cells. Modeling predicts that molecular trapping by dendritic spines causes diffusion along spiny dendrites to be anomalous and that the value of the anomalous exponent (d(w) ) is proportional to spine density in both cell types. To test these predictions we combined the local photorelease of an inert dye, rhodamine dextran, with two-photon fluorescence imaging to track diffusion along dendrites. Our results show that anomalous diffusion is present in spiny dendrites of both cell types. Further, the anomalous exponent is linearly related to the density of spines in pyramidal cells and d(w) in Purkinje cells is consistent with such a relationship. We conclude that anomalous diffusion occurs in the dendrites of multiple types of neurons. Because spine density is dynamic and depends on neuronal activity, the degree of anomalous diffusion induced by spines can dynamically regulate the movement of molecules along dendrites.

Multiphoton fluorescence recovery after photobleaching in bounded systems

Multiphoton fluorescence recovery after photobleaching (MP-FRAP) is a laser microscopy technique used to measure diffusion coefficients of macromolecules in biological systems. The three-dimensional resolution and superior depth penetration within scattering samples offered by MP-FRAP make it an important tool for investigating both in vitro and in vivo systems. However, biological systems frequently confine diffusion within solid barriers, and to date the effect of such barriers on the measurement of absolute diffusion coefficients via MP-FRAP has not been studied. We have used Monte Carlo simulations of diffusion and MP-FRAP to understand the effect of barriers of varying geometries and positions relative to the two-photon focal volume. Furthermore, we supply ranges of barrier positions within which MP-FRAP can confidently be employed to measure accurate diffusion coefficients. Finally, we produce two new MP-FRAP models that can produce accurate diffusion coefficients in the presence of a single plane boundary or parallel infinite plane boundaries positioned parallel to the optical axis, up to the resolution limit of the multiphoton laser scanning microscope.

Second messengers and membrane trafficking direct and organize growth cone steering

Graded distributions of extracellular cues guide developing axons toward their targets. A network of second messengers - Ca(2+) and cyclic nucleotides - shapes cue-derived information into either attractive or repulsive signals that steer growth cones bidirectionally. Emerging evidence suggests that such guidance signals create a localized imbalance between exocytosis and endocytosis, which in turn redirects membrane, adhesion and cytoskeletal components asymmetrically across the growth cone to bias the direction of axon extension. These recent advances allow us to propose a unifying model of how the growth cone translates shallow gradients of environmental information into polarized activity of the steering machinery for axon guidance.

Numerical analysis of Ca2+ signaling in rat ventricular myocytes with realistic transverse-axial tubular geometry and inhibited sarcoplasmic reticulum

The t-tubules of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca²⁺). To investigate how the t-tubule microanatomy and the distribution of membrane Ca²⁺ flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca²⁺ signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca²⁺ signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca²⁺ flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca²⁺ buffers, including the Ca²⁺ indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca²⁺ transients was found when the Ca²⁺ flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca²⁺ signals are predicted. Even at modest elevation of Ca²⁺, reached during Ca²⁺ influx, large and steep Ca²⁺ gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca²⁺ flux density along the cell membrane support initiation and propagation of Ca²⁺ waves in rat myocytes.

In cardiac muscle cells, calcium (Ca²⁺) is best known for its role in contraction activation. A remarkable amount of quantitative data on cardiac cell structure, ion-transporting protein distributions and intracellular Ca²⁺ dynamics has been accumulated. Various alterations in the protein distributions or cell ultra-structure are now recognized to be the primary mechanisms of cardiac dysfunction in a diverse range of common pathologies including cardiac arrhythmias and hypertrophy. Using a 3-D computational model, incorporating more realistic transverse-axial t-tubule geometry and considering geometric irregularities and inhomogeneities in the distribution of ion-transporting proteins, we analyze several important spatial and temporal features of Ca²⁺ signaling in rat ventricular myocytes. This study demonstrates that the computational models could serve as powerful tools for prediction and analyses of how the Ca²⁺ dynamics and cardiac excitation-contraction coupling are regulated under normal conditions or certain pathologies. The use of computational and mathematical approaches will help also to better understand aspects of cell functions that are not currently amenable to experimental investigation.

Cytosolic Ca2+ buffers

"Ca(2+) buffers," a class of cytosolic Ca(2+)-binding proteins, act as modulators of short-lived intracellular Ca(2+) signals; they affect both the temporal and spatial aspects of these transient increases in [Ca(2+)](i). Examples of Ca(2+) buffers include parvalbumins (α and β isoforms), calbindin-D9k, calbindin-D28k, and calretinin. Besides their proven Ca(2+) buffer function, some might additionally have Ca(2+) sensor functions. Ca(2+) buffers have to be viewed as one of the components implicated in the precise regulation of Ca(2+) signaling and Ca(2+) homeostasis. Each cell is equipped with proteins, including Ca(2+) channels, transporters, and pumps that, together with the Ca(2+) buffers, shape the intracellular Ca(2+) signals. All of these molecules are not only functionally coupled, but their expression is likely to be regulated in a Ca(2+)-dependent manner to maintain normal Ca(2+) signaling, even in the absence or malfunctioning of one of the components.

The role of local protein synthesis and degradation in axon regeneration

In axotomised regenerating axons, the first step toward successful regeneration is the formation of a growth cone. This requires a variety of dynamic morphological and biochemical changes in the axon, including the appearance of many new cytoskeletal, cell surface and signalling molecules. These changes suggest the activation of coordinated complex cellular processes. A recent development has been the demonstration that the regenerative ability of some axons depends on their capacity to locally synthesise new proteins and degrade others at the injury site autonomously from the cell body. There are also events involving the degradation of cytoskeletal and other molecules, and activation of signalling pathways, with axotomy-induced calcium changes probably being an initiating event. A future challenge will be to understand how this complex network of processes interacts in order to find therapeutic ways of promoting the regeneration of CNS axons.

Modeling of quantal neurotransmitter release kinetics in the presence of fixed and mobile calcium buffers

The local calcium concentration in the active zone of secretion determines the number and kinetics of neurotransmitter quanta released after the arrival of a nerve action potential in chemical synapses. The small size of mammalian neuromuscular junctions does not allow direct measurement of the correlation between calcium influx, the state of endogenous calcium buffers determining the local concentration of calcium and the time course of quanta exocytosis. In this work, we used computer modeling of quanta release kinetics with various levels of calcium influx and in the presence of endogenous calcium buffers with varying mobilities. The results of this modeling revealed the desynchronization of quanta release under low calcium influx in the presence of an endogenous fixed calcium buffer, with a diffusion coefficient much smaller than that of free Ca(2+), and synchronization occurred upon adding a mobile buffer. This corresponds to changes in secretion time course parameters found experimentally (Samigullin et al., Physiol Res 54:129-132, 2005; Bukharaeva et al., J Neurochem 100:939-949, 2007).

Ca2+-mobility in the sarcoplasmic reticulum of ventricular myocytes is low

The sarcoplasmic reticulum (SR) in ventricular myocytes contains releasable Ca(2+) for activating cellular contraction. Recent measurements of intra-SR (luminal) Ca(2+) suggest a high diffusive Ca(2+)-mobility constant (D(CaSR)). This could help spatially to unify SR Ca(2+)-content ([Ca(2+)](SRT)) and standardize Ca(2+)-release throughout the cell. But measurements of localized depletions of luminal Ca(2+) (Ca(2+)-blinks), associated with local Ca(2+)-release (Ca(2+)-sparks), suggest D(CaSR) may actually be low. Here we describe a novel method for measuring D(CaSR). Using a cytoplasmic Ca(2+)-fluorophore, we estimate regional [Ca(2+)](SRT) from localized, caffeine-induced SR Ca(2+)-release. Caffeine microperfusion of one end of a guinea pig or rat myocyte diffusively empties the whole SR at a rate indicating D(CaSR) is 8-9 microm(2)/s, up to tenfold lower than previous estimates. Ignoring background SR Ca(2+)-leakage in our measurement protocol produces an artifactually high D(CaSR) (>40 microm(2)/s), which may also explain the previous high values. Diffusion-reaction modeling suggests that a low D(CaSR) would be sufficient to support local SR Ca(2+)-signaling within sarcomeres during excitation-contraction coupling. Low D(CaSR) also implies that [Ca(2+)](SRT) may readily become spatially nonuniform, particularly under pathological conditions of spatially nonuniform Ca(2+)-release. Local control of luminal Ca(2+), imposed by low D(CaSR), may complement the well-established local control of SR Ca(2+)-release by Ca(2+)-channel/ryanodine receptor couplons.

Ryanodine receptor allosteric coupling and the dynamics of calcium sparks

Puffs and sparks are localized intracellular Ca(2+) elevations that arise from the cooperative activity of Ca(2+)-regulated inositol 1,4,5-trisphosphate receptors and ryanodine receptors clustered at Ca(2+) release sites on the surface of the endoplasmic reticulum or the sarcoplasmic reticulum. While the synchronous gating of Ca(2+)-regulated Ca(2+) channels can be mediated entirely though the buffered diffusion of intracellular Ca(2+), interprotein allosteric interactions also contribute to the dynamics of ryanodine receptor (RyR) gating and Ca(2+) sparks. In this article, Markov chain models of Ca(2+) release sites are used to investigate how the statistics of Ca(2+) spark generation and termination are related to the coupling of RyRs via local [Ca(2+)] changes and allosteric interactions. Allosteric interactions are included in a manner that promotes the synchronous gating of channels by stabilizing neighboring closed-closed and/or open-open channel pairs. When the strength of Ca(2+)-mediated channel coupling is systematically varied (e.g., by changing the Ca(2+) buffer concentration), simulations that include synchronizing allosteric interactions often exhibit more robust Ca(2+) sparks; however, for some Ca(2+) coupling strengths the sparks are less robust. We find no evidence that the distribution of spark durations can be used to distinguish between allosteric interactions that stabilize closed channel pairs, open channel pairs, or both in a balanced fashion. On the other hand, the changes in spark duration, interspark interval, and frequency observed when allosteric interactions that stabilize closed channel pairs are gradually removed from simulations are qualitatively different than the changes observed when open or both closed and open channel pairs are stabilized. Thus, our simulations clarify how changes in spark statistics due to pharmacological washout of the accessory proteins mediating allosteric coupling may indicate the type of synchronizing allosteric interactions exhibited by physically coupled RyRs. We also investigate the validity of a mean-field reduction applicable to the dynamics of a ryanodine receptor cluster coupled via local [Ca(2+)] and allosteric interactions. In addition to facilitating parameter studies of the effect of allosteric coupling on spark statistics, the derivation of the mean-field model establishes the correct functional form for cooperativity factors representing the coupled gating of RyRs. This mean-field formulation is well suited for use in computationally efficient whole cell simulations of excitation-contraction coupling.