Usefulness and limitations of linear approximations to the understanding of Ca++ signals

Probing neuronal activity with genetically encoded calcium and voltage fluorescent indicators

Monitoring neural activity in individual neurons is crucial for understanding neural circuits and brain functions. The emergence of optical imaging technologies has dramatically transformed the field of neuroscience, enabling detailed observation of large-scale neuronal populations with both cellular and subcellular resolution. This transformation will be further accelerated by the integration of these imaging technologies and advanced big data analysis. Genetically encoded fluorescent indicators to detect neural activity with high signal-to-noise ratios are pivotal in this advancement. In recent years, these indicators have undergone significant developments, greatly enhancing the understanding of neural dynamics and networks. This review highlights the recent progress in genetically encoded calcium and voltage indicators and discusses the future direction of imaging techniques with big data analysis that deepens our understanding of the complexities of the brain.

Developmental transformation of Ca2+ channel-vesicle nanotopography at a central GABAergic synapse

The coupling between Ca2+ channels and release sensors is a key factor defining the signaling properties of a synapse. However, the coupling nanotopography at many synapses remains unknown, and it is unclear how it changes during development. To address these questions, we examined coupling at the cerebellar inhibitory basket cell (BC)-Purkinje cell (PC) synapse. Biophysical analysis of transmission by paired recording and intracellular pipette perfusion revealed that the effects of exogenous Ca2+ chelators decreased during development, despite constant reliance of release on P/Q-type Ca2+ channels. Structural analysis by freeze-fracture replica labeling (FRL) and transmission electron microscopy (EM) indicated that presynaptic P/Q-type Ca2+ channels formed nanoclusters throughout development, whereas docked vesicles were only clustered at later developmental stages. Modeling suggested a developmental transformation from a more random to a more clustered coupling nanotopography. Thus, presynaptic signaling developmentally approaches a point-to-point configuration, optimizing speed, reliability, and energy efficiency of synaptic transmission.

Optical profiling of autonomous Ca2+ nanodomains generated by lysosomal TPC2 and TRPML1

Multiple families of Ca2+-permeable channels co-exist on lysosomal Ca2+ stores but how each family couples to its own unique downstream physiology is unclear. We have therefore investigated the Ca2+-signalling architecture underpinning different channels on the same vesicle that drive separate pathways, using phagocytosis as a physiological stimulus. Lysosomal Ca2+-channels are a major Ca2+ source driving particle uptake in macrophages, but different channels drive different aspects of Fc-receptor-mediated phagocytosis: TPC2 couples to dynamin activation, whilst TRPML1 couples to lysosomal exocytosis. We hypothesised that they are driven by discrete local plumes of Ca2+ around open channels (Ca2+ nanodomains). To test this, we optimized Ca2+-nanodomain recordings by screening panels of genetically encoded Ca2+ indicators (GECIs) fused to TPC2 to monitor the [Ca2+] next to the channel. Signal calibration accounting for the distance of the GECI from the channel mouth reveals that, during phagocytosis, TPC2 generates local Ca2+ nanodomains around itself of up to 42 µM, nearly a hundred-fold greater than the global cytosolic [Ca2+] rise. We further show that TPC2 and TRPML1, though on the same lysosomes, generate autonomous Ca2+ nanodomains of high [Ca2+] that are largely insulated from one another, a platform allowing their discrete Ca2+-decoding to promote unique respective physiologies.

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.

Photoswitching alters fluorescence readout of jGCaMP8 Ca2+ indicators tethered to Orai1 channels

We used electrophysiology and Ca2+ channel tethering to evaluate the performance of jGCaMP8 genetically encoded Ca2+ indicators (GECIs). Orai1 Ca2+ channel-jGCaMP8 fusions were transfected into HEK 293A cells and jGCaMP8 fluorescence responses recorded by simultaneous total internal reflection fluorescence microscopy and whole-cell patch clamp electrophysiology. Noninactivating currents from the Orai1 Y80E mutant provided a steady flux of Ca2+ controlled on a millisecond time scale by step changes in membrane potential. Test pulses to -100 mV produced Orai1 Y80E-jGCaMP8f fluorescence traces that unexpectedly declined by ~50% over 100 ms before reaching a stable plateau. Testing of Orai1-jGCaMP8f using unroofed cells further demonstrated that rapid and partial fluorescence inactivation is a property of the indicator itself, rather than channel function. Photoinactivation spontaneously recovered over 5 min in the dark, and recovery was accelerated in the absence of Ca2+. Mutational analysis of residues near the tripeptide fluorophore of jGCaMP8f pointed to a mechanism: Q69M/C70V greatly increased (~90%) photoinactivation, reminiscent of fluorescent protein fluorophore cis-trans photoswitching. Indeed, 405-nm illumination of jGCaMP8f or 8m/8s/6f led to immediate photorecovery, and simultaneous illumination with 405 and 488-nm light blocked photoinactivation. Subsequent mutagenesis produced a variant, V203Y, that lacks photoinactivation but largely preserves the desirable properties of jGCaMP8f. Our results point to caution in interpreting rapidly changing Ca2+ signals using jGCaMP8 and earlier series GECIs, suggest strategies to avoid photoswitching, and serve as a starting point to produce more photostable, and thus more accurate, GECI derivatives.

Assessing brain state and anesthesia level with two-photon calcium signals

Brain states, such as wake, sleep, or different depths of anesthesia are usually assessed using electrophysiological techniques, such as the local field potential (LFP) or the electroencephalogram (EEG), which are ideal signals for detecting activity patterns such as asynchronous or oscillatory activities. However, it is technically challenging to have these types of measures during calcium imaging recordings such as two-photon or wide-field techniques. Here, using simultaneous two-photon and LFP measurements, we demonstrate that despite the slower dynamics of the calcium signal, there is a high correlation between the LFP and two-photon signals taken from the neuropil outside neuronal somata. Moreover, we find the calcium signal to be systematically delayed from the LFP signal, and we use a model to show that the delay between the two signals is due to the physical distance between the recording sites. These results suggest that calcium signals alone can be used to detect activity patterns such as slow oscillations and ultimately assess the brain state and level of anesthesia.

Unraveling the mysteries of dendritic spine dynamics: Five key principles shaping memory and cognition

Recent research extends our understanding of brain processes beyond just action potentials and chemical transmissions within neural circuits, emphasizing the mechanical forces generated by excitatory synapses on dendritic spines to modulate presynaptic function. From in vivo and in vitro studies, we outline five central principles of synaptic mechanics in brain function: P1: Stability - Underpinning the integral relationship between the structure and function of the spine synapses. P2: Extrinsic dynamics - Highlighting synapse-selective structural plasticity which plays a crucial role in Hebbian associative learning, distinct from pathway-selective long-term potentiation (LTP) and depression (LTD). P3: Neuromodulation - Analyzing the role of G-protein-coupled receptors, particularly dopamine receptors, in time-sensitive modulation of associative learning frameworks such as Pavlovian classical conditioning and Thorndike's reinforcement learning (RL). P4: Instability - Addressing the intrinsic dynamics crucial to memory management during continual learning, spotlighting their role in "spine dysgenesis" associated with mental disorders. P5: Mechanics - Exploring how synaptic mechanics influence both sides of synapses to establish structural traces of short- and long-term memory, thereby aiding the integration of mental functions. We also delve into the historical background and foresee impending challenges.

Involvement of Ca2+ in Signaling Mechanisms Mediating Muscarinic Inhibition of M Currents in Sympathetic Neurons

Acetylcholine can excite neurons by suppressing M-type (KCNQ) potassium channels. This effect is mediated by M1 muscarinic receptors coupled to the Gq protein. Although PIP2 depletion and PKC activation have been strongly suggested to contribute to muscarinic inhibition of M currents (IM), direct evidence is lacking. We investigated the mechanism involved in muscarinic inhibition of IM with Ca2+ measurement and electrophysiological studies in both neuronal (rat sympathetic neurons) and heterologous (HEK cells expressing KCNQ2/KCNQ3) preparations. We found that muscarinic inhibition of IM was not blocked either by PIP2 or by calphostin C, a PKC inhibitor. We then examined whether muscarinic inhibition of IM uses multiple signaling pathways by blocking both PIP2 depletion and PKC activation. This maneuver, however, did not block muscarinic inhibition of IM. Additionally, muscarinic inhibition of IM was not prevented either by sequestering of G-protein βγ subunits from Gα-transducin or anti-Gβγ antibody or by preventing intracellular trafficking of channel proteins with blebbistatin, a class-II myosin inhibitor. Finally, we re-examined the role of Ca2+ signals in muscarinic inhibition of IM. Ca2+ measurements showed that muscarinic stimulation increased intracellular Ca2+ and was comparable to the Ca2+ mobilizing effect of bradykinin. Accordingly, 20-mM of BAPTA significantly suppressed muscarinic inhibition of IM. In contrast, muscarinic inhibition of IM was completely insensitive to 20-mM EGTA. Taken together, these data suggest a role of Ca2+ signaling in muscarinic modulation of IM. The differential effects of EGTA and BAPTA imply that Ca2+ microdomains or spatially local Ca2+ signals contribute to inhibition of IM.

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.

Presynaptic Mitochondria Communicate With Release Sites for Spatio-Temporal Regulation of Exocytosis at the Motor Nerve Terminal

Presynaptic Ca2+ regulation is critical for accurate neurotransmitter release, vesicle reloading of release sites, and plastic changes in response to electrical activity. One of the main players in the regulation of cytosolic Ca2+ in nerve terminals is mitochondria, which control the size and spread of the Ca2+ wave during sustained electrical activity. However, the role of mitochondria in Ca2+ signaling during high-frequency short bursts of action potentials (APs) is not well known. Here, we studied spatial and temporal relationships between mitochondrial Ca2+ (mCa2+) and exocytosis by live imaging and electrophysiology in adult motor nerve terminals of transgenic mice expressing synaptophysin-pHluorin (SypHy). Our results show that hot spots of exocytosis and mitochondria are organized in subsynaptic functional regions and that mitochondria start to uptake Ca2+ after a few APs. We also show that mitochondria contribute to the regulation of the mode of fusion (synchronous and asynchronous) and the kinetics of release and replenishment of the readily releasable pool (RRP) of vesicles. We propose that mitochondria modulate the timing and reliability of neurotransmission in motor nerve terminals during brief AP trains.

A theory of synaptic transmission

Rapid and precise neuronal communication is enabled through a highly synchronous release of signaling molecules neurotransmitters within just milliseconds of the action potential. Yet neurotransmitter release lacks a theoretical framework that is both phenomenologically accurate and mechanistically realistic. Here, we present an analytic theory of the action-potential-triggered neurotransmitter release at the chemical synapse. The theory is demonstrated to be in detailed quantitative agreement with existing data on a wide variety of synapses from electrophysiological recordings in vivo and fluorescence experiments in vitro. Despite up to ten orders of magnitude of variation in the release rates among the synapses, the theory reveals that synaptic transmission obeys a simple, universal scaling law, which we confirm through a collapse of the data from strikingly diverse synapses onto a single master curve. This universality is complemented by the capacity of the theory to readily extract, through a fit to the data, the kinetic and energetic parameters that uniquely identify each synapse. The theory provides a means to detect cooperativity among the SNARE complexes that mediate vesicle fusion and reveals such cooperativity in several existing data sets. The theory is further applied to establish connections between molecular constituents of synapses and synaptic function. The theory allows competing hypotheses of short-term plasticity to be tested and identifies the regimes where particular mechanisms of synaptic facilitation dominate or, conversely, fail to account for the existing data for the paired-pulse ratio. The derived trade-off relation between the transmission rate and fidelity shows how transmission failure can be controlled by changing the microscopic properties of the vesicle pool and SNARE complexes. The established condition for the maximal synaptic efficacy reveals that no fine tuning is needed for certain synapses to maintain near-optimal transmission. We discuss the limitations of the theory and propose possible routes to extend it. These results provide a quantitative basis for the notion that the molecular-level properties of synapses are crucial determinants of the computational and information-processing functions in synaptic transmission.

Voltage-gated calcium channels contribute to spontaneous glutamate release directly via nanodomain coupling or indirectly via calmodulin

Neurotransmitter release occurs either synchronously with action potentials (evoked release) or spontaneously (spontaneous release). Whether the molecular mechanisms underlying evoked and spontaneous release are identical, especially whether voltage-gated calcium channels (VGCCs) can trigger spontaneous events, is still a matter of debate in glutamatergic synapses. To elucidate this issue, we characterized the VGCC dependence of miniature excitatory postsynaptic currents (mEPSCs) in various synapses with different coupling distances between VGCCs and synaptic vesicles, known as a critical factor in evoked release. We found that most of the extracellular calcium-dependent mEPSCs were attributable to VGCCs in cultured autaptic hippocampal neurons and the mature calyx of Held where VGCCs and vesicles were tightly coupled. Among loosely coupled synapses, mEPSCs were not VGCC-dependent at immature calyx of Held and CA1 pyramidal neuron synapses, whereas VGCCs contribution was significant at CA3 pyramidal neuron synapses. Interestingly, the contribution of VGCCs to spontaneous glutamate release in CA3 pyramidal neurons was abolished by a calmodulin antagonist, calmidazolium. These data suggest that coupling distance between VGCCs and vesicles determines VGCC dependence of spontaneous release at tightly coupled synapses, yet VGCC contribution can be achieved indirectly at loosely coupled synapses.

Imaging Voltage with Microbial Rhodopsins

Membrane potential is the critical parameter that reflects the excitability of a neuron, and it is usually measured by electrophysiological recordings with electrodes. However, this is an invasive approach that is constrained by the problems of lacking spatial resolution and genetic specificity. Recently, the development of a variety of fluorescent probes has made it possible to measure the activity of individual cells with high spatiotemporal resolution. The adaptation of this technique to image electrical activity in neurons has become an informative method to study neural circuits. Genetically encoded voltage indicators (GEVIs) can be used with superior performance to accurately target specific genetic populations and reveal neuronal dynamics on a millisecond scale. Microbial rhodopsins are commonly used as optogenetic actuators to manipulate neuronal activities and to explore the circuit mechanisms of brain function, but they also can be used as fluorescent voltage indicators. In this review, we summarize recent advances in the design and the application of rhodopsin-based GEVIs.

Calbindin regulates Kv4.1 trafficking and excitability in dentate granule cells via CaMKII-dependent phosphorylation

Calbindin, a major Ca2+ buffer in dentate granule cells (GCs), plays a critical role in shaping Ca2+ signals, yet how it regulates neuronal function remains largely unknown. Here, we found that calbindin knockout (CBKO) mice exhibited dentate GC hyperexcitability and impaired pattern separation, which co-occurred with reduced K+ current due to downregulated surface expression of Kv4.1. Relatedly, manipulation of calbindin expression in HT22 cells led to changes in CaMKII activation and the level of surface localization of Kv4.1 through phosphorylation at serine 555, confirming the mechanism underlying neuronal hyperexcitability in CBKO mice. We also discovered that Ca2+ buffering capacity was significantly reduced in the GCs of Tg2576 mice to the level of CBKO GCs, and this reduction was restored to normal levels by antioxidants, suggesting that calbindin is a target of oxidative stress. Our data suggest that the regulation of CaMKII signaling by Ca2+ buffering is crucial for neuronal excitability regulation.

Stationary Ca2+ nanodomains in the presence of buffers with two binding sites

We examine closed-form approximations for the equilibrium Ca²⁺ and buffer concentrations near a point Ca²⁺ source representing a Ca²⁺ channel, in the presence of a mobile buffer with two Ca²⁺ binding sites activated sequentially and possessing distinct binding affinities and kinetics. This allows us to model the impact on Ca²⁺ nanodomains of realistic endogenous Ca²⁺ buffers characterized by cooperative Ca²⁺ binding, such as calretinin. The approximations we present involve a combination or rational and exponential functions, whose parameters are constrained using the series interpolation method that we recently introduced for the case of simpler Ca²⁺ buffers with a single Ca²⁺ binding site. We conduct extensive parameter sensitivity analysis and show that the obtained closed-form approximations achieve reasonable qualitative accuracy for a wide range of buffer's Ca²⁺ binding properties and other relevant model parameters. In particular, the accuracy of the derived approximants exceeds that of the rapid buffering approximation in large portions of the relevant parameter space.

Simulating cardiac Ca2+ release units: effects of RyR cluster size and Ca2+ buffers on diastolic Ca2+ leak

Leak of Ca²⁺ out of the cardiac sarcoplasmic reticulum (SR) via ryanodine receptors (RyRs) during diastole is vital to regulate SR Ca²⁺ levels. This leak can become deleterious when large spontaneous RyR-mediated Ca²⁺ release events evoke proarrhythmic Ca²⁺ waves that can lead to delayed after-depolarizations. Here, we model diastolic SR Ca²⁺ leak at individual SR Ca²⁺ release sites using computer simulations of RyR arrays like those in the dyadic cleft. The results show that RyR arrays size has a significant effect on SR Ca²⁺ leak, with bigger arrays producing larger and more frequent Ca²⁺ release events. Moreover, big RyR arrays are more susceptible to small changes in the levels of dyadic Ca²⁺ buffers. Such changes in buffering shift Ca²⁺ leak from small Ca²⁺ release events (involving few open RyRs) to larger events (with many open RyRs). Moreover, by analyzing a large parameter space of possible buffering and SR Ca²⁺ loads, we find further evidence for the hypothesis that SR Ca²⁺ leak by RyR arrays can undergo a sudden phase transition.

Inter-spike mitochondrial Ca2+ release enhances high frequency synaptic transmission

KEY POINTS

Presynaptic mitochondria not only absorb but also release Ca²⁺ during high frequency stimulation (HFS) when presynaptic [Ca²⁺ ] is kept low (<500 nm) by high cytosolic Ca²⁺ buffer or strong plasma membrane calcium clearance mechanisms under physiological external [Ca²⁺ ]. Mitochondrial Ca²⁺ release (MCR) does not alter the global presynaptic Ca²⁺ transients. MCR during HFS enhances short-term facilitation and steady state excitatory postsynaptic currents by increasing vesicular release probability. The intra-train MCR may provide residual calcium at interspike intervals, and thus support high frequency neurotransmission at central glutamatergic synapses.

ABSTRACT

Emerging evidence indicates that mitochondrial Ca²⁺ buffering contributes to local regulation of synaptic transmission. It is unknown, however, whether mitochondrial Ca²⁺ release (MCR) occurs during high frequency synaptic transmission. Confirming the previous notion that 2 μm tetraphenylphosphonium (TPP⁺ ) is a specific inhibitor of the mitochondrial Na⁺ /Ca²⁺ exchanger (mNCX), we studied the role of MCR via mNCX in short-term plasticity during high frequency stimulation (HFS) at the calyx of Held synapse of the rat. TPP⁺ reduced short-term facilitation (STF) and steady state excitatory postsynaptic currents during HFS at mature calyx synapses under physiological extracellular [Ca²⁺ ] ([Ca²⁺ ]_o  = 1.2 mm), but not at immature calyx or at 2 mm [Ca²⁺ ]_o . The inhibitory effects of TPP⁺ were stronger at synapses with morphologically complex calyces harbouring many swellings and at 32°C than at simple calyx synapses and at room temperature. These effects of TPP⁺ on STF were well correlated with those on the presynaptic mitochondrial [Ca²⁺ ] build-up during HFS. Mitochondrial [Ca²⁺ ] during HFS was increased by TPP⁺ at mature calyces under 1.2 mm [Ca²⁺ ]_o , and further enhanced at 32°C, but not under 2 mm [Ca²⁺ ]_o or at immature calyces. The close correlation of the effects of TPP⁺ on mitochondrial [Ca²⁺ ] with those on STF suggests that mNCX contributes to STF at the calyx of Held synapses. The intra-train MCR enhanced vesicular release probability without altering global presynaptic [Ca²⁺ ]. Our results suggest that MCR during HFS elevates local [Ca²⁺ ] near synaptic sites at interspike intervals to enhance STF and to support stable synaptic transmission under physiological [Ca²⁺ ]_o .

Efficient Approximations for Stationary Single-Channel Ca2+ Nanodomains across Length Scales

We consider the stationary solution for the Ca²⁺ concentration near a point Ca²⁺ source describing a single-channel Ca²⁺ nanodomain in the presence of a single mobile Ca²⁺ buffer with 1:1 Ca²⁺ binding. We present computationally efficient approximants that estimate stationary single-channel Ca²⁺ nanodomains with great accuracy in broad regions of parameter space. The presented approximants have a functional form that combines rational and exponential functions, which is similar to that of the well-known excess buffer approximation and the linear approximation but with parameters estimated using two novel, to our knowledge, methods. One of the methods involves interpolation between the short-range Taylor series of the free buffer concentration and its long-range asymptotic series in inverse powers of distance from the channel. Although this method has already been used to find Padé (rational-function) approximants to single-channel Ca²⁺ and buffer concentrations, extending this method to interpolants combining exponential and rational functions improves accuracy in a significant fraction of the relevant parameter space. A second method is based on the variational approach and involves a global minimization of an appropriate functional with respect to parameters of the chosen approximations. An extensive parameter-sensitivity analysis is presented, comparing these two methods with previously developed approximants. Apart from increased accuracy, the strength of these approximants is that they can be extended to more realistic buffers with multiple binding sites characterized by cooperative Ca²⁺ binding, such as calmodulin and calretinin.

Simulating diffusion from a cluster of point sources using propagation integrals

A computational methodology to simulate the diffusion of ions from point sources (e.g., ion channels) is described. The outlined approach computes the ion concentration from a cluster of many ion channels at pre-specified locations as a function of time using the theory of propagation integrals. How the channels' open/closed states evolve in time does not need to be known at the start of the simulation, but can be updated on-the-fly as the simulation goes along. The technique uses analytic formulas for the solutions of the diffusion equation for three common geometries: (1) ions diffusing from a membrane (planar symmetry); (2) ions diffusing into a narrow cleft for effective two-dimensional diffusion (cylindrical symmetry); and (3) ions diffusing into open space like the cytosol (spherical symmetry). Because these formulas are exact solutions valid for arbitrarily long timesteps, no spatial or time discretizations are necessary. The only discrete locations are where the ion concentration is computed, and the only discrete timesteps are when the channels' open/closed states are updated. Beyond pure diffusion, the technique is generalized to the Excess Buffer Approximation of ion chelation to give an analytic solution of this approximation of the full reaction/diffusion system. Both the pure diffusion and the diffusion/buffering algorithms scale linearly with the number of channels and the number of ion concentration locations.

The Role of CaV2.1 Channel Facilitation in Synaptic Facilitation

Activation of Ca_V2.1 voltage-gated calcium channels is facilitated by preceding calcium entry. Such self-modulatory facilitation is thought to contribute to synaptic facilitation. Using knockin mice with mutated Ca_V2.1 channels that do not facilitate (Ca IM-AA mice), we surprisingly found that, under conditions of physiological calcium and near-physiological temperatures, synaptic facilitation at hippocampal CA3 to CA1 synapses was not attenuated in Ca IM-AA mice and facilitation was paradoxically more prominent at two cerebellar synapses. Enhanced facilitation at these synapses is consistent with a decrease in initial calcium entry, suggested by an action-potential-evoked Ca_V2.1 current reduction in Purkinje cells from Ca IM-AA mice. In wild-type mice, Ca_V2.1 facilitation during high-frequency action potential trains was very small. Thus, for the synapses studied, facilitation of calcium entry through Ca_V2.1 channels makes surprisingly little contribution to synaptic facilitation under physiological conditions. Instead, Ca_V2.1 facilitation offsets Ca_V2.1 inactivation to produce remarkably stable calcium influx during high-frequency activation.

Weyrer et al. use Ca IM-AA mice in which Ca_V2.1 calcium channel facilitation is eliminated to study synaptic facilitation at hippocampal and cerebellar synapses. Under conditions of physiological temperature, external calcium, and presynaptic waveforms, facilitation of Ca_V2.1 channels is small and does not contribute to synaptic facilitation at these synapses.

Comparative Evaluation of Genetically Encoded Voltage Indicators

Imaging voltage using fluorescent-based sensors could be an ideal technique to probe neural circuits with high spatiotemporal resolution. However, due to insufficient signal-to-noise ratio (SNR), imaging membrane potential in mammalian preparations is still challenging. In recent years, many genetically encoded voltage indicators (GEVIs) have been developed. To compare them and guide decisions on which GEVI to use, we have characterized side by side the performance of eight GEVIs that represent different families of molecular constructs. We tested GEVIs in vitro with 1-photon imaging and in vivo with 1-photon wide-field imaging and 2-photon imaging. We find that QuasAr2 exhibited the best performance in vitro, whereas only ArcLight-MT could be used to reliably detect electrical activity in vivo with 2-photon excitation. No single GEVI was ideal for every experiment. These results provide a guide for choosing optimal GEVIs for specific applications.

Calcium Buffering in the Heart in Health and Disease

Changes of intracellular Ca²⁺ concentration regulate many aspects of cardiac myocyte function. About 99% of the cytoplasmic calcium in cardiac myocytes is bound to buffers, and their properties will therefore have a major influence on Ca²⁺ signaling. This article considers the fundamental properties and identities of the buffers and how to measure them. It reviews the effects of buffering on the systolic Ca²⁺ transient and how this may change physiologically, and in heart failure and both atrial and ventricular arrhythmias, as well. It is concluded that the consequences of this strong buffering may be more significant than currently appreciated, and a fuller understanding is needed for proper understanding of cardiac calcium cycling and contractility.

Reductions in Calcium Signaling Limit Inhibition to Diabetic Retinal Rod Bipolar Cells

Purpose

The balance of neuronal excitation and inhibition is important for proper retinal signaling. A previous report showed that diabetes selectively reduces light-evoked inhibition to the retinal dim light rod pathway, changing this balance. Here, changes in mechanisms of retinal inhibitory synaptic transmission after 6 weeks of diabetes are investigated.

Methods

Diabetes was induced in C57BL/6J mice by three intraperitoneal injections of streptozotocin (STZ, 75 mg/kg), and confirmed by blood glucose levels more than 200 mg/dL. After 6 weeks, whole-cell voltage-clamp recordings of electrically evoked inhibitory postsynaptic currents from rod bipolar cells and light-evoked excitatory postsynaptic currents from A17-amacrine cells were made in dark-adapted retinal slices.

Results

Diabetes shortened the timecourse of directly activated lateral GABAergic inhibitory amacrine cell inputs to rod bipolar cells. The timing of GABA release onto rod bipolar cells depends on a prolonged amacrine cell calcium signal that is reduced by slow calcium buffering. Therefore, the effects of calcium buffering with EGTA-acetoxymethyl ester (AM) on diabetic GABAergic signaling were tested. EGTA-AM reduced GABAergic signaling in diabetic retinas more strongly, suggesting that diabetic amacrine cells have reduced calcium signals. Additionally, the timing of release from reciprocal inhibitory inputs to diabetic rod bipolar cells was reduced, but the activation of the A17 amacrine cells responsible for this inhibition was not changed.

Conclusions

These results suggest that reduced light-evoked inhibitory input to rod bipolar cells is due to reduced and shortened calcium signals in presynaptic GABAergic amacrine cells. A reduction in calcium signaling may be a common mechanism limiting inhibition in the retina.

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.

Noise analysis of cytosolic calcium image data

Cellular Ca²⁺ signals are often constrained to cytosolic micro- or nano-domains where stochastic openings of Ca²⁺ channels cause large fluctuations in local Ca²⁺ concentration (Ca²⁺ 'noise'). With the advent of TIRF microscopy to image the fluorescence of Ca²⁺-sensitive probes from attoliter volumes it has become possible to directly monitor these signals, which closely track the gating of plasmalemmal and ER Ca²⁺-permeable channels. Nevertheless, it is likely that many physiologically important Ca²⁺ signals are too small to resolve as discrete events in fluorescence recordings. By analogy with noise analysis of electrophysiological data, we explore here the use of statistical approaches to detect and analyze such Ca²⁺ noise in images obtained using Ca²⁺-sensitive indicator dyes. We describe two techniques - power spectrum analysis and spatio-temporal correlation - and demonstrate that both effectively identify discrete, spatially localized calcium release events (Ca²⁺ puffs). Moreover, we show they are able to detect localized noise fluctuations in a case where discrete events cannot directly be resolved.

Spatial Coupling Tunes NMDA Receptor Responses via Ca2+ Diffusion

In the CNS, NMDA receptors generate large and highly regulated Ca2+ signals, which are critical for synaptic development and plasticity. They are highly clustered at postsynaptic sites and along dendritic arbors, but whether this spatial arrangement affects their output is unknown. Synaptic NMDA receptor currents are subject to Ca2+-dependent inactivation (CDI), a type of activity-dependent inhibition that requires intracellular Ca2+ and calmodulin (CaM). We asked whether Ca2+ influx through a single NMDA receptor influences the activity of nearby NMDA receptors, as a possible coupling mechanism. Using cell-attached unitary current recordings from GluN1-2a/GluN2A receptors expressed in human HEK293 cells and from NMDA receptors native to hippocampal neurons from male and female rats, we recorded unitary currents from multichannel patches and used a coupled Markov model to determine the extent of signal coupling (κ). In the absence of extracellular Ca2+, we observed no cooperativity (κ < 0.1), whereas in 1.8 mm external Ca2+, both recombinant and native channels showed substantial negative cooperativity (κ = 0.27). Intracellular Ca2+ chelation or overexpression of a Ca2+-insensitive CaM mutant, reduced coupling, which is consistent with CDI representing the coupling mechanism. In contrast, cooperativity increased substantially (κ = 0.68) when overexpressing the postsynaptic scaffolding protein PSD-95, which increased receptor clustering. Together, these new results demonstrate that NMDA receptor currents are negatively coupled through CDI, and the degree of coupling can be tuned by the distance between receptors. Therefore, channel clustering can influence the activity-dependent reduction in NMDA receptor currents.SIGNIFICANCE STATEMENT At central synapses, NMDA receptors are a major class of excitatory glutamate-gated channels and a source of activity-dependent Ca2+ influx. In turn, fluxed Ca2+ ions bind to calmodulin-primed receptors and reduce further entry, through an autoinhibitory mechanism known as Ca2+ -dependent inactivation (CDI). Here, we show that the diffusion of fluxed Ca2+ between active channels situated within submicroscopic distances amplified receptor inactivation. Thus, calmodulin-mediated gating modulation, an evolutionarily conserved regulatory mechanism, endows synapses with sensitivity to both the temporal sequence and spatial distribution of Ca2+ signals. Perturbations in this mechanism, which coordinates the activity of NMDA receptors within a cluster, may cause signaling alterations that contribute to neuropsychiatric conditions.

EGTA Can Inhibit Vesicular Release in the Nanodomain of Single Ca2+ Channels

The exogenous Ca²⁺ chelator EGTA (ethylene glycol tetraacetic acid) has been widely used to probe the coupling distance between Ca²⁺ channels and vesicular Ca²⁺ sensors for neurotransmitter release. Because of its slow forward rate for binding, EGTA is thought to not capture calcium ions in very proximity to a channel, whereas it does capture calcium ions at the remote distance. However, in this study, our reaction diffusion simulations (RDSs) of Ca²⁺ combined with a release calculation using vesicular sensor models indicate that a high concentration of EGTA decreases Ca²⁺ and vesicular release in the nanodomain of single channels. We found that a key determinant of the effect of EGTA on neurotransmitter release is the saturation of the vesicular sensor. When the sensor is saturated, the reduction in the Ca²⁺ concentration by EGTA is masked. By contrast, when the sensor is in a linear range, even a small reduction in Ca²⁺ by EGTA can decrease vesicular release. In proximity to a channel, the vesicular sensor is often saturated for a long voltage step, but not for a brief Ca²⁺ influx typically evoked by an action potential. Therefore, when EGTA is used as a diagnostic tool to probe the coupling distance, care must be taken regarding the presynaptic Ca²⁺ entry duration as well as the property of the vesicular Ca²⁺ sensor.

Quantitation and Simulation of Single Action Potential-Evoked Ca2+ Signals in CA1 Pyramidal Neuron Presynaptic Terminals

Presynaptic Ca²⁺ evokes exocytosis, endocytosis, and synaptic plasticity. However, Ca²⁺ flux and interactions at presynaptic molecular targets are difficult to quantify because fluorescence imaging has limited resolution. In rats of either sex, we measured single varicosity presynaptic Ca²⁺ using Ca²⁺ dyes as buffers, and constructed models of Ca²⁺ dispersal. Action potentials evoked Ca²⁺ transients with little variation when measured with low-affinity dye (peak amplitude 789 ± 39 nM, within 2 ms of stimulation; decay times, 119 ± 10 ms). Endogenous Ca²⁺ buffering capacity, action potential-evoked free [Ca²⁺]_i, and total Ca²⁺ amounts entering terminals were determined using Ca²⁺ dyes as buffers. These data constrained Monte Carlo (MCell) simulations of Ca²⁺ entry, buffering, and removal. Simulations of experimentally-determined Ca²⁺ fluxes, buffered by simulated calbindin_28K well fit data, and were consistent with clustered Ca²⁺ entry followed within 4 ms by diffusion throughout the varicosity. Repetitive stimulation caused free varicosity Ca²⁺ to sum. However, simulated in nanometer domains, its removal by pumps and buffering was negligible, while local diffusion dominated. Thus, Ca²⁺ within tens of nanometers of entry, did not accumulate. A model of synaptotagmin1 (syt1)-Ca²⁺ binding indicates that even with 10 µM free varicosity evoked Ca²⁺, syt1 must be within tens of nanometers of channels to ensure occupation of all its Ca²⁺-binding sites. Repetitive stimulation, evoking short-term synaptic enhancement, does not modify probabilities of Ca²⁺ fully occupying syt1’s C2 domains, suggesting that enhancement is not mediated by Ca²⁺-syt1 interactions. We conclude that at spatiotemporal scales of fusion machines, Ca²⁺ necessary for their activation is diffusion dominated.

Ca-dependence of synaptic vesicle exocytosis and endocytosis at the hippocampal mossy fibre terminal

KEY POINTS

We used presynaptic capacitance measurements at the hippocampal mossy fibre terminal at room temperature to measure Ca-dependence of exo- and endocytotic kinetics. The readily releasable pool (RRP) of synaptic vesicles was released with a time constant of 30-40 ms and was sensitive to Ca buffers, BAPTA and EGTA. Our data suggest that recruitment of the vesicles to the RRP was Ca-insensitive and had a time constant of 1 s. In addition to the RRP, the reserve pool of vesicles, which had a similar size to RRP, was depleted during repetitive stimulation. Our data suggest that synaptic vesicle endocytosis was also Ca-insensitive.

ABSTRACT

Hippocampal mossy fibre terminals comprise one of the cortical terminals, which are sufficiently large to be accessible by patch clamp recordings. To measure Ca-dependence of exo- and endocytotic kinetics quantitatively, we applied presynaptic capacitance measurements to the mossy fibre terminal at room temperature. The time course of synaptic vesicle fusion was slow, with a time constant of tens of milliseconds, and was sensitive to Ca buffers EGTA and BAPTA, suggesting a loose coupling between Ca channels and synaptic vesicles. The size of the readily-releasable pool (RRP) of synaptic vesicles was relatively insensitive to Ca buffers. Once the RRP was depleted, it was recovered by a single exponential with a time constant of ∼1 s independent of the presence of Ca buffers, suggesting Ca independent vesicle replenishment. In addition to the RRP, the reserve pool of vesicles was released slowly during repetitive stimulation. Endocytosis was also insensitive to Ca buffers and had a slow time course, excluding the involvement of rapid vesicle cycling in vesicle replenishment. Although mossy fibre terminals are known to have various forms of Ca-dependent plasticity, some features of vesicle dynamics are robust and Ca-insensitive.

Calcium, Dopamine and Neuronal Calcium Sensor 1: Their Contribution to Parkinson's Disease

Parkinson’s disease (PD) is a debilitating neurodegenerative disorder characterized by loss of dopaminergic neurons in the substantia nigra pars compacta. The causes of PD in humans are still unknown, although metabolic characteristics of the neurons affected by the disease have been implicated in their selective susceptibility. Mitochondrial dysfunction and proteostatic stress are recognized to be important in the pathogenesis of both familial and sporadic PD, and they both culminate in bioenergetic deficits. Exposure to calcium overload has recently emerged as a key determinant, and pharmacological treatment that inhibits Ca²⁺ entry diminishes neuronal damage in chemical models of PD. In this review, we first introduce general concepts on neuronal Ca²⁺ signaling and then summarize the current knowledge on fundamental properties of substantia nigra pars compacta dopaminergic neurons, on the role of the interplay between Ca²⁺ and dopamine signaling in neuronal activity and susceptibility to cell death. We also discuss the possible involvement of a “neglected” player, the Neuronal Calcium Sensor-1 (NCS-1), which has been shown to participate to dopaminergic signaling by regulating dopamine dependent receptor desensitization in normal brain but, data supporting a direct role in PD pathogenesis are still missing. However, it is intriguing to speculate that the Ca²⁺-dependent modulation of NCS-1 activity could eventually counteract dopaminergic neurons degeneration.

Extension of Rapid Buffering Approximation to Ca2+ Buffers with Two Binding Sites

Fundamental cell processes such as synaptic neurotransmitter release, endocrine hormone secretion, and myocyte contraction are controlled by highly localized calcium (Ca²⁺) signals resulting from brief openings of trans-membrane Ca²⁺ channels. On short temporal and spatial scales, the corresponding local Ca²⁺ nanodomains formed in the vicinity of a single or several open Ca²⁺ channels can be effectively approximated by quasi-stationary solutions. The rapid buffering approximation (RBA) is one of the most powerful of such approximations, and is based on the assumption of instantaneous equilibration of the bimolecular Ca²⁺ buffering reaction, combined with the conservation condition for the total Ca²⁺ and buffer molecule numbers. Previously, RBA has been generalized to an arbitrary arrangement of Ca²⁺ channels on a flat membrane, in the presence of any number of simple Ca²⁺ buffers with one-to-one Ca²⁺ binding stoichiometry. However, many biological buffers have multiple binding sites. For example, buffers and sensors phylogenetically related to calmodulin consist of two Ca²⁺-binding domains (lobes), with each domain binding two Ca²⁺ ions in a cooperative manner. Here we consider an extension of RBA to such buffers with two interdependent Ca²⁺ binding sites. We show that in the presence of such buffers, RBA solution is given by the solution to a cubic equation, analogous to the quadratic equation describing RBA in the case of a simple, one-to-one Ca²⁺ buffer. We examine in detail the dependence of RBA accuracy on buffering parameters, to reveal conditions under which RBA provides sufficient precision.

Synaptotagmin Ca2+ Sensors and Their Spatial Coupling to Presynaptic Cav Channels in Central Cortical Synapses

Ca²⁺ concentrations drop rapidly over a distance of a few tens of nanometers from an open voltage-gated Ca²⁺ channel (Ca_v), thereby, generating a spatially steep and temporally short-lived Ca²⁺ gradient that triggers exocytosis of a neurotransmitter filled synaptic vesicle. These non-steady state conditions make the Ca²⁺-binding kinetics of the Ca²⁺ sensors for release and their spatial coupling to the Ca_vs important parameters of synaptic efficacy. In the mammalian central nervous system, the main release sensors linking action potential mediated Ca²⁺ influx to synchronous release are Synaptotagmin (Syt) 1 and 2. We review here quantitative work focusing on the Ca²⁺ kinetics of Syt2-mediated release. At present similar quantitative detail is lacking for Syt1-mediated release. In addition to triggering release, Ca²⁺ remaining bound to Syt after the first of two successive high-frequency activations was found to be capable of facilitating release during the second activation. More recently, the Ca²⁺ sensor Syt7 was identified as additional facilitation sensor. We further review how several recent functional studies provided quantitative insights into the spatial topographical relationships between Syts and Ca_vs and identified mechanisms regulating the sensor-to-channel coupling distances at presynaptic active zones. Most synapses analyzed in matured cortical structures were found to operate at tight, nanodomain coupling. For fast signaling synapses a developmental switch from loose, microdomain to tight, nanodomain coupling was found. The protein Septin5 has been known for some time as a developmentally down-regulated “inhibitor” of tight coupling, while Munc13-3 was found only recently to function as a developmentally up-regulated mediator of tight coupling. On the other hand, a highly plastic synapse was found to operate at loose coupling in the matured hippocampus. Together these findings suggest that the coupling topography and its regulation is a specificity of the type of synapse. However, to definitely draw such conclusion our knowledge of functional active zone topographies of different types of synapses in different areas of the mammalian brain is too incomplete.

Two Forms of Synaptic Depression Produced by Differential Neuromodulation of Presynaptic Calcium Channels

Neuromodulators are important regulators of synaptic transmission throughout the brain. At the presynaptic terminal, neuromodulation of calcium channels (CaVs) can affect transmission not only by changing neurotransmitter release probability, but also by shaping short-term plasticity (STP). Indeed, changes in STP are often considered a requirement for defining a presynaptic site of action. Nevertheless, some synapses exhibit non-canonical forms of neuromodulation, where release probability is altered without a corresponding change in STP. Here, we identify biophysical mechanisms whereby both canonical and non-canonical presynaptic neuromodulation can occur at the same synapse. At a subset of glutamatergic terminals in prefrontal cortex, GABAB and D1/D5 dopamine receptors suppress release probability with and without canonical increases in short-term facilitation by modulating different aspects of presynaptic CaV function. These findings establish a framework whereby signaling from multiple neuromodulators can converge on presynaptic CaVs to differentially tune release dynamics at the same synapse.

Regulation of synaptic release-site Ca2+ channel coupling as a mechanism to control release probability and short-term plasticity

Synaptic transmission relies on the rapid fusion of neurotransmitter-containing synaptic vesicles (SVs), which happens in response to action potential (AP)-induced Ca²⁺ influx at active zones (AZs). A highly conserved molecular machinery cooperates at SV-release sites to mediate SV plasma membrane attachment and maturation, Ca²⁺ sensing, and membrane fusion. Despite this high degree of conservation, synapses - even within the same organism, organ or neuron - are highly diverse regarding the probability of APs to trigger SV fusion. Additionally, repetitive activation can lead to either strengthening or weakening of transmission. In this review, we discuss mechanisms controlling release probability and this short-term plasticity. We argue that an important layer of control is exerted by evolutionarily conserved AZ scaffolding proteins, which determine the coupling distance between SV fusion sites and voltage-gated Ca²⁺ channels (VGCC) and, thereby, shape synapse-specific input/output behaviors. We propose that AZ-scaffold modifications may occur to adapt the coupling distance during synapse maturation and plastic regulation of synapse strength.

Challenges in Reproducibility, Replicability, and Comparability of Computational Models and Tools for Neuronal and Glial Networks, Cells, and Subcellular Structures

The possibility to replicate and reproduce published research results is one of the biggest challenges in all areas of science. In computational neuroscience, there are thousands of models available. However, it is rarely possible to reimplement the models based on the information in the original publication, let alone rerun the models just because the model implementations have not been made publicly available. We evaluate and discuss the comparability of a versatile choice of simulation tools: tools for biochemical reactions and spiking neuronal networks, and relatively new tools for growth in cell cultures. The replicability and reproducibility issues are considered for computational models that are equally diverse, including the models for intracellular signal transduction of neurons and glial cells, in addition to single glial cells, neuron-glia interactions, and selected examples of spiking neuronal networks. We also address the comparability of the simulation results with one another to comprehend if the studied models can be used to answer similar research questions. In addition to presenting the challenges in reproducibility and replicability of published results in computational neuroscience, we highlight the need for developing recommendations and good practices for publishing simulation tools and computational models. Model validation and flexible model description must be an integral part of the tool used to simulate and develop computational models. Constant improvement on experimental techniques and recording protocols leads to increasing knowledge about the biophysical mechanisms in neural systems. This poses new challenges for computational neuroscience: extended or completely new computational methods and models may be required. Careful evaluation and categorization of the existing models and tools provide a foundation for these future needs, for constructing multiscale models or extending the models to incorporate additional or more detailed biophysical mechanisms. Improving the quality of publications in computational neuroscience, enabling progressive building of advanced computational models and tools, can be achieved only through adopting publishing standards which underline replicability and reproducibility of research results.

Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: Insights into ER refilling and the spatial signature of Ca2+ signals

The spatial organisation of Orai channels and SERCA pumps within ER-PM junctions is important for enhancing the versatility and specificity of sub-cellular Ca²⁺ signals generated during store operated Ca²⁺ entry (SOCE). In this paper, we present a novel three dimensional spatio-temporal model describing Ca²⁺ dynamics in the ER-PM junction and sub-PM ER during SOCE. We investigate the role of Orai channel and SERCA pump location to provide insights into how these components shape the Ca²⁺ signals generated and affect ER refilling. We find that the organisation of Orai channels within the ER-PM junction controls the amplitude and shape of the Ca²⁺ profile but does not enhance ER refilling. The model shows that ER refilling is only weakly affected by the location of SERCA2b pumps within the ER-PM junction and that the placement of SERCA2a pumps within the ER-PM junction has much greater control over ER refilling.

Variations in Ca2+ Influx Can Alter Chelator-Based Estimates of Ca2+ Channel-Synaptic Vesicle Coupling Distance

The timing and probability of synaptic vesicle fusion from presynaptic terminals is governed by the distance between voltage-gated Ca²⁺ channels (VGCCs) and Ca²⁺ sensors for exocytosis. This VGCC-sensor coupling distance can be determined from the fractional block of vesicular release by exogenous Ca²⁺ chelators, which depends on biophysical factors that have not been thoroughly explored. Using numerical simulations of Ca²⁺ reaction and diffusion, as well as vesicular release, we examined the contributions of conductance, density, and open duration of VGCCs, and the influence of endogenous Ca²⁺ buffers on the inhibition of exocytosis by EGTA. We found that estimates of coupling distance are critically influenced by the duration and amplitude of Ca²⁺ influx at active zones, but relatively insensitive to variations of mobile endogenous buffer. High concentrations of EGTA strongly inhibit vesicular release in close proximity (20-30 nm) to VGCCs if the flux duration is brief, but have little influence for longer flux durations that saturate the Ca²⁺ sensor. Therefore, the diversity in presynaptic action potential duration is sufficient to alter EGTA inhibition, resulting in errors potentially as large as 300% if Ca²⁺ entry durations are not considered when estimating VGCC-sensor coupling distances.SIGNIFICANT STATEMENT The coupling distance between voltage-gated Ca²⁺ channels and Ca²⁺ sensors for exocytosis critically determines the timing and probability of neurotransmitter release. Perfusion of presynaptic terminals with the exogenous Ca²⁺ chelator EGTA has been widely used for both qualitative and quantitative estimates of this distance. However, other presynaptic terminal parameters such as the amplitude and duration of Ca²⁺ entry can also influence EGTA inhibition of exocytosis, thus confounding conclusions based on EGTA alone. Here, we performed reaction-diffusion simulations of Ca²⁺-driven synaptic vesicle fusion, which delineate the critical parameters influencing an accurate prediction of coupling distance. Our study provides guidelines for characterizing and understanding how variability in coupling distance across chemical synapses could be estimated accurately.

Vesicle release site organization at synaptic active zones

Information transfer between nerve cells (neurons) forms the basis of behavior, emotion, and survival. Signal transduction from one neuron to another occurs at synapses, and relies on both electrical and chemical signal propagation. At chemical synapses, incoming electrical action potentials trigger the release of chemical neurotransmitters that are sensed by the connected cell and here reconverted to an electrical signal. The presynaptic conversion of an electrical to a chemical signal is an energy demanding, highly regulated process that relies on a complex, evolutionarily conserved molecular machinery. Here, we review the biophysical characteristics of this process, the current knowledge of the molecules operating in this reaction and genetic specializations that may have evolved to shape inter-neuronal signaling.

Inseparable tandem: evolution chooses ATP and Ca2+ to control life, death and cellular signalling

From the very dawn of biological evolution, ATP was selected as a multipurpose energy-storing molecule. Metabolism of ATP required intracellular free Ca(2+) to be set at exceedingly low concentrations, which in turn provided the background for the role of Ca(2+) as a universal signalling molecule. The early-eukaryote life forms also evolved functional compartmentalization and vesicle trafficking, which used Ca(2+) as a universal signalling ion; similarly, Ca(2+) is needed for regulation of ciliary and flagellar beat, amoeboid movement, intracellular transport, as well as of numerous metabolic processes. Thus, during evolution, exploitation of atmospheric oxygen and increasingly efficient ATP production via oxidative phosphorylation by bacterial endosymbionts were a first step for the emergence of complex eukaryotic cells. Simultaneously, Ca(2+) started to be exploited for short-range signalling, despite restrictions by the preset phosphate-based energy metabolism, when both phosphates and Ca(2+) interfere with each other because of the low solubility of calcium phosphates. The need to keep cytosolic Ca(2+) low forced cells to restrict Ca(2+) signals in space and time and to develop energetically favourable Ca(2+) signalling and Ca(2+) microdomains. These steps in tandem dominated further evolution. The ATP molecule (often released by Ca(2+)-regulated exocytosis) rapidly grew to be the universal chemical messenger for intercellular communication; ATP effects are mediated by an extended family of purinoceptors often linked to Ca(2+) signalling. Similar to atmospheric oxygen, Ca(2+) must have been reverted from a deleterious agent to a most useful (intra- and extracellular) signalling molecule. Invention of intracellular trafficking further increased the role for Ca(2+) homeostasis that became critical for regulation of cell survival and cell death. Several mutually interdependent effects of Ca(2+) and ATP have been exploited in evolution, thus turning an originally unholy alliance into a fascinating success story.This article is part of the themed issue 'Evolution brings Ca(2+) and ATP together to control life and death'.

Concise Whole-Cell Modeling of BKCa-CaV Activity Controlled by Local Coupling and Stoichiometry

Large-conductance Ca²⁺-dependent K⁺ (BK_Ca) channels are important regulators of electrical activity. These channels colocalize and form ion channel complexes with voltage-dependent Ca²⁺ (CaV) channels. Recent stochastic simulations of the BK_Ca-CaV complex with 1:1 stoichiometry have given important insight into the local control of BK_Ca channels by fluctuating nanodomains of Ca²⁺. However, such Monte Carlo simulations are computationally expensive, and are therefore not suitable for large-scale simulations of cellular electrical activity. In this work we extend the stochastic model to more realistic BK_Ca-CaV complexes with 1:n stoichiometry, and analyze the single-complex model with Markov chain theory. From the description of a single BK_Ca-CaV complex, using arguments based on timescale analysis, we derive a concise model of whole-cell BK_Ca currents, which can readily be analyzed and inserted into models of cellular electrical activity. We illustrate the usefulness of our results by inserting our BK_Ca description into previously published whole-cell models, and perform simulations of electrical activity in various cell types, which show that BK_Ca-CaV stoichiometry can affect whole-cell behavior substantially. Our work provides a simple formulation for the whole-cell BK_Ca current that respects local interactions in BK_Ca-CaV complexes, and indicates how local-global coupling of ion channels may affect cell behavior.

The Mechanisms and Functions of Synaptic Facilitation

The ability of the brain to store and process information relies on changing the strength of connections between neurons. Synaptic facilitation is a form of short-term plasticity that enhances synaptic transmission for less than a second. Facilitation is a ubiquitous phenomenon thought to play critical roles in information transfer and neural processing. Yet our understanding of the function of facilitation remains largely theoretical. Here we review proposed roles for facilitation and discuss how recent progress in uncovering the underlying molecular mechanisms could enable experiments that elucidate how facilitation, and short-term plasticity in general, contributes to circuit function and animal behavior.

Padé Approximation of a Stationary Single-Channel Ca2+ Nanodomain

We consider the stationary solution for the Ca²⁺ concentration near a point Ca²⁺ source describing a single-channel Ca²⁺ nanodomain, in the presence of a single mobile buffer with one-to-one Ca²⁺ binding stoichiometry. Previously, a number of Ca²⁺ nanodomains approximations have been developed, for instance the excess buffer approximation (EBA), the rapid buffering approximation (RBA), and the linear approximation (LIN), each valid for appropriate buffering conditions. Apart from providing a simple method of estimating Ca²⁺ and buffer concentrations without resorting to computationally expensive numerical solution of reaction-diffusion equations, such approximations proved useful in revealing the dependence of nanodomain Ca²⁺ distribution on crucial parameters such as buffer mobility and its Ca²⁺ binding properties. In this study, we present a different form of analytic approximation, which is based on matching the short-range Taylor series of the nanodomain concentration with the long-range asymptotic series expressed in inverse powers of distance from channel location. Namely, we use a "dual" Padé rational function approximation to simultaneously match terms in the short- and the long-range series, and we show that this provides an accurate approximation to the nanodomain Ca²⁺ and buffer concentrations. We compare this approximation with the previously obtained approximations and show that it yields a better estimate of the free buffer concentration for a wide range of buffering conditions. The drawback of our method is that it has a complex algebraic form for any order higher than the lowest bilinear order, and cannot be readily extended to multiple Ca²⁺ channels. However, it may be possible to extend the Padé method to estimate Ca²⁺ nanodomains in the presence of cooperative Ca²⁺ buffers with two Ca²⁺ binding sites, the case that existing methods do not address.

Regulation of PI3K by PKC and MARCKS: Single-Molecule Analysis of a Reconstituted Signaling Pathway

In chemotaxing ameboid cells, a complex leading-edge signaling circuit forms on the cytoplasmic leaflet of the plasma membrane and directs both actin and membrane remodeling to propel the leading edge up an attractant gradient. This leading-edge circuit includes a putative amplification module in which Ca(2+)-protein kinase C (Ca(2+)-PKC) is hypothesized to phosphorylate myristoylated alanine-rich C kinase substrate (MARCKS) and release phosphatidylinositol-4,5-bisphosphate (PIP2), thereby stimulating production of the signaling lipid phosphatidylinositol-3,4,5-trisphosphate (PIP3) by the lipid kinase phosphoinositide-3-kinase (PI3K). We investigated this hypothesized Ca(2+)-PKC-MARCKS-PIP2-PI3K-PIP3 amplification module and tested its key predictions using single-molecule fluorescence to measure the surface densities and activities of its protein components. Our findings demonstrate that together Ca(2+)-PKC and the PIP2-binding peptide of MARCKS modulate the level of free PIP2, which serves as both a docking target and substrate lipid for PI3K. In the off state of the amplification module, the MARCKS peptide sequesters PIP2 and thereby inhibits PI3K binding to the membrane. In the on state, Ca(2+)-PKC phosphorylation of the MARCKS peptide reverses the PIP2 sequestration, thereby releasing multiple PIP2 molecules that recruit multiple active PI3K molecules to the membrane surface. These findings 1) show that the Ca(2+)-PKC-MARCKS-PIP2-PI3K-PIP3 system functions as an activation module in vitro, 2) reveal the molecular mechanism of activation, 3) are consistent with available in vivo data, and 4) yield additional predictions that are testable in live cells. More broadly, the Ca(2+)-PKC-stimulated release of free PIP2 may well regulate the membrane association of other PIP2-binding proteins, and the findings illustrate the power of single-molecule analysis to elucidate key dynamic and mechanistic features of multiprotein signaling pathways on membrane surfaces.

The complex nature of calcium cation interactions with phospholipid bilayers

Understanding interactions of calcium with lipid membranes at the molecular level is of great importance in light of their involvement in calcium signaling, association of proteins with cellular membranes, and membrane fusion. We quantify these interactions in detail by employing a combination of spectroscopic methods with atomistic molecular dynamics simulations. Namely, time-resolved fluorescent spectroscopy of lipid vesicles and vibrational sum frequency spectroscopy of lipid monolayers are used to characterize local binding sites of calcium in zwitterionic and anionic model lipid assemblies, while dynamic light scattering and zeta potential measurements are employed for macroscopic characterization of lipid vesicles in calcium-containing environments. To gain additional atomic-level information, the experiments are complemented by molecular simulations that utilize an accurate force field for calcium ions with scaled charges effectively accounting for electronic polarization effects. We demonstrate that lipid membranes have substantial calcium-binding capacity, with several types of binding sites present. Significantly, the binding mode depends on calcium concentration with important implications for calcium buffering, synaptic plasticity, and protein-membrane association.

Regulation of a Coupled MARCKS-PI3K Lipid Kinase Circuit by Calmodulin: Single-Molecule Analysis of a Membrane-Bound Signaling Module

Amoeboid cells that employ chemotaxis to travel up an attractant gradient possess a signaling network assembled on the leading edge of the plasma membrane that senses the gradient and remodels the actin mesh and cell membrane to drive movement in the appropriate direction. In leukocytes such as macrophages and neutrophils, and perhaps in other amoeboid cells as well, the leading edge network includes a positive feedback loop in which the signaling of multiple pathway components is cooperatively coupled. Cytoplasmic Ca²⁺ is a recently recognized component of the feedback loop at the leading edge where it stimulates phosphoinositide-3-kinase (PI3K) and the production of its product signaling lipid phosphatidylinositol 3,4,5-trisphosphate (PIP₃). A previous study implicated Ca²⁺-activated protein kinase C (PKC) and the phosphatidylinositol 4,5-bisphosphate (PIP₂) binding protein MARCKS as two important players in this signaling, because PKC phosphorylation of MARCKS releases free PIP₂ that serves as the membrane binding target and substrate for PI3K. This study asks whether calmodulin (CaM), which is known to directly bind MARCKS, also stimulates PIP₃ production by releasing free PIP₂. Single-molecule fluorescence microscopy is used to quantify the surface density and enzyme activity of key protein components of the hypothesized Ca²⁺-CaM-MARCKS-PIP₂-PI3K-PIP₃ circuit. The findings show that CaM does stimulate PI3K lipid kinase activity by binding MARCKS and displacing it from PIP₂ headgroups, thereby releasing free PIP₂ that recruits active PI3K to the membrane and serves as the substrate for the generation of PIP₃. The resulting CaM-triggered activation of PI3K is complete in seconds and is much faster than PKC-triggered activation, which takes minutes. Overall, the available evidence implicates both PKC and CaM in the coupling of Ca²⁺ and PIP₃ signals and suggests these two different pathways have slow and fast activation kinetics, respectively.

Recent advances in mathematical modeling and statistical analysis of exocytosis in endocrine cells

Most endocrine cells secrete hormones as a result of Ca²⁺-regulated exocytosis, i.e., fusion of the membranes of hormone-containing secretory granules with the cell membrane, which allows the hormone molecules to escape to the extracellular space. As in neurons, electrical activity and cell depolarization open voltage-sensitive Ca²⁺ channels, and the resulting Ca²⁺ influx elevate the intracellular Ca²⁺ concentration, which in turn causes exocytosis. Whereas the main molecular components involved in exocytosis are increasingly well understood, quantitative understanding of the dynamical aspects of exocytosis is still lacking. Due to the nontrivial spatiotemporal Ca²⁺ dynamics, which depends on the particular pattern of electrical activity as well as Ca²⁺ channel kinetics, exocytosis is dependent on the spatial arrangement of Ca²⁺ channels and secretory granules. For example, the creation of local Ca²⁺ microdomains, where the Ca²⁺ concentration reaches tens of µM, are believed to be important for triggering exocytosis. Spatiotemporal simulations of buffered Ca²⁺ diffusion have provided important insight into the interplay between electrical activity, Ca²⁺ channel kinetics, and the location of granules and Ca²⁺ channels. By confronting simulations with statistical time-to-event (or survival) regression analysis of single granule exocytosis monitored with TIRF microscopy, a direct connection between location and rate of exocytosis can be obtained at the local, single-granule level. To get insight into whole-cell secretion, simplifications of the full spatiotemporal dynamics have shown to be highly helpful. Here, we provide an overview of recent approaches and results for quantitative analysis of Ca²⁺ regulated exocytosis of hormone-containing granules.

Ca2+ controls gating of voltage-gated calcium channels by releasing the β2e subunit from the plasma membrane

Voltage-gated calcium (Cav) channels, which are regulated by membrane potential, cytosolic Ca(2+), phosphorylation, and membrane phospholipids, govern Ca(2+) entry into excitable cells. Cav channels contain a pore-forming α1 subunit, an auxiliary α2δ subunit, and a regulatory β subunit, each encoded by several genes in mammals. In addition to a domain that interacts with the α1 subunit, β2e and β2a also interact with the cytoplasmic face of the plasma membrane through an electrostatic interaction for β2e and posttranslational acylation for β2a. We found that an increase in cytosolic Ca(2+) promoted the release of β2e from the membrane without requiring substantial depletion of the anionic phospholipid phosphatidylinositol 4,5-bisphosphate (PIP2) from the plasma membrane. Experiments with liposomes indicated that Ca(2+) disrupted the interaction of the β2e amino-terminal peptide with membranes containing PIP2 Ca(2+) binding to calmodulin (CaM) leads to CaM-mediated inactivation of Cav currents. Although Cav2.2 coexpressed with β2a required Ca(2+)-dependent activation of CaM for Ca(2+)-mediated reduction in channel activity, Cav2.2 coexpressed with β2e exhibited Ca(2+)-dependent inactivation of the channel even in the presence of Ca(2+)-insensitive CaM. Inducible depletion of PIP2 reduced Cav2.2 currents, and in cells coexpressing β2e, but not a form that lacks the polybasic region, increased intracellular Ca(2+) further reduced Cav2.2 currents. Many hormone- or neurotransmitter-activated receptors stimulate PIP2 hydrolysis and increase cytosolic Ca(2+); thus, our findings suggest that β2e may integrate such receptor-mediated signals to limit Cav activity.