Hybrid Markov-mass action law model for cell activation by rare binding events: Application to calcium induced vesicular release at neuronal synapses

Close agreement between deterministic versus stochastic modeling of first-passage time to vesicle fusion

Ca2+-dependent cell processes, such as neurotransmitter or endocrine vesicle fusion, are inherently stochastic due to large fluctuations in Ca2+ channel gating, Ca2+ diffusion, and Ca2+ binding to buffers and target sensors. However, previous studies revealed closer-than-expected agreement between deterministic and stochastic simulations of Ca2+ diffusion, buffering, and sensing if Ca2+ channel gating is not Ca2+ dependent. To understand this result more fully, we present a comparative study complementing previous work, focusing on Ca2+ dynamics downstream of Ca2+ channel gating. Specifically, we compare deterministic (mean-field/mass-action) and stochastic simulations of vesicle exocytosis latency, quantified by the probability density of the first-passage time (FPT) to the Ca2+-bound state of a vesicle fusion sensor, following a brief Ca2+ current pulse. We show that under physiological constraints, the discrepancy between FPT densities obtained using the two approaches remains small even if as few as ∼50 Ca2+ ions enter per single channel-vesicle release unit. Using a reduced two-compartment model for ease of analysis, we illustrate how this close agreement arises from the smallness of correlations between fluctuations of the reactant molecule numbers, despite the large magnitude of fluctuation amplitudes. This holds if all relevant reactions are heteroreaction between molecules of different species, as is the case for bimolecular Ca2+ binding to buffers and downstream sensor targets. In this case, diffusion and buffering effectively decorrelate the state of the Ca2+ sensor from local Ca2+ fluctuations. Thus, fluctuations in the Ca2+ sensor's state underlying the FPT distribution are only weakly affected by the fluctuations in the local Ca2+ concentration around its average, deterministically computable value.

Reversible target-binding kinetics of multiple impatient particles

Certain biochemical reactions can only be triggered after binding a sufficient number of particles to a specific target region such as an enzyme or a protein sensor. We investigate the distribution of the reaction time, i.e., the first instance when all independently diffusing particles are bound to the target. When each particle binds irreversibly, this is equivalent to the first-passage time of the slowest (last) particle. In turn, reversible binding to the target renders the problem much more challenging and drastically changes the distribution of the reaction time. We derive the exact solution of this problem and investigate the short-time and long-time asymptotic behaviors of the reaction time probability density. We also analyze how the mean reaction time depends on the unbinding rate and the number of particles. Our exact and asymptotic solutions are compared to Monte Carlo simulations.

A first-passage approach to diffusion-influenced reversible binding and its insights into nanoscale signaling at the presynapse

Synaptic transmission between neurons is governed by a cascade of stochastic calcium ion reaction–diffusion events within nerve terminals leading to vesicular release of neurotransmitter. Since experimental measurements of such systems are challenging due to their nanometer and sub-millisecond scale, numerical simulations remain the principal tool for studying calcium-dependent neurotransmitter release driven by electrical impulses, despite the limitations of time-consuming calculations. In this paper, we develop an analytical solution to rapidly explore dynamical stochastic reaction–diffusion problems based on first-passage times. This is the first analytical model that accounts simultaneously for relevant statistical features of calcium ion diffusion, buffering, and its binding/unbinding reaction with a calcium sensor for synaptic vesicle fusion. In particular, unbinding kinetics are shown to have a major impact on submillisecond sensor occupancy probability and therefore cannot be neglected. Using Monte Carlo simulations we validated our analytical solution for instantaneous calcium influx and that through voltage-gated calcium channels. We present a fast and rigorous analytical tool that permits a systematic exploration of the influence of various biophysical parameters on molecular interactions within cells, and which can serve as a building block for more general cell signaling simulators.

Suppression of Presynaptic Glutamate Release by Postsynaptic Metabotropic NMDA Receptor Signalling to Pannexin-1

The impact of pannexin-1 (Panx1) channels on synaptic transmission is poorly understood. Here, we show that selective block of Panx1 in single postsynaptic hippocampal CA1 neurons from male rat or mouse brain slices causes intermittent, seconds long increases in the frequency of sEPSC following Schaffer collateral stimulation. The increase in sEPSC frequency occurred without an effect on evoked neurotransmission. Consistent with a presynaptic origin of the augmented glutamate release, the increased sEPSC frequency was prevented by bath-applied EGTA-AM or TTX. Manipulation of a previously described metabotropic NMDAR pathway (i.e., by preventing ligand binding to NMDARs with competitive antagonists or blocking downstream Src kinase) also increased sEPSC frequency similar to that seen when Panx1 was blocked. This facilitated glutamate release was absent in transient receptor potential vanilloid 1 (TRPV1) KO mice and prevented by the TRPV1 antagonist, capsazepine, suggesting it required presynaptic TRPV1. We show presynaptic expression of TRPV1 by immunoelectron microscopy and link TRPV1 to Panx1 because Panx1 block increases tissue levels of the endovanilloid, anandamide. Together, these findings demonstrate an unexpected role for metabotropic NMDARs and postsynaptic Panx1 in suppression of facilitated glutamate neurotransmission.SIGNIFICANCE STATEMENT The postsynaptic ion and metabolite channel, pannexin-1, is regulated by metabotropic NMDAR signaling through Src kinase. This pathway suppresses facilitated release of presynaptic glutamate during synaptic activity by regulating tissue levels of the transient receptor potential vanilloid 1 agonist anandamide.

Transient Confinement of CaV2.1 Ca2+-Channel Splice Variants Shapes Synaptic Short-Term Plasticity

The precision and reliability of synaptic information transfer depend on the molecular organization of voltage-gated calcium channels (VGCCs) within the presynaptic membrane. Alternative splicing of exon 47 affects the C-terminal structure of VGCCs and their affinity to intracellular partners and synaptic vesicles (SVs). We show that hippocampal synapses expressing VGCCs either with exon 47 (Ca_V2.1₊₄₇) or without (Ca_V2.1_Δ47) differ in release probability and short-term plasticity. Tracking single channels revealed transient visits (∼100 ms) of presynaptic VGCCs in nanodomains (∼80 nm) that were controlled by neuronal network activity. Surprisingly, despite harboring prominent binding sites to scaffold proteins, Ca_V2.1₊₄₇ persistently displayed higher mobility within nanodomains. Synaptic accumulation of Ca_V2.1 was accomplished by optogenetic clustering, but only Ca_V2.1₊₄₇ increased transmitter release and enhanced synaptic short-term depression. We propose that exon 47-related alternative splicing of Ca_V2.1 channels controls synapse-specific release properties at the level of channel mobility-dependent coupling between VGCCs and SVs.

Perineuronal nets decrease membrane capacitance of peritumoral fast spiking interneurons in a model of epilepsy

Brain tumor patients commonly present with epileptic seizures. We show that tumor-associated seizures are the consequence of impaired GABAergic inhibition due to an overall loss of peritumoral fast spiking interneurons (FSNs) concomitant with a significantly reduced firing rate of those that remain. The reduced firing is due to the degradation of perineuronal nets (PNNs) that surround FSNs. We show that PNNs decrease specific membrane capacitance of FSNs permitting them to fire action potentials at supra-physiological frequencies. Tumor-released proteolytic enzymes degrade PNNs, resulting in increased membrane capacitance, reduced firing, and hence decreased GABA release. These studies uncovered a hitherto unknown role of PNNs as an electrostatic insulator that reduces specific membrane capacitance, functionally akin to myelin sheaths around axons, thereby permitting FSNs to exceed physiological firing rates. Disruption of PNNs may similarly account for excitation-inhibition imbalances in other forms of epilepsy and PNN protection through proteolytic inhibition may provide therapeutic benefits.

The First 100 nm Inside the Pre-synaptic Terminal Where Calcium Diffusion Triggers Vesicular Release

Calcium diffusion in the thin 100 nm layer located between the plasma membrane and docked vesicles in the pre-synaptic terminal of neuronal cells mediates vesicular fusion and synaptic transmission. Accounting for the narrow-cusp geometry located underneath the vesicle is a key ingredient that defines the probability and the time scale of calcium diffusion to bind calcium sensors for the initiation of vesicular release. We review here the time scale, the calcium binding dynamics and the consequences for asynchronous versus synchronous release. To conclude, three-dimensional modeling approaches and the associated coarse-grained simulations can now account efficiently for the precise co-organization of vesicles and Voltage-Gated-Calcium-Channel (VGCC). This co-organization is a key determinant of short-term plasticity and it shapes asynchronous release. Moreover, changing the location of VGCC from few nanometers underneath the vesicle modifies significantly the release probability. Finally, by modifying the calcium buffer concentration, a single synapse can switch from facilitation to depression.

Bridging intracellular scales by mechanistic computational models

The impact of intracellular spatial organization beyond classical compartments on processes such as cell signaling is increasingly recognized. A quantitative, mechanistic understanding of cellular systems therefore needs to account for different scales in at least three coordinates: time, molecular abundances, and space. Mechanistic mathematical models may span all these scales, but corresponding multi-scale models need to resolve mechanistic details on small scales while maintaining computational tractability for larger ones. This typically results in models that combine different levels of description: from a microscopic representation of chemical reactions up to continuum dynamics in space and time. We highlight recent progress in bridging these model classes and outline current challenges in multi-scale models such as active transport and dynamic geometries.

Electrodiffusion phenomena in neuroscience: a neglected companion

The emerging technological revolution in genetically encoded molecular sensors and super-resolution imaging provides neuroscientists with a pass to the real-time nano-world. On this small scale, however, classical principles of electrophysiology do not always apply. This is in large part because the nanoscopic heterogeneities in ionic concentrations and the local electric fields associated with individual ions and their movement can no longer be ignored. Here, we review basic principles of molecular electrodiffusion in the cellular environment of organized brain tissue. We argue that accurate interpretation of physiological observations on the nanoscale requires a better understanding of the underlying electrodiffusion phenomena.