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Vahdat Z, Gambrell O, Singh A. Characterizing the role of autaptic feedback in enhancing precision of neuronal firing times. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.10.06.561207. [PMID: 37873216 PMCID: PMC10592613 DOI: 10.1101/2023.10.06.561207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2023]
Abstract
In a chemical synapse, information flow occurs via the release of neurotransmitters from a presynaptic neuron that triggers an Action potential (AP) in the postsynaptic neuron. At its core, this occurs via the postsynaptic membrane potential integrating neurotransmitter-induced synaptic currents, and AP generation occurs when potential reaches a critical threshold. This manuscript investigates feedback implementation via an autapse, where the axon from the postsynaptic neuron forms an inhibitory synapse onto itself. Using a stochastic model of neuronal synaptic transmission, we formulate AP generation as a first-passage time problem and derive expressions for both the mean and noise of AP-firing times. Our analytical results supported by stochastic simulations identify parameter regimes where autaptic feedback transmission enhances the precision of AP firing times consistent with experimental data. These noise attenuating regimes are intuitively based on two orthogonal mechanisms - either expanding the time window to integrate noisy upstream signals; or by linearizing the mean voltage increase over time. Interestingly, we find regimes for noise amplification that specifically occur when the inhibitory synapse has a low probability of release for synaptic vesicles. In summary, this work explores feedback modulation of the stochastic dynamics of autaptic neurotransmission and reveals its function of creating more regular AP firing patterns.
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Affiliation(s)
- Zahra Vahdat
- Department of Electrical and Computer Engineering, University of Delaware, Newark, DE USA 19716
| | - Oliver Gambrell
- Department of Electrical and Computer Engineering, University of Delaware, Newark, DE USA 19716
| | - Abhyudai Singh
- Department of Electrical and Computer Engineering, Biomedical Engineering, Mathematical Sciences, Center for Bioinformatics and Computational Biology, University of Delaware, Newark, DE USA 19716
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Misra S, Bland LC, Cardwell SG, Incorvia JAC, James CD, Kent AD, Schuman CD, Smith JD, Aimone JB. Probabilistic Neural Computing with Stochastic Devices. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2204569. [PMID: 36395387 DOI: 10.1002/adma.202204569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Revised: 08/03/2022] [Indexed: 06/16/2023]
Abstract
The brain has effectively proven a powerful inspiration for the development of computing architectures in which processing is tightly integrated with memory, communication is event-driven, and analog computation can be performed at scale. These neuromorphic systems increasingly show an ability to improve the efficiency and speed of scientific computing and artificial intelligence applications. Herein, it is proposed that the brain's ubiquitous stochasticity represents an additional source of inspiration for expanding the reach of neuromorphic computing to probabilistic applications. To date, many efforts exploring probabilistic computing have focused primarily on one scale of the microelectronics stack, such as implementing probabilistic algorithms on deterministic hardware or developing probabilistic devices and circuits with the expectation that they will be leveraged by eventual probabilistic architectures. A co-design vision is described by which large numbers of devices, such as magnetic tunnel junctions and tunnel diodes, can be operated in a stochastic regime and incorporated into a scalable neuromorphic architecture that can impact a number of probabilistic computing applications, such as Monte Carlo simulations and Bayesian neural networks. Finally, a framework is presented to categorize increasingly advanced hardware-based probabilistic computing technologies.
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Affiliation(s)
- Shashank Misra
- Microsystems Engineering, Science and Applications, Sandia National Laboratories, Albuquerque, NM, 87123, USA
| | - Leslie C Bland
- Department of Physics, Temple University, Philadelphia, PA, 19122-1801, USA
| | - Suma G Cardwell
- Neural Exploration and Research Laboratory, Sandia National Laboratories, Albuquerque, NM, 87123, USA
| | - Jean Anne C Incorvia
- Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, 78712, USA
| | - Conrad D James
- Microsystems Engineering, Science and Applications, Sandia National Laboratories, Albuquerque, NM, 87123, USA
| | - Andrew D Kent
- Department of Physics, New York University, New York, NY, 10003, USA
| | - Catherine D Schuman
- Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996, USA
| | - J Darby Smith
- Neural Exploration and Research Laboratory, Sandia National Laboratories, Albuquerque, NM, 87123, USA
| | - James B Aimone
- Neural Exploration and Research Laboratory, Sandia National Laboratories, Albuquerque, NM, 87123, USA
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Hays CL, Sladek AL, Field GD, Thoreson WB. Properties of multivesicular release from mouse rod photoreceptors support transmission of single-photon responses. eLife 2021; 10:67446. [PMID: 33769285 PMCID: PMC8032395 DOI: 10.7554/elife.67446] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2021] [Accepted: 03/20/2021] [Indexed: 01/18/2023] Open
Abstract
Vision under starlight requires rod photoreceptors to transduce and transmit single-photon responses to the visual system. Small single-photon voltage changes must therefore cause detectable reductions in glutamate release. We found that rods achieve this by employing mechanisms that enhance release regularity and its sensitivity to small voltage changes. At the resting membrane potential in darkness, mouse rods exhibit coordinated and regularly timed multivesicular release events, each consisting of ~17 vesicles and occurring two to three times more regularly than predicted by Poisson statistics. Hyperpolarizing rods to mimic the voltage change produced by a single photon abruptly reduced the probability of multivesicular release nearly to zero with a rebound increase at stimulus offset. Simulations of these release dynamics indicate that this regularly timed, multivesicular release promotes transmission of single-photon responses to post-synaptic rod-bipolar cells. Furthermore, the mechanism is efficient, requiring lower overall release rates than uniquantal release governed by Poisson statistics.
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Affiliation(s)
- Cassandra L Hays
- Truhlsen Eye Institute and Department of Ophthalmology and Visual Sciences, College of Medicine, University of Nebraska Medical Center, Omaha, United States.,Cellular and Integrative Physiology, Omaha, United States
| | - Asia L Sladek
- Pharmacology and Experimental Neuroscience, Omaha, United States
| | - Greg D Field
- Department of Neurobiology, Duke University School of Medicine, Durham, United States
| | - Wallace B Thoreson
- Truhlsen Eye Institute and Department of Ophthalmology and Visual Sciences, College of Medicine, University of Nebraska Medical Center, Omaha, United States.,Pharmacology and Experimental Neuroscience, Omaha, United States
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Esmaeilpour Z, Kronberg G, Reato D, Parra LC, Bikson M. Temporal interference stimulation targets deep brain regions by modulating neural oscillations. Brain Stimul 2020; 14:55-65. [PMID: 33186778 PMCID: PMC9382891 DOI: 10.1016/j.brs.2020.11.007] [Citation(s) in RCA: 39] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2020] [Revised: 11/06/2020] [Accepted: 11/07/2020] [Indexed: 12/11/2022] Open
Abstract
BACKGROUND Temporal interference (TI) stimulation of the brain generates amplitude-modulated electric fields oscillating in the kHz range with the goal of non-invasive targeted deep brain stimulation. Yet, the current intensities required in human (sensitivity) to modulate deep brain activity and if superficial brain region are spared (selectivity) at these intensities remains unclear. OBJECTIVE We developed an experimentally constrained theory for TI sensitivity to kHz electric field given the attenuation by membrane low-pass filtering property, and for TI selectivity to deep structures given the distribution of modulated and unmodulated electric fields in brain. METHODS The electric field threshold to modulate carbachol-induced gamma oscillations in rat hippocampal slices was determined for unmodulated 0.05-2 kHz sine waveforms, and 5 Hz amplitude-modulated waveforms with 0.1-2 kHz carrier frequencies. The neuronal effects are replicated with a computational network model to explore the underlying mechanisms, and then coupled to a validated current-flow model of the human head. RESULTS Amplitude-modulated electric fields are stronger in deep brain regions, while unmodulated electric fields are maximal at the cortical regions. Both experiment and model confirmed the hypothesis that spatial selectivity of temporal interference stimulation depends on the phasic modulation of neural oscillations only in deep brain regions. Adaptation mechanism (e.g. GABAb) enhanced sensitivity to amplitude modulated waveform in contrast to unmodulated kHz and produced selectivity in modulating gamma oscillation (i.e. Higher gamma modulation in amplitude modulated vs unmodulated kHz stimulation). Selection of carrier frequency strongly affected sensitivity to amplitude modulation stimulation. Amplitude modulated stimulation with 100 Hz carrier frequency required ∼5 V/m (corresponding to ∼13 mA at the scalp surface), whereas, 1 kHz carrier frequency ∼60 V/m (∼160 mA) and 2 kHz carrier frequency ∼80 V/m (∼220 mA) to significantly modulate gamma oscillation. Sensitivity is increased (scalp current required decreased) for theoretical neuronal membranes with faster time constants. CONCLUSION The TI sensitivity (current required at the scalp) depends on the neuronal membrane time-constant (e.g. axons) approaching the kHz carrier frequency. TI selectivity is governed by network adaption (e.g. GABAb) that is faster than the amplitude-modulation frequency. Thus, we show neuronal and network oscillations time-constants determine the scalp current required and the selectivity achievable with TI in humans.
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Affiliation(s)
- Zeinab Esmaeilpour
- Department of Biomedical Engineering, The City College of the City University of New York, New York, NY, USA.
| | - Greg Kronberg
- Department of Biomedical Engineering, The City College of the City University of New York, New York, NY, USA
| | - Davide Reato
- Champalimaud Centre for the Unknown, Neuroscience Program, Lisbon, Portugal
| | - Lucas C Parra
- Department of Biomedical Engineering, The City College of the City University of New York, New York, NY, USA
| | - Marom Bikson
- Department of Biomedical Engineering, The City College of the City University of New York, New York, NY, USA
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Local Design Principles at Hippocampal Synapses Revealed by an Energy-Information Trade-Off. eNeuro 2020; 7:ENEURO.0521-19.2020. [PMID: 32847867 PMCID: PMC7540928 DOI: 10.1523/eneuro.0521-19.2020] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Revised: 03/16/2020] [Accepted: 03/17/2020] [Indexed: 12/01/2022] Open
Abstract
Synapses across different brain regions display distinct structure-function relationships. We investigated the interplay of fundamental design constraints that shape the transmission properties of the excitatory CA3-CA1 pyramidal cell connection, a prototypic synapse for studying the mechanisms of learning in the mammalian hippocampus. This small synapse is characterized by probabilistic release of transmitter, which is markedly facilitated in response to naturally occurring trains of action potentials. Based on a physiologically motivated computational model of the rat CA3 presynaptic terminal, we show how unreliability and short-term dynamics of vesicular release work together to regulate the trade-off of information transfer versus energy use. We propose that individual CA3-CA1 synapses are designed to operate near the maximum possible capacity of information transmission in an efficient manner. Experimental measurements reveal a wide range of vesicular release probabilities at hippocampal synapses, which may be a necessary consequence of long-term plasticity and homeostatic mechanisms that manifest as presynaptic modifications of the release probability. We show that the timescales and magnitude of short-term plasticity (STP) render synaptic information transfer nearly independent of differences in release probability. Thus, individual synapses transmit optimally while maintaining a heterogeneous distribution of presynaptic strengths indicative of synaptically-encoded memory representations. Our results support the view that organizing principles that are evident on higher scales of neural organization percolate down to the design of an individual synapse.
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Barros-Zulaica N, Rahmon J, Chindemi G, Perin R, Markram H, Muller E, Ramaswamy S. Estimating the Readily-Releasable Vesicle Pool Size at Synaptic Connections in the Neocortex. Front Synaptic Neurosci 2019; 11:29. [PMID: 31680928 PMCID: PMC6813366 DOI: 10.3389/fnsyn.2019.00029] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Accepted: 09/30/2019] [Indexed: 12/21/2022] Open
Abstract
Previous studies based on the 'Quantal Model' for synaptic transmission suggest that neurotransmitter release is mediated by a single release site at individual synaptic contacts in the neocortex. However, recent studies seem to contradict this hypothesis and indicate that multi-vesicular release (MVR) could better explain the synaptic response variability observed in vitro. In this study we present a novel method to estimate the number of release sites per synapse, also known as the size of the readily releasable pool (NRRP), from paired whole-cell recordings of connections between layer 5 thick tufted pyramidal cell (L5_TTPC) in the juvenile rat somatosensory cortex. Our approach extends the work of Loebel et al. (2009) by leveraging a recently published data-driven biophysical model of neocortical tissue. Using this approach, we estimated NRRP to be between two to three for synaptic connections between L5_TTPCs. To constrain NRRP values for other connections in the microcircuit, we developed and validated a generalization approach using published data on the coefficient of variation (CV) of the amplitudes of post-synaptic potentials (PSPs) from literature and comparing them against in silico experiments. Our study predicts that transmitter release at synaptic connections in the neocortex could be mediated by MVR and provides a data-driven approach to constrain the MVR model parameters in the microcircuit.
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Affiliation(s)
| | - John Rahmon
- Blue Brain Project, École Polytechnique Fédérale de Lausanne, Geneva, Switzerland
| | - Giuseppe Chindemi
- Blue Brain Project, École Polytechnique Fédérale de Lausanne, Geneva, Switzerland
| | - Rodrigo Perin
- Laboratory of Neural Microcircuitry, Brain Mind Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Henry Markram
- Blue Brain Project, École Polytechnique Fédérale de Lausanne, Geneva, Switzerland.,Laboratory of Neural Microcircuitry, Brain Mind Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Eilif Muller
- Blue Brain Project, École Polytechnique Fédérale de Lausanne, Geneva, Switzerland
| | - Srikanth Ramaswamy
- Blue Brain Project, École Polytechnique Fédérale de Lausanne, Geneva, Switzerland
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Roles for the Endoplasmic Reticulum in Regulation of Neuronal Calcium Homeostasis. Cells 2019; 8:cells8101232. [PMID: 31658749 PMCID: PMC6829861 DOI: 10.3390/cells8101232] [Citation(s) in RCA: 47] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Revised: 10/01/2019] [Accepted: 10/03/2019] [Indexed: 02/06/2023] Open
Abstract
By influencing Ca2+ homeostasis in spatially and architecturally distinct neuronal compartments, the endoplasmic reticulum (ER) illustrates the notion that form and function are intimately related. The contribution of ER to neuronal Ca2+ homeostasis is attributed to the organelle being the largest reservoir of intracellular Ca2+ and having a high density of Ca2+ channels and transporters. As such, ER Ca2+ has incontrovertible roles in the regulation of axodendritic growth and morphology, synaptic vesicle release, and neural activity dependent gene expression, synaptic plasticity, and mitochondrial bioenergetics. Not surprisingly, many neurological diseases arise from ER Ca2+ dyshomeostasis, either directly due to alterations in ER resident proteins, or indirectly via processes that are coupled to the regulators of ER Ca2+ dynamics. In this review, we describe the mechanisms involved in the establishment of ER Ca2+ homeostasis in neurons. We elaborate upon how changes in the spatiotemporal dynamics of Ca2+ exchange between the ER and other organelles sculpt neuronal function and provide examples that demonstrate the involvement of ER Ca2+ dyshomeostasis in a range of neurological and neurodegenerative diseases.
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Llera-Montero M, Sacramento J, Costa RP. Computational roles of plastic probabilistic synapses. Curr Opin Neurobiol 2018; 54:90-97. [PMID: 30308457 DOI: 10.1016/j.conb.2018.09.002] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2018] [Revised: 07/02/2018] [Accepted: 09/06/2018] [Indexed: 11/18/2022]
Abstract
The probabilistic nature of synaptic transmission has remained enigmatic. However, recent developments have started to shed light on why the brain may rely on probabilistic synapses. Here, we start out by reviewing experimental evidence on the specificity and plasticity of synaptic response statistics. Next, we overview different computational perspectives on the function of plastic probabilistic synapses for constrained, statistical and deep learning. We highlight that all of these views require some form of optimisation of probabilistic synapses, which has recently gained support from theoretical analysis of long-term synaptic plasticity experiments. Finally, we contrast these different computational views and propose avenues for future research. Overall, we argue that the time is ripe for a better understanding of the computational functions of probabilistic synapses.
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Affiliation(s)
- Milton Llera-Montero
- Computational Neuroscience Unit, Department of Computer Science, School of Computer Science, Electrical and Electronic Engineering, and Engineering Mathematics, Faculty of Engineering, University of Bristol, United Kingdom; Bristol Neuroscience, University of Bristol, United Kingdom; School of Psychological Science, Faculty of Life Sciences, University of Bristol, United Kingdom
| | | | - Rui Ponte Costa
- Computational Neuroscience Unit, Department of Computer Science, School of Computer Science, Electrical and Electronic Engineering, and Engineering Mathematics, Faculty of Engineering, University of Bristol, United Kingdom; Bristol Neuroscience, University of Bristol, United Kingdom; Department of Physiology, University of Bern, Switzerland; Centre for Neural Circuits and Behaviour, Department of Physiology, Anatomy and Genetics, University of Oxford, United Kingdom.
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Bird AD, Richardson MJE. Transmission of temporally correlated spike trains through synapses with short-term depression. PLoS Comput Biol 2018; 14:e1006232. [PMID: 29933363 PMCID: PMC6039054 DOI: 10.1371/journal.pcbi.1006232] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2017] [Revised: 07/10/2018] [Accepted: 05/24/2018] [Indexed: 11/18/2022] Open
Abstract
Short-term synaptic depression, caused by depletion of releasable neurotransmitter, modulates the strength of neuronal connections in a history-dependent manner. Quantifying the statistics of synaptic transmission requires stochastic models that link probabilistic neurotransmitter release with presynaptic spike-train statistics. Common approaches are to model the presynaptic spike train as either regular or a memory-less Poisson process: few analytical results are available that describe depressing synapses when the afferent spike train has more complex, temporally correlated statistics such as bursts. Here we present a series of analytical results—from vesicle release-site occupancy statistics, via neurotransmitter release, to the post-synaptic voltage mean and variance—for depressing synapses driven by correlated presynaptic spike trains. The class of presynaptic drive considered is that fully characterised by the inter-spike-interval distribution and encompasses a broad range of models used for neuronal circuit and network analyses, such as integrate-and-fire models with a complete post-spike reset and receiving sufficiently short-time correlated drive. We further demonstrate that the derived post-synaptic voltage mean and variance allow for a simple and accurate approximation of the firing rate of the post-synaptic neuron, using the exponential integrate-and-fire model as an example. These results extend the level of biological detail included in models of synaptic transmission and will allow for the incorporation of more complex and physiologically relevant firing patterns into future studies of neuronal networks. Synapses between neurons transmit signals with strengths that vary with the history of their activity, over scales from milliseconds to decades. Short-term changes in synaptic strength modulate and sculpt ongoing neuronal activity, whereas long-term changes underpin memory formation. Here we focus on changes of strength over timescales of less than a second caused by transitory depletion of the neurotransmitters that carry signals across the synapse. Neurotransmitters are stored in small vesicles that release their contents, with a certain probability, when the presynaptic neuron is active. Once a vesicle has been used it is replenished after a variable delay. There is therefore a complex interaction between the pattern of incoming signals to the synapse and the probablistic release and restock of packaged neurotransmitter. Here we extend existing models to examine how correlated synaptic activity is transmitted through synapses and affects the voltage fluctuations and firing rate of the target neuron. Our results provide a framework that will allow for the inclusion of biophysically realistic synaptic behaviour in studies of neuronal circuits.
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Affiliation(s)
- Alex D. Bird
- Warwick Systems Biology Centre, University of Warwick, Coventry, United Kingdom
- Ernst Strüngmann Institute for Neuroscience, Max Planck Society, Frankfurt, Germany
- Frankfurt Institute for Advanced Studies, Frankfurt, Germany
- * E-mail: (ADB); (MJER)
| | - Magnus J. E. Richardson
- Warwick Mathematics Institute, University of Warwick, Coventry, United Kingdom
- * E-mail: (ADB); (MJER)
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Hybrid Markov-mass action law model for cell activation by rare binding events: Application to calcium induced vesicular release at neuronal synapses. Sci Rep 2016; 6:35506. [PMID: 27752087 PMCID: PMC5067597 DOI: 10.1038/srep35506] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2016] [Accepted: 09/30/2016] [Indexed: 11/08/2022] Open
Abstract
Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian. The large ensemble of particles is described by mass action laws. We use this novel model to predict the time distribution of vesicular release at neuronal synapses. Vesicular release is triggered by the binding of few calcium ions that can originate either from the synaptic bulk or from the entry through calcium channels. We report here that the distribution of release time is bimodal although it is triggered by a single fast action potential. While the first peak follows a stimulation, the second corresponds to the random arrival over much longer time of ions located in the synaptic terminal to small binding vesicular targets. To conclude, the present multiscale stochastic modeling approach allows studying cellular events based on integrating discrete molecular events over several time scales.
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