Electrophysical cardiac remodeling at the molecular level: insights into Ryanodine Receptor activation and calcium-induced calcium release from a stochastic explicit-particle model.

We present the first-ever, fully-discrete, stochastic model of triggered cardiac calcium dynamics. Using anatomically accurate subcellular cardiac myocyte geometries, we simulate the molecular players involved in calcium handling using high-resolution stochastic and explicit-particle methods at the level of an individual cardiac dyadic junction. Integrating data from multiple experimental sources, the model not only replicates the findings of traditional in silico studies and complements in vitro experimental data, but also reveals new insights into the molecular mechanisms driving cardiac dysfunction under stress and disease conditions. We improve upon older, non-discrete models using the same realistic geometry by incorporating molecular mechanisms for spontaneous, as well as triggered Calcium-Induced Calcium Release (CICR). Action potentials are used to activate L-type calcium channels (LTCCs), triggering CICR through Ryanodine receptors (RyR) on the surface of the sarcoplasmic reticulum. These improvements allow for the specific focus on the couplon: the structure-function relationship between LTCC and RyR. We investigate the electrophysical effects of normal and diseased action potentials on CICR and interrogate the effects of dyadic junction deformation through detubulation and orphaning of RyR. Our work demonstrates the importance of the electrophysical integrity of the CRU on CICR fidelity, giving insights into the molecular basis of heart disease. Finally, we provide a unique, detailed, molecular view of the CICR process using advanced rendering techniques. This easy-to-use model comes complete with tutorials and all necessary software for use and analysis so as to maximize usability and reproducibility. Our work focuses on quantifying, qualifying, and visualizing the behavior of the molecular species that underlie the function and dysfunction of subcellular cardiomyocyte systems.

Transcranial Magnetic Stimulation Facilitates Neural Speech Decoding.

Transcranial magnetic stimulation (TMS) has been widely used to study the mechanisms that underlie motor output. Yet, the extent to which TMS acts upon the cortical neurons implicated in volitional motor commands and the focal limitations of TMS remain subject to debate. Previous research links TMS to improved subject performance in behavioral tasks, including a bias in phoneme discrimination. Our study replicates this result, which implies a causal relationship between electro-magnetic stimulation and psychomotor activity, and tests whether TMS-facilitated psychomotor activity recorded via electroencephalography (EEG) may thus serve as a superior input for neural decoding. First, we illustrate that site-specific TMS elicits a double dissociation in discrimination ability for two phoneme categories. Next, we perform a classification analysis on the EEG signals recorded during TMS and find a dissociation between the stimulation site and decoding accuracy that parallels the behavioral results. We observe weak to moderate evidence for the alternative hypothesis in a Bayesian analysis of group means, with more robust results upon stimulation to a brain region governing multiple phoneme features. Overall, task accuracy was a significant predictor of decoding accuracy for phoneme categories (F(1,135) = 11.51, p < 0.0009) and individual phonemes (F(1,119) = 13.56, p < 0.0003), providing new evidence for a causal link between TMS, neural function, and behavior.

Transformers and cortical waves: encoders for pulling in context across time.

The capabilities of transformer networks such as ChatGPT and other large language models (LLMs) have captured the world's attention. The crucial computational mechanism underlying their performance relies on transforming a complete input sequence - for example, all the words in a sentence - into a long 'encoding vector' that allows transformers to learn long-range temporal dependencies in naturalistic sequences. Specifically, 'self-attention' applied to this encoding vector enhances temporal context in transformers by computing associations between pairs of words in the input sequence. We suggest that waves of neural activity traveling across single cortical areas, or multiple regions on the whole-brain scale, could implement a similar encoding principle. By encapsulating recent input history into a single spatial pattern at each moment in time, cortical waves may enable a temporal context to be extracted from sequences of sensory inputs, the same computational principle as that used in transformers.

Decoding imagined speech with delay differential analysis.

Speech decoding from non-invasive EEG signals can achieve relatively high accuracy (70-80%) for strictly delimited classification tasks, but for more complex tasks non-invasive speech decoding typically yields a 20-50% classification accuracy. However, decoder generalization, or how well algorithms perform objectively across datasets, is complicated by the small size and heterogeneity of existing EEG datasets. Furthermore, the limited availability of open access code hampers a comparison between methods. This study explores the application of a novel non-linear method for signal processing, delay differential analysis (DDA), to speech decoding. We provide a systematic evaluation of its performance on two public imagined speech decoding datasets relative to all publicly available deep learning methods. The results support DDA as a compelling alternative or complementary approach to deep learning methods for speech decoding. DDA is a fast and efficient time-domain open-source method that fits data using only few strong features and does not require extensive preprocessing.

MCell4 with BioNetGen: A Monte Carlo simulator of rule-based reaction-diffusion systems with Python interface.

Biochemical signaling pathways in living cells are often highly organized into spatially segregated volumes, membranes, scaffolds, subcellular compartments, and organelles comprising small numbers of interacting molecules. At this level of granularity stochastic behavior dominates, well-mixed continuum approximations based on concentrations break down and a particle-based approach is more accurate and more efficient. We describe and validate a new version of the open-source MCell simulation program (MCell4), which supports generalized 3D Monte Carlo modeling of diffusion and chemical reaction of discrete molecules and macromolecular complexes in solution, on surfaces representing membranes, and combinations thereof. The main improvements in MCell4 compared to the previous versions, MCell3 and MCell3-R, include a Python interface and native BioNetGen reaction language (BNGL) support. MCell4's Python interface opens up completely new possibilities for interfacing with external simulators to allow creation of sophisticated event-driven multiscale/multiphysics simulations. The native BNGL support, implemented through a new open-source library libBNG (also introduced in this paper), provides the capability to run a given BNGL model spatially resolved in MCell4 and, with appropriate simplifying assumptions, also in the BioNetGen simulation environment, greatly accelerating and simplifying model validation and comparison.

Synaptic Information Storage Capacity Measured With Information Theory.

Variation in the strength of synapses can be quantified by measuring the anatomical properties of synapses. Quantifying precision of synaptic plasticity is fundamental to understanding information storage and retrieval in neural circuits. Synapses from the same axon onto the same dendrite have a common history of coactivation, making them ideal candidates for determining the precision of synaptic plasticity based on the similarity of their physical dimensions. Here, the precision and amount of information stored in synapse dimensions were quantified with Shannon information theory, expanding prior analysis that used signal detection theory (Bartol et al., 2015). The two methods were compared using dendritic spine head volumes in the middle of the stratum radiatum of hippocampal area CA1 as well-defined measures of synaptic strength. Information theory delineated the number of distinguishable synaptic strengths based on nonoverlapping bins of dendritic spine head volumes. Shannon entropy was applied to measure synaptic information storage capacity (SISC) and resulted in a lower bound of 4.1 bits and upper bound of 4.59 bits of information based on 24 distinguishable sizes. We further compared the distribution of distinguishable sizes and a uniform distribution using Kullback-Leibler divergence and discovered that there was a nearly uniform distribution of spine head volumes across the sizes, suggesting optimal use of the distinguishable values. Thus, SISC provides a new analytical measure that can be generalized to probe synaptic strengths and capacity for plasticity in different brain regions of different species and among animals raised in different conditions or during learning. How brain diseases and disorders affect the precision of synaptic plasticity can also be probed.

A spatial model of autophosphorylation of Ca 2+ /calmodulin-dependent protein kinase II in a glutamatergic spine reveals dynamics of kinase activation in the first several seconds after a complex synaptic stimulus.

Long-term potentiation (LTP) is a biochemical process in excitatory glutamatergic synapses in the Central Nervous System (CNS). It is initiated by a bout of synaptic activation that is strong enough to contribute to production of an action potential in the axon of the postsynaptic neuron, and it results in an increase in the size of postsynaptic depolarization during subsequent activity. The first step leading to LTP is activation and autophosphorylation of an abundant postsynaptic enzyme, Ca 2+ /calmodulin-dependent protein kinase II (CaMKII). We use simulation of activation of CaMKII holoenzymes in a realistic spatial model of a spine synapse, created in MCell4, to test three hypotheses about how the autophosphorylation response of CaMKII is shaped during a repeated high-frequency stimulus. First, the simulation results indicate that autophosphorylation of CaMKII does not constitute a bistable switch under biologically realistic conditions. Instead, prolonged autophosphorylation of CaMKII may contribute to a biochemical "kinetic proof-reading" mechanism that controls induction of synaptic plasticity. Second, concentration of CaMKII near the postsynaptic membrane increases the local concentration of kinase activity. However, neither localization nor "Ca 2+ -calmodulin-trapping (CaM-trapping)" increase the proportion of autophosphorylated subunits in holoenzymes after a complex stimulus, as previously hypothesized. Finally, we show that, as hypothesized, the amplitude of autophosphorylation in the first 30 seconds after a stimulus is extremely sensitive to the level and location of PP1 activity when PP1 is present in biologically accurate amounts. We further show that prolonged steric hindrance of dephosphorylation of CaMKII, caused by CaM-trapping, can increase the amplitude of autophosphorylation after a complex stimulus. These simulation results sharpen our quantitative understanding of the early events leading to LTP at excitatory synapses. Author Summary: Neurons in the brain are interconnected in an organized fashion by synapses that transmit neuronal activity from one neuron to another. Most of the billions of neurons in the brain have about 10,000 synapses spread over the neuronal membrane. Information is stored in the brain when the ability of specific synapses to pass along neuronal activity is strengthened resulting in formation of new networks. The increase in strength of a synapse is tightly controlled by the frequency and amplitude of its activity, and by neurohormonal signals, which, in combination, can cause long-lasting biochemical changes at the synapse that underlie learning and memory. Defects in these biochemical pathways cause mental and neurological diseases. To develop treatments, we need to understand the precise choreography of these critical biochemical changes. However, the tiny size of the synaptic compartment makes precise measurements of the biochemical reactions impossible. We have used computer simulation techniques and information gathered from experiments on purified synaptic proteins to simulate, within a single synapse, the choreography of the first biochemical step in synaptic strengthening: activation of the enzyme Ca 2+ / calmodulin-dependent protein kinase II. Our results provide insights that can be used in future studies to develop treatments for neuronal diseases.

Long-Term Potentiation Produces a Sustained Expansion of Synaptic Information Storage Capacity in Adult Rat Hippocampus.

Long-term potentiation (LTP) has become a standard model for investigating synaptic mechanisms of learning and memory. Increasingly, it is of interest to understand how LTP affects the synaptic information storage capacity of the targeted population of synapses. Here, structural synaptic plasticity during LTP was explored using three-dimensional reconstruction from serial section electron microscopy. Storage capacity was assessed by applying a new analytical approach, Shannon information theory, to delineate the number of functionally distinguishable synaptic strengths. LTP was induced by delta-burst stimulation of perforant pathway inputs to the middle molecular layer of hippocampal dentate granule cells in adult rats. Spine head volumes were measured as predictors of synaptic strength and compared between LTP and control hemispheres at 30 min and 2 hr after the induction of LTP. Synapses from the same axon onto the same dendrite were used to determine the precision of synaptic plasticity based on the similarity of their physical dimensions. Shannon entropy was measured by exploiting the frequency of spine heads in functionally distinguishable sizes to assess the degree to which LTP altered the number of bits of information storage. Outcomes from these analyses reveal that LTP expanded storage capacity; the distribution of spine head volumes was increased from 2 bits in controls to 3 bits at 30 min and 2.7 bits at 2 hr after the induction of LTP. Furthermore, the distribution of spine head volumes was more uniform across the increased number of functionally distinguishable sizes following LTP, thus achieving more efficient use of coding space across the population of synapses.

Computer simulations predict the impact of neuronal atrophy on the calcium dynamics in Huntington's disease.

One of the early hallmarks of Huntington's disease (HD) is neuronal cell atrophy, especially in the striatum, underlying motor dysfunction in HD. Here using a computer model, we have predicted the impact of cell shrinkage on calcium dynamics at the cellular level. Our model indicates that as cytosolic volume decreases, the amplitude of calcium transients increases and the endoplasmic reticulum (ER) becomes more leaky due to calcium-induced calcium release and a "toxic" positive feedback mechanism mediated by ryanodine receptors that greatly increases calcium release into the cytosol. The excessive calcium release from ER saturates the calcium buffering capacity of calbindin and forces further accumulation of free calcium in the cytosol and cellular compartments including mitochondria. This leads to imbalance of calcium in both cytosol and ER regions. Excessive calcium accumulation in the cytosol can damage the mitochondria resulting in metabolic dysfunction in the cell consistent with the pathology of HD. Our computational model points toward potential drug targets and can accelerate and greatly help the experimental studies of HD paving the way for treatments of patients suffering from HD.

Network-motif delay differential analysis of brain activity during seizures.

Delay Differential Analysis (DDA) is a nonlinear method for analyzing time series based on principles from nonlinear dynamical systems. DDA is extended here to incorporate network aspects to improve the dynamical characterization of complex systems. To demonstrate its effectiveness, DDA with network capabilities was first applied to the well-known Rössler system under different parameter regimes and noise conditions. Network-motif DDA, based on cortical regions, was then applied to invasive intracranial electroencephalographic data from drug-resistant epilepsy patients undergoing presurgical monitoring. The directional network motifs between brain areas that emerge from this analysis change dramatically before, during, and after seizures. Neural systems provide a rich source of complex data, arising from varying internal states generated by network interactions.

Exploring strategy differences between humans and monkeys with recurrent neural networks.

Animal models are used to understand principles of human biology. Within cognitive neuroscience, non-human primates are considered the premier model for studying decision-making behaviors in which direct manipulation experiments are still possible. Some prominent studies have brought to light major discrepancies between monkey and human cognition, highlighting problems with unverified extrapolation from monkey to human. Here, we use a parallel model system-artificial neural networks (ANNs)-to investigate a well-established discrepancy identified between monkeys and humans with a working memory task, in which monkeys appear to use a recency-based strategy while humans use a target-selective strategy. We find that ANNs trained on the same task exhibit a progression of behavior from random behavior (untrained) to recency-like behavior (partially trained) and finally to selective behavior (further trained), suggesting monkeys and humans may occupy different points in the same overall learning progression. Surprisingly, what appears to be recency-like behavior in the ANN, is in fact an emergent non-recency-based property of the organization of the neural network's state space during its development through training. We find that explicit encouragement of recency behavior during training has a dual effect, not only causing an accentuated recency-like behavior, but also speeding up the learning process altogether, resulting in an efficient shaping mechanism to achieve the optimal strategy. Our results suggest a new explanation for the discrepency observed between monkeys and humans and reveal that what can appear to be a recency-based strategy in some cases may not be recency at all.

Transformations that preserve the uniqueness of the differential form for Lorenz-like systems.

Differential equations serve as models for many physical systems. But, are these equations unique? We prove here that when a 3D system of ordinary differential equations for a dynamical system is transformed to the jerk or differential form, the jerk form is preserved in relation to a given variable and, therefore, the transformed system shares the time series of that given variable with the original untransformed system. Multiple algebraically different systems of ordinary differential equations can share the same jerk form. They may also share the same time series of the transformed variable depending on the parameters of the jerk form. Here, we studied 17 algebraically different Lorenz-like systems that share the same functional jerk form. There are groups of these systems that share the jerk parameters and, therefore, also have the same time series of the transformed variable.

Internal feedback in the cortical perception-action loop enables fast and accurate behavior.

Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control, drawing on control theory, have assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single, unidirectional perception-action loop. However, the sensorimotor loop contains internal delays in sensory and motor pathways, which can lead to unstable control. We show here that these delays can be compensated by internal feedback signals that flow backward, from motor toward sensory areas. This internal feedback is ubiquitous in neural sensorimotor systems, and we show how internal feedback compensates internal delays. This is accomplished by filtering out self-generated and other predictable changes so that unpredicted, actionable information can be rapidly transmitted toward action by the fastest components, effectively compressing the sensory input to more efficiently use feedforward pathways: Tracts of fast, giant neurons necessarily convey less accurate signals than tracts with many smaller neurons, but they are crucial for fast and accurate behavior. We use a mathematically tractable control model to show that internal feedback has an indispensable role in achieving state estimation, localization of function (how different parts of the cortex control different parts of the body), and attention, all of which are crucial for effective sensorimotor control. This control model can explain anatomical, physiological, and behavioral observations, including motor signals in the visual cortex, heterogeneous kinetics of sensory receptors, and the presence of giant cells in the cortex of humans as well as internal feedback patterns and unexplained heterogeneity in neural systems.

Mitochondrial morphology governs ATP production rate.

Life is based on energy conversion. In particular, in the nervous system, significant amounts of energy are needed to maintain synaptic transmission and homeostasis. To a large extent, neurons depend on oxidative phosphorylation in mitochondria to meet their high energy demand. For a comprehensive understanding of the metabolic demands in neuronal signaling, accurate models of ATP production in mitochondria are required. Here, we present a thermodynamically consistent model of ATP production in mitochondria based on previous work. The significant improvement of the model is that the reaction rate constants are set such that detailed balance is satisfied. Moreover, using thermodynamic considerations, the dependence of the reaction rate constants on membrane potential, pH, and substrate concentrations are explicitly provided. These constraints assure that the model is physically plausible. Furthermore, we explore different parameter regimes to understand in which conditions ATP production or its export are the limiting steps in making ATP available in the cytosol. The outcomes reveal that, under the conditions used in our simulations, ATP production is the limiting step and not its export. Finally, we performed spatial simulations with nine 3-D realistic mitochondrial reconstructions and linked the ATP production rate in the cytosol with morphological features of the organelles.

Large Language Models and the Reverse Turing Test.

Large language models (LLMs) have been transformative. They are pretrained foundational models that are self-supervised and can be adapted with fine-tuning to a wide range of natural language tasks, each of which previously would have required a separate network model. This is one step closer to the extraordinary versatility of human language. GPT-3 and, more recently, LaMDA, both of them LLMs, can carry on dialogs with humans on many topics after minimal priming with a few examples. However, there has been a wide range of reactions and debate on whether these LLMs understand what they are saying or exhibit signs of intelligence. This high variance is exhibited in three interviews with LLMs reaching wildly different conclusions. A new possibility was uncovered that could explain this divergence. What appears to be intelligence in LLMs may in fact be a mirror that reflects the intelligence of the interviewer, a remarkable twist that could be considered a reverse Turing test. If so, then by studying interviews, we may be learning more about the intelligence and beliefs of the interviewer than the intelligence of the LLMs. As LLMs become more capable, they may transform the way we interact with machines and how they interact with each other. Increasingly, LLMs are being coupled with sensorimotor devices. LLMs can talk the talk, but can they walk the walk? A road map for achieving artificial general autonomy is outlined with seven major improvements inspired by brain systems and how LLMs could in turn be used to uncover new insights into brain function.

Brain network dynamics codify heterogeneity in seizure evolution.

Dynamic functional brain connectivity facilitates adaptive cognition and behaviour. Abnormal alterations within such connectivity could result in disrupted functions observed across various neurological conditions. As one of the most common neurological disorders, epilepsy is defined by the seemingly random occurrence of spontaneous seizures. A central but unresolved question concerns the mechanisms by which extraordinarily diverse propagation dynamics of seizures emerge. Here, we applied a graph-theoretical approach to assess dynamic reconfigurations in the functional brain connectivity before, during and after seizures that display heterogeneous propagation patterns despite sharing similar cortical onsets. We computed time-varying functional brain connectivity networks from human intracranial recordings of 67 seizures (across 14 patients) that had a focal origin-49 of these focal seizures remained focal and 18 underwent a bilateral spread (focal to bilateral tonic-clonic seizures). We utilized functional connectivity networks estimated from interictal periods across patients as control. Our results characterize network features that quantify the underlying functional dynamics associated with the observed heterogeneity of seizure propagation across these two types of focal seizures. Decoding these network features demonstrate that bilateral propagation of seizure activity is an outcome of the imbalance of global integration and segregation in the brain prior to seizure onset. We show that there exist intrinsic network signatures preceding seizure onset that are associated with the extent to which an impending seizure will propagate throughout the brain (i.e. staying within one hemisphere versus spreading transcallosally). Additionally, these features characterize an increase in segregation and a decrease in excitability within the brain network (i.e. high modularity and low spectral radius). Importantly, seizure-type-specific differences in these features emerge several minutes prior to seizure onset, suggesting the potential utility of such measures in intervention strategies. Finally, our results reveal network characteristics after the onset that are unique to the propagation mechanisms of two most common focal seizure subtypes, indicative of distinct reconfiguration processes that may assist termination of each seizure type. Together, our findings provide insights into the relationship between the temporal evolution of seizure activity and the underlying functional connectivity dynamics. These results offer exciting avenues where graph-theoretical measures could potentially guide personalized clinical interventions for epilepsy and other neurological disorders in which extensive heterogeneity is observed across subtypes as well as across and within individual patients.

Functional connectivity of fMRI using differential covariance predicts structural connectivity and behavioral reaction times.

Recordings from resting-state functional magnetic resonance imaging (rs-fMRI) reflect the influence of pathways between brain areas. A wide range of methods have been proposed to measure this functional connectivity (FC), but the lack of "ground truth" has made it difficult to systematically validate them. Most measures of FC produce connectivity estimates that are symmetrical between brain areas. Differential covariance (dCov) is an algorithm for analyzing FC with directed graph edges. When we applied dCov to rs-fMRI recordings from the human connectome project (HCP) and anesthetized mice, dCov-FC accurately identified strong cortical connections from diffusion magnetic resonance imaging (dMRI) in individual humans and viral tract tracing in mice. In addition, those HCP subjects whose dCov-FCs were more integrated, as assessed by a graph-theoretic measure, tended to have shorter reaction times in several behavioral tests. Thus, dCov-FC was able to identify anatomically verified connectivity that yielded measures of brain integration significantly correlated with behavior.

Dynamical differential covariance recovers directional network structure in multiscale neural systems.

Investigating neural interactions is essential to understanding the neural basis of behavior. Many statistical methods have been used for analyzing neural activity, but estimating the direction of network interactions correctly and efficiently remains a difficult problem. Here, we derive dynamical differential covariance (DDC), a method based on dynamical network models that detects directional interactions with low bias and high noise tolerance under nonstationarity conditions. Moreover, DDC scales well with the number of recording sites and the computation required is comparable to that needed for covariance. DDC was validated and compared favorably with other methods on networks with false positive motifs and multiscale neural simulations where the ground-truth connectivity was known. When applied to recordings of resting-state functional magnetic resonance imaging (rs-fMRI), DDC consistently detected regional interactions with strong structural connectivity in over 1,000 individual subjects obtained by diffusion MRI (dMRI). DDC is a promising family of methods for estimating connectivity that can be generalized to a wide range of dynamical models and recording techniques and to other applications where system identification is needed.

Dnmt3a knockout in excitatory neurons impairs postnatal synapse maturation and increases the repressive histone modification H3K27me3.

Two epigenetic pathways of transcriptional repression, DNA methylation and polycomb repressive complex 2 (PRC2), are known to regulate neuronal development and function. However, their respective contributions to brain maturation are unknown. We found that conditional loss of the de novo DNA methyltransferase Dnmt3a in mouse excitatory neurons altered expression of synapse-related genes, stunted synapse maturation, and impaired working memory and social interest. At the genomic level, loss of Dnmt3a abolished postnatal accumulation of CG and non-CG DNA methylation, leaving adult neurons with an unmethylated, fetal-like epigenomic pattern at ~222,000 genomic regions. The PRC2-associated histone modification, H3K27me3, increased at many of these sites. Our data support a dynamic interaction between two fundamental modes of epigenetic repression during postnatal maturation of excitatory neurons, which together confer robustness on neuronal regulation.

Multiscale modeling of presynaptic dynamics from molecular to mesoscale.

Chemical synapses exhibit a diverse array of internal mechanisms that affect the dynamics of transmission efficacy. Many of these processes, such as release of neurotransmitter and vesicle recycling, depend strongly on activity-dependent influx and accumulation of Ca2+. To model how each of these processes may affect the processing of information in neural circuits, and how their dysfunction may lead to disease states, requires a computationally efficient modelling framework, capable of generating accurate phenomenology without incurring a heavy computational cost per synapse. Constructing a phenomenologically realistic model requires the precise characterization of the timing and probability of neurotransmitter release. Difficulties arise in that functional forms of instantaneous release rate can be difficult to extract from noisy data without running many thousands of trials, and in biophysical synapses, facilitation of per-vesicle release probability is confounded by depletion. To overcome this, we obtained traces of free Ca2+ concentration in response to various action potential stimulus trains from a molecular MCell model of a hippocampal Schaffer collateral axon. Ca2+ sensors were placed at varying distance from a voltage-dependent calcium channel (VDCC) cluster, and Ca2+ was buffered by calbindin. Then, using the calcium traces to drive deterministic state vector models of synaptotagmin 1 and 7 (Syt-1/7), which respectively mediate synchronous and asynchronous release in excitatory hippocampal synapses, we obtained high-resolution profiles of instantaneous release rate, to which we applied functional fits. Synchronous vesicle release occurred predominantly within half a micron of the source of spike-evoked Ca2+ influx, while asynchronous release occurred more consistently at all distances. Both fast and slow mechanisms exhibited multi-exponential release rate curves, whose magnitudes decayed exponentially with distance from the Ca2+ source. Profile parameters facilitate on different time scales according to a single, general facilitation function. These functional descriptions lay the groundwork for efficient mesoscale modelling of vesicular release dynamics.