Reliable evaluation of the quantal determinants of synaptic efficacy using Bayesian analysis

Spinal microcircuits go through multiphasic homeostatic compensations in a mouse model of motoneuron degeneration

In neurological conditions affecting the brain, early-stage neural circuit adaption is key for long-term preservation of normal behaviour. We tested if motoneurons and respective microcircuits also adapt in the initial stages of disease progression in a mouse model of progressive motoneuron degeneration. Using a combination of in vitro and in vivo electrophysiology and super-resolution microscopy, we found that, preceding muscle denervation and motoneuron death, recurrent inhibition mediated by Renshaw cells is reduced in half due to impaired quantal size associated with decreased glycine receptor density. Additionally, higher probability of release from proprioceptive Ia terminals leads to increased monosynaptic excitation to motoneurons. Surprisingly, the initial impairment in recurrent inhibition is not a widespread feature of inhibitory spinal circuits, such as group I inhibitory afferents, and is compensated at later stages of disease progression. We reveal that in disease conditions, spinal microcircuits undergo specific multiphasic homeostatic compensations to preserve force output.

Efficient sampling-based Bayesian Active Learning for synaptic characterization

Bayesian Active Learning (BAL) is an efficient framework for learning the parameters of a model, in which input stimuli are selected to maximize the mutual information between the observations and the unknown parameters. However, the applicability of BAL to experiments is limited as it requires performing high-dimensional integrations and optimizations in real time. Current methods are either too time consuming, or only applicable to specific models. Here, we propose an Efficient Sampling-Based Bayesian Active Learning (ESB-BAL) framework, which is efficient enough to be used in real-time biological experiments. We apply our method to the problem of estimating the parameters of a chemical synapse from the postsynaptic responses to evoked presynaptic action potentials. Using synthetic data and synaptic whole-cell patch-clamp recordings, we show that our method can improve the precision of model-based inferences, thereby paving the way towards more systematic and efficient experimental designs in physiology.

Targeted sensors for glutamatergic neurotransmission

Optical report of neurotransmitter release allows visualisation of excitatory synaptic transmission. Sensitive genetically-encoded fluorescent glutamate reporters operating with a range of affinities and emission wavelengths are available. However, without targeting to synapses, the specificity of the fluorescent signal is uncertain, compared to sensors directed at vesicles or other synaptic markers. We fused the state-of-the-art reporter iGluSnFR to glutamate receptor auxiliary proteins in order to target it to postsynaptic sites. Chimeras of Stargazin and gamma-8 that we named SnFR-γ2 and SnFR-γ8, were enriched at synapses, retained function and reported spontaneous glutamate release in rat hippocampal cells, with apparently diffraction-limited spatial precision. In autaptic mouse neurons cultured on astrocytic microislands, evoked neurotransmitter release could be quantitatively detected at tens of synapses in a field of view whilst evoked currents were recorded simultaneously. These experiments revealed a specific postsynaptic deficit from Stargazin overexpression, resulting in synapses with normal neurotransmitter release but without postsynaptic responses. This defect was reverted by delaying overexpression. By working at different calcium concentrations, we determined that SnFR-γ2 is a linear reporter of the global quantal parameters and short-term synaptic plasticity, whereas iGluSnFR is not. On average, half of iGluSnFR regions of interest (ROIs) showing evoked fluorescence changes had intense rundown, whereas less than 5% of SnFR-γ2 ROIs did. We provide an open-source analysis suite for extracting quantal parameters including release probability from fluorescence time series of individual and grouped synaptic responses. Taken together, postsynaptic targeting improves several properties of iGluSnFR and further demonstrates the importance of subcellular targeting for optogenetic actuators and reporters.

Predominantly linear summation of metabotropic postsynaptic potentials follows coactivation of neurogliaform interneurons

Summation of ionotropic receptor-mediated responses is critical in neuronal computation by shaping input-output characteristics of neurons. However, arithmetics of summation for metabotropic signals are not known. We characterized the combined ionotropic and metabotropic output of neocortical neurogliaform cells (NGFCs) using electrophysiological and anatomical methods in the rat cerebral cortex. These experiments revealed that GABA receptors are activated outside release sites and confirmed coactivation of putative NGFCs in superficial cortical layers in vivo. Triple recordings from presynaptic NGFCs converging to a postsynaptic neuron revealed sublinear summation of ionotropic GABA_A responses and linear summation of metabotropic GABA_B responses. Based on a model combining properties of volume transmission and distributions of all NGFC axon terminals, we predict that in 83% of cases one or two NGFCs can provide input to a point in the neuropil. We suggest that interactions of metabotropic GABAergic responses remain linear even if most superficial layer interneurons specialized to recruit GABA_B receptors are simultaneously active.

Linear-nonlinear cascades capture synaptic dynamics

Short-term synaptic dynamics differ markedly across connections and strongly regulate how action potentials communicate information. To model the range of synaptic dynamics observed in experiments, we have developed a flexible mathematical framework based on a linear-nonlinear operation. This model can capture various experimentally observed features of synaptic dynamics and different types of heteroskedasticity. Despite its conceptual simplicity, we show that it is more adaptable than previous models. Combined with a standard maximum likelihood approach, synaptic dynamics can be accurately and efficiently characterized using naturalistic stimulation patterns. These results make explicit that synaptic processing bears algorithmic similarities with information processing in convolutional neural networks.

Excess Neuronal Branching Allows for Local Innervation of Specific Dendritic Compartments in Mature Cortex

The connectivity of cortical microcircuits is a major determinant of brain function; defining how activity propagates between different cell types is key to scaling our understanding of individual neuronal behavior to encompass functional networks. Furthermore, the integration of synaptic currents within a dendrite depends on the spatial organization of inputs, both excitatory and inhibitory. We identify a simple equation to estimate the number of potential anatomical contacts between neurons; finding a linear increase in potential connectivity with cable length and maximum spine length, and a decrease with overlapping volume. This enables us to predict the mean number of candidate synapses for reconstructed cells, including those realistically arranged. We identify an excess of potential local connections in mature cortical data, with densities of neurite higher than is necessary to reliably ensure the possible implementation of any given axo-dendritic connection. We show that the number of local potential contacts allows specific innervation of distinct dendritic compartments.

Identifiability of a Binomial Synapse

Synapses are highly stochastic transmission units. A classical model describing this stochastic transmission is called the binomial model, and its underlying parameters can be estimated from postsynaptic responses to evoked stimuli. The accuracy of parameter estimates obtained via such a model-based approach depends on the identifiability of the model. A model is said to be structurally identifiable if its parameters can be uniquely inferred from the distribution of its outputs. However, this theoretical property does not necessarily imply practical identifiability. For instance, if the number of observations is low or if the recording noise is high, the model's parameters can only be loosely estimated. Structural identifiability, which is an intrinsic property of a model, has been widely characterized; but practical identifiability, which is a property of both the model and the experimental protocol, is usually only qualitatively assessed. Here, we propose a formal definition for the practical identifiability domain of a statistical model. For a given experimental protocol, this domain corresponds to the set of parameters for which the model is correctly identified as the ground truth compared to a simpler alternative model. Considering a model selection problem instead of a parameter inference problem allows to derive a non-arbitrary criterion for practical identifiability. We apply our definition to the study of neurotransmitter release at a chemical synapse. Our contribution to the analysis of synaptic stochasticity is three-fold: firstly, we propose a quantitative criterion for the practical identifiability of a statistical model, and compute the identifiability domains of different variants of the binomial release model (uni or multi-quantal, with or without short-term plasticity); secondly, we extend the Bayesian Information Criterion (BIC), a classically used tool for model selection, to models with correlated data (which is the case for most models of chemical synapses); finally, we show that our approach allows to perform data free model selection, i.e., to verify if a model used to fit data was indeed identifiable even without access to the data, but having only access to the fitted parameters.

Sensory neuron-derived NaV1.7 contributes to dorsal horn neuron excitability

Expression of the voltage-gated sodium channel Na_V1.7 in sensory neurons is required for pain sensation. We examined the role of Na_V1.7 in the dorsal horn of the spinal cord using an epitope-tagged Na_V1.7 knock-in mouse. Immuno-electron microscopy showed the presence of Na_V1.7 in dendrites of superficial dorsal horn neurons, despite the absence of mRNA. Rhizotomy of L5 afferent nerves lowered the levels of Na_V1.7 in the dorsal horn. Peripheral nervous system-specific Na_V1.7 null mutant mice showed central deficits, with lamina II dorsal horn tonic firing neurons more than halved and single spiking neurons more than doubled. Na_V1.7 blocker PF05089771 diminished excitability in dorsal horn neurons but had no effect on Na_V1.7 null mutant mice. These data demonstrate an unsuspected functional role of primary afferent neuron-generated Na_V1.7 in dorsal horn neurons and an expression pattern that would not be predicted by transcriptomic analysis.

Strong preference for autaptic self-connectivity of neocortical PV interneurons facilitates their tuning to γ-oscillations

Parvalbumin (PV)-positive interneurons modulate cortical activity through highly specialized connectivity patterns onto excitatory pyramidal neurons (PNs) and other inhibitory cells. PV cells are autoconnected through powerful autapses, but the contribution of this form of fast disinhibition to cortical function is unknown. We found that autaptic transmission represents the most powerful inhibitory input of PV cells in neocortical layer V. Autaptic strength was greater than synaptic strength onto PNs as a result of a larger quantal size, whereas autaptic and heterosynaptic PV-PV synapses differed in the number of release sites. Overall, single-axon autaptic transmission contributed to approximately 40% of the global inhibition (mostly perisomatic) that PV interneurons received. The strength of autaptic transmission modulated the coupling of PV-cell firing with optogenetically induced γ-oscillations, preventing high-frequency bursts of spikes. Autaptic self-inhibition represents an exceptionally large and fast disinhibitory mechanism, favoring synchronization of PV-cell firing during cognitive-relevant cortical network activity.

Parvalbumin-positive interneurons modulate cortical activity via highly specialized connections to excitatory pyramidal neurons and other inhibitory cells. However, this study shows that fast autaptic self-inhibition is the major output of parvalbumin-positive basket cells in the neocortex and serves to modulate phase-locking of these interneurons during gamma-oscillations.

Model-Based Inference of Synaptic Transmission

Synaptic computation is believed to underlie many forms of animal behavior. A correct identification of synaptic transmission properties is thus crucial for a better understanding of how the brain processes information, stores memories and learns. Recently, a number of new statistical methods for inferring synaptic transmission parameters have been introduced. Here we review and contrast these developments, with a focus on methods aimed at inferring both synaptic release statistics and synaptic dynamics. Furthermore, based on recent proposals we discuss how such methods can be applied to data across different levels of investigation: from intracellular paired experiments to in vivo network-wide recordings. Overall, these developments open the window to reliably estimating synaptic parameters in behaving animals.

Parsing Out the Variability of Transmission at Central Synapses Using Optical Quantal Analysis

Properties of synaptic release dictates the core of information transfer in neural circuits. Despite decades of technical and theoretical advances, distinguishing bona fide information content from the multiple sources of synaptic variability remains a challenging problem. Here, we employed a combination of computational approaches with cellular electrophysiology, two-photon uncaging of MNI-Glutamate and imaging at single synapses. We describe and calibrate the use of the fluorescent glutamate sensor iGluSnFR and found that its kinetic profile is close to that of AMPA receptors, therefore providing several distinct advantages over slower methods relying on NMDA receptor activation (i.e., chemical or genetically encoded calcium indicators). Using an array of statistical methods, we further developed, and validated on surrogate data, an expectation-maximization algorithm that, by biophysically constraining release variability, extracts the quantal parameters n (maximum number of released vesicles) and p (unitary probability of release) from single-synapse iGluSnFR-mediated transients. Together, we present a generalizable mathematical formalism which, when applied to optical recordings, paves the way to an increasingly precise investigation of information transfer at central synapses.

Functional consequences of pre- and postsynaptic expression of synaptic plasticity

Growing experimental evidence shows that both homeostatic and Hebbian synaptic plasticity can be expressed presynaptically as well as postsynaptically. In this review, we start by discussing this evidence and methods used to determine expression loci. Next, we discuss the functional consequences of this diversity in pre- and postsynaptic expression of both homeostatic and Hebbian synaptic plasticity. In particular, we explore the functional consequences of a biologically tuned model of pre- and postsynaptically expressed spike-timing-dependent plasticity complemented with postsynaptic homeostatic control. The pre- and postsynaptic expression in this model predicts (i) more reliable receptive fields and sensory perception, (ii) rapid recovery of forgotten information (memory savings), and (iii) reduced response latencies, compared with a model with postsynaptic expression only. Finally, we discuss open questions that will require a considerable research effort to better elucidate how the specific locus of expression of homeostatic and Hebbian plasticity alters synaptic and network computations.This article is part of the themed issue 'Integrating Hebbian and homeostatic plasticity'.

Segregation of glutamatergic and cholinergic transmission at the mixed motoneuron Renshaw cell synapse

In neonatal mice motoneurons excite Renshaw cells by releasing both acetylcholine (ACh) and glutamate. These two neurotransmitters activate two types of nicotinic receptors (nAChRs) (the homomeric α₇ receptors and the heteromeric α*ß* receptors) as well as the two types of glutamate receptors (GluRs) (AMPARs and NMDARs). Using paired recordings, we confirm that a single motoneuron can release both transmitters on a single post-synaptic Renshaw cell. We then show that co-transmission is preserved in adult animals. Kinetic analysis of miniature EPSCs revealed quantal release of mixed events associating AMPARs and NMDARs, as well as α₇ and α*ß* nAChRs, but no evidence was found for mEPSCs associating nAChRs with GluRs. Bayesian Quantal Analysis (BQA) of evoked EPSCs showed that the number of functional contacts on a single Renshaw cell is more than halved when the nicotinic receptors are blocked, confirming that the two neurotransmitters systems are segregated. Our observations can be explained if ACh and glutamate are released from common vesicles onto spatially segregated post-synaptic receptors clusters, but a pre-synaptic segregation of cholinergic and glutamatergic release sites is also possible.

The readily releasable pool of synaptic vesicles

Each presynaptic bouton is densely packed with many vesicles, only a small fraction of which are available for immediate release. These vesicles constitute the readily releasable pool (RRP). The RRP size, and the probability of release of each vesicle within the RRP, together determine synaptic strength. Here, we discuss complications and recent advances in determining the size of the physiologically relevant RRP. We consider molecular mechanisms to generate and regulate the RRP, and discuss the relationship between vesicle docking and the RRP. We conclude that many RRP vesicles are docked, that some docked vesicles may not be part of the RRP, and that undocked vesicles can contribute to the RRP by rapid recruitment to unoccupied, molecularly activated ready-to-release sites.

Bayesian Inference of Synaptic Quantal Parameters from Correlated Vesicle Release

Synaptic transmission is both history-dependent and stochastic, resulting in varying responses to presentations of the same presynaptic stimulus. This complicates attempts to infer synaptic parameters and has led to the proposal of a number of different strategies for their quantification. Recently Bayesian approaches have been applied to make more efficient use of the data collected in paired intracellular recordings. Methods have been developed that either provide a complete model of the distribution of amplitudes for isolated responses or approximate the amplitude distributions of a train of post-synaptic potentials, with correct short-term synaptic dynamics but neglecting correlations. In both cases the methods provided significantly improved inference of model parameters as compared to existing mean-variance fitting approaches. However, for synapses with high release probability, low vesicle number or relatively low restock rate and for data in which only one or few repeats of the same pattern are available, correlations between serial events can allow for the extraction of significantly more information from experiment: a more complete Bayesian approach would take this into account also. This has not been possible previously because of the technical difficulty in calculating the likelihood of amplitudes seen in correlated post-synaptic potential trains; however, recent theoretical advances have now rendered the likelihood calculation tractable for a broad class of synaptic dynamics models. Here we present a compact mathematical form for the likelihood in terms of a matrix product and demonstrate how marginals of the posterior provide information on covariance of parameter distributions. The associated computer code for Bayesian parameter inference for a variety of models of synaptic dynamics is provided in the Supplementary Material allowing for quantal and dynamical parameters to be readily inferred from experimental data sets.

Quantifying Repetitive Transmission at Chemical Synapses: A Generative-Model Approach

The dependence of the synaptic responses on the history of activation and their large variability are both distinctive features of repetitive transmission at chemical synapses. Quantitative investigations have mostly focused on trial-averaged responses to characterize dynamic aspects of the transmission—thus disregarding variability—or on the fluctuations of the responses in steady conditions to characterize variability—thus disregarding dynamics. We present a statistically principled framework to quantify the dynamics of the probability distribution of synaptic responses under arbitrary patterns of activation. This is achieved by constructing a generative model of repetitive transmission, which includes an explicit description of the sources of stochasticity present in the process. The underlying parameters are then selected via an expectation-maximization algorithm that is exact for a large class of models of synaptic transmission, so as to maximize the likelihood of the observed responses. The method exploits the information contained in the correlation between responses to produce highly accurate estimates of both quantal and dynamic parameters from the same recordings. The method also provides important conceptual and technical advances over existing state-of-the-art techniques. In particular, the repetition of the same stimulation in identical conditions becomes unnecessary. This paves the way to the design of optimal protocols to estimate synaptic parameters, to the quantitative comparison of synaptic models over benchmark datasets, and, most importantly, to the study of repetitive transmission under physiologically relevant patterns of synaptic activation.

Synaptic Connectivity between Renshaw Cells and Motoneurons in the Recurrent Inhibitory Circuit of the Spinal Cord

Renshaw cells represent a fundamental component of one of the first discovered neuronal circuits, but their function in motor control has not been established. They are the only central neurons that receive collateral projections from motor outputs, yet the efficacy of the excitatory synapses from single and converging motoneurons remains unknown. Here we present the results of dual whole-cell recordings from identified, synaptically connected Renshaw cell-motoneuron pairs in the mouse lumbar spinal cord. The responses from single Renshaw cells demonstrate that motoneuron synapses elicit large excitatory conductances with few or no failures. We show that the strong excitatory input from motoneurons results from a high probability of neurotransmitter release onto multiple postsynaptic contacts. Dual current-clamp recordings confirm that single motoneuron inputs were sufficient to depolarize the Renshaw cell beyond threshold for firing. Reciprocal connectivity was observed in approximately one-third of the paired recordings tested. Ventral root stimulation was used to evoke currents from Renshaw cells or motoneurons to characterize responses of single neurons to the activation of their corresponding presynaptic cell populations. Excitatory or inhibitory synaptic inputs in the recurrent inhibitory loop induced substantial effects on the excitability of respective postsynaptic cells. Quantal analysis estimates showed a large number of converging inputs from presynaptic motoneuron and Renshaw cell populations. The combination of considerable synaptic efficacy and extensive connectivity within the recurrent circuitry indicates a role of Renshaw cells in modulating motor outputs that may be considerably more important than has been previously supposed.

SIGNIFICANCE STATEMENT

We have recently shown that Renshaw cells mediate powerful shunt inhibition on motoneuron excitability. Here we complete a quantitative description of the recurrent circuit using recordings of excitatory synapses between identified motoneuron and Renshaw cell pairs. We show that the excitation is highly effective as a result of a high probability of neurotransmitter release onto multiple release sites and that efficient neurotransmission is maintained at physiologically relevant firing rates in motoneurons. Our results also show that both excitatory and inhibitory connections exhibit considerable convergence of inputs. Because evaluation of the determinants of synaptic strength and the extent of connectivity constitute fundamental parameters affecting the operation of the recurrent circuit, our findings are critical for informing any future models of motor control.

Extracting quantal properties of transmission at central synapses

Chemical synapses enable neurons to communicate rapidly, process and filter signals and to store information. However, studying their functional properties is difficult because synaptic connections typically consist of multiple synaptic contacts that release vesicles stochastically and exhibit time-dependent behavior. Moreover, most central synapses are small and inaccessible to direct measurements. Estimation of synaptic properties from responses recorded at the soma is complicated by the presence of nonuniform release probability and nonuniform quantal properties. The presence of multivesicular release and postsynaptic receptor saturation at some synapses can also complicate the interpretation of quantal parameters. Multiple-probability fluctuation analysis (MPFA; also known as variance-mean analysis) is a method that has been developed for estimating synaptic parameters from the variance and mean amplitude of synaptic responses recorded at different release probabilities. This statistical approach, which incorporates nonuniform synaptic properties, has become widely used for studying synaptic transmission. In this chapter, we describe the statistical models used to extract quantal parameters and discuss their interpretation when applying MPFA.

The recurrent case for the Renshaw cell

Although Renshaw cells (RCs) were discovered over half a century ago, their precise role in recurrent inhibition and ability to modulate motoneuron excitability have yet to be established. Indirect measurements of recurrent inhibition have suggested only a weak modulatory effect but are limited by the lack of observed motoneuron responses to inputs from single RCs. Here we present dual recordings between connected RC-motoneuron pairs, performed on mouse spinal cord. Motoneuron responses demonstrated that Renshaw synapses elicit large inhibitory conductances and show short-term potentiation. Anatomical reconstruction, combined with a novel method of quantal analysis, showed that the strong inhibitory input from RCs results from the large number of synaptic contacts that they make onto individual motoneurons. We used the NEURON simulation environment to construct realistic electrotonic models, which showed that inhibitory conductances from Renshaw inputs exert considerable shunting effects in motoneurons and reduce the frequency of spikes generated by excitatory inputs. This was confirmed experimentally by showing that excitation of a single RC or selective activation of the recurrent inhibitory pathway to generate equivalent inhibitory conductances both suppress motoneuron firing. We conclude that recurrent inhibition is remarkably effective, in that a single action potential from one RC is sufficient to silence a motoneuron. Although our results may differ from previous indirect observations, they underline a need for a reevaluation of the role that RCs perform in one of the first neuronal circuits to be discovered.

Probabilistic inference of short-term synaptic plasticity in neocortical microcircuits

Short-term synaptic plasticity is highly diverse across brain area, cortical layer, cell type, and developmental stage. Since short-term plasticity (STP) strongly shapes neural dynamics, this diversity suggests a specific and essential role in neural information processing. Therefore, a correct characterization of short-term synaptic plasticity is an important step towards understanding and modeling neural systems. Phenomenological models have been developed, but they are usually fitted to experimental data using least-mean-square methods. We demonstrate that for typical synaptic dynamics such fitting may give unreliable results. As a solution, we introduce a Bayesian formulation, which yields the posterior distribution over the model parameters given the data. First, we show that common STP protocols yield broad distributions over some model parameters. Using our result we propose a experimental protocol to more accurately determine synaptic dynamics parameters. Next, we infer the model parameters using experimental data from three different neocortical excitatory connection types. This reveals connection-specific distributions, which we use to classify synaptic dynamics. Our approach to demarcate connection-specific synaptic dynamics is an important improvement on the state of the art and reveals novel features from existing data.