The sloppy relationship between neural circuit structure and function.

Investigating and describing the relationships between the structure of a circuit and its function has a long tradition in neuroscience. Since neural circuits acquire their structure through sophisticated developmental programmes, and memories and experiences are maintained through synaptic modification, it is to be expected that structure is closely linked to function. Recent findings challenge this hypothesis from three different angles: function does not strongly constrain circuit parameters, many parameters in neural circuits are irrelevant and contribute little to function, and circuit parameters are unstable and subject to constant random drift. At the same time, however, recent work also showed that dynamics in neural circuit activity that is related to function are robust over time and across individuals. Here this apparent contradiction is addressed by considering the properties of neural manifolds that restrict circuit activity to functionally relevant subspaces, and it will be suggested that degenerate, anisotropic and unstable parameter spaces are closely related to the structure and implementation of functionally relevant neural manifolds.

Receptive field estimation in large visual neuron assemblies using a super-resolution approach.

Computing the spike-triggered average (STA) is a simple method to estimate linear receptive fields (RFs) in sensory neurons. For random, uncorrelated stimuli, the STA provides an unbiased RF estimate, but in practice, white noise at high resolution is not an optimal stimulus choice as it usually evokes only weak responses. Therefore, for a visual stimulus, images of randomly modulated blocks of pixels are often used. This solution naturally limits the resolution at which an RF can be measured. Here, we present a simple super-resolution technique that can overcome these limitations. We define a novel stimulus type, the shifted white noise (SWN), by introducing random spatial shifts in the usual stimulus to increase the resolution of the measurements. In simulated data, we show that the average error using the SWN was 1.7 times smaller than when using the classical stimulus, with successful mapping of 2.3 times more neurons, covering a broader range of RF sizes. Moreover, successful RF mapping was achieved with brief recordings of light responses, lasting only about 1 min of activity, which is more than 10 times more efficient than the classical white noise stimulus. In recordings from mouse retinal ganglion cells with large scale multielectrode arrays, we successfully mapped 21 times more RFs than when using the traditional white noise stimuli. In summary, randomly shifting the usual white noise stimulus significantly improves RFs estimation, and requires only short recordings.NEW & NOTEWORTHY We present a novel approach to measure receptive fields in large and heterogeneous populations of sensory neurons recorded with large-scale, high-density multielectrode arrays. Our approach leverages super-resolution principles to improve the yield of the spike-triggered average method. By simply designing a new stimulus, we provide experimentalists with a new and fast technique to simultaneously detect more receptive fields at higher resolution in population of hundreds to thousands of neurons.

The information theory of developmental pruning: Optimizing global network architectures using local synaptic rules.

During development, biological neural networks produce more synapses and neurons than needed. Many of these synapses and neurons are later removed in a process known as neural pruning. Why networks should initially be over-populated, and the processes that determine which synapses and neurons are ultimately pruned, remains unclear. We study the mechanisms and significance of neural pruning in model neural networks. In a deep Boltzmann machine model of sensory encoding, we find that (1) synaptic pruning is necessary to learn efficient network architectures that retain computationally-relevant connections, (2) pruning by synaptic weight alone does not optimize network size and (3) pruning based on a locally-available measure of importance based on Fisher information allows the network to identify structurally important vs. unimportant connections and neurons. This locally-available measure of importance has a biological interpretation in terms of the correlations between presynaptic and postsynaptic neurons, and implies an efficient activity-driven pruning rule. Overall, we show how local activity-dependent synaptic pruning can solve the global problem of optimizing a network architecture. We relate these findings to biology as follows: (I) Synaptic over-production is necessary for activity-dependent connectivity optimization. (II) In networks that have more neurons than needed, cells compete for activity, and only the most important and selective neurons are retained. (III) Cells may also be pruned due to a loss of synapses on their axons. This occurs when the information they convey is not relevant to the target population.

Neural field models for latent state inference: Application to large-scale neuronal recordings.

Large-scale neural recording methods now allow us to observe large populations of identified single neurons simultaneously, opening a window into neural population dynamics in living organisms. However, distilling such large-scale recordings to build theories of emergent collective dynamics remains a fundamental statistical challenge. The neural field models of Wilson, Cowan, and colleagues remain the mainstay of mathematical population modeling owing to their interpretable, mechanistic parameters and amenability to mathematical analysis. Inspired by recent advances in biochemical modeling, we develop a method based on moment closure to interpret neural field models as latent state-space point-process models, making them amenable to statistical inference. With this approach we can infer the intrinsic states of neurons, such as active and refractory, solely from spiking activity in large populations. After validating this approach with synthetic data, we apply it to high-density recordings of spiking activity in the developing mouse retina. This confirms the essential role of a long lasting refractory state in shaping spatiotemporal properties of neonatal retinal waves. This conceptual and methodological advance opens up new theoretical connections between mathematical theory and point-process state-space models in neural data analysis.

Optimal Encoding in Stochastic Latent-Variable Models.

In this work we explore encoding strategies learned by statistical models of sensory coding in noisy spiking networks. Early stages of sensory communication in neural systems can be viewed as encoding channels in the information-theoretic sense. However, neural populations face constraints not commonly considered in communications theory. Using restricted Boltzmann machines as a model of sensory encoding, we find that networks with sufficient capacity learn to balance precision and noise-robustness in order to adaptively communicate stimuli with varying information content. Mirroring variability suppression observed in sensory systems, informative stimuli are encoded with high precision, at the cost of more variable responses to frequent, hence less informative stimuli. Curiously, we also find that statistical criticality in the neural population code emerges at model sizes where the input statistics are well captured. These phenomena have well-defined thermodynamic interpretations, and we discuss their connection to prevailing theories of coding and statistical criticality in neural populations.

Glucose and lactate as metabolic constraints on presynaptic transmission at an excitatory synapse.

KEY POINTS: Synapses have high energy demands which increase during intense activity. We show that presynaptic terminals can utilise extracellular glucose or lactate to generate energy to maintain synaptic transmission. Reducing energy substrates induces a metabolic stress: presynaptic ATP depletion impaired synaptic transmission through a reduction in the number of functional synaptic vesicle release sites and a slowing of vesicle pool replenishment, without a consistent change in release probability. Metabolic function is compromised in many pathological conditions (e.g. stroke, traumatic brain injury and neurodegeneration). Knowledge of how synaptic transmission is constrained by metabolic stress, especially during intense brain activity, will provide insights to improve cognition following pathological insults. ABSTRACT: The synapse has high energy demands, which increase during intense activity. Presynaptic ATP production depends on substrate availability and usage will increase during activity, which in turn could influence transmitter release and information transmission. We investigated transmitter release at the mouse calyx of Held synapse using glucose or lactate (10, 1 or 0 mm) as the extracellular substrates while inducing metabolic stress. High-frequency stimulation (HFS) and recovery paradigms evoked trains of EPSCs monitored under voltage-clamp. Whilst postsynaptic intracellular ATP was stabilised by diffusion from the patch pipette, depletion of glucose increased EPSC depression during HFS and impaired subsequent recovery. Computational modelling of these data demonstrated a reduction in the number of functional release sites and slowed vesicle pool replenishment during metabolic stress, with little change in release probability. Directly depleting presynaptic terminal ATP impaired transmitter release in an analogous manner to glucose depletion. In the absence of glucose, presynaptic terminal metabolism could utilise lactate from the aCSF and this was blocked by inhibition of monocarboxylate transporters (MCTs). MCT inhibitors significantly suppressed transmission in low glucose, implying that lactate is a presynaptic substrate. Additionally, block of glycogenolysis accelerated synaptic transmission failure in the absence of extracellular glucose, consistent with supplemental supply of lactate by local astrocytes. We conclude that both glucose and lactate support presynaptic metabolism and that limited availability, exacerbated by high-intensity firing, constrains presynaptic ATP, impeding transmission through a reduction in functional presynaptic release sites as vesicle recycling slows when ATP levels are low.

Spike-Based Bayesian-Hebbian Learning of Temporal Sequences.

Many cognitive and motor functions are enabled by the temporal representation and processing of stimuli, but it remains an open issue how neocortical microcircuits can reliably encode and replay such sequences of information. To better understand this, a modular attractor memory network is proposed in which meta-stable sequential attractor transitions are learned through changes to synaptic weights and intrinsic excitabilities via the spike-based Bayesian Confidence Propagation Neural Network (BCPNN) learning rule. We find that the formation of distributed memories, embodied by increased periods of firing in pools of excitatory neurons, together with asymmetrical associations between these distinct network states, can be acquired through plasticity. The model's feasibility is demonstrated using simulations of adaptive exponential integrate-and-fire model neurons (AdEx). We show that the learning and speed of sequence replay depends on a confluence of biophysically relevant parameters including stimulus duration, level of background noise, ratio of synaptic currents, and strengths of short-term depression and adaptation. Moreover, sequence elements are shown to flexibly participate multiple times in the sequence, suggesting that spiking attractor networks of this type can support an efficient combinatorial code. The model provides a principled approach towards understanding how multiple interacting plasticity mechanisms can coordinate hetero-associative learning in unison.

Sloppiness in spontaneously active neuronal networks.

Various plasticity mechanisms, including experience-dependent, spontaneous, as well as homeostatic ones, continuously remodel neural circuits. Yet, despite fluctuations in the properties of single neurons and synapses, the behavior and function of neuronal assemblies are generally found to be very stable over time. This raises the important question of how plasticity is coordinated across the network. To address this, we investigated the stability of network activity in cultured rat hippocampal neurons recorded with high-density multielectrode arrays over several days. We used parametric models to characterize multineuron activity patterns and analyzed their sensitivity to changes. We found that the models exhibited sloppiness, a property where the model behavior is insensitive to changes in many parameter combinations, but very sensitive to a few. The activity of neurons with sloppy parameters showed faster and larger fluctuations than the activity of a small subset of neurons associated with sensitive parameters. Furthermore, parameter sensitivity was highly correlated with firing rates. Finally, we tested our observations from cell cultures on an in vivo recording from monkey visual cortex and we confirm that spontaneous cortical activity also shows hallmarks of sloppy behavior and firing rate dependence. Our findings suggest that a small subnetwork of highly active and stable neurons supports group stability, and that this endows neuronal networks with the flexibility to continuously remodel without compromising stability and function.

Acoustic trauma slows AMPA receptor-mediated EPSCs in the auditory brainstem, reducing GluA4 subunit expression as a mechanism to rescue binaural function.

KEY POINTS: Lateral superior olive (LSO) principal neurons receive AMPA receptor (AMPAR) - and NMDA receptor (NMDAR)-mediated EPSCs and glycinergic IPSCs. Both EPSCs and IPSCs have slow kinetics in prehearing animals, which during developmental maturation accelerate to sub-millisecond decay time-constants. This correlates with a change in glutamate and glycine receptor subunit composition quantified via mRNA levels. The NMDAR-EPSCs accelerate over development to achieve decay time-constants of 2.5 ms. This is the fastest NMDAR-mediated EPSC reported. Acoustic trauma (AT, loud sounds) slow AMPAR-EPSC decay times, increasing GluA1 and decreasing GluA4 mRNA. Modelling of interaural intensity difference suggests that the increased EPSC duration after AT shifts interaural level difference to the right and compensates for hearing loss. Two months after AT the EPSC decay times recovered to control values. Synaptic transmission in the LSO matures by postnatal day 20, with EPSCs and IPSCs having fast kinetics. AT changes the AMPAR subunits expressed and slows the EPSC time-course at synapses in the central auditory system. ABSTRACT: Damaging levels of sound (acoustic trauma, AT) diminish peripheral synapses, but what is the impact on the central auditory pathway? Developmental maturation of synaptic function and hearing were characterized in the mouse lateral superior olive (LSO) from postnatal day 7 (P7) to P96 using voltage-clamp and auditory brainstem responses. IPSCs and EPSCs show rapid acceleration during development, so that decay kinetics converge to similar sub-millisecond time-constants (τ, 0.87 ± 0.11 and 0.77 ± 0.08 ms, respectively) in adult mice. This correlated with LSO mRNA levels for glycinergic and glutamatergic ionotropic receptor subunits, confirming a switch from Glyα2 to Glyα1 for IPSCs and increased expression of GluA3 and GluA4 subunits for EPSCs. The NMDA receptor (NMDAR)-EPSC decay τ accelerated from >40 ms in prehearing animals to 2.6 ± 0.4 ms in adults, as GluN2C expression increased. In vivo induction of AT at around P20 disrupted IPSC and EPSC integration in the LSO, so that 1 week later the AMPA receptor (AMPAR)-EPSC decay was slowed and mRNA for GluA1 increased while GluA4 decreased. In contrast, GlyR IPSC and NMDAR-EPSC decay times were unchanged. Computational modelling confirmed that matched IPSC and EPSC kinetics are required to generate mature interaural level difference functions, and that longer-lasting EPSCs compensate to maintain binaural function with raised auditory thresholds after AT. We conclude that LSO excitatory and inhibitory synaptic drive matures to identical time-courses, that AT changes synaptic AMPARs by expression of subunits with slow kinetics (which recover over 2 months) and that loud sounds reversibly modify excitatory synapses in the brain, changing synaptic function for several weeks after exposure.

A Diffusive Homeostatic Signal Maintains Neural Heterogeneity and Responsiveness in Cortical Networks.

Gaseous neurotransmitters such as nitric oxide (NO) provide a unique and often overlooked mechanism for neurons to communicate through diffusion within a network, independent of synaptic connectivity. NO provides homeostatic control of intrinsic excitability. Here we conduct a theoretical investigation of the distinguishing roles of NO-mediated diffusive homeostasis in comparison with canonical non-diffusive homeostasis in cortical networks. We find that both forms of homeostasis provide a robust mechanism for maintaining stable activity following perturbations. However, the resulting networks differ, with diffusive homeostasis maintaining substantial heterogeneity in activity levels of individual neurons, a feature disrupted in networks with non-diffusive homeostasis. This results in networks capable of representing input heterogeneity, and linearly responding over a broader range of inputs than those undergoing non-diffusive homeostasis. We further show that these properties are preserved when homeostatic and Hebbian plasticity are combined. These results suggest a mechanism for dynamically maintaining neural heterogeneity, and expose computational advantages of non-local homeostatic processes.

Following the ontogeny of retinal waves: pan-retinal recordings of population dynamics in the neonatal mouse.

The immature retina generates spontaneous waves of spiking activity that sweep across the ganglion cell layer during a limited period of development before the onset of visual experience. The spatiotemporal patterns encoded in the waves are believed to be instructive for the wiring of functional connections throughout the visual system. However, the ontogeny of retinal waves is still poorly documented as a result of the relatively low resolution of conventional recording techniques. Here, we characterize the spatiotemporal features of mouse retinal waves from birth until eye opening in unprecedented detail using a large-scale, dense, 4096-channel multielectrode array that allowed us to record from the entire neonatal retina at near cellular resolution. We found that early cholinergic waves propagate with random trajectories over large areas with low ganglion cell recruitment. They become slower, smaller and denser when GABAA signalling matures, as occurs beyond postnatal day (P) 7. Glutamatergic influences dominate from P10, coinciding with profound changes in activity dynamics. At this time, waves cease to be random and begin to show repetitive trajectories confined to a few localized hotspots. These hotspots gradually tile the retina with time, and disappear after eye opening. Our observations demonstrate that retinal waves undergo major spatiotemporal changes during ontogeny. Our results support the hypotheses that cholinergic waves guide the refinement of retinal targets and that glutamatergic waves may also support the wiring of retinal receptive fields.

Age-dependent homeostatic plasticity of GABAergic signaling in developing retinal networks.

Developing retinal ganglion cells fire in correlated spontaneous bursts, resulting in propagating waves with robust spatiotemporal features preserved across development and species. Here we investigate the effects of homeostatic adaptation on the circuits controlling retinal waves. Mouse retinal waves were recorded in vitro for up to 35 h with a multielectrode array in presence of the GABA(A) antagonist bicuculline, allowing us to obtain a precise, time-resolved characterization of homeostatic effects in this preparation. Experiments were performed at P4-P6, when GABA(A) signaling is depolarizing in ganglion cells, and at P7-P10, when GABA(A) signaling is hyperpolarizing. At all ages, bicuculline initially increased the wave sizes and other activity metrics. At P5-P6, wave sizes decreased toward control levels within a few hours while firing remained strong, but this ability to compensate disappeared entirely from P7 onwards. This demonstrates that homeostatic control of spontaneous retinal activity maintains specific network dynamic properties in an age-dependent manner, and suggests that the underlying mechanism is linked to GABA(A) signaling.

Movement-specific signaling is differentially distributed across motor cortex layer 5 projection neuron classes.

Motor cortex generates descending output necessary for executing a wide range of limb movements. Although movement-related activity has been described throughout motor cortex, the spatiotemporal organization of movement-specific signaling in deep layers remains largely unknown. Here we record layer 5B population dynamics in the caudal forelimb area of motor cortex while mice perform a forelimb push/pull task and find that most neurons show movement-invariant responses, with a minority displaying movement specificity. Using cell-type-specific imaging, we identify that invariant responses dominate pyramidal tract (PT) neuron activity, with a small subpopulation representing movement type, whereas a larger proportion of intratelencephalic (IT) neurons display movement-type-specific signaling. The proportion of IT neurons decoding movement-type peaks prior to movement initiation, whereas for PT neurons, this occurs during movement execution. Our data suggest that layer 5B population dynamics largely reflect movement-invariant signaling, with information related to movement-type being routed through relatively small, distributed subpopulations of projection neurons.

Low-voltage activated Kv1.1 subunits are crucial for the processing of sound source location in the lateral superior olive in mice.

Voltage-gated potassium (Kv) channels containing Kv1.1 subunits are strongly expressed in neurons that fire temporally precise action potentials (APs). In the auditory system, AP timing is used to localize sound sources by integrating interaural differences in time (ITD) and intensity (IID) using sound arriving at both cochleae. In mammals, the first nucleus to encode IIDs is the lateral superior olive (LSO), which integrates excitation from the ipsilateral ventral cochlear nucleus and contralateral inhibition mediated via the medial nucleus of the trapezoid body. Previously we reported that neurons in this pathway show reduced firing rates, longer latencies and increased jitter in Kv1.1 knockout (Kcna1−/−) mice. Here, we investigate whether these differences have direct impact on IID processing by LSO neurons. Single-unit recordings were made from LSO neurons of wild-type (Kcna1+/+) and from Kcna1−/− mice. IID functions were measured to evaluate genotype-specific changes in integrating excitatory and inhibitory inputs. In Kcna1+/+ mice, IID sensitivity ranged from +27 dB (excitatory ear more intense) to −20 dB (inhibitory ear more intense), thus covering the physiologically relevant range of IIDs. However, the distribution of IID functions in Kcna1−/− mice was skewed towards positive IIDs, favouring ipsilateral sound positions. Our computational model revealed that the reduced performance of IID encoding in the LSO of Kcna1−/− mice is mainly caused by a decrease in temporal fidelity along the inhibitory pathway. These results imply a fundamental role for Kv1.1 in temporal integration of excitation and inhibition during sound source localization.

Building population models for large-scale neural recordings: Opportunities and pitfalls.

Modern recording technologies now enable simultaneous recording from large numbers of neurons. This has driven the development of new statistical models for analyzing and interpreting neural population activity. Here, we provide a broad overview of recent developments in this area. We compare and contrast different approaches, highlight strengths and limitations, and discuss biological and mechanistic insights that these methods provide.

Early-stage waves in the retinal network emerge close to a critical state transition between local and global functional connectivity.

A novel, biophysically realistic model for early-stage, acetylcholine-mediated retinal waves is presented. In this model, neural excitability is regulated through a slow after-hyperpolarization (sAHP) operating on two different temporal scales. As a result, the simulated network exhibits competition between a desynchronizing effect of spontaneous, cell-intrinsic bursts, and the synchronizing effect of synaptic transmission during retinal waves. Cell-intrinsic bursts decouple the retinal network through activation of the sAHP current, and we show that the network is capable of operating at a transition point between purely local and global functional connectedness, which corresponds to a percolation phase transition. Multielectrode array recordings show that, at this point, the properties of retinal waves are reliably predicted by the model. These results indicate that early spontaneous activity in the developing retina is regulated according to a very specific principle, which maximizes randomness and variability in the resulting activity patterns.

SpikeInterface, a unified framework for spike sorting.

Much development has been directed toward improving the performance and automation of spike sorting. This continuous development, while essential, has contributed to an over-saturation of new, incompatible tools that hinders rigorous benchmarking and complicates reproducible analysis. To address these limitations, we developed SpikeInterface, a Python framework designed to unify preexisting spike sorting technologies into a single codebase and to facilitate straightforward comparison and adoption of different approaches. With a few lines of code, researchers can reproducibly run, compare, and benchmark most modern spike sorting algorithms; pre-process, post-process, and visualize extracellular datasets; validate, curate, and export sorting outputs; and more. In this paper, we provide an overview of SpikeInterface and, with applications to real and simulated datasets, demonstrate how it can be utilized to reduce the burden of manual curation and to more comprehensively benchmark automated spike sorters.

Scaling Spike Detection and Sorting for Next-Generation Electrophysiology.

Reliable spike detection and sorting, the process of assigning each detected spike to its originating neuron, are essential steps in the analysis of extracellular electrical recordings from neurons. The volume and complexity of the data from recently developed large-scale, high-density microelectrode arrays and probes, which allow recording from thousands of channels simultaneously, substantially complicate this task conceptually and computationally. This chapter provides a summary and discussion of recently developed methods to tackle these challenges and discusses the important aspect of algorithm validation, and assessment of detection and sorting quality.

Slow NMDA-Mediated Excitation Accelerates Offset-Response Latencies Generated via a Post-Inhibitory Rebound Mechanism.

In neural circuits, action potentials (spikes) are conventionally caused by excitatory inputs whereas inhibitory inputs reduce or modulate neuronal excitability. We previously showed that neurons in the superior paraolivary nucleus (SPN) require solely synaptic inhibition to generate their hallmark offset response, a burst of spikes at the end of a sound stimulus, via a post-inhibitory rebound mechanism. In addition SPN neurons receive excitatory inputs, but their functional significance is not yet known. Here we used mice of both sexes to demonstrate that in SPN neurons, the classical roles for excitation and inhibition are switched, with inhibitory inputs driving spike firing and excitatory inputs modulating this response. Hodgkin-Huxley modeling suggests that a slow, NMDA receptor (NMDAR)-mediated excitation would accelerate the offset response. We find corroborating evidence from in vitro and in vivo recordings that lack of excitation prolonged offset-response latencies and rendered them more variable to changing sound intensity levels. Our results reveal an unsuspected function for slow excitation in improving the timing of post-inhibitory rebound firing even when the firing itself does not depend on excitation. This shows the auditory system employs highly specialized mechanisms to encode timing-sensitive features of sound offsets which are crucial for sound-duration encoding and have profound biological importance for encoding the temporal structure of speech.

Interactions between multiple sources of short-term plasticity during evoked and spontaneous activity at the rat calyx of Held.

Sustained activity at most central synapses is accompanied by a number of short-term changes in synaptic strength which act over a range of time scales. Here we examine experimental data and develop a model of synaptic depression at the calyx of Held synaptic terminal that combines many of these mechanisms (acting at differing sites and across a range of time scales). This new model incorporates vesicle recycling, facilitation, activity-dependent vesicle retrieval and multiple mechanisms affecting calcium channel activity and release probability. It can accurately reproduce the time course of experimentally measured short-term depression across different stimulus frequencies and exhibits a slow decay in EPSC amplitude during sustained stimulation. We show that the slow decay is a consequence of vesicle release inhibition by multiple mechanisms and is accompanied by a partial recovery of the releasable vesicle pool. This prediction is supported by patch-clamp data, using long duration repetitive EPSC stimulation at up to 400 Hz. The model also explains the recovery from depression in terms of interaction between these multiple processes, which together generate a stimulus-history-dependent recovery after repetitive stimulation. Given the high rates of spontaneous activity in the auditory pathway, the model also demonstrates how these multiple interactions cause chronic synaptic depression under in vivo conditions. While the magnitude of the depression converges to the same steady state for a given frequency, the time courses of onset and recovery are faster in the presence of spontaneous activity. We conclude that interactions between multiple sources of short-term plasticity can account for the complex kinetics during high frequency stimulation and cause stimulus-history-dependent recovery at this relay synapse.