Dendritic Mechanisms for In Vivo Neural Computations and Behavior.

Dendrites receive the vast majority of a single neuron's inputs, and coordinate the transformation of these signals into neuronal output. Ex vivo and theoretical evidence has shown that dendrites possess powerful processing capabilities, yet little is known about how these mechanisms are engaged in the intact brain or how they influence circuit dynamics. New experimental and computational technologies have led to a surge in interest to unravel and harness their computational potential. This review highlights recent and emerging work that combines established and cutting-edge technologies to identify the role of dendrites in brain function. We discuss active dendritic mediation of sensory perception and learning in neocortical and hippocampal pyramidal neurons. Complementing these physiological findings, we present theoretical work that provides new insights into the underlying computations of single neurons and networks by using biologically plausible implementations of dendritic processes. Finally, we present a novel brain-computer interface task, which assays somatodendritic coupling to study the mechanisms of biological credit assignment. Together, these findings present exciting progress in understanding how dendrites are critical for in vivo learning and behavior, and highlight how subcellular processes can contribute to our understanding of both biological and artificial neural computation.

Silences, spikes and bursts: Three-part knot of the neural code.

When a neuron breaks silence, it can emit action potentials in a number of patterns. Some responses are so sudden and intense that electrophysiologists felt the need to single them out, labelling action potentials emitted at a particularly high frequency with a metonym - bursts. Is there more to bursts than a figure of speech? After all, sudden bouts of high-frequency firing are expected to occur whenever inputs surge. The burst coding hypothesis advances that the neural code has three syllables: silences, spikes and bursts. We review evidence supporting this ternary code in terms of devoted mechanisms for burst generation, synaptic transmission and synaptic plasticity. We also review the learning and attention theories for which such a triad is beneficial.

Self-organization of a doubly asynchronous irregular network state for spikes and bursts.

Cortical pyramidal cells (PCs) have a specialized dendritic mechanism for the generation of bursts, suggesting that these events play a special role in cortical information processing. In vivo, bursts occur at a low, but consistent rate. Theory suggests that this network state increases the amount of information they convey. However, because burst activity relies on a threshold mechanism, it is rather sensitive to dendritic input levels. In spiking network models, network states in which bursts occur rarely are therefore typically not robust, but require fine-tuning. Here, we show that this issue can be solved by a homeostatic inhibitory plasticity rule in dendrite-targeting interneurons that is consistent with experimental data. The suggested learning rule can be combined with other forms of inhibitory plasticity to self-organize a network state in which both spikes and bursts occur asynchronously and irregularly at low rate. Finally, we show that this network state creates the network conditions for a recently suggested multiplexed code and thereby indeed increases the amount of information encoded in bursts.

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.

A User's Guide to Generalized Integrate-and-Fire Models.

The generalized integrate-and-fire (GIF) neuron model accounts for some of the most fundamental behaviours of neurons within a compact and extensible mathematical framework. Here, we introduce the main concepts behind the design of the GIF model in terms that will be familiar to electrophysiologists, and show why its simple design makes this model particularly well suited to mimicking behaviours observed in experimental data. Along the way, we will build an intuition for how specific neuronal behaviours, such as spike-frequency adaptation, or electrical properties, such as ionic currents, can be formulated mathematically and used to extend integrate-and-fire models to overcome their limitations. This chapter will provide readers with no previous exposure to modelling a clear understanding of the strengths and limitations of GIF models, along with the mathematical intuitions required to digest more detailed and technical treatments of this topic.

Sparse bursts optimize information transmission in a multiplexed neural code.

Many cortical neurons combine the information ascending and descending the cortical hierarchy. In the classical view, this information is combined nonlinearly to give rise to a single firing-rate output, which collapses all input streams into one. We analyze the extent to which neurons can simultaneously represent multiple input streams by using a code that distinguishes spike timing patterns at the level of a neural ensemble. Using computational simulations constrained by experimental data, we show that cortical neurons are well suited to generate such multiplexing. Interestingly, this neural code maximizes information for short and sparse bursts, a regime consistent with in vivo recordings. Neurons can also demultiplex this information, using specific connectivity patterns. The anatomy of the adult mammalian cortex suggests that these connectivity patterns are used by the nervous system to maintain sparse bursting and optimal multiplexing. Contrary to firing-rate coding, our findings indicate that the physiology and anatomy of the cortex may be interpreted as optimizing the transmission of multiple independent signals to different targets.

Automated High-Throughput Characterization of Single Neurons by Means of Simplified Spiking Models.

Single-neuron models are useful not only for studying the emergent properties of neural circuits in large-scale simulations, but also for extracting and summarizing in a principled way the information contained in electrophysiological recordings. Here we demonstrate that, using a convex optimization procedure we previously introduced, a Generalized Integrate-and-Fire model can be accurately fitted with a limited amount of data. The model is capable of predicting both the spiking activity and the subthreshold dynamics of different cell types, and can be used for online characterization of neuronal properties. A protocol is proposed that, combined with emergent technologies for automatic patch-clamp recordings, permits automated, in vitro high-throughput characterization of single neurons.

Speed-invariant encoding of looming object distance requires power law spike rate adaptation.

Neural representations of a moving object's distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent's response to "looming" object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent's response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent's firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli.

Counting on dis-inhibition: a circuit motif for interval counting and selectivity in the anuran auditory system.

Information can be encoded in the temporal patterning of spikes. How the brain reads these patterns is of general importance and represents one of the greatest challenges in neuroscience. We addressed this issue in relation to temporal pattern recognition in the anuran auditory system. Many species of anurans perform mating decisions based on the temporal structure of advertisement calls. One important temporal feature is the number of sound pulses that occur with a species-specific interpulse interval. Neurons representing this pulse count have been recorded in the anuran inferior colliculus, but the mechanisms underlying their temporal selectivity are incompletely understood. Here, we construct a parsimonious model that can explain the key dynamical features of these cells with biologically plausible elements. We demonstrate that interval counting arises naturally when combining interval-selective inhibition with pulse-per-pulse excitation having both fast- and slow-conductance synapses. Interval-dependent inhibition is modeled here by a simple architecture based on known physiology of afferent nuclei. Finally, we consider simple implementations of previously proposed mechanistic explanations for these counting neurons and show that they do not account for all experimental observations. Our results demonstrate that tens of millisecond-range temporal selectivities can arise from simple connectivity motifs of inhibitory neurons, without recourse to internal clocks, spike-frequency adaptation, or appreciable short-term plasticity.

Dendritic excitability controls overdispersion.

The brain is an intricate assembly of intercommunicating neurons whose input-output function is only partially understood. The role of active dendrites in shaping spiking responses, in particular, is unclear. Although existing models account for active dendrites and spiking responses, they are too complex to analyze analytically and demand long stochastic simulations. Here we combine cable and renewal theory to describe how input fluctuations shape the response of neuronal ensembles with active dendrites. We found that dendritic input readily and potently controls interspike interval dispersion. This phenomenon can be understood by considering that neurons display three fundamental operating regimes: one mean-driven regime and two fluctuation-driven regimes. We show that these results are expected to appear for a wide range of dendritic properties and verify predictions of the model in experimental data. These findings have implications for the role of interspike interval dispersion in learning and for theories of attractor states.

Functional subtypes of synaptic dynamics in mouse and human.

Synapses preferentially respond to particular temporal patterns of activity with a large degree of heterogeneity that is informally or tacitly separated into classes. Yet, the precise number and properties of such classes are unclear. Do they exist on a continuum and, if so, when is it appropriate to divide that continuum into functional regions? In a large dataset of glutamatergic cortical connections, we perform model-based characterization to infer the number and characteristics of functionally distinct subtypes of synaptic dynamics. In rodent data, we find five clusters that partially converge with transgenic-associated subtypes. Strikingly, the application of the same clustering method in human data infers a highly similar number of clusters, supportive of stable clustering. This nuanced dictionary of functional subtypes shapes the heterogeneity of cortical synaptic dynamics and provides a lens into the basic motifs of information transmission in the brain.

Coding and decoding with adapting neurons: a population approach to the peri-stimulus time histogram.

The response of a neuron to a time-dependent stimulus, as measured in a Peri-Stimulus-Time-Histogram (PSTH), exhibits an intricate temporal structure that reflects potential temporal coding principles. Here we analyze the encoding and decoding of PSTHs for spiking neurons with arbitrary refractoriness and adaptation. As a modeling framework, we use the spike response model, also known as the generalized linear neuron model. Because of refractoriness, the effect of the most recent spike on the spiking probability a few milliseconds later is very strong. The influence of the last spike needs therefore to be described with high precision, while the rest of the neuronal spiking history merely introduces an average self-inhibition or adaptation that depends on the expected number of past spikes but not on the exact spike timings. Based on these insights, we derive a 'quasi-renewal equation' which is shown to yield an excellent description of the firing rate of adapting neurons. We explore the domain of validity of the quasi-renewal equation and compare it with other rate equations for populations of spiking neurons. The problem of decoding the stimulus from the population response (or PSTH) is addressed analogously. We find that for small levels of activity and weak adaptation, a simple accumulator of the past activity is sufficient to decode the original input, but when refractory effects become large decoding becomes a non-linear function of the past activity. The results presented here can be applied to the mean-field analysis of coupled neuron networks, but also to arbitrary point processes with negative self-interaction.

Temporal derivative computation in the dorsal raphe network revealed by an experimentally driven augmented integrate-and-fire modeling framework.

By means of an expansive innervation, the serotonin (5-HT) neurons of the dorsal raphe nucleus (DRN) are positioned to enact coordinated modulation of circuits distributed across the entire brain in order to adaptively regulate behavior. Yet the network computations that emerge from the excitability and connectivity features of the DRN are still poorly understood. To gain insight into these computations, we began by carrying out a detailed electrophysiological characterization of genetically identified mouse 5-HT and somatostatin (SOM) neurons. We next developed a single-neuron modeling framework that combines the realism of Hodgkin-Huxley models with the simplicity and predictive power of generalized integrate-and-fire models. We found that feedforward inhibition of 5-HT neurons by heterogeneous SOM neurons implemented divisive inhibition, while endocannabinoid-mediated modulation of excitatory drive to the DRN increased the gain of 5-HT output. Our most striking finding was that the output of the DRN encodes a mixture of the intensity and temporal derivative of its input, and that the temporal derivative component dominates this mixture precisely when the input is increasing rapidly. This network computation primarily emerged from prominent adaptation mechanisms found in 5-HT neurons, including a previously undescribed dynamic threshold. By applying a bottom-up neural network modeling approach, our results suggest that the DRN is particularly apt to encode input changes over short timescales, reflecting one of the salient emerging computations that dominate its output to regulate behavior.

Parameter extraction and classification of three cortical neuron types reveals two distinct adaptation mechanisms.

Cortical information processing originates from the exchange of action potentials between many cell types. To capture the essence of these interactions, it is of critical importance to build mathematical models that reflect the characteristic features of spike generation in individual neurons. We propose a framework to automatically extract such features from current-clamp experiments, in particular the passive properties of a neuron (i.e., membrane time constant, reversal potential, and capacitance), the spike-triggered adaptation currents, as well as the dynamics of the action potential threshold. The stochastic model that results from our maximum likelihood approach accurately predicts the spike times, the subthreshold voltage, the firing patterns, and the type of frequency-current curve. Extracting the model parameters for three cortical cell types revealed that cell types show highly significant differences in the time course of the spike-triggered currents and moving threshold, that is, in their adaptation and refractory properties but not in their passive properties. In particular, GABAergic fast-spiking neurons mediate weak adaptation through spike-triggered currents only, whereas regular spiking excitatory neurons mediate adaptation with both moving threshold and spike-triggered currents. GABAergic nonfast-spiking neurons combine the two distinct adaptation mechanisms with reduced strength. Differences between cell types are large enough to enable automatic classification of neurons into three different classes. Parameter extraction is performed for individual neurons so that we find not only the mean parameter values for each neuron type but also the spread of parameters within a group of neurons, which will be useful for future large-scale computer simulations.

Overwriting the past with supervised plasticity.

Triggered activity bursts in place cells can increase and decrease the strength of some inputs.

Cell-type-specific responses to associative learning in the primary motor cortex.

The primary motor cortex (M1) is known to be a critical site for movement initiation and motor learning. Surprisingly, it has also been shown to possess reward-related activity, presumably to facilitate reward-based learning of new movements. However, whether reward-related signals are represented among different cell types in M1, and whether their response properties change after cue-reward conditioning remains unclear. Here, we performed longitudinal in vivo two-photon Ca2+ imaging to monitor the activity of different neuronal cell types in M1 while mice engaged in a classical conditioning task. Our results demonstrate that most of the major neuronal cell types in M1 showed robust but differential responses to both the conditioned cue stimulus (CS) and reward, and their response properties undergo cell-type-specific modifications after associative learning. PV-INs' responses became more reliable to the CS, while VIP-INs' responses became more reliable to reward. Pyramidal neurons only showed robust responses to novel reward, and they habituated to it after associative learning. Lastly, SOM-INs' responses emerged and became more reliable to both the CS and reward after conditioning. These observations suggest that cue- and reward-related signals are preferentially represented among different neuronal cell types in M1, and the distinct modifications they undergo during associative learning could be essential in triggering different aspects of local circuit reorganization in M1 during reward-based motor skill learning.

Parallel and Recurrent Cascade Models as a Unifying Force for Understanding Subcellular Computation.

Neurons are very complicated computational devices, incorporating numerous non-linear processes, particularly in their dendrites. Biophysical models capture these processes directly by explicitly modelling physiological variables, such as ion channels, current flow, membrane capacitance, etc. However, another option for capturing the complexities of real neural computation is to use cascade models, which treat individual neurons as a cascade of linear and non-linear operations, akin to a multi-layer artificial neural network. Recent research has shown that cascade models can capture single-cell computation well, but there are still a number of sub-cellular, regenerative dendritic phenomena that they cannot capture, such as the interaction between sodium, calcium, and NMDA spikes in different compartments. Here, we propose that it is possible to capture these additional phenomena using parallel, recurrent cascade models, wherein an individual neuron is modelled as a cascade of parallel linear and non-linear operations that can be connected recurrently, akin to a multi-layer, recurrent, artificial neural network. Given their tractable mathematical structure, we show that neuron models expressed in terms of parallel recurrent cascades can themselves be integrated into multi-layered artificial neural networks and trained to perform complex tasks. We go on to discuss potential implications and uses of these models for artificial intelligence. Overall, we argue that parallel, recurrent cascade models provide an important, unifying tool for capturing single-cell computation and exploring the algorithmic implications of physiological phenomena.

Improved similarity measures for small sets of spike trains.

Multiple measures have been developed to quantify the similarity between two spike trains. These measures have been used for the quantification of the mismatch between neuron models and experiments as well as for the classification of neuronal responses in neuroprosthetic devices and electrophysiological experiments. Frequently only a few spike trains are available in each class. We derive analytical expressions for the small-sample bias present when comparing estimators of the time-dependent firing intensity. We then exploit analogies between the comparison of firing intensities and previously used spike train metrics and show that improved spike train measures can be successfully used for fitting neuron models to experimental data, for comparisons of spike trains, and classification of spike train data. In classification tasks, the improved similarity measures can increase the recovered information. We demonstrate that when similarity measures are used for fitting mathematical models, all previous methods systematically underestimate the noise. Finally, we show a striking implication of this deterministic bias by reevaluating the results of the single-neuron prediction challenge.

Neural burst codes disguised as rate codes.

The burst coding hypothesis posits that the occurrence of sudden high-frequency patterns of action potentials constitutes a salient syllable of the neural code. Many neurons, however, do not produce clearly demarcated bursts, an observation invoked to rule out the pervasiveness of this coding scheme across brain areas and cell types. Here we ask how detrimental ambiguous spike patterns, those that are neither clearly bursts nor isolated spikes, are for neuronal information transfer. We addressed this question using information theory and computational simulations. By quantifying how information transmission depends on firing statistics, we found that the information transmitted is not strongly influenced by the presence of clearly demarcated modes in the interspike interval distribution, a feature often used to identify the presence of burst coding. Instead, we found that neurons having unimodal interval distributions were still able to ascribe different meanings to bursts and isolated spikes. In this regime, information transmission depends on dynamical properties of the synapses as well as the length and relative frequency of bursts. Furthermore, we found that common metrics used to quantify burstiness were unable to predict the degree with which bursts could be used to carry information. Our results provide guiding principles for the implementation of coding strategies based on spike-timing patterns, and show that even unimodal firing statistics can be consistent with a bivariate neural code.