Spike-timing prediction in cortical neurons with active dendrites

Cortical interneurons: fit for function and fit to function? Evidence from development and evolution

Cortical inhibitory interneurons form a broad spectrum of subtypes. This diversity suggests a division of labor, in which each cell type supports a distinct function. In the present era of optimisation-based algorithms, it is tempting to speculate that these functions were the evolutionary or developmental driving force for the spectrum of interneurons we see in the mature mammalian brain. In this study, we evaluated this hypothesis using the two most common interneuron types, parvalbumin (PV) and somatostatin (SST) expressing cells, as examples. PV and SST interneurons control the activity in the cell bodies and the apical dendrites of excitatory pyramidal cells, respectively, due to a combination of anatomical and synaptic properties. But was this compartment-specific inhibition indeed the function for which PV and SST cells originally evolved? Does the compartmental structure of pyramidal cells shape the diversification of PV and SST interneurons over development? To address these questions, we reviewed and reanalyzed publicly available data on the development and evolution of PV and SST interneurons on one hand, and pyramidal cell morphology on the other. These data speak against the idea that the compartment structure of pyramidal cells drove the diversification into PV and SST interneurons. In particular, pyramidal cells mature late, while interneurons are likely committed to a particular fate (PV vs. SST) during early development. Moreover, comparative anatomy and single cell RNA-sequencing data indicate that PV and SST cells, but not the compartment structure of pyramidal cells, existed in the last common ancestor of mammals and reptiles. Specifically, turtle and songbird SST cells also express the Elfn1 and Cbln4 genes that are thought to play a role in compartment-specific inhibition in mammals. PV and SST cells therefore evolved and developed the properties that allow them to provide compartment-specific inhibition before there was selective pressure for this function. This suggest that interneuron diversity originally resulted from a different evolutionary driving force and was only later co-opted for the compartment-specific inhibition it seems to serve in mammals today. Future experiments could further test this idea using our computational reconstruction of ancestral Elfn1 protein sequences.

Parallel functional architectures within a single dendritic tree

The input-output transformation of individual neurons is a key building block of neural circuit dynamics. While previous models of this transformation vary widely in their complexity, they all describe the underlying functional architecture as unitary, such that each synaptic input makes a single contribution to the neuronal response. Here, we show that the input-output transformation of CA1 pyramidal cells is instead best captured by two distinct functional architectures operating in parallel. We used statistically principled methods to fit flexible, yet interpretable, models of the transformation of input spikes into the somatic "output" voltage and to automatically select among alternative functional architectures. With dendritic Na+ channels blocked, responses are accurately captured by a single static and global nonlinearity. In contrast, dendritic Na+-dependent integration requires a functional architecture with multiple dynamic nonlinearities and clustered connectivity. These two architectures incorporate distinct morphological and biophysical properties of the neuron and its synaptic organization.

Optimizing interneuron circuits for compartment-specific feedback inhibition

Cortical circuits process information by rich recurrent interactions between excitatory neurons and inhibitory interneurons. One of the prime functions of interneurons is to stabilize the circuit by feedback inhibition, but the level of specificity on which inhibitory feedback operates is not fully resolved. We hypothesized that inhibitory circuits could enable separate feedback control loops for different synaptic input streams, by means of specific feedback inhibition to different neuronal compartments. To investigate this hypothesis, we adopted an optimization approach. Leveraging recent advances in training spiking network models, we optimized the connectivity and short-term plasticity of interneuron circuits for compartment-specific feedback inhibition onto pyramidal neurons. Over the course of the optimization, the interneurons diversified into two classes that resembled parvalbumin (PV) and somatostatin (SST) expressing interneurons. Using simulations and mathematical analyses, we show that the resulting circuit can be understood as a neural decoder that inverts the nonlinear biophysical computations performed within the pyramidal cells. Our model provides a proof of concept for studying structure-function relations in cortical circuits by a combination of gradient-based optimization and biologically plausible phenomenological models.

The brain contains billions of nerve cells—neurons—that can be classified into different types depending on their shape, connectivity and activity. A particularly diverse group of neurons is that of inhibitory neurons, named after their suppressive effect on neural activity. Presumably, their diverse properties allow inhibitory neurons to fulfil different functions, but what these functions are is currently unclear. In this paper, we investigated if a particular function can explain the existence and properties of the two most common inhibitory cell classes: The need to regulate activity in different physical parts (compartments) of the neurons they target. We investigated this function in a computer model, using optimization to find the neuron properties best-suited for compartment-specific inhibition. Our key result is that after the optimization, model neurons largely fell into two classes that resembled the two types of biological neurons. In particular, the optimized neurons were connected to only one compartment of other neurons. This suggests that the diversity of inhibitory neurons is well suited for compartment-specific inhibition. In the future, our approach of optimizing neural properties might be used to investigate other functions (or dysfunctions) of neuron diversity.

Dynamic compartmental computations in tuft dendrites of layer 5 neurons during motor behavior

Tuft dendrites of layer 5 pyramidal neurons form specialized compartments important for motor learning and performance, yet their computational capabilities remain unclear. Structural-functional mapping of the tuft tree from the motor cortex during motor tasks revealed two morphologically distinct populations of layer 5 pyramidal tract neurons (PTNs) that exhibit specific tuft computational properties. Early bifurcating and large nexus PTNs showed marked tuft functional compartmentalization, representing different motor variable combinations within and between their two tuft hemi-trees. By contrast, late bifurcating and smaller nexus PTNs showed synchronous tuft activation. Dendritic structure and dynamic recruitment of the N-methyl-d-aspartate (NMDA)-spiking mechanism explained the differential compartmentalization patterns. Our findings support a morphologically dependent framework for motor computations, in which independent amplification units can be combinatorically recruited to represent different motor sequences within the same tree.

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.

Dendritic Computing: Branching Deeper into Machine Learning

In this paper, we discuss the nonlinear computational power provided by dendrites in biological and artificial neurons. We start by briefly presenting biological evidence about the type of dendritic nonlinearities, respective plasticity rules and their effect on biological learning as assessed by computational models. Four major computational implications are identified as improved expressivity, more efficient use of resources, utilizing internal learning signals, and enabling continual learning. We then discuss examples of how dendritic computations have been used to solve real-world classification problems with performance reported on well known data sets used in machine learning. The works are categorized according to the three primary methods of plasticity used-structural plasticity, weight plasticity, or plasticity of synaptic delays. Finally, we show the recent trend of confluence between concepts of deep learning and dendritic computations and highlight some future research directions.

Single cortical neurons as deep artificial neural networks

Utilizing recent advances in machine learning, we introduce a systematic approach to characterize neurons' input/output (I/O) mapping complexity. Deep neural networks (DNNs) were trained to faithfully replicate the I/O function of various biophysical models of cortical neurons at millisecond (spiking) resolution. A temporally convolutional DNN with five to eight layers was required to capture the I/O mapping of a realistic model of a layer 5 cortical pyramidal cell (L5PC). This DNN generalized well when presented with inputs widely outside the training distribution. When NMDA receptors were removed, a much simpler network (fully connected neural network with one hidden layer) was sufficient to fit the model. Analysis of the DNNs' weight matrices revealed that synaptic integration in dendritic branches could be conceptualized as pattern matching from a set of spatiotemporal templates. This study provides a unified characterization of the computational complexity of single neurons and suggests that cortical networks therefore have a unique architecture, potentially supporting their computational power.

Parallel and Recurrent Cascade Models as a Unifying Force for Understanding Sub-cellular 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.

Rethinking Single Neuron Electrical Compartmentalization: Dendritic Contributions to Network Computation In Vivo

Decades of experimental and theoretical work support a now well-established theory that active dendritic processing contributes to the computational power of individual neurons. This theory is based on the high degree of electrical compartmentalization observed in the dendrites of single neurons in ex vivo preparations. Compartmentalization allows dendrites to conduct semi-independent operations on their inputs before final integration and output at the axon, producing a "network-in-a-neuron." However, recent in vivo functional imaging experiments in mouse cortex have reported surprisingly little evidence for strong dendritic compartmentalization. In this review, we contextualize these new findings and discuss their impact on the future of the field. Specifically, we consider how highly coordinated, and thus less compartmentalized, activity in soma and dendrites can contribute to cortical computations including nonlinear mixed selectivity, prediction/expectation, multiplexing, and credit assignment.

Data-driven reduction of dendritic morphologies with preserved dendro-somatic responses

Dendrites shape information flow in neurons. Yet, there is little consensus on the level of spatial complexity at which they operate. Through carefully chosen parameter fits, solvable in the least-squares sense, we obtain accurate reduced compartmental models at any level of complexity. We show that (back-propagating) action potentials, Ca²⁺ spikes, and N-methyl-D-aspartate spikes can all be reproduced with few compartments. We also investigate whether afferent spatial connectivity motifs admit simplification by ablating targeted branches and grouping affected synapses onto the next proximal dendrite. We find that voltage in the remaining branches is reproduced if temporal conductance fluctuations stay below a limit that depends on the average difference in input resistance between the ablated branches and the next proximal dendrite. Furthermore, our methodology fits reduced models directly from experimental data, without requiring morphological reconstructions. We provide software that automatizes the simplification, eliminating a common hurdle toward including dendritic computations in network models.

Illuminating dendritic function with computational models

Dendrites have always fascinated researchers: from the artistic drawings by Ramon y Cajal to the beautiful recordings of today, neuroscientists have been striving to unravel the mysteries of these structures. Theoretical work in the 1960s predicted important dendritic effects on neuronal processing, establishing computational modelling as a powerful technique for their investigation. Since then, modelling of dendrites has been instrumental in driving neuroscience research in a targeted manner, providing experimentally testable predictions that range from the subcellular level to the systems level, and their relevance extends to fields beyond neuroscience, such as machine learning and artificial intelligence. Validation of modelling predictions often requires - and drives - new technological advances, thus closing the loop with theory-driven experimentation that moves the field forward. This Review features the most important, to our understanding, contributions of modelling of dendritic computations, including those pending experimental verification, and highlights studies of successful interactions between the modelling and experimental neuroscience communities.

Stochastic point process models for multi-compartment dendritic-tree input-output transformations in spiking neurons

We extend stochastic point-process generalized linear models (PPGLMs) to the estimation of input-output transformations in dendritic trees and their contribution to the generation of soma action potentials in multi-compartmental models of single neurons. We used simulations of a model enthorinal cortex pyramidal neuron, with known dentritic tree and soma spatial organization, including active compartments defined in terms of standard cable and standard Hodgkin-Huxley equations. Each dendritic compartment (391 total) was endowed with either excitatory (E) or inhibitory (I) synaptic inputs whose strength was randomly specified. We examined the cases of both homogeneous and inhomogeneous spatial distributions for E and I synaptic inputs. The times for synaptic inputs followed a Poisson process with different mean rate regimes varying from 50 to 600 inputs/s. The soma membrane potential received also a background noise in the form of an Ornstein-Uhlenbeck process. Our main findings are: (1) Power spectra of soma membrane potentials revealed subthreshold resonances at ~40 Hz and ~80 Hz; (2) The contribution of different dendritic compartments, under the examined input ranges and spatial distributions, depended not only of the dendrite-soma path distance, but also on the number of compartments in the dendritic segment. (3) Estimated conditional intensity functions (CIFs) with PPGLMs successfully predicted spiking activity based on given E-I input times; area under ROC curves computed on test data varied from 0.8 - 0.95. (4) The CIF models identified compartments and regions receiving E-I synaptic inputs; Estimated temporal filters were consistent with dendrite-soma path distances and input weights. We expect this type of PPGLMs to contribute to data-driven identification of input-output transformations in dentritic trees based on single-neuron Ca²⁺ and voltage indicator imaging data.

Classes of dendritic information processing

Dendrites are much more than passive neuronal components. Mounting experimental evidence and decades of computational work have decisively shown that dendrites leverage a host of nonlinear biophysical phenomena and actively participate in sophisticated computations, at the level of the single neuron and at the level of the network. However, a coherent view of their processing power is still lacking and dendrites are largely neglected in neural network models. Here, we describe four classes of dendritic information processing and delineate their implications at the algorithmic level. We propose that beyond the well-known spatiotemporal filtering of their inputs, dendrites are capable of selecting, routing and multiplexing information. By separating dendritic processing from axonal outputs, neuron networks gain a degree of freedom with implications for perception and learning.

Global and Multiplexed Dendritic Computations under In Vivo-like Conditions

Dendrites integrate inputs nonlinearly, but it is unclear how these nonlinearities contribute to the overall input-output transformation of single neurons. We developed statistically principled methods using a hierarchical cascade of linear-nonlinear subunits (hLN) to model the dynamically evolving somatic response of neurons receiving complex, in vivo-like spatiotemporal synaptic input patterns. We used the hLN to predict the somatic membrane potential of an in vivo-validated detailed biophysical model of a L2/3 pyramidal cell. Linear input integration with a single global dendritic nonlinearity achieved above 90% prediction accuracy. A novel hLN motif, input multiplexing into parallel processing channels, could improve predictions as much as conventionally used additional layers of local nonlinearities. We obtained similar results in two other cell types. This approach provides a data-driven characterization of a key component of cortical circuit computations: the input-output transformation of neurons during in vivo-like conditions.

Linking demyelination to compound action potential dispersion with a spike-diffuse-spike approach

To establish and exploit novel biomarkers of demyelinating diseases requires a mechanistic understanding of axonal propagation. Here, we present a novel computational framework called the stochastic spike-diffuse-spike (SSDS) model for assessing the effects of demyelination on axonal transmission. It models transmission through nodal and internodal compartments with two types of operations: a stochastic integrate-and-fire operation captures nodal excitability and a linear filtering operation describes internodal propagation. The effects of demyelinated segments on the probability of transmission, transmission delay and spike time jitter are explored. We argue that demyelination-induced impedance mismatch prevents propagation mostly when the action potential leaves a demyelinated region, not when it enters a demyelinated region. In addition, we model sodium channel remodeling as a homeostatic control of nodal excitability. We find that the effects of mild demyelination on transmission probability and delay can be largely counterbalanced by an increase in excitability at the nodes surrounding the demyelination. The spike timing jitter, however, reflects the level of demyelination whether excitability is fixed or is allowed to change in compensation. This jitter can accumulate over long axons and leads to a broadening of the compound action potential, linking microscopic defects to a mesoscopic observable. Our findings articulate why action potential jitter and compound action potential dispersion can serve as potential markers of weak and sporadic demyelination.

Synaptic modifications driven by spike-timing-dependent plasticity in weakly coupled bursting neurons

In the course of development, sleep, or mental disorders, certain neurons in the brain display spontaneous spike-burst activity. The synaptic plasticity evoked by such activity is here studied in the presence of spike-timing-dependent plasticity (STDP). In two chemically coupled bursting model neurons, the spike-burst activity can translate the STDP related to pre- and postsynaptic spike activity into burst-timing-dependent plasticity (BTDP), based on the timing of bursts of pre- and postsynaptic neurons. The resulting BTDP exhibits exponential decays with the same time scales as those of STDP. In weakly coupled bursting neuron networks, the synaptic modification driven by the spike-burst activity obeys a power-law distribution. The model can also produce a power-law distribution of synaptic weights. Here, the considered bursting behavior is made of stereotypical groups of spikes, and bursting is evenly spaced by long intervals.

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.

Action potential initiation in a two-compartment model of pyramidal neuron mediated by dendritic Ca2+ spike

Dendritic Ca²⁺ spike endows cortical pyramidal cell with powerful ability of synaptic integration, which is critical for neuronal computation. Here we propose a two-compartment conductance-based model to investigate how the Ca²⁺ activity of apical dendrite participates in the action potential (AP) initiation to affect the firing properties of pyramidal neurons. We have shown that the apical input with sufficient intensity triggers a dendritic Ca²⁺ spike, which significantly boosts dendritic inputs as it propagates to soma. Such event instantaneously shifts the limit cycle attractor of the neuron and results in a burst of APs, which makes its firing rate reach a plateau steady-state level. Delivering current to two chambers simultaneously increases the level of neuronal excitability and decreases the threshold of input-output relation. Here the back-propagating APs facilitate the initiation of dendritic Ca²⁺ spike and evoke BAC firing. These findings indicate that the proposed model is capable of reproducing in vitro experimental observations. By determining spike initiating dynamics, we have provided a fundamental link between dendritic Ca²⁺ spike and output APs, which could contribute to mechanically interpreting how dendritic Ca²⁺ activity participates in the simple computations of pyramidal neuron.

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.