Inferring synaptic inputs from spikes with a conductance-based neural encoding model

Disparate nonlinear neural dynamics measured with different techniques in macaque and human V1

Diverse neuro-imaging techniques measure different aspects of neural responses with distinct spatial and temporal resolutions. Relating measured neural responses across different methods has been challenging. Here, we take a step towards overcoming this challenge, by comparing the nonlinearity of neural dynamics measured across methods. We used widefield voltage-sensitive dye imaging (VSDI) to measure neural population responses in macaque V1 to visual stimuli with a wide range of temporal waveforms. We found that stimulus-evoked VSDI responses are surprisingly near-additive in time. These results are qualitatively different from the strong sub-additive dynamics previously measured using fMRI and electrocorticography (ECoG) in human visual cortex with a similar set of stimuli. To test whether this discrepancy is specific to VSDI-a signal dominated by subthreshold neural activity, we repeated our measurements using widefield imaging of a genetically encoded calcium indicator (GcaMP6f)-a signal dominated by spiking activity, and found that GCaMP signals in macaque V1 are also near-additive. Therefore, the discrepancies in the extent of sub-additivity between the macaque and the human measurements are unlikely due to differences between sub- and supra-threshold neural responses. Finally, we use a simple yet flexible delayed normalization model to capture these different dynamics across measurements (with different model parameters). The model can potentially generalize to a broader set of stimuli, which aligns with previous suggestion that dynamic gain-control is a canonical computation contributing to neural processing in the brain.

Dynamic Nonlinear Spatial Integrations on Encoding Contrasting Stimuli of Tectal Neurons

Animals detect targets using a variety of visual cues, with the visual salience of these cues determining which environmental features receive priority attention and further processing. Surround modulation plays a crucial role in generating visual saliency, which has been extensively studied in avian tectal neurons. Recent work has reported that the suppression of tectal neurons induced by motion contrasting stimulus is stronger than that by luminance contrasting stimulus. However, the underlying mechanism remains poorly understood. In this study, we built a computational model (called Generalized Linear-Dynamic Modulation) which incorporates independent nonlinear tuning mechanisms for excitatory and inhibitory inputs. This model aims to describe how tectal neurons encode contrasting stimuli. The results showed that: (1) The dynamic nonlinear integration structure substantially improved the accuracy (significant difference (p < 0.001, paired t-test) in the goodness of fit between the two models) of the predicted responses to contrasting stimuli, verifying the nonlinear processing performed by tectal neurons. (2) The modulation difference between luminance and motion contrasting stimuli emerged from the predicted response by the full model but not by that with only excitatory synaptic input (spatial luminance: 89 ± 2.8% (GL_DM) vs. 87 ± 2.1% (GL_DMexc); motion contrasting stimuli: 87 ± 1.7% (GL_DM) vs. 83 ± 2.2% (GL_DMexc)). These results validate the proposed model and further suggest the role of dynamic nonlinear spatial integrations in contextual visual information processing, especially in spatial integration, which is important for object detection performed by birds.

Time-varying generalized linear models: characterizing and decoding neuronal dynamics in higher visual areas

To create a behaviorally relevant representation of the visual world, neurons in higher visual areas exhibit dynamic response changes to account for the time-varying interactions between external (e.g., visual input) and internal (e.g., reward value) factors. The resulting high-dimensional representational space poses challenges for precisely quantifying individual factors' contributions to the representation and readout of sensory information during a behavior. The widely used point process generalized linear model (GLM) approach provides a powerful framework for a quantitative description of neuronal processing as a function of various sensory and non-sensory inputs (encoding) as well as linking particular response components to particular behaviors (decoding), at the level of single trials and individual neurons. However, most existing variations of GLMs assume the neural systems to be time-invariant, making them inadequate for modeling nonstationary characteristics of neuronal sensitivity in higher visual areas. In this review, we summarize some of the existing GLM variations, with a focus on time-varying extensions. We highlight their applications to understanding neural representations in higher visual areas and decoding transient neuronal sensitivity as well as linking physiology to behavior through manipulation of model components. This time-varying class of statistical models provide valuable insights into the neural basis of various visual behaviors in higher visual areas and hold significant potential for uncovering the fundamental computational principles that govern neuronal processing underlying various behaviors in different regions of the brain.

Grid cells, border cells, and discrete complex analysis

We propose a mechanism enabling the appearance of border cells-neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity toward the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.

Grid Cells, Border Cells and Discrete Complex Analysis

We propose a mechanism enabling the appearance of border cells-neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity towards the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.

SpikeSEE: An energy-efficient dynamic scenes processing framework for retinal prostheses

Intelligent and low-power retinal prostheses are highly demanded in this era, where wearable and implantable devices are used for numerous healthcare applications. In this paper, we propose an energy-efficient dynamic scenes processing framework (SpikeSEE) that combines a spike representation encoding technique and a bio-inspired spiking recurrent neural network (SRNN) model to achieve intelligent processing and extreme low-power computation for retinal prostheses. The spike representation encoding technique could interpret dynamic scenes with sparse spike trains, decreasing the data volume. The SRNN model, inspired by the human retina's special structure and spike processing method, is adopted to predict the response of ganglion cells to dynamic scenes. Experimental results show that the Pearson correlation coefficient of the proposed SRNN model achieves 0.93, which outperforms the state-of-the-art processing framework for retinal prostheses. Thanks to the spike representation and SRNN processing, the model can extract visual features in a multiplication-free fashion. The framework achieves 8 times power reduction compared with the convolutional recurrent neural network (CRNN) processing-based framework. Our proposed SpikeSEE predicts the response of ganglion cells more accurately with lower energy consumption, which alleviates the precision and power issues of retinal prostheses and provides a potential solution for wearable or implantable prostheses.

Artificial intelligence techniques for retinal prostheses: a comprehensive review and future direction

Objective. Retinal prostheses are promising devices to restore vision for patients with severe age-related macular degeneration or retinitis pigmentosa disease. The visual processing mechanism embodied in retinal prostheses play an important role in the restoration effect. Its performance depends on our understanding of the retina's working mechanism and the evolvement of computer vision models. Recently, remarkable progress has been made in the field of processing algorithm for retinal prostheses where the new discovery of the retina's working principle and state-of-the-arts computer vision models are combined together.Approach. We investigated the related research on artificial intelligence techniques for retinal prostheses. The processing algorithm in these studies could be attributed to three types: computer vision-related methods, biophysical models, and deep learning models.Main results. In this review, we first illustrate the structure and function of the normal and degenerated retina, then demonstrate the vision rehabilitation mechanism of three representative retinal prostheses. It is necessary to summarize the computational frameworks abstracted from the normal retina. In addition, the development and feature of three types of different processing algorithms are summarized. Finally, we analyze the bottleneck in existing algorithms and propose our prospect about the future directions to improve the restoration effect.Significance. This review systematically summarizes existing processing models for predicting the response of the retina to external stimuli. What's more, the suggestions for future direction may inspire researchers in this field to design better algorithms for retinal prostheses.

Fitting of TC model according to key parameters affecting Parkinson's state based on improved particle swarm optimization algorithm

Biophysical models contain a large number of parameters, while the spiking characteristics of neurons are related to a few key parameters. For thalamic neurons, relay reliability is an important characteristic that affects Parkinson's state. This paper proposes a method to fit key parameters of the model based on the spiking characteristics of neurons, and improves the traditional particle swarm optimization algorithm. That is, a nonlinear concave function and a Logistic chaotic mapping are combined to adjust the inertia weight of particles to avoid the particle falling into a local optimum in the search process or appearing premature convergence. In this paper, three parameters that play an important role in Parkinson's state of the thalamic cell model are selected and fitted by the improved particle swarm optimization algorithm. Using the fitted parameters to reconstruct the neuron model can predict the spiking trajectories well, which verifies the effectiveness of the fitting method. By comparing the fitting results with other particle swarm optimization algorithms, it is shown that the proposed particle swarm optimization algorithm can better avoid local optima and converge to the optimal values quickly.

An in silico model for determining the influence of neuronal co-activity on rodent spatial behavior

BACKGROUND

Neuropsychological and neurophysiological analyses focus on understanding how neuronal activity and co-activity predict behavior. Experimental techniques allow for modulation of neuronal activity, but do not control neuronal ensemble spatiotemporal firing patterns, and there are few, if any, sophisticated in silico techniques which accurately reconstruct physiological neural spike trains and behavior using unit co-activity as an input parameter.

NEW METHOD

Our approach to simulation of neuronal spike trains is based on using state space modeling to estimate a weighted graph of interaction strengths between pairs of neurons along with separate estimations of spiking threshold voltage and neuronal membrane leakage. These parameters allow us to tune a biophysical model which is then employed to accurately reconstruct spike trains from freely behaving animals and then use these spike trains to estimate an animal's spatial behavior. The reconstructed spatial behavior allows us to confirm the same information is present in both the recorded and simulated spike trains.

RESULTS

Our method reconstructs spike trains (98 ± 0.0013% like original spike trains, mean ± SEM) and animal position (9.468 ± 0.240 cm, mean ± SEM) with high fidelity.

COMPARISON WITH EXISTING METHOD(S)

To our knowledge, this is the first method that uses empirically derived network connectivity to constrain biophysical parameters and predict spatial behavior. Together, these methods allow in silico quantification of the contribution of specific unit activity and co-activity to animal spatial behavior.

CONCLUSIONS

Our novel approach provides a flexible, robust in silico technique for determining the contribution of specific neuronal activity and co-activity to spatial behavior.

Dissecting cascade computational components in spiking neural networks

Finding out the physical structure of neuronal circuits that governs neuronal responses is an important goal for brain research. With fast advances for large-scale recording techniques, identification of a neuronal circuit with multiple neurons and stages or layers becomes possible and highly demanding. Although methods for mapping the connection structure of circuits have been greatly developed in recent years, they are mostly limited to simple scenarios of a few neurons in a pairwise fashion; and dissecting dynamical circuits, particularly mapping out a complete functional circuit that converges to a single neuron, is still a challenging question. Here, we show that a recent method, termed spike-triggered non-negative matrix factorization (STNMF), can address these issues. By simulating different scenarios of spiking neural networks with various connections between neurons and stages, we demonstrate that STNMF is a persuasive method to dissect functional connections within a circuit. Using spiking activities recorded at neurons of the output layer, STNMF can obtain a complete circuit consisting of all cascade computational components of presynaptic neurons, as well as their spiking activities. For simulated simple and complex cells of the primary visual cortex, STNMF allows us to dissect the pathway of visual computation. Taken together, these results suggest that STNMF could provide a useful approach for investigating neuronal systems leveraging recorded functional neuronal activity.

It is well known that the computation of neuronal circuits is carried out through the staged and cascade structure of different types of neurons. Nevertheless, the information, particularly sensory information, is processed in a network primarily with feedforward connections through different pathways. A peculiar example is the early visual system, where light is transcoded by the retinal cells, routed by the lateral geniculate nucleus, and reached the primary visual cortex. One meticulous interest in recent years is to map out these physical structures of neuronal pathways. However, most methods so far are limited to taking snapshots of a static view of connections between neurons. It remains unclear how to obtain a functional and dynamical neuronal circuit beyond the simple scenarios of a few randomly sampled neurons. Using simulated spiking neural networks of visual pathways with different scenarios of multiple stages, mixed cell types, and natural image stimuli, we demonstrate that a recent computational tool, named spike-triggered non-negative matrix factorization, can resolve these issues. It enables us to recover the entire structural components of neural networks underlying the computation, together with the functional components of each individual neuron. Utilizing it for complex cells of the primary visual cortex allows us to reveal every underpinning of the nonlinear computation. Our results, together with other recent experimental and computational efforts, show that it is possible to systematically dissect neural circuitry with detailed structural and functional components.

Efficient spline regression for neural spiking data

Point process generalized linear models (GLMs) provide a powerful tool for characterizing the coding properties of neural populations. Spline basis functions are often used in point process GLMs, when the relationship between the spiking and driving signals are nonlinear, but common choices for the structure of these spline bases often lead to loss of statistical power and numerical instability when the signals that influence spiking are bounded above or below. In particular, history dependent spike train models often suffer these issues at times immediately following a previous spike. This can make inferences related to refractoriness and bursting activity more challenging. Here, we propose a modified set of spline basis functions that assumes a flat derivative at the endpoints and show that this limits the uncertainty and numerical issues associated with cardinal splines. We illustrate the application of this modified basis to the problem of simultaneously estimating the place field and history dependent properties of a set of neurons from the CA1 region of rat hippocampus, and compare it with the other commonly used basis functions. We have made code available in MATLAB to implement spike train regression using these modified basis functions.

Nonlinear Spatial Integration Underlies the Diversity of Retinal Ganglion Cell Responses to Natural Images

How neurons encode natural stimuli is a fundamental question for sensory neuroscience. In the early visual system, standard encoding models assume that neurons linearly filter incoming stimuli through their receptive fields, but artificial stimuli, such as contrast-reversing gratings, often reveal nonlinear spatial processing. We investigated to what extent such nonlinear processing is relevant for the encoding of natural images in retinal ganglion cells in mice of either sex.

How neurons encode natural stimuli is a fundamental question for sensory neuroscience. In the early visual system, standard encoding models assume that neurons linearly filter incoming stimuli through their receptive fields, but artificial stimuli, such as contrast-reversing gratings, often reveal nonlinear spatial processing. We investigated to what extent such nonlinear processing is relevant for the encoding of natural images in retinal ganglion cells in mice of either sex. We found that standard linear receptive field models yielded good predictions of responses to flashed natural images for a subset of cells but failed to capture the spiking activity for many others. Cells with poor model performance displayed pronounced sensitivity to fine spatial contrast and local signal rectification as the dominant nonlinearity. By contrast, sensitivity to high-frequency contrast-reversing gratings, a classical test for nonlinear spatial integration, was not a good predictor of model performance and thus did not capture the variability of nonlinear spatial integration under natural images. In addition, we also observed a class of nonlinear ganglion cells with inverse tuning for spatial contrast, responding more strongly to spatially homogeneous than to spatially structured stimuli. These findings highlight the diversity of receptive field nonlinearities as a crucial component for understanding early sensory encoding in the context of natural stimuli.

SIGNIFICANCE STATEMENT Experiments with artificial visual stimuli have revealed that many types of retinal ganglion cells pool spatial input signals nonlinearly. However, it is still unclear how relevant this nonlinear spatial integration is when the input signals are natural images. Here we analyze retinal responses to natural scenes in large populations of mouse ganglion cells. We show that nonlinear spatial integration strongly influences responses to natural images for some ganglion cells, but not for others. Cells with nonlinear spatial integration were sensitive to spatial structure inside their receptive fields, and a small group of cells displayed a surprising sensitivity to spatially homogeneous stimuli. Traditional analyses with contrast-reversing gratings did not predict this variability of nonlinear spatial integration under natural images.

Poisson balanced spiking networks

An important problem in computational neuroscience is to understand how networks of spiking neurons can carry out various computations underlying behavior. Balanced spiking networks (BSNs) provide a powerful framework for implementing arbitrary linear dynamical systems in networks of integrate-and-fire neurons. However, the classic BSN model requires near-instantaneous transmission of spikes between neurons, which is biologically implausible. Introducing realistic synaptic delays leads to an pathological regime known as "ping-ponging", in which different populations spike maximally in alternating time bins, causing network output to overshoot the target solution. Here we document this phenomenon and provide a novel solution: we show that a network can have realistic synaptic delays while maintaining accuracy and stability if neurons are endowed with conditionally Poisson firing. Formally, we propose two alternate formulations of Poisson balanced spiking networks: (1) a "local" framework, which replaces the hard integrate-and-fire spiking rule within each neuron by a "soft" threshold function, such that firing probability grows as a smooth nonlinear function of membrane potential; and (2) a "population" framework, which reformulates the BSN objective function in terms of expected spike counts over the entire population. We show that both approaches offer improved robustness, allowing for accurate implementation of network dynamics with realistic synaptic delays between neurons. Both Poisson frameworks preserve the coding accuracy and robustness to neuron loss of the original model and, moreover, produce positive correlations between similarly tuned neurons, a feature of real neural populations that is not found in the deterministic BSN. This work unifies balanced spiking networks with Poisson generalized linear models and suggests several promising avenues for future research.

Capturing Multiple Timescales of Adaptation to Second-Order Statistics With Generalized Linear Models: Gain Scaling and Fractional Differentiation

Single neurons can dynamically change the gain of their spiking responses to take into account shifts in stimulus variance. Moreover, gain adaptation can occur across multiple timescales. Here, we examine the ability of a simple statistical model of spike trains, the generalized linear model (GLM), to account for these adaptive effects. The GLM describes spiking as a Poisson process whose rate depends on a linear combination of the stimulus and recent spike history. The GLM successfully replicates gain scaling observed in Hodgkin-Huxley simulations of cortical neurons that occurs when the ratio of spike-generating potassium and sodium conductances approaches one. Gain scaling in the GLM depends on the length and shape of the spike history filter. Additionally, the GLM captures adaptation that occurs over multiple timescales as a fractional derivative of the stimulus envelope, which has been observed in neurons that include long timescale afterhyperpolarization conductances. Fractional differentiation in GLMs requires long spike history that span several seconds. Together, these results demonstrate that the GLM provides a tractable statistical approach for examining single-neuron adaptive computations in response to changes in stimulus variance.

Accurate detection of spontaneous seizures using a generalized linear model with external validation

OBJECTIVE

Seizure detection is a major facet of electroencephalography (EEG) analysis in neurocritical care, epilepsy diagnosis and management, and the instantiation of novel therapies such as closed-loop stimulation or optogenetic control of seizures. It is also of increased importance in high-throughput, robust, and reproducible pre-clinical research. However, seizure detectors are not widely relied upon in either clinical or research settings due to limited validation. In this study, we create a high-performance seizure-detection approach, validated in multiple data sets, with the intention that such a system could be available to users for multiple purposes.

METHODS

We introduce a generalized linear model trained on 141 EEG signal features for classification of seizures in continuous EEG for two data sets. In the first (Focal Epilepsy) data set consisting of 16 rats with focal epilepsy, we collected 1012 spontaneous seizures over 3 months of 24/7 recording. We trained a generalized linear model on the 141 features representing 20 feature classes, including univariate and multivariate, linear and nonlinear, time, and frequency domains. We tested performance on multiple hold-out test data sets. We then used the trained model in a second (Multifocal Epilepsy) data set consisting of 96 rats with 2883 spontaneous multifocal seizures.

RESULTS

From the Focal Epilepsy data set, we built a pooled classifier with an Area Under the Receiver Operating Characteristic (AUROC) of 0.995 and leave-one-out classifiers with an AUROC of 0.962. We validated our method within the independently constructed Multifocal Epilepsy data set, resulting in a pooled AUROC of 0.963. We separately validated a model trained exclusively on the Focal Epilepsy data set and tested on the held-out Multifocal Epilepsy data set with an AUROC of 0.890. Latency to detection was under 5 seconds for over 80% of seizures and under 12 seconds for over 99% of seizures.

SIGNIFICANCE

This method achieves the highest performance published for seizure detection on multiple independent data sets. This method of seizure detection can be applied to automated EEG analysis pipelines as well as closed loop interventional approaches, and can be especially useful in the setting of research using animals in which there is an increased need for standardization and high-throughput analysis of large number of seizures.

Modeling the Short-Term Dynamics of in Vivo Excitatory Spike Transmission

Information transmission in neural networks is influenced by both short-term synaptic plasticity (STP) as well as nonsynaptic factors, such as after-hyperpolarization currents and changes in excitability. Although these effects have been widely characterized in vitro using intracellular recordings, how they interact in vivo is unclear. Here, we develop a statistical model of the short-term dynamics of spike transmission that aims to disentangle the contributions of synaptic and nonsynaptic effects based only on observed presynaptic and postsynaptic spiking. The model includes a dynamic functional connection with short-term plasticity as well as effects due to the recent history of postsynaptic spiking and slow changes in postsynaptic excitability. Using paired spike recordings, we find that the model accurately describes the short-term dynamics of in vivo spike transmission at a diverse set of identified and putative excitatory synapses, including a pair of connected neurons within thalamus in mouse, a thalamocortical connection in a female rabbit, and an auditory brainstem synapse in a female gerbil. We illustrate the utility of this modeling approach by showing how the spike transmission patterns captured by the model may be sufficient to account for stimulus-dependent differences in spike transmission in the auditory brainstem (endbulb of Held). Finally, we apply this model to large-scale multielectrode recordings to illustrate how such an approach has the potential to reveal cell type-specific differences in spike transmission in vivo Although STP parameters estimated from ongoing presynaptic and postsynaptic spiking are highly uncertain, our results are partially consistent with previous intracellular observations in these synapses.SIGNIFICANCE STATEMENT Although synaptic dynamics have been extensively studied and modeled using intracellular recordings of postsynaptic currents and potentials, inferring synaptic effects from extracellular spiking is challenging. Whether or not a synaptic current contributes to postsynaptic spiking depends not only on the amplitude of the current, but also on many other factors, including the activity of other, typically unobserved, synapses, the overall excitability of the postsynaptic neuron, and how recently the postsynaptic neuron has spiked. Here, we developed a model that, using only observations of presynaptic and postsynaptic spiking, aims to describe the dynamics of in vivo spike transmission by modeling both short-term synaptic plasticity (STP) and nonsynaptic effects. This approach may provide a novel description of fast, structured changes in spike transmission.

Dynamic input-dependent encoding of individual basal ganglia neurons

Computational models are crucial to studying the encoding of individual neurons. Static models are composed of a fixed set of parameters, thus resulting in static encoding properties that do not change under different inputs. Here, we challenge this basic concept which underlies these models. Using generalized linear models, we quantify the encoding and information processing properties of basal ganglia neurons recorded in-vitro. These properties are highly sensitive to the internal state of the neuron due to factors such as dependency on the baseline firing rate. Verification of these experimental results with simulations provides insights into the mechanisms underlying this input-dependent encoding. Thus, static models, which are not context dependent, represent only part of the neuronal encoding capabilities, and are not sufficient to represent the dynamics of a neuron over varying inputs. Input-dependent encoding is crucial for expanding our understanding of neuronal behavior in health and disease and underscores the need for a new generation of dynamic neuronal models.