Connectivity inference from neural recording data: Challenges, mathematical bases and research directions

Inference of monosynaptic connections from parallel spike trains: A review

This article presents a mini-review about the progress in inferring monosynaptic connections from spike trains of multiple neurons over the past twenty years. First, we explain a variety of meanings of "neuronal connectivity" in different research areas of neuroscience, such as structural connectivity, monosynaptic connectivity, and functional connectivity. Among these, we focus on the methods used to infer the monosynaptic connectivity from spike data. We then summarize the inference methods based on two main approaches, i.e., correlation-based and model-based approaches. Finally, we describe available source codes for connectivity inference and future challenges. Although inference will never be perfect, the accuracy of identifying the monosynaptic connections has improved dramatically in recent years due to continuous efforts.

Decoding neuronal networks: A Reservoir Computing approach for predicting connectivity and functionality

In this study, we address the challenge of analyzing electrophysiological measurements in neuronal networks. Our computational model, based on the Reservoir Computing Network (RCN) architecture, deciphers spatio-temporal data obtained from electrophysiological measurements of neuronal cultures. By reconstructing the network structure on a macroscopic scale, we reveal the connectivity between neuronal units. Notably, our model outperforms common methods such as Cross-Correlation, Transfer-Entropy, and a recently developed related algorithm in predicting the network's connectivity map. Furthermore, we experimentally validate its ability to forecast network responses to specific inputs, including localized optogenetic stimuli.

Network reconstruction may not mean dynamics prediction

With an increasing number of observations on the dynamics of many complex systems, it is necessary to reveal the underlying mechanisms behind these complex dynamics, which is fundamentally important in many scientific fields such as climate, financial, ecological, and neural systems. The underlying mechanisms are commonly encoded into network structures, e.g., capturing how constituents interact with each other to produce emergent behavior. Here, we address whether a good network reconstruction suggests a good dynamics prediction. The answer depends on the nature of the supplied (observed) dynamics sequences measured on the complex system. When the dynamics are not chaotic, network reconstruction implies dynamics prediction. In contrast, even if a network can be well reconstructed from the chaotic time series (chaos means that many unstable dynamics states coexist), the prediction of the future dynamics can become impossible as at some future point the prediction error will be amplified. This is explained using dynamical mean-field theory on a toy model of random recurrent neural networks.

The Functional Connectome Mediating Circadian Synchrony in the Suprachiasmatic Nucleus

Circadian rhythms in mammals arise from the spatiotemporal synchronization of ~20,000 neuronal clocks in the Suprachiasmatic Nucleus (SCN). While anatomical, molecular, and genetic approaches have revealed diverse cell types and signaling mechanisms, the network wiring that enables SCN cells to communicate and synchronize remains unclear. To overcome the challenges of revealing functional connectivity from fixed tissue, we developed MITE (Mutual Information & Transfer Entropy), an information theory approach that infers directed cell-cell connections with high fidelity. By analyzing 3447 hours of continuously recorded clock gene expression from 9011 cells in 17 mice, we found that the functional connectome of SCN was highly conserved bilaterally and across mice, sparse, and organized into a dorsomedial and a ventrolateral module. While most connections were local, we discovered long-range connections from ventral cells to cells in both the ventral and dorsal SCN. Based on their functional connectivity, SCN cells can be characterized as circadian signal generators, broadcasters, sinks, or bridges. For example, a subset of VIP neurons acts as hubs that generate circadian signals critical to synchronize daily rhythms across the SCN neural network. Simulations of the experimentally inferred SCN networks recapitulated the stereotypical dorsal-to-ventral wave of daily PER2 expression and ability to spontaneously synchronize, revealing that SCN emergent dynamics are sculpted by cell-cell connectivity. We conclude that MITE provides a powerful method to infer functional connectomes, and that the conserved architecture of cell-cell connections mediates circadian synchrony across space and time in the mammalian SCN.

Integrated information decomposition unveils major structural traits of in silico and in vitro neuronal networks

The properties of complex networked systems arise from the interplay between the dynamics of their elements and the underlying topology. Thus, to understand their behavior, it is crucial to convene as much information as possible about their topological organization. However, in large systems, such as neuronal networks, the reconstruction of such topology is usually carried out from the information encoded in the dynamics on the network, such as spike train time series, and by measuring the transfer entropy between system elements. The topological information recovered by these methods does not necessarily capture the connectivity layout, but rather the causal flow of information between elements. New theoretical frameworks, such as Integrated Information Decomposition (Φ-ID), allow one to explore the modes in which information can flow between parts of a system, opening a rich landscape of interactions between network topology, dynamics, and information. Here, we apply Φ-ID on in silico and in vitro data to decompose the usual transfer entropy measure into different modes of information transfer, namely, synergistic, redundant, or unique. We demonstrate that the unique information transfer is the most relevant measure to uncover structural topological details from network activity data, while redundant information only introduces residual information for this application. Although the retrieved network connectivity is still functional, it captures more details of the underlying structural topology by avoiding to take into account emergent high-order interactions and information redundancy between elements, which are important for the functional behavior, but mask the detection of direct simple interactions between elements constituted by the structural network topology.

Identifying Effective Connectivity between Stochastic Neurons with Variable-Length Memory Using a Transfer Entropy Rate Estimator

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X:=Xt:t∈Z and Y:=Yt:t∈Z, which take values in binary alphabets. When the bivariate process (X,Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test-no causal influence-requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons.

Ensemble learning and ground-truth validation of synaptic connectivity inferred from spike trains

Probing the architecture of neuronal circuits and the principles that underlie their functional organization remains an important challenge of modern neurosciences. This holds true, in particular, for the inference of neuronal connectivity from large-scale extracellular recordings. Despite the popularity of this approach and a number of elaborate methods to reconstruct networks, the degree to which synaptic connections can be reconstructed from spike-train recordings alone remains controversial. Here, we provide a framework to probe and compare connectivity inference algorithms, using a combination of synthetic ground-truth and in vitro data sets, where the connectivity labels were obtained from simultaneous high-density microelectrode array (HD-MEA) and patch-clamp recordings. We find that reconstruction performance critically depends on the regularity of the recorded spontaneous activity, i.e., their dynamical regime, the type of connectivity, and the amount of available spike-train data. We therefore introduce an ensemble artificial neural network (eANN) to improve connectivity inference. We train the eANN on the validated outputs of six established inference algorithms and show how it improves network reconstruction accuracy and robustness. Overall, the eANN demonstrated strong performance across different dynamical regimes, worked well on smaller datasets, and improved the detection of synaptic connectivity, especially inhibitory connections. Results indicated that the eANN also improved the topological characterization of neuronal networks. The presented methodology contributes to advancing the performance of inference algorithms and facilitates our understanding of how neuronal activity relates to synaptic connectivity.

The impact of input node placement in the controllability of structural brain networks

Network controllability refers to the ability to steer the state of a network towards a target state by driving certain nodes, known as input nodes. This concept can be applied to brain networks for studying brain function and its relation to the structure, which has numerous practical applications. Brain network controllability involves using external signals such as electrical stimulation to drive specific brain regions and navigate the neurophysiological activity level of the brain around the state space. Although controllability is mainly theoretical, the energy required for control is critical in real-world implementations. With a focus on the structural brain networks, this study explores the impact of white matter fiber architecture on the control energy in brain networks using the theory of how input node placement affects the LCC (the longest distance between inputs and other network nodes). Initially, we use a single input node as it is theoretically possible to control brain networks with just one input. We show that highly connected brain regions that lead to lower LCCs are more energy-efficient as a single input node. However, there may still be a need for a significant amount of control energy with one input, and achieving controllability with less energy could be of interest. We identify the minimum number of input nodes required to control brain networks with smaller LCCs, demonstrating that reducing the LCC can significantly decrease the control energy in brain networks. Our results show that relying solely on highly connected nodes is not effective in controlling brain networks with lower energy by using multiple inputs because of densely interconnected brain network hubs. Instead, a combination of low and high-degree nodes is necessary.

Analysis of Multiscale Corticomuscular Coupling Networks Based on Ordinal Patterns

The coupled analysis of corticomuscular function based on physiological electrical signals can identify differences in causal relationships between electroencephalogram (EEG) and surface electromyogram (sEMG) in different motor states. The existing methods are mainly devoted to the analysis in the same frequency band, while ignoring the cross-band coupling, which plays an active role in motion control. Considering the inherent multiscale characteristics of physiological signals, a method combining Ordinal Partition Transition Networks (OPTNs) and Multivariate Variational Modal Decomposition (MVMD) was proposed in this paper. The EEG and sEMG were firstly decomposed on a time-frequency scale using MVMD, and then the coupling strength was calculated by the OPTNs to construct a corticomuscular coupling network, which was analyzed with complex network parameters. Experimental data were obtained from a self-acquired dataset consisting of EEG and sEMG of 16 healthy subjects at different sizes of constant grip force. The results showed that the method was superior in representing changes in the causal link among multichannel signals characterized by different frequency bands and grip strength patterns. Complex information transfer between the cerebral cortex and the corresponding muscle groups during constant grip force output from the human upper limb. Furthermore, the sEMG of the flexor digitorum superficialis (FDS) in the low frequency band is the hub in the effective information transmission between the cortex and the muscle, while the importance of each frequency component in this transmission network becomes more dispersed as the grip strength grows, and the increase in coupling strength and node status is mainly in the γ band (30~60Hz). This study provides new ideas for deconstructing the mechanisms of neural control of muscle movements.

A recurrent Hopfield network for estimating meso-scale effective connectivity in MEG

The architecture of communication within the brain, represented by the human connectome, has gained a paramount role in the neuroscience community. Several features of this communication, e.g., the frequency content, spatial topology, and temporal dynamics are currently well established. However, identifying generative models providing the underlying patterns of inhibition/excitation is very challenging. To address this issue, we present a novel generative model to estimate large-scale effective connectivity from MEG. The dynamic evolution of this model is determined by a recurrent Hopfield neural network with asymmetric connections, and thus denoted Recurrent Hopfield Mass Model (RHoMM). Since RHoMM must be applied to binary neurons, it is suitable for analyzing Band Limited Power (BLP) dynamics following a binarization process. We trained RHoMM to predict the MEG dynamics through a gradient descent minimization and we validated it in two steps. First, we showed a significant agreement between the similarity of the effective connectivity patterns and that of the interregional BLP correlation, demonstrating RHoMM's ability to capture individual variability of BLP dynamics. Second, we showed that the simulated BLP correlation connectomes, obtained from RHoMM evolutions of BLP, preserved some important topological features, e.g, the centrality of the real data, assuring the reliability of RHoMM. Compared to other biophysical models, RHoMM is based on recurrent Hopfield neural networks, thus, it has the advantage of being data-driven, less demanding in terms of hyperparameters and scalable to encompass large-scale system interactions. These features are promising for investigating the dynamics of inhibition/excitation at different spatial scales.

Efficient inference of synaptic plasticity rule with Gaussian process regression

Finding the form of synaptic plasticity is critical to understanding its functions underlying learning and memory. We investigated an efficient method to infer synaptic plasticity rules in various experimental settings. We considered biologically plausible models fitting a wide range of in-vitro studies and examined the recovery of their firing-rate dependence from sparse and noisy data. Among the methods assuming low-rankness or smoothness of plasticity rules, Gaussian process regression (GPR), a nonparametric Bayesian approach, performs the best. Under the conditions measuring changes in synaptic weights directly or measuring changes in neural activities as indirect observables of synaptic plasticity, which leads to different inference problems, GPR performs well. Also, GPR could simultaneously recover multiple plasticity rules and robustly perform under various plasticity rules and noise levels. Such flexibility and efficiency, particularly at the low sampling regime, make GPR suitable for recent experimental developments and inferring a broader class of plasticity models.

Reconstruction of sparse recurrent connectivity and inputs from the nonlinear dynamics of neuronal networks

Reconstructing the recurrent structural connectivity of neuronal networks is a challenge crucial to address in characterizing neuronal computations. While directly measuring the detailed connectivity structure is generally prohibitive for large networks, we develop a novel framework for reverse-engineering large-scale recurrent network connectivity matrices from neuronal dynamics by utilizing the widespread sparsity of neuronal connections. We derive a linear input-output mapping that underlies the irregular dynamics of a model network composed of both excitatory and inhibitory integrate-and-fire neurons with pulse coupling, thereby relating network inputs to evoked neuronal activity. Using this embedded mapping and experimentally feasible measurements of the firing rate as well as voltage dynamics in response to a relatively small ensemble of random input stimuli, we efficiently reconstruct the recurrent network connectivity via compressive sensing techniques. Through analogous analysis, we then recover high dimensional natural stimuli from evoked neuronal network dynamics over a short time horizon. This work provides a generalizable methodology for rapidly recovering sparse neuronal network data and underlines the natural role of sparsity in facilitating the efficient encoding of network data in neuronal dynamics.

In vivo direct imaging of neuronal activity at high temporospatial resolution

There has been a long-standing demand for noninvasive neuroimaging methods that can detect neuronal activity at both high temporal and high spatial resolution. We present a two-dimensional fast line-scan approach that enables direct imaging of neuronal activity with millisecond precision while retaining the high spatial resolution of magnetic resonance imaging (MRI). This approach was demonstrated through in vivo mouse brain imaging at 9.4 tesla during electrical whisker-pad stimulation. In vivo spike recording and optogenetics confirmed the high correlation of the observed MRI signal with neural activity. It also captured the sequential and laminar-specific propagation of neuronal activity along the thalamocortical pathway. This high-resolution, direct imaging of neuronal activity will open up new avenues in brain science by providing a deeper understanding of the brain's functional organization, including the temporospatial dynamics of neural networks.

Deep learning for neural decoding in motor cortex

Objective. Neural decoding is an important tool in neural engineering and neural data analysis. Of various machine learning algorithms adopted for neural decoding, the recently introduced deep learning is promising to excel. Therefore, we sought to apply deep learning to decode movement trajectories from the activity of motor cortical neurons.Approach. In this paper, we assessed the performance of deep learning methods in three different decoding schemes, concurrent, time-delay, and spatiotemporal. In the concurrent decoding scheme where the input to the network is the neural activity coincidental to the movement, deep learning networks including artificial neural network (ANN) and long-short term memory (LSTM) were applied to decode movement and compared with traditional machine learning algorithms. Both ANN and LSTM were further evaluated in the time-delay decoding scheme in which temporal delays are allowed between neural signals and movements. Lastly, in the spatiotemporal decoding scheme, we trained convolutional neural network (CNN) to extract movement information from images representing the spatial arrangement of neurons, their activity, and connectomes (i.e. the relative strengths of connectivity between neurons) and combined CNN and ANN to develop a hybrid spatiotemporal network. To reveal the input features of the CNN in the hybrid network that deep learning discovered for movement decoding, we performed a sensitivity analysis and identified specific regions in the spatial domain.Main results. Deep learning networks (ANN and LSTM) outperformed traditional machine learning algorithms in the concurrent decoding scheme. The results of ANN and LSTM in the time-delay decoding scheme showed that including neural data from time points preceding movement enabled decoders to perform more robustly when the temporal relationship between the neural activity and movement dynamically changes over time. In the spatiotemporal decoding scheme, the hybrid spatiotemporal network containing the concurrent ANN decoder outperformed single-network concurrent decoders.Significance. Taken together, our study demonstrates that deep learning could become a robust and effective method for the neural decoding of behavior.

Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes

Thanks to technological advances leading to near-continuous time observations, emerging multivariate point process data offer new opportunities for causal discovery. However, a key obstacle in achieving this goal is that many relevant processes may not be observed in practice. Naïve estimation approaches that ignore these hidden variables can generate misleading results because of the unadjusted confounding. To plug this gap, we propose a deconfounding procedure to estimate high-dimensional point process networks with only a subset of the nodes being observed. Our method allows flexible connections between the observed and unobserved processes. It also allows the number of unobserved processes to be unknown and potentially larger than the number of observed nodes. Theoretical analyses and numerical studies highlight the advantages of the proposed method in identifying causal interactions among the observed processes.

FARCI: Fast and Robust Connectome Inference

The inference of neuronal connectome from large-scale neuronal activity recordings, such as two-photon Calcium imaging, represents an active area of research in computational neuroscience. In this work, we developed FARCI (Fast and Robust Connectome Inference), a MATLAB package for neuronal connectome inference from high-dimensional two-photon Calcium fluorescence data. We employed partial correlations as a measure of the functional association strength between pairs of neurons to reconstruct a neuronal connectome. We demonstrated using in silico datasets from the Neural Connectomics Challenge (NCC) and those generated using the state-of-the-art simulator of Neural Anatomy and Optimal Microscopy (NAOMi) that FARCI provides an accurate connectome and its performance is robust to network sizes, missing neurons, and noise levels. Moreover, FARCI is computationally efficient and highly scalable to large networks. In comparison with the best performing connectome inference algorithm in the NCC, Generalized Transfer Entropy (GTE), and Fluorescence Single Neuron and Network Analysis Package (FluoroSNNAP), FARCI produces more accurate networks over different network sizes, while providing significantly better computational speed and scaling.

Minimum spanning tree based graph neural network for emotion classification using EEG

Emotion classification based on neurophysiology signals has been a challenging issue in the literature. Recent neuroscience findings suggest that brain network structure underlying the different emotions provides a window in understanding human affection. In this paper, we propose a novel method to capture the distinct minimum spanning tree (MST) topology underpinning the different emotions. Specifically, we propose a hierarchical aggregation-based graph neural network to investigate the MST structure in emotion recognition. Extensive experiments on the public available DEAP dataset demonstrate the superior performance of the model in emotion classification as compared to existing methods. In addition, the results show that the theta, lower beta and gamma frequency band network information are more sensitive to emotions, suggesting a multi-frequency interaction in emotion processing.

Super-Selective Reconstruction of Causal and Direct Connectivity With Application to in vitro iPSC Neuronal Networks

Despite advancements in the development of cell-based in-vitro neuronal network models, the lack of appropriate computational tools limits their analyses. Methods aimed at deciphering the effective connections between neurons from extracellular spike recordings would increase utility of in vitro local neural circuits, especially for studies of human neural development and disease based on induced pluripotent stem cells (hiPSC). Current techniques allow statistical inference of functional couplings in the network but are fundamentally unable to correctly identify indirect and apparent connections between neurons, generating redundant maps with limited ability to model the causal dynamics of the network. In this paper, we describe a novel mathematically rigorous, model-free method to map effective-direct and causal-connectivity of neuronal networks from multi-electrode array data. The inference algorithm uses a combination of statistical and deterministic indicators which, first, enables identification of all existing functional links in the network and then reconstructs the directed and causal connection diagram via a super-selective rule enabling highly accurate classification of direct, indirect, and apparent links. Our method can be generally applied to the functional characterization of any in vitro neuronal networks. Here, we show that, given its accuracy, it can offer important insights into the functional development of in vitro hiPSC-derived neuronal cultures.

Estimating Transfer Entropy in Continuous Time Between Neural Spike Trains or Other Event-Based Data

Transfer entropy (TE) is a widely used measure of directed information flows in a number of domains including neuroscience. Many real-world time series for which we are interested in information flows come in the form of (near) instantaneous events occurring over time. Examples include the spiking of biological neurons, trades on stock markets and posts to social media, amongst myriad other systems involving events in continuous time throughout the natural and social sciences. However, there exist severe limitations to the current approach to TE estimation on such event-based data via discretising the time series into time bins: it is not consistent, has high bias, converges slowly and cannot simultaneously capture relationships that occur with very fine time precision as well as those that occur over long time intervals. Building on recent work which derived a theoretical framework for TE in continuous time, we present an estimation framework for TE on event-based data and develop a k-nearest-neighbours estimator within this framework. This estimator is provably consistent, has favourable bias properties and converges orders of magnitude more quickly than the current state-of-the-art in discrete-time estimation on synthetic examples. We demonstrate failures of the traditionally-used source-time-shift method for null surrogate generation. In order to overcome these failures, we develop a local permutation scheme for generating surrogate time series conforming to the appropriate null hypothesis in order to test for the statistical significance of the TE and, as such, test for the conditional independence between the history of one point process and the updates of another. Our approach is shown to be capable of correctly rejecting or accepting the null hypothesis of conditional independence even in the presence of strong pairwise time-directed correlations. This capacity to accurately test for conditional independence is further demonstrated on models of a spiking neural circuit inspired by the pyloric circuit of the crustacean stomatogastric ganglion, succeeding where previous related estimators have failed.

The amygdala instructs insular feedback for affective learning

Affective responses depend on assigning value to environmental predictors of threat or reward. Neuroanatomically, this affective value is encoded at both cortical and subcortical levels. However, the purpose of this distributed representation across functional hierarchies remains unclear. Using fMRI in mice, we mapped a discrete cortico-limbic loop between insular cortex (IC), central amygdala (CE), and nucleus basalis of Meynert (NBM), which decomposes the affective value of a conditioned stimulus (CS) into its salience and valence components. In IC, learning integrated unconditioned stimulus (US)-evoked bodily states into CS valence. In turn, CS salience in the CE recruited these CS representations bottom-up via the cholinergic NBM. This way, the CE incorporated interoceptive feedback from IC to improve discrimination of CS valence. Consequently, opto-/chemogenetic uncoupling of hierarchical information flow disrupted affective learning and conditioned responding. Dysfunctional interactions in the IC↔CE/NBM network may underlie intolerance to uncertainty, observed in autism and related psychiatric conditions.

Optimal Interplay between Synaptic Strengths and Network Structure Enhances Activity Fluctuations and Information Propagation in Hierarchical Modular Networks

In network models of spiking neurons, the joint impact of network structure and synaptic parameters on activity propagation is still an open problem. Here, we use an information-theoretical approach to investigate activity propagation in spiking networks with a hierarchical modular topology. We observe that optimized pairwise information propagation emerges due to the increase of either (i) the global synaptic strength parameter or (ii) the number of modules in the network, while the network size remains constant. At the population level, information propagation of activity among adjacent modules is enhanced as the number of modules increases until a maximum value is reached and then decreases, showing that there is an optimal interplay between synaptic strength and modularity for population information flow. This is in contrast to information propagation evaluated among pairs of neurons, which attains maximum value at the maximum values of these two parameter ranges. By examining the network behavior under the increase of synaptic strength and the number of modules, we find that these increases are associated with two different effects: (i) the increase of autocorrelations among individual neurons and (ii) the increase of cross-correlations among pairs of neurons. The second effect is associated with better information propagation in the network. Our results suggest roles that link topological features and synaptic strength levels to the transmission of information in cortical networks.

Computationally going where experiments cannot: a dynamical assessment of dendritic ion channel currents during in vivo-like states

Background: Despite technological advances, how specific cell types are involved in brain function remains shrouded in mystery. Further, little is known about the contribution of different ion channel currents to cell excitability across different neuronal subtypes and their dendritic compartments in vivo. The picture that we do have is largely based on somatic recordings performed in vitro. Uncovering dendritic ion channel current contributions in neuron subtypes that represent a minority of the neuronal population is not currently a feasible task using purely experimental means.

Methods: We employ two morphologically-detailed multi-compartment models of a specific type of inhibitory interneuron, the oriens lacunosum moleculare (OLM) cell. The OLM cell is a well-studied cell type in CA1 hippocampus that is important in gating sensory and contextual information. We create in vivo-like states for these cellular models by including levels of synaptic bombardment that would occur in vivo. Using visualization tools and analyses we assess the ion channel current contribution profile across the different somatic and dendritic compartments of the models.

Results: We identify changes in dendritic excitability, ion channel current contributions and co-activation patterns between in vitro and in vivo-like states. Primarily, we find that the relative timing between ion channel currents are mostly invariant between states, but exhibit changes in magnitudes and decreased propagation across dendritic compartments. We also find enhanced dendritic hyperpolarization-activated cyclic nucleotide-gated channel (h-channel) activation during in vivo-like states, which suggests that dendritically located h-channels are functionally important in altering signal propagation in the behaving animal.

Conclusions: Overall, we have demonstrated, using computational modelling, the dynamical changes that can occur to ion channel mechanisms governing neuronal spiking. Simultaneous access to dendritic compartments during simulated in vivo states shows that the magnitudes of some ion channel current contributions are differentially altered during in vivo-like states relative to in vitro.

Pre-Synaptic Pool Modification (PSPM): A supervised learning procedure for recurrent spiking neural networks

Learning synaptic weights of spiking neural network (SNN) models that can reproduce target spike trains from provided neural firing data is a central problem in computational neuroscience and spike-based computing. The discovery of the optimal weight values can be posed as a supervised learning task wherein the weights of the model network are chosen to maximize the similarity between the target spike trains and the model outputs. It is still largely unknown whether optimizing spike train similarity of highly recurrent SNNs produces weight matrices similar to those of the ground truth model. To this end, we propose flexible heuristic supervised learning rules, termed Pre-Synaptic Pool Modification (PSPM), that rely on stochastic weight updates in order to produce spikes within a short window of the desired times and eliminate spikes outside of this window. PSPM improves spike train similarity for all-to-all SNNs and makes no assumption about the post-synaptic potential of the neurons or the structure of the network since no gradients are required. We test whether optimizing for spike train similarity entails the discovery of accurate weights and explore the relative contributions of local and homeostatic weight updates. Although PSPM improves similarity between spike trains, the learned weights often differ from the weights of the ground truth model, implying that connectome inference from spike data may require additional constraints on connectivity statistics. We also find that spike train similarity is sensitive to local updates, but other measures of network activity such as avalanche distributions, can be learned through synaptic homeostasis.

Inference of synaptic connectivity and external variability in neural microcircuits

A major goal in neuroscience is to estimate neural connectivity from large scale extracellular recordings of neural activity in vivo. This is challenging in part because any such activity is modulated by the unmeasured external synaptic input to the network, known as the common input problem. Many different measures of functional connectivity have been proposed in the literature, but their direct relationship to synaptic connectivity is often assumed or ignored. For in vivo data, measurements of this relationship would require a knowledge of ground truth connectivity, which is nearly always unavailable. Instead, many studies use in silico simulations as benchmarks for investigation, but such approaches necessarily rely upon a variety of simplifying assumptions about the simulated network and can depend on numerous simulation parameters. We combine neuronal network simulations, mathematical analysis, and calcium imaging data to address the question of when and how functional connectivity, synaptic connectivity, and latent external input variability can be untangled. We show numerically and analytically that, even though the precision matrix of recorded spiking activity does not uniquely determine synaptic connectivity, it is in practice often closely related to synaptic connectivity. This relation becomes more pronounced when the spatial structure of neuronal variability is jointly considered.

Dynamic Tracking Algorithm for Time-Varying Neuronal Network Connectivity using Wide-Field Optical Image Video Sequences

Propagation of signals between neurons and brain regions provides information about the functional properties of neural networks, and thus information transfer. Advances in optical imaging and statistical analyses of acquired optical signals have yielded various metrics for inferring neural connectivity, and hence for mapping signal intercorrelation. However, a single coefficient is traditionally derived to classify the connection strength between two cells, ignoring the fact that neural systems are inherently time-variant systems. To overcome these limitations, we utilized a time-varying Pearson's correlation coefficient, spike-sorting, wavelet transform, and wavelet coherence of calcium transients from DIV 12-15 hippocampal neurons from GCaMP6s mice after applying various concentrations of glutamate. Results provide a comprehensive overview of resulting firing patterns, network connectivity, signal directionality, and network properties. Together, these metrics provide a more comprehensive and robust method of analyzing transient neural signals, and enable future investigations for tracking the effects of different stimuli on network properties.

Studying complex brain dynamics using Drosophila

The field has successfully used Drosophila genetic tools to identify neurons and sub-circuits important for specific functions. However, for an organism with complex and changing internal states to succeed in a complex and changing natural environment, many neurons and circuits need to interact dynamically. Drosophila's many advantages, combined with new imaging tools, offer unique opportunities to study how the brain functions as a complex dynamical system. We give an overview of complex activity patterns and how they can be observed, as well as modeling strategies, adding proof of principle in some cases.