Inferring synaptic structure in presence of neural interaction time scales

Simulations approaching data: cortical slow waves in inferred models of the whole hemisphere of mouse

The development of novel techniques to record wide-field brain activity enables estimation of data-driven models from thousands of recording channels and hence across large regions of cortex. These in turn improve our understanding of the modulation of brain states and the richness of traveling waves dynamics. Here, we infer data-driven models from high-resolution in-vivo recordings of mouse brain obtained from wide-field calcium imaging. We then assimilate experimental and simulated data through the characterization of the spatio-temporal features of cortical waves in experimental recordings. Inference is built in two steps: an inner loop that optimizes a mean-field model by likelihood maximization, and an outer loop that optimizes a periodic neuro-modulation via direct comparison of observables that characterize cortical slow waves. The model reproduces most of the features of the non-stationary and non-linear dynamics present in the high-resolution in-vivo recordings of the mouse brain. The proposed approach offers new methods of characterizing and understanding cortical waves for experimental and computational neuroscientists.

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.

Target spike patterns enable efficient and biologically plausible learning for complex temporal tasks

Recurrent spiking neural networks (RSNN) in the brain learn to perform a wide range of perceptual, cognitive and motor tasks very efficiently in terms of energy consumption and their training requires very few examples. This motivates the search for biologically inspired learning rules for RSNNs, aiming to improve our understanding of brain computation and the efficiency of artificial intelligence. Several spiking models and learning rules have been proposed, but it remains a challenge to design RSNNs whose learning relies on biologically plausible mechanisms and are capable of solving complex temporal tasks. In this paper, we derive a learning rule, local to the synapse, from a simple mathematical principle, the maximization of the likelihood for the network to solve a specific task. We propose a novel target-based learning scheme in which the learning rule derived from likelihood maximization is used to mimic a specific spatio-temporal spike pattern that encodes the solution to complex temporal tasks. This method makes the learning extremely rapid and precise, outperforming state of the art algorithms for RSNNs. While error-based approaches, (e.g. e-prop) trial after trial optimize the internal sequence of spikes in order to progressively minimize the MSE we assume that a signal randomly projected from an external origin (e.g. from other brain areas) directly defines the target sequence. This facilitates the learning procedure since the network is trained from the beginning to reproduce the desired internal sequence. We propose two versions of our learning rule: spike-dependent and voltage-dependent. We find that the latter provides remarkable benefits in terms of learning speed and robustness to noise. We demonstrate the capacity of our model to tackle several problems like learning multidimensional trajectories and solving the classical temporal XOR benchmark. Finally, we show that an online approximation of the gradient ascent, in addition to guaranteeing complete locality in time and space, allows learning after very few presentations of the target output. Our model can be applied to different types of biological neurons. The analytically derived plasticity learning rule is specific to each neuron model and can produce a theoretical prediction for experimental validation.

Inferring Neuronal Couplings From Spiking Data Using a Systematic Procedure With a Statistical Criterion

Recent remarkable advances in experimental techniques have provided a background for inferring neuronal couplings from point process data that include a great number of neurons. Here, we propose a systematic procedure for pre- and postprocessing generic point process data in an objective manner to handle data in the framework of a binary simple statistical model, the Ising or generalized McCulloch-Pitts model. The procedure has two steps: (1) determining time bin size for transforming the point process data into discrete-time binary data and (2) screening relevant couplings from the estimated couplings. For the first step, we decide the optimal time bin size by introducing the null hypothesis that all neurons would fire independently, then choosing a time bin size so that the null hypothesis is rejected with the strict criteria. The likelihood associated with the null hypothesis is analytically evaluated and used for the rejection process. For the second postprocessing step, after a certain estimator of coupling is obtained based on the preprocessed data set (any estimator can be used with the proposed procedure), the estimate is compared with many other estimates derived from data sets obtained by randomizing the original data set in the time direction. We accept the original estimate as relevant only if its absolute value is sufficiently larger than those of randomized data sets. These manipulations suppress false positive couplings induced by statistical noise. We apply this inference procedure to spiking data from synthetic and in vitro neuronal networks. The results show that the proposed procedure identifies the presence or absence of synaptic couplings fairly well, including their signs, for the synthetic and experimental data. In particular, the results support that we can infer the physical connections of underlying systems in favorable situations, even when using a simple statistical model.

Altered Neocortical Dynamics in a Mouse Model of Williams-Beuren Syndrome

Williams-Beuren syndrome (WBS) is a rare neurodevelopmental disorder characterized by moderate intellectual disability and learning difficulties alongside behavioral abnormalities such as hypersociability. Several structural and functional brain alterations are characteristic of this syndrome, as well as disturbed sleep and sleeping patterns. However, the detailed physiological mechanisms underlying WBS are mostly unknown. Here, we characterized the cortical dynamics in a mouse model of WBS previously reported to replicate most of the behavioral alterations described in humans. We recorded the laminar local field potential generated in the frontal cortex during deep anesthesia and characterized the properties of the emergent slow oscillation activity. Moreover, we performed micro-electrocorticogram recordings using multielectrode arrays covering the cortical surface of one hemisphere. We found significant differences between the cortical emergent activity and functional connectivity between wild-type mice and WBS model mice. Slow oscillations displayed Up states with diminished firing rate and lower high-frequency content in the gamma range. Lower firing rates were also recorded in the awake WBS animals while performing a marble burying task and could be associated with the decreased spine density and thus synaptic connectivity in this cortical area. We also found an overall increase in functional connectivity between brain areas, reflected in lower clustering and abnormally high integration, especially in the gamma range. These results expand previous findings in humans, suggesting that the cognitive deficits characterizing WBS might be associated with reduced excitability, plus an imbalance in the capacity to functionally integrate and segregate information.

Inference of the kinetic Ising model with heterogeneous missing data

We consider the problem of inferring a causality structure from multiple binary time series by using the kinetic Ising model in datasets where a fraction of observations is missing. Inspired by recent work on mean field methods for the inference of the model with hidden spins, we develop a pseudo-expectation-maximization algorithm that is able to work even in conditions of severe data sparsity. The methodology relies on the Martin-Siggia-Rose path integral method with second-order saddle-point solution to make it possible to approximate the log-likelihood in polynomial time, giving as output an estimate of the couplings matrix and of the missing observations. We also propose a recursive version of the algorithm, where at every iteration some missing values are substituted by their maximum-likelihood estimate, showing that the method can be used together with sparsification schemes such as lasso regularization or decimation. We test the performance of the algorithm on synthetic data and find interesting properties regarding the dependency on heterogeneity of the observation frequency of spins and when some of the hypotheses that are necessary to the saddle-point approximation are violated, such as the small couplings limit and the assumption of statistical independence between couplings.

Spontaneous activity emerging from an inferred network model captures complex spatio-temporal dynamics of spike data

Inference methods are widely used to recover effective models from observed data. However, few studies attempted to investigate the dynamics of inferred models in neuroscience, and none, to our knowledge, at the network level. We introduce a principled modification of a widely used generalized linear model (GLM), and learn its structural and dynamic parameters from in-vitro spike data. The spontaneous activity of the new model captures prominent features of the non-stationary and non-linear dynamics displayed by the biological network, where the reference GLM largely fails, and also reflects fine-grained spatio-temporal dynamical features. Two ingredients were key for success. The first is a saturating transfer function: beyond its biological plausibility, it limits the neuron's information transfer, improving robustness against endogenous and external noise. The second is a super-Poisson spikes generative mechanism; it accounts for the undersampling of the network, and allows the model neuron to flexibly incorporate the observed activity fluctuations.

Maximum-entropy models reveal the excitatory and inhibitory correlation structures in cortical neuronal activity

Maximum entropy models can be inferred from large datasets to uncover how collective dynamics emerge from local interactions. Here, such models are employed to investigate neurons recorded by multi-electrode arrays in the human and monkey cortex. Taking advantage of the separation of excitatory and inhibitory neuron types, we construct a model including this distinction. This approach allows us to shed light on differences between excitatory and inhibitory activity across different brain states such as wakefulness and deep sleep, in agreement with previous findings. Additionally, maximum entropy models can also unveil novel features of neuronal interactions, which are found to be dominated by pairwise interactions during wakefulness, but are population-wide during deep sleep. Overall, we demonstrate that maximum entropy models can be useful to analyze datasets with classified neuron types and to reveal the respective roles of excitatory and inhibitory neurons in organizing coherent dynamics in the cerebral cortex.

Differential Covariance: A New Class of Methods to Estimate Sparse Connectivity from Neural Recordings

With our ability to record more neurons simultaneously, making sense of these data is a challenge. Functional connectivity is one popular way to study the relationship of multiple neural signals. Correlation-based methods are a set of currently well-used techniques for functional connectivity estimation. However, due to explaining away and unobserved common inputs (Stevenson, Rebesco, Miller, & Körding, 2008 ), they produce spurious connections. The general linear model (GLM), which models spike trains as Poisson processes (Okatan, Wilson, & Brown, 2005 ; Truccolo, Eden, Fellows, Donoghue, & Brown, 2005 ; Pillow et al., 2008 ), avoids these confounds. We develop here a new class of methods by using differential signals based on simulated intracellular voltage recordings. It is equivalent to a regularized AR(2) model. We also expand the method to simulated local field potential recordings and calcium imaging. In all of our simulated data, the differential covariance-based methods achieved performance better than or similar to the GLM method and required fewer data samples. This new class of methods provides alternative ways to analyze neural signals.

Density-based clustering: A 'landscape view' of multi-channel neural data for inference and dynamic complexity analysis

Two, partially interwoven, hot topics in the analysis and statistical modeling of neural data, are the development of efficient and informative representations of the time series derived from multiple neural recordings, and the extraction of information about the connectivity structure of the underlying neural network from the recorded neural activities. In the present paper we show that state-space clustering can provide an easy and effective option for reducing the dimensionality of multiple neural time series, that it can improve inference of synaptic couplings from neural activities, and that it can also allow the construction of a compact representation of the multi-dimensional dynamics, that easily lends itself to complexity measures. We apply a variant of the ‘mean-shift’ algorithm to perform state-space clustering, and validate it on an Hopfield network in the glassy phase, in which metastable states are largely uncorrelated from memories embedded in the synaptic matrix. In this context, we show that the neural states identified as clusters’ centroids offer a parsimonious parametrization of the synaptic matrix, which allows a significant improvement in inferring the synaptic couplings from the neural activities. Moving to the more realistic case of a multi-modular spiking network, with spike-frequency adaptation inducing history-dependent effects, we propose a procedure inspired by Boltzmann learning, but extending its domain of application, to learn inter-module synaptic couplings so that the spiking network reproduces a prescribed pattern of spatial correlations; we then illustrate, in the spiking network, how clustering is effective in extracting relevant features of the network’s state-space landscape. Finally, we show that the knowledge of the cluster structure allows casting the multi-dimensional neural dynamics in the form of a symbolic dynamics of transitions between clusters; as an illustration of the potential of such reduction, we define and analyze a measure of complexity of the neural time series.

Correlations and functional connections in a population of grid cells

We study the statistics of spike trains of simultaneously recorded grid cells in freely behaving rats. We evaluate pairwise correlations between these cells and, using a maximum entropy kinetic pairwise model (kinetic Ising model), study their functional connectivity. Even when we account for the covariations in firing rates due to overlapping fields, both the pairwise correlations and functional connections decay as a function of the shortest distance between the vertices of the spatial firing pattern of pairs of grid cells, i.e. their phase difference. They take positive values between cells with nearby phases and approach zero or negative values for larger phase differences. We find similar results also when, in addition to correlations due to overlapping fields, we account for correlations due to theta oscillations and head directional inputs. The inferred connections between neurons in the same module and those from different modules can be both negative and positive, with a mean close to zero, but with the strongest inferred connections found between cells of the same module. Taken together, our results suggest that grid cells in the same module do indeed form a local network of interconnected neurons with a functional connectivity that supports a role for attractor dynamics in the generation of grid pattern.

The way mammals navigate in space is hypothesized to depend on neural structures in the temporal lobe including the hippocampus and medial entorhinal cortex (MEC). In particular, grid cells, neurons whose firing is mostly restricted to regions of space that form a hexagonal pattern, are believed to be an important part of this circuitry. Despite several years of work, not much is known about the correlated activity of neurons in the MEC and how grid cells are functionally coupled to each other. Here, we have taken a statistical approach to these questions and studied pairwise correlations and functional connections between simultaneously recorded grid cells. Through careful statistical analysis, we demonstrate that grid cells with nearby firing vertices tend to have positive effects on eliciting responses in each other, while those further apart tend to have inhibitory or no effects. Cells that respond similarly to manipulations of the environment are considered to belong to the same module. Cells belonging to a module have stronger interactions with each other than those in different modules. These results are consistent with and shed light on the population-based mechanisms suggested by models for the generation of grid cell firing.