Functional networks from inverse modeling of neural population activity

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Enhanced simulations of whole-brain dynamics using hybrid resting-state structural connectomes

The human brain, composed of billions of neurons and synaptic connections, is an intricate network coordinating a sophisticated balance of excitatory and inhibitory activities between brain regions. The dynamical balance between excitation and inhibition is vital for adjusting neural input/output relationships in cortical networks and regulating the dynamic range of their responses to stimuli. To infer this balance using connectomics, we recently introduced a computational framework based on the Ising model, which was first developed to explain phase transitions in ferromagnets, and proposed a novel hybrid resting-state structural connectome (rsSC). Here, we show that a generative model based on the Kuramoto phase oscillator can be used to simulate static and dynamic functional connectomes (FC) with rsSC as the coupling weight coefficients, such that the simulated FC aligns well with the observed FC when compared with that simulated traditional structural connectome.

Disrupted excitation-inhibition balance in cognitively normal individuals at risk of Alzheimer's disease

Background

Sex differences impact Alzheimer's disease (AD) neuropathology, but cell-to-network level dysfunctions in the prodromal phase are unclear. Alterations in hippocampal excitation-inhibition balance (EIB) have recently been linked to early AD pathology.

Objective

Examine how AD risk factors (age, APOE-ɛ4, amyloid-β) relate to hippocampal EIB in cognitively normal males and females using connectome-level measures.

Methods

Individuals from the OASIS-3 cohort (age 42-95) were studied (N = 437), with a subset aged 65+ undergoing neuropsychological testing (N = 231).

Results

In absence of AD risk factors (APOE-ɛ4/Aβ+), whole-brain EIB decreases with age more significantly in males than females (p = 0.021, β = -0.007). Regression modeling including APOE-ɛ4 allele carriers (Aβ-) yielded a significant positive AGE-by-APOE interaction in the right hippocampus for females only (p = 0.013, β = 0.014), persisting with inclusion of Aβ+ individuals (p = 0.012, β = 0.014). Partial correlation analyses of neuropsychological testing showed significant associations with EIB in females: positive correlations between right hippocampal EIB with categorical fluency and whole-brain EIB with the trail-making test (p < 0.05).

Conclusion

Sex differences in EIB emerge during normal aging and progresses differently with AD risk. Results suggest APOE-ɛ4 disrupts hippocampal balance more than amyloid in females. Increased excitation correlates positively with neuropsychological performance in the female group, suggesting a duality in terms of potential beneficial effects prior to cognitive impairment. This underscores the translational relevance of APOE-ɛ4 related hyperexcitation in females, potentially informing therapeutic targets or early interventions to mitigate AD progression in this vulnerable population.

Enhanced simulations of whole-brain dynamics using hybrid resting-state structural connectomes

The human brain, composed of billions of neurons and synaptic connections, is an intricate network coordinating a sophisticated balance of excitatory and inhibitory activity between brain regions. The dynamical balance between excitation and inhibition is vital for adjusting neural input/output relationships in cortical networks and regulating the dynamic range of their responses to stimuli. To infer this balance using connectomics, we recently introduced a computational framework based on the Ising model, first developed to explain phase transitions in ferromagnets, and proposed a novel hybrid resting-state structural connectome (rsSC). Here, we show that a generative model based on the Kuramoto phase oscillator can be used to simulate static and dynamic functional connectomes (FC) with rsSC as the coupling weight coefficients, such that the simulated FC well aligns with the observed FC when compared to that simulated with traditional structural connectome. Simulations were performed using the open source framework The Virtual Brain on High Performance Computing infrastructure.

Disrupted Excitation-Inhibition Balance in Cognitively Normal Individuals at Risk of Alzheimer's Disease

BACKGROUND

Sex differences impact Alzheimer's disease (AD) neuropathology, but cell-to-network level dysfunctions in the prodromal phase are unclear. Alterations in hippocampal excitation-inhibition balance (EIB) have recently been linked to early AD pathology.

OBJECTIVE

Examine how AD risk factors (age, APOEɛ4, amyloid-β) relate to hippocampal EIB in cognitively normal males and females using connectome-level measures.

METHODS

Individuals from the OASIS-3 cohort (age 42-95) were studied (N = 437), with a subset aged 65+ undergoing neuropsychological testing (N = 231).

RESULTS

In absence of AD risk factors (APOEɛ4/Aβ+), whole-brain EIB decreases with age more significantly in males than females (p = 0.021, β= -0.007). Regression modeling including APOEɛ4 allele carriers (Aβ-) yielded a significant positive AGE-by-APOE interaction in the right hippocampus for females only (p = 0.013, β= 0.014), persisting with inclusion of Aβ+ individuals (p = 0.012, β= 0.014). Partial correlation analyses of neuropsychological testing showed significant associations with EIB in females: positive correlations between right hippocampal EIB with categorical fluency and whole-brain EIB with the Trail Making Test (p < 0.05).

CONCLUSIONS

Sex differences in EIB emerge during normal aging and progresses differently with AD risk. Results suggest APOEɛ4 disrupts hippocampal balance more than amyloid in females. Increased excitation correlates positively with neuropsychological performance in the female group, suggesting a duality in terms of potential beneficial effects prior to cognitive impairment. This underscores the translational relevance of APOEɛ4 related hyperexcitation in females, potentially informing therapeutic targets or early interventions to mitigate AD progression in this vulnerable population.

Inferring excitation-inhibition dynamics using a maximum entropy model unifying brain structure and function

Neural activity coordinated across different scales from neuronal circuits to large-scale brain networks gives rise to complex cognitive functions. Bridging the gap between micro- and macroscale processes, we present a novel framework based on the maximum entropy model to infer a hybrid resting-state structural connectome, representing functional interactions constrained by structural connectivity. We demonstrate that the structurally informed network outperforms the unconstrained model in simulating brain dynamics, wherein by constraining the inference model with the network structure we may improve the estimation of pairwise BOLD signal interactions. Further, we simulate brain network dynamics using Monte Carlo simulations with the new hybrid connectome to probe connectome-level differences in excitation-inhibition balance between apolipoprotein E (APOE)-ε4 carriers and noncarriers. Our results reveal sex differences among APOE-ε4 carriers in functional dynamics at criticality; specifically, female carriers appear to exhibit a lower tolerance to network disruptions resulting from increased excitatory interactions. In sum, the new multimodal network explored here enables analysis of brain dynamics through the integration of structure and function, providing insight into the complex interactions underlying neural activity such as the balance of excitation and inhibition.

Blind deconvolution for spike inference from fluorescence recordings

The parallel developments of genetically-encoded calcium indicators and fast fluorescence imaging techniques allows one to simultaneously record neural activity of extended neuronal populations in vivo. To fully harness the potential of functional imaging, one needs to infer the sequence of action potentials from fluorescence traces. Here we build on recently proposed computational approaches to develop a blind sparse deconvolution (BSD) algorithm based on a generative model for inferring spike trains from fluorescence traces. BSD features, (1) automatic (fully unsupervised) estimation of the hyperparameters, such as spike amplitude, noise level and rise and decay time constants, (2) a novel analytical estimate of the sparsity prior, which yields enhanced robustness and computational speed with respect to existing methods, (3) automatic thresholding for binarizing spikes that maximizes the precision-recall performance, (4) super-resolution capabilities increasing the temporal resolution beyond the fluorescence signal acquisition rate. BSD also uniquely provides theoretically-grounded estimates of the expected performance of the spike reconstruction in terms of precision-recall and temporal accuracy for each recording. The performance of the algorithm is established using synthetic data and through the SpikeFinder challenge, a community-based initiative for spike-rate inference benchmarking based on a collection of joint electrophysiological and fluorescence recordings. Our method outperforms classical sparse deconvolution algorithms in terms of robustness, speed and/or accuracy and performs competitively in the SpikeFinder challenge. This algorithm is modular, easy-to-use and made freely available. Its novel features can thus be incorporated in a straightforward way into existing calcium imaging packages.

Inference of compressed Potts graphical models

We consider the problem of inferring a graphical Potts model on a population of variables. This inverse Potts problem generally involves the inference of a large number of parameters, often larger than the number of available data, and, hence, requires the introduction of regularization. We study here a double regularization scheme, in which the number of Potts states (colors) available to each variable is reduced and interaction networks are made sparse. To achieve the color compression, only Potts states with large empirical frequency (exceeding some threshold) are explicitly modeled on each site, while the others are grouped into a single state. We benchmark the performances of this mixed regularization approach, with two inference algorithms, adaptive cluster expansion (ACE) and pseudolikelihood maximization (PLM), on synthetic data obtained by sampling disordered Potts models on Erdős-Rényi random graphs. We show in particular that color compression does not affect the quality of reconstruction of the parameters corresponding to high-frequency symbols, while drastically reducing the number of the other parameters and thus the computational time. Our procedure is also applied to multisequence alignments of protein families, with similar results.

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.

Unsupervised identification of states from voltage recordings of neural networks

BACKGROUND

Modern techniques for multi-neuronal recording produce large amounts of data. There is no automatic procedure for the identification of states in recurrent voltage patterns.

NEW METHOD

We propose NetSAP (Network States And Pathways), a data-driven analysis method that is able to recognize multi-neuron voltage patterns (states). To capture the subtle differences between snapshots in voltage recordings, NetSAP infers the underlying functional neural network in a time-resolved manner with a sliding window approach. Then NetSAP identifies states from a reordering of the time series of inferred networks according to a user-defined metric. The procedure for unsupervised identification of states was developed originally for the analysis of molecular dynamics simulations of proteins.

RESULTS

We tested NetSAP on neural network simulations of GABAergic inhibitory interneurons. Most simulation parameters are chosen to reproduce literature observations, and we keep noise terms as control parameters to regulate the coherence of the simulated signals. NetSAP is able to identify multiple states even in the case of high internal noise and low signal coherence. We provide evidence that NetSAP is robust for networks with up to about 50% of the neurons spiking randomly. NetSAP is scalable and its code is open source.

COMPARISON WITH EXISTING METHODS

NetSAP outperforms common analysis techniques, such as PCA and k-means clustering, on a simulated recording of voltage traces of 50 neurons.

CONCLUSIONS

NetSAP analysis is an efficient tool to identify voltage patterns from neuronal recordings.

Functional connectivity models for decoding of spatial representations from hippocampal CA1 recordings

Hippocampus stores spatial representations, or maps, which are recalled each time a subject is placed in the corresponding environment. Across different environments of similar geometry, these representations show strong orthogonality in CA3 of hippocampus, whereas in the CA1 subfield a considerable overlap between the maps can be seen. The lower orthogonality decreases reliability of various decoders developed in an attempt to identify which of the stored maps is active at the moment. Especially, the problem with decoding emerges with a need to analyze data at high temporal resolution. Here, we introduce a functional-connectivity-based decoder, which accounts for the pairwise correlations between the spiking activities of neurons in each map and does not require any positional information, i.e. any knowledge about place fields. We first show, on recordings of hippocampal activity in constant environmental conditions, that our decoder outperforms existing decoding methods in CA1. Our decoder is then applied to data from teleportation experiments, in which an instantaneous switch between the environment identity triggers a recall of the corresponding spatial representation . We test the sensitivity of our approach on the transition dynamics between the respective memory states (maps). We find that the rate of spontaneous state shifts (flickering) after a teleportation event is increased not only within the first few seconds as already reported, but this instability is sustained across much longer (> 1 min.) periods.