Rahul Biswas

Brain state modulates sensory processing across visual cortex, yet how it relates to the organization of functional circuitry at the level of individual neurons and cell types remains largely unknown. To address this, we constructed one of the largest microscale directed functional circuit maps in mouse visual cortex from calcium imaging of more than 57,000 neurons across four visual areas and five cortical layers. Using a time-aware causal inference framework, we found that intra-areal connections dominate across arousal states, consistent with experimental findings on the local bias of cortical anatomy. Among intra-areal connections, anterolateral area (AL) had the highest density, and among inter-areal connections, the AL-rostrolateral area (RL) axis formed the strongest pathway. Laminar circuit organization was dominated by layer 6 recurrence within-layer, while the most prominent between-layer pathway was layer 5-to-layer 6 in low arousal and layer 4-to-layer 5 in high arousal. Spatial extent was selectively greater for excitatory-to-inhibitory connections in high arousal, but not for excitatory-to-excitatory connections. Across 6,597 electron-microscopy reconstructions of neuron pairs, synapse count predicted functional connection strength in both arousal states, but structure-function coupling was weaker in high arousal. In stimulus-driven response prediction, neuron pairs with stronger functional connections exhibited more similar predictive performance in both states, with performance varying by layer and cell type. Overall, our findings map, at single-neuron resolution, the multi-scale organization of directed functional circuitry in mouse visual cortex across brain states.

Identifying causal interactions in complex dynamical systems is a fundamental challenge across the computational sciences. Existing functional connectivity methods capture correlations but not causation. While addressing directionality, popular causal inference tools such as Granger causality and the Peter-Clark algorithm rely on restrictive assumptions that limit their applicability to high-resolution time-series data, such as the large-scale recordings now standard in neuroscience. Here, we introduce CITS (Causal Inference in Time Series), a nonparametric framework for inferring statistically causal structure from multivariate time series. CITS models dynamics using a structural causal model of arbitrary Markov order and statistical tests for lagged conditional independence. We prove consistency under mild assumptions and demonstrate superior accuracy over state-of-the-art baselines across simulated linear, nonlinear, and recurrent neural network benchmarks. Applying CITS to large-scale neuronal recordings from the mouse visual cortex, thalamus, and hippocampus, we uncover stimulus-specific causal pathways and inter-regional hierarchies that align with known anatomy while revealing new functional insights. We further highlight CITS ability in accurately identifying conditional dependencies within small inferred neuronal motifs. These results establish CITS as a theoretically grounded and empirically validated method for discovering interpretable statistically causal networks in neural time series. Beyond neuroscience, the framework is broadly applicable to causal discovery in complex temporal systems across domains.

Functional connectivity between brain regions is known to be altered in Alzheimer’s disease and promises to be a biomarker for early diagnosis. Several approaches for functional connectivity obtain an undirected network representing stochastic associations (correlations) between brain regions. However, association does not necessarily imply causation. In contrast, Causal Functional Connectivity (CFC) is more informative, providing a directed network representing causal relationships between brain regions. In this paper, we obtained the causal functional connectome for the whole brain from resting-state functional magnetic resonance imaging (rs-fMRI) recordings of subjects from three clinical groups: cognitively normal, mild cognitive impairment, and Alzheimer’s disease. We applied the recently developed Time-aware PC (TPC) algorithm to infer the causal functional connectome for the whole brain. TPC supports model-free estimation of whole brain CFC based on directed graphical modeling in a time series setting. We compared the CFC outcome of TPC with that of other related approaches in the literature. Then, we used the CFC outcomes of TPC and performed an exploratory analysis of the difference in strengths of CFC edges between Alzheimer’s and cognitively normal groups, based on edge-wise p-values obtained by Welch’s t-test. The brain regions thus identified are found to be in agreement with literature on brain regions impacted by Alzheimer’s disease, published by researchers from clinical/medical institutions.

The estimator of a causal directed acyclic graph (DAG) with the PC algorithm is known to be consistent based on independent and identically distributed samples. In this paper, we consider the scenario when the multivariate samples are identically distributed but not independent. A common example is a stationary multivariate time series. We show that under a standard set of assumptions on the underlying time series involving rho-mixing, the PC algorithm is consistent in this dependent sample scenario. Further, we show that for the popular time series models such as vector auto-regressive moving average and linear processes, consistency of the PC algorithm holds. We also prove the consistency for the Time-Aware PC algorithm, a recent adaptation of the PC algorithm for the time series scenario. Our findings are supported by simulations and benchmark real data analyses provided towards the end of the paper.

The representation of the flow of information between neurons in the brain based on their activity is termed the causal functional connectome. Such representation incorporates the dynamic nature of neuronal activity and causal interactions between them. In contrast to connectome, the causal functional connectome is not directly observed and needs to be inferred from neural time series. A popular statistical framework for inferring causal connectivity from observations is the directed probabilistic graphical modeling. Its common formulation is not suitable for neural time series since it was developed for variables with independent and identically distributed static samples. In this work, we propose to model and estimate the causal functional connectivity from neural time series using a novel approach that adapts directed probabilistic graphical modeling to the time series scenario. In particular, we develop the Time-Aware PC (TPC) algorithm for estimating the causal functional connectivity, which adapts the PC algorithm, a state-of-the-art method for statistical causal inference. We show that the model outcome of TPC has the properties of reflecting causality of neural interactions such as being non-parametric, exhibits the directed Markov property in a time-series setting, and is predictive of the consequence of counterfactual interventions on the time series. We demonstrate the utility of the methodology to obtain the causal functional connectome for several datasets including simulations, benchmark datasets, and recent multi-array electro-physiological recordings from the mouse visual cortex.