Latent Dynamical Variables Produce Signatures of Spatiotemporal Criticality in Large Biological Systems

Contextual modulation emerges by integrating feedforward and feedback processing in mouse visual cortex

Sensory systems use context to infer meaning. Accordingly, context profoundly influences neural responses to sensory stimuli. However, a cohesive understanding of the circuit mechanisms governing contextual effects across different stimulus conditions is still lacking. Here we present a unified circuit model of mouse visual cortex that accounts for the main standard forms of contextual modulation. This data-driven and biologically realistic circuit, including three primary inhibitory cell types, sheds light on how bottom-up, top-down, and recurrent inputs are integrated across retinotopic space to generate contextual effects in layer 2/3. We establish causal relationships between neural responses, geometrical features of the inputs, and the connectivity patterns. The model not only reveals how a single canonical cortical circuit differently modulates sensory response depending on context but also generates multiple testable predictions, offering insights that apply to broader neural circuitry.

Multiscale organization of neuronal activity unifies scale-dependent theories of brain function

Brain recordings collected at different resolutions support distinct signatures of neural coding, leading to scale-dependent theories of brain function. Here, we show that these disparate signatures emerge from a heavy-tailed, multiscale functional organization of neuronal activity observed across calcium-imaging recordings collected from the whole brains of zebrafish and C. elegans as well as from sensory regions in Drosophila, mice, and macaques. Network simulations demonstrate that this conserved hierarchical structure enhances information processing. Finally, we find that this organization is maintained despite significant cross-scale reconfiguration of cellular coordination during behavior. Our findings suggest that this nonlinear organization of neuronal activity is a universal principle conserved for its ability to adaptively link behavior to neural dynamics across multiple spatiotemporal scales while balancing functional resiliency and information processing efficiency.

Latent dynamics of primary sensory cortical population activity structured by fluctuations in the local field potential

Introduction

As emerging technologies enable measurement of precise details of the activity within microcircuits at ever-increasing scales, there is a growing need to identify the salient features and patterns within the neural populations that represent physiologically and behaviorally relevant aspects of the network. Accumulating evidence from recordings of large neural populations suggests that neural population activity frequently exhibits relatively low-dimensional structure, with a small number of variables explaining a substantial fraction of the structure of the activity. While such structure has been observed across the brain, it is not known how reduced-dimension representations of neural population activity relate to classical metrics of "brain state," typically described in terms of fluctuations in the local field potential (LFP), single-cell activity, and behavioral metrics.

Methods

Hidden state models were fit to spontaneous spiking activity of populations of neurons, recorded in the whisker area of primary somatosensory cortex of awake mice. Classic measures of cortical state in S1, including the LFP and whisking activity, were compared to the dynamics of states inferred from spiking activity.

Results

A hidden Markov model fit the population spiking data well with a relatively small number of states, and putative inhibitory neurons played an outsize role in determining the latent state dynamics. Spiking states inferred from the model were more informative of the cortical state than a direct readout of the spiking activity of single neurons or of the population. Further, the spiking states predicted both the trial-by-trial variability in sensory responses and one aspect of behavior, whisking activity.

Discussion

Our results show how classical measurements of brain state relate to neural population spiking dynamics at the scale of the microcircuit and provide an approach for quantitative mapping of brain state dynamics across brain areas.

Searching for long timescales without fine tuning

Animal behavior occurs on timescales much longer than the response times of individual neurons. In many cases, it is plausible that these long timescales emerge from the recurrent dynamics of electrical activity in networks of neurons. In linear models, timescales are set by the eigenvalues of a dynamical matrix whose elements measure the strengths of synaptic connections between neurons. It is not clear to what extent these matrix elements need to be tuned to generate long timescales; in some cases, one needs not just a single long timescale but a whole range. Starting from the simplest case of random symmetric connections, we combine maximum entropy and random matrix theory methods to construct ensembles of networks, exploring the constraints required for long timescales to become generic. We argue that a single long timescale can emerge generically from realistic constraints, but a full spectrum of slow modes requires more tuning. Langevin dynamics that generates patterns of synaptic connections drawn from these ensembles involves a combination of Hebbian learning and activity-dependent synaptic scaling.

Designing host-associated microbiomes using the consumer/resource model

A key step towards rational microbiome engineering is in silico sampling of realistic microbial communities that correspond to desired host phenotypes, and vice versa. This remains challenging due to a lack of generative models that simultaneously capture compositions of host-associated microbiomes and host phenotypes. To that end, we present a generative model based on the mechanistic consumer/resource (C/R) framework. In the model, variation in microbial ecosystem composition arises due to differences in the availability of effective resources (inferred latent variables) while species' resource preferences remain conserved. The same latent variables are used to model phenotypic states of hosts. In silico microbiomes generated by our model accurately reproduce universal and dataset-specific statistics of bacterial communities. The model allows us to address three salient questions in host-associated microbial ecologies: (1) which host phenotypes maximally constrain the composition of the host-associated microbiomes? (2) how context-specific are phenotype/microbiome associations, and (3) what are plausible microbiome compositions that correspond to desired host phenotypes? Our approach aids the analysis and design of microbial communities associated with host phenotypes of interest.

Neural criticality from effective latent variables

Observations of power laws in neural activity data have raised the intriguing notion that brains may operate in a critical state. One example of this critical state is 'avalanche criticality', which has been observed in various systems, including cultured neurons, zebrafish, rodent cortex, and human EEG. More recently, power laws were also observed in neural populations in the mouse under an activity coarse-graining procedure, and they were explained as a consequence of the neural activity being coupled to multiple latent dynamical variables. An intriguing possibility is that avalanche criticality emerges due to a similar mechanism. Here, we determine the conditions under which latent dynamical variables give rise to avalanche criticality. We find that populations coupled to multiple latent variables produce critical behavior across a broader parameter range than those coupled to a single, quasi-static latent variable, but in both cases, avalanche criticality is observed without fine-tuning of model parameters. We identify two regimes of avalanches, both critical but differing in the amount of information carried about the latent variable. Our results suggest that avalanche criticality arises in neural systems in which activity is effectively modeled as a population driven by a few dynamical variables and these variables can be inferred from the 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.

Statistical properties of large data sets with linear latent features

Analytical understanding of how low-dimensional latent features reveal themselves in large-dimensional data is still lacking. We study this by defining a probabilistic linear latent features model with additive noise and by analytically and numerically computing the statistical distributions of pairwise correlations and eigenvalues of the data correlation matrix. This allows us to resolve the latent feature structure across a wide range of data regimes set by the number of recorded variables, observations, latent features, and the signal-to-noise ratio. We find a characteristic imprint of latent features in the distribution of correlations and eigenvalues and provide an analytic estimate for the boundary between signal and noise, even in the absence of a spectral gap.

Mutual information in changing environments: Nonlinear interactions, out-of-equilibrium systems, and continuously varying diffusivities

Biochemistry, ecology, and neuroscience are examples of prominent fields aiming at describing interacting systems that exhibit nontrivial couplings to complex, ever-changing environments. We have recently shown that linear interactions and a switching environment are encoded separately in the mutual information of the overall system. Here we first generalize these findings to a broad class of nonlinear interacting models. We find that a new term in the mutual information appears, quantifying the interplay between nonlinear interactions and environmental changes, and leading to either constructive or destructive information interference. Furthermore, we show that a higher mutual information emerges in out-of-equilibrium environments with respect to an equilibrium scenario. Finally, we generalize our framework to the case of continuously varying environments. We find that environmental changes can be mapped exactly into an effective spatially varying diffusion coefficient, shedding light on modeling of biophysical systems in inhomogeneous media.

Inferring couplings in networks across order-disorder phase transitions

Statistical inference is central to many scientific endeavors, yet how it works remains unresolved. Answering this requires a quantitative understanding of the intrinsic interplay between statistical models, inference methods, and the structure in the data. To this end, we characterize the efficacy of direct coupling analysis (DCA) - a highly successful method for analyzing amino acid sequence data-in inferring pairwise interactions from samples of ferromagnetic Ising models on random graphs. Our approach allows for physically motivated exploration of qualitatively distinct data regimes separated by phase transitions. We show that inference quality depends strongly on the nature of data-generating distributions: optimal accuracy occurs at an intermediate temperature where the detrimental effects from macroscopic order and thermal noise are minimal. Importantly our results indicate that DCA does not always outperform its local-statistics-based predecessors; while DCA excels at low temperatures, it becomes inferior to simple correlation thresholding at virtually all temperatures when data are limited. Our findings offer insights into the regime in which DCA operates so successfully, and more broadly, how inference interacts with the structure in the data.

Short- and Long-Range Connections Differentially Modulate the Dynamics and State of Small-World Networks

The human brain contains billions of neurons that flexibly interconnect to support local and global computational spans. As neuronal activity propagates through the neural medium, it approaches a critical state hedged between ordered and disordered system regimes. Recent work demonstrates that this criticality coincides with the small-world topology, a network arrangement that accommodates both local (subcritical) and global (supercritical) system properties. On one hand, operating near criticality is thought to offer several neurocomputational advantages, e.g., high-dynamic range, efficient information capacity, and information transfer fidelity. On the other hand, aberrations from the critical state have been linked to diverse pathologies of the brain, such as post-traumatic epileptiform seizures and disorders of consciousness. Modulation of brain activity, through neuromodulation, presents an attractive mode of treatment to alleviate such neurological disorders, but a tractable neural framework is needed to facilitate clinical progress. Using a variation on the generative small-world model of Watts and Strogatz and Kuramoto's model of coupled oscillators, we show that the topological and dynamical properties of the small-world network are divided into two functional domains based on the range of connectivity, and that these domains play distinct roles in shaping the behavior of the critical state. We demonstrate that short-range network connections shape the dynamics of the system, e.g., its volatility and metastability, whereas long-range connections drive the system state, e.g., a seizure. Together, these findings lend support to combinatorial neuromodulation approaches that synergistically normalize the system dynamic while mobilizing the system state.