A Geometric Approach for the Study of Functional Connectivity Dynamics
Functional connectivity has been the focus of many research groups aiming to study the interaction between cells and brain regions. A standard method for analyzing connectivity is to statistically compare pairwise interactions between cells or brain regions across behavioral states or conditions. This methodology ignores the intrinsic properties of functional connectivity as a multivariate and dynamic signal, expressing the correlational configuration of the network. In this talk, I will present a geometric approach, combining Graph Theory and Riemannian Geometry to build "a graph of graphs" and extract the latent dynamics of the overall correlational structure. Using this approach, we formulate the statistical relations between network dynamics and spontaneous behavior as a second-order Taylor’s expansion. Our analysis shows that fast fluctuations in functional connectivity of large-scale cortical networks are closely linked to variations in behavioral metrics related to the arousal state. We further expand this methodology to longer time scales to study the effect of dopamine on network dynamics in the primary motor cortex (M1) during learning. We developed a series of analysis methods indicating that as animals learn to perform a motor task, the network of pyramidal neurons in layer 2-3 gradually and monotonically reorganizes toward an "expert" configuration. Our results highlight the critical role of dopamine in driving synaptic plasticity: Blocking dopaminergic neurotransmission locally in M1 prevented motor learning at the behavioral level and concomitantly halted plasticity changes in network activity and in functional connectivity. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-01-29. Recording duration: 00:27:08.
Characterizing the causal role of large-scale network interactions in supporting complex cognition
Neuroimaging has greatly extended our capacity to study the workings of the human brain. Despite the wealth of knowledge this tool has generated however, there are still critical gaps in our understanding. While tremendous progress has been made in mapping areas of the brain that are specialized for particular stimuli, or cognitive processes, we still know very little about how large-scale interactions between different cortical networks facilitate the integration of information and the execution of complex tasks. Yet even the simplest behavioral tasks are complex, requiring integration over multiple cognitive domains. Our knowledge falls short not only in understanding how this integration takes place, but also in what drives the profound variation in behavior that can be observed on almost every task, even within the typically developing (TD) population. The search for the neural underpinnings of individual differences is important not only philosophically, but also in the service of precision medicine. We approach these questions using a three-pronged approach. First, we create a battery of behavioral tasks from which we can calculate objective measures for different aspects of the behaviors of interest, with sufficient variance across the TD population. Second, using these individual differences in behavior, we identify the neural variance which explains the behavioral variance at the network level. Finally, using covert neurofeedback, we perturb the networks hypothesized to correspond to each of these components, thus directly testing their casual contribution. I will discuss our overall approach, as well as a few of the new directions we are currently pursuing.
Roles of inhibition in stabilizing and shaping the response of cortical networks
Inhibition has long been thought to stabilize the activity of cortical networks at low rates, and to shape significantly their response to sensory inputs. In this talk, I will describe three recent collaborative projects that shed light on these issues. (1) I will show how optogenetic excitation of inhibition neurons is consistent with cortex being inhibition stabilized even in the absence of sensory inputs, and how this data can constrain the coupling strengths of E-I cortical network models. (2) Recent analysis of the effects of optogenetic excitation of pyramidal cells in V1 of mice and monkeys shows that in some cases this optogenetic input reshuffles the firing rates of neurons of the network, leaving the distribution of rates unaffected. I will show how this surprising effect can be reproduced in sufficiently strongly coupled E-I networks. (3) Another puzzle has been to understand the respective roles of different inhibitory subtypes in network stabilization. Recent data reveal a novel, state dependent, paradoxical effect of weakening AMPAR mediated synaptic currents onto SST cells. Mathematical analysis of a network model with multiple inhibitory cell types shows that this effect tells us in which conditions SST cells are required for network stabilization.
The strongly recurrent regime of cortical networks
Modern electrophysiological recordings simultaneously capture single-unit spiking activities of hundreds of neurons. These neurons exhibit highly complex coordination patterns. Where does this complexity stem from? One candidate is the ubiquitous heterogeneity in connectivity of local neural circuits. Studying neural network dynamics in the linearized regime and using tools from statistical field theory of disordered systems, we derive relations between structure and dynamics that are readily applicable to subsampled recordings of neural circuits: Measuring the statistics of pairwise covariances allows us to infer statistical properties of the underlying connectivity. Applying our results to spontaneous activity of macaque motor cortex, we find that the underlying network operates in a strongly recurrent regime. In this regime, network connectivity is highly heterogeneous, as quantified by a large radius of bulk connectivity eigenvalues. Being close to the point of linear instability, this dynamical regime predicts a rich correlation structure, a large dynamical repertoire, long-range interaction patterns, relatively low dimensionality and a sensitive control of neuronal coordination. These predictions are verified in analyses of spontaneous activity of macaque motor cortex and mouse visual cortex. Finally, we show that even microscopic features of connectivity, such as connection motifs, systematically scale up to determine the global organization of activity in neural circuits.
Universal function approximation in balanced spiking networks through convex-concave boundary composition
The spike-threshold nonlinearity is a fundamental, yet enigmatic, component of biological computation — despite its role in many theories, it has evaded definitive characterisation. Indeed, much classic work has attempted to limit the focus on spiking by smoothing over the spike threshold or by approximating spiking dynamics with firing-rate dynamics. Here, we take a novel perspective that captures the full potential of spike-based computation. Based on previous studies of the geometry of efficient spike-coding networks, we consider a population of neurons with low-rank connectivity, allowing us to cast each neuron’s threshold as a boundary in a space of population modes, or latent variables. Each neuron divides this latent space into subthreshold and suprathreshold areas. We then demonstrate how a network of inhibitory (I) neurons forms a convex, attracting boundary in the latent coding space, and a network of excitatory (E) neurons forms a concave, repellant boundary. Finally, we show how the combination of the two yields stable dynamics at the crossing of the E and I boundaries, and can be mapped onto a constrained optimization problem. The resultant EI networks are balanced, inhibition-stabilized, and exhibit asynchronous irregular activity, thereby closely resembling cortical networks of the brain. Moreover, we demonstrate how such networks can be tuned to either suppress or amplify noise, and how the composition of inhibitory convex and excitatory concave boundaries can result in universal function approximation. Our work puts forth a new theory of biologically-plausible computation in balanced spiking networks, and could serve as a novel framework for scalable and interpretable computation with spikes.
Response of cortical networks to optogenetic stimulation: Experiment vs. theory
Optogenetics is a powerful tool that allows experimentalists to perturb neural circuits. What can we learn about a network from observing its response to perturbations? I will first describe the results of optogenetic activation of inhibitory neurons in mice cortex, and show that the results are consistent with inhibition stabilization. I will then move to experiments in which excitatory neurons are activated optogenetically, with or without visual inputs, in mice and monkeys. In some conditions, these experiments show a surprising result that the distribution of firing rates is not significantly changed by stimulation, even though firing rates of individual neurons are strongly modified. I will show in which conditions a network model of excitatory and inhibitory neurons can reproduce this feature.
Multisensory encoding of self-motion in the retrosplenial cortex and beyond
In order to successfully navigate through the environment, animals must accurately estimate the status of their motion with respect to the surrounding scene and objects. In this talk, I will present our recent work on how retrosplenial cortical (RSC) neurons combine vestibular and visual signals to reliably encode the direction and speed of head turns during passive motion and active navigation. I will discuss these data in the context of RSC long-range connectivity and further show our ongoing work on building population-level models of motion representation across cortical and subcortical networks.
Error correction and reliability timescale in converging cortical networks
Rapidly changing inputs such as visual scenes and auditory landscapes are transmitted over several synaptic interfaces and perceived with little loss of detail, but individual neurons are typically “noisy” and cortico-cortical connections are typically “weak”. To understand how information embodied in spike train is transmitted in a lossless manner, we focus on a single synaptic interface: between pyramidal cells and putative interneurons. Using arbitrary white noise patterns injected intra-cortically as photocurrents to freely-moving mice, we find that directly-activated cells exhibit precision of several milliseconds, but post-synaptic, indirectly-activated cells exhibit higher precision. Considering multiple identical messages, the reliability of directly-activated cells peaks at a timescale of dozens of milliseconds, whereas indirectly-activated cells exhibit an order-of-magnitude faster timescale. Using data-driven modelling, we find that error correction is consistent with non-linear amplification of coincident spikes.
Understanding sensorimotor control at global and local scales
The brain is remarkably flexible, and appears to instantly reconfigure its processing depending on what’s needed to solve a task at hand: fMRI studies indicate that distal brain areas appear to fluidly couple and decouple with one another depending on behavioral context. But the structural architecture of the brain is comprised of long-range axonal projections that are relatively fixed by adulthood. How does the global dynamism evident in fMRI recordings manifest at a cellular level? To bridge the gap between the activity of single neurons and cortex-wide networks, we correlated electrophysiological recordings of individual neurons in primary visual (V1) and retrosplenial (RSP) associational cortex with activity across dorsal cortex, recorded simultaneously using widefield calcium imaging. We found that individual neurons in both cortical areas independently engaged in different distributed cortical networks depending on the animal’s behavioral state, suggesting that locomotion puts cortex into a more sensory driven mode relevant for navigation.
Correlations, chaos, and criticality in neural networks
The remarkable properties of information-processing of biological and of artificial neuronal networks alike arise from the interaction of large numbers of neurons. A central quest is thus to characterize their collective states. The directed coupling between pairs of neurons and their continuous dissipation of energy, moreover, cause dynamics of neuronal networks outside thermodynamic equilibrium. Tools from non-equilibrium statistical mechanics and field theory are thus instrumental to obtain a quantitative understanding. We here present progress with this recent approach [1]. On the experimental side, we show how correlations between pairs of neurons are informative on the dynamics of cortical networks: they are poised near a transition to chaos [2]. Close to this transition, we find prolongued sequential memory for past signals [3]. In the chaotic regime, networks offer representations of information whose dimensionality expands with time. We show how this mechanism aids classification performance [4]. Together these works illustrate the fruitful interplay between theoretical physics, neuronal networks, and neural information processing.
The interaction of sensory and motor information to shape neuronal representations in mouse cortical networks
The neurons in our brain never function in isolation; they are organized into complex circuits which perform highly specialized information processing tasks and transfer information through large neuronal networks. The aim of Janelle Pakan's research group is to better understand how neural circuits function during the transformation of information from sensory perception to behavioural output. Importantly, they also aim to further understand the cell-type specific processes that interrupt the flow of information through neural circuits in neurodegenerative disorders with dementia. The Pakan group utilizes innovative neuroanatomical tracing techniques, advanced in vivo two-photon imaging, and genetically targeted manipulations of neuronal activity to investigate the cell-type specific microcircuitry of the cerebral cortex, the macrocircuitry of cortical output to subcortical structures, and the functional circuitry underlying processes of sensory perception and motor behaviour.
Positive and negative feedback in seizure initiation
Seizure onset is a critically important brain state transition that has proved very difficult to predict accurately from recordings of brain activity. I will present new data acquired using a range of optogenetic and imaging tools to characterize exactly how cortical networks change in the build-up to a seizure. I will show how intermittent optogenetic stimulation ("active probing") reveals a latent change in dendritic excitability that is tightly correlated to the onset of seizure activity. This data relates back to old work from the 1980s suggesting a critical role in epileptic pathophysiology for dendritic plateau potentials. Our data show how the precipitous nature of the transition can be understood in terms of multiple, synergistic positive feedback mechanisms.
Computational Models of Large-Scale Brain Networks - Dynamics & Function
Theoretical and computational models of neural systems have been traditionally focused on small neural circuits, given the lack of reliable data on large-scale brain structures. The situation has started to change in recent years, with novel recording technologies and large organized efforts to describe the brain at a larger scale. In this talk, Professor Mejias from the University of Amsterdam will review his recent work on developing anatomically constrained computational models of large-scale cortical networks of monkeys, and how this approach can help to answer important questions in large-scale neuroscience. He will focus on three main aspects: (i) the emergence of functional interactions in different frequency regimes, (ii) the role of balance for efficient large-scale communication, and (iii) new paradigms of brain function, such as working memory, in large-scale networks.