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.
Prediction of neural activity in connectome-constrained recurrent networks
In this talk, I will explain a theory of connectome-constrained neural networks in which a “student” networks is trained to reproduce the activity of a ground-truth “teacher”, representing a neural system for which a connectome is available. Unlike standard paradigms with unconstrained connectivity, here both networks have the same connectivity but they have different biophysical parameters, reflecting uncertainty in neuronal and synaptic properties. We find that the connectome is often insufficient to constrain the dynamics of networks that perform a specific task, illustrating the difficulty of inferring function from connectivity alone. However, recordings from a small subset of neurons can remove this degeneracy, producing dynamics in the student that agree with the teacher. Our theory can prioritize which neurons to record from to most efficiently unmeasured network activity. The analysis shows that the solution spaces of connectome-constrained and unconstrained models are qualitatively different, and provides a framework to determine when such models yield consistent dynamics. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-04-03. Recording duration: 00:42:28.
Conversions between space and time in network dynamics by neural assemblies
The connectivity structure of many biological systems, including neural circuits, is highly non-uniform. Recent technologies allow detailed mapping of these irregularities, but our understanding of their effect on the overall circuit dynamics is still lacking. By developing complex system analytical tools that perform reduction of the network, I determine the impact of connectivity features on network dynamics. I will demonstrate the use of these tools on neural assemblies (clusters), a ubiquitous non-uniform structure in our brains. I will show how neural assemblies of different sizes naturally generate multiple timescales of activity spanning several orders of magnitude. I will demonstrate how the analytical theory we develop for rate networks, supported by spiking network simulations, reveals the dependency between neural timescales and assembly sizes and how new recordings of spontaneous activity from a million neurons support this analysis. I will also show how our model can naturally explain the particular long-tailed timescale distribution observed in the awake primate cortex. In olfactory cortex, neural assemblies represent odor stimuli. Previously, I showed how the diffuse recurrent excitation among these assemblies allows the conversion of time-encoded inputs from the bulb to spacial neural assembly representations in olfactory cortex. Here, I will show how changes in the dynamical properties of these assemblies alter both their timing response and properties of the time-encoded inputs via feedback. This demonstrates the role of neural assemblies in time-sensitive modulation needed for cognitive tasks, such as attention. Our results offer a biologically plausible mechanism of assemblies in network connectivity for explaining multiple puzzling dynamical phenomena: The ability of neural circuits to transform external simultaneous temporal fluctuations into spatial representations and alter them; and the ability of neuronal circuits to generate simultaneous temporal fluctuations across a large range of timescales; Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-03-20. Recording duration: 00:41:28.
Neural Mechanisms of Subsecond Temporal Encoding in Primary Visual Cortex
Subsecond timing underlies nearly all sensory and motor activities across species and is critical to survival. While subsecond temporal information has been found across cortical and subcortical regions, it is unclear if it is generated locally and intrinsically or if it is a read out of a centralized clock-like mechanism. Indeed, mechanisms of subsecond timing at the circuit level are largely obscure. Primary sensory areas are well-suited to address these question as they have early access to sensory information and provide minimal processing to it: if temporal information is found in these regions, it is likely to be generated intrinsically and locally. We test this hypothesis by training mice to perform an audio-visual temporal pattern sensory discrimination task as we use 2-photon calcium imaging, a technique capable of recording population level activity at single cell resolution, to record activity in primary visual cortex (V1). We have found significant changes in network dynamics through mice’s learning of the task from naive to middle to expert levels. Changes in network dynamics and behavioral performance are well accounted for by an intrinsic model of timing in which the trajectory of q network through high dimensional state space represents temporal sensory information. Conversely, while we found evidence of other temporal encoding models, such as oscillatory activity, we did not find that they accounted for increased performance but were in fact correlated with the intrinsic model itself. These results provide insight into how subsecond temporal information is encoded mechanistically at the circuit level.
Heterogeneity and non-random connectivity in reservoir computing
Reservoir computing is a promising framework to study cortical computation, as it is based on continuous, online processing and the requirements and operating principles are compatible with cortical circuit dynamics. However, the framework has issues that limit its scope as a generic model for cortical processing. The most obvious of these is that, in traditional models, learning is restricted to the output projections and takes place in a fully supervised manner. If such an output layer is interpreted at face value as downstream computation, this is biologically questionable. If it is interpreted merely as a demonstration that the network can accurately represent the information, this immediately raises the question of what would be biologically plausible mechanisms for transmitting the information represented by a reservoir and incorporating it in downstream computations. Another major issue is that we have as yet only modest insight into how the structural and dynamical features of a network influence its computational capacity, which is necessary not only for gaining an understanding of those features in biological brains, but also for exploiting reservoir computing as a neuromorphic application. In this talk, I will first demonstrate a method for quantifying the representational capacity of reservoirs without training them on tasks. Based on this technique, which allows systematic comparison of systems, I then present our recent work towards understanding the roles of heterogeneity and connectivity patterns in enhancing both the computational properties of a network and its ability to reliably transmit to downstream networks. Finally, I will give a brief taster of our current efforts to apply the reservoir computing framework to magnetic systems as an approach to neuromorphic computing.
Homeostatic structural plasticity of neuronal connectivity triggered by optogenetic stimulation
Ever since Bliss and Lømo discovered the phenomenon of long-term potentiation (LTP) in rabbit dentate gyrus in the 1960s, Hebb’s rule—neurons that fire together wire together—gained popularity to explain learning and memory. Accumulating evidence, however, suggests that neural activity is homeostatically regulated. Homeostatic mechanisms are mostly interpreted to stabilize network dynamics. However, recent theoretical work has shown that linking the activity of a neuron to its connectivity within the network provides a robust alternative implementation of Hebb’s rule, although entirely based on negative feedback. In this setting, both natural and artificial stimulation of neurons can robustly trigger network rewiring. We used computational models of plastic networks to simulate the complex temporal dynamics of network rewiring in response to external stimuli. In parallel, we performed optogenetic stimulation experiments in the mouse anterior cingulate cortex (ACC) and subsequently analyzed the temporal profile of morphological changes in the stimulated tissue. Our results suggest that the new theoretical framework combining neural activity homeostasis and structural plasticity provides a consistent explanation of our experimental observations.
Network dynamics in the basal ganglia and possible implications for Parkinson’s disease
The basal ganglia are a collection of brain areas that are connected by a variety of synaptic pathways and are a site of significant reward-related dopamine release. These properties suggest a possible role for the basal ganglia in action selection, guided by reinforcement learning. In this talk, I will discuss a framework for how this function might be performed. I will also present some recent experimental results and theory that call for a re-evaluation of certain aspects of this framework. Next, I will turn to the changes in basal ganglia activity observed to occur with the dopamine depletion associated with Parkinson’s disease. I will discuss some of the potential functional implications of some of these changes and, if time permits, will conclude with some new results that focus on delta oscillations under dopamine depletion.
A macaque connectome for simulating large-scale network dynamics in The VirtualBrain
TheVirtualBrain (TVB; thevirtualbrain.org) is a software platform for simulating whole-brain network dynamics. TVB models link biophysical parameters at the cellular level with systems-level functional neuroimaging signals. Data available from animal models can provide vital constraints for the linkage across spatial and temporal scales. I will describe the construction of a macaque cortical connectome as an initial step towards a comprehensive multi-scale macaque TVB model. I will also describe our process of validating the connectome and show an example simulation of macaque resting-state dynamics using TVB. This connectome opens the opportunity for the addition of other available data from the macaque, such as electrophysiological recordings and receptor distributions, to inform multi-scale models of brain dynamics. Future work will include extensions to neurological conditions and other nonhuman primate species.
Slow global population dynamics propagating through the medial entorhinal cortex
The medial entorhinal cortex (MEC) supports the brain’s representation of space with distinct cell types whose firing is tuned to features of the environment (grid, border, and object-vector cells) or navigation (head-direction and speed cells). While the firing properties of these functionally-distinct cell types are well characterized, how they interact with one another remains unknown. To determine how activity self-organizes in the MEC network, we tested mice in a spontaneous locomotion task under sensory-deprived conditions. Using 2-photon calcium imaging, we monitored the activity of large populations of MEC neurons in head-fixed mice running on a wheel in darkness, in the absence of external sensory feedback tuned to navigation. We unveiled the presence of motifs that involve the sequential activation of cells in layer II of MEC (MEC-L2). We call these motifs waves. Waves lasted tens of seconds to minutes, were robust, swept through the entire network of active cells and did not exhibit any anatomical organization. Furthermore, waves did not map the position of the mouse on the wheel and were not restricted to running epochs. The majority of MEC-L2 neurons participate in this global sequential dynamics, that ties all functional cell types together. We found the waves in the most lateral region of MEC, but not in adjacent areas such as PaS or in a sensory cortex such as V1.
Using noise to probe recurrent neural network structure and prune synapses
Many networks in the brain are sparsely connected, and the brain eliminates synapses during development and learning. How could the brain decide which synapses to prune? In a recurrent network, determining the importance of a synapse between two neurons is a difficult computational problem, depending on the role that both neurons play and on all possible pathways of information flow between them. Noise is ubiquitous in neural systems, and often considered an irritant to be overcome. In the first part of this talk, I will suggest that noise could play a functional role in synaptic pruning, allowing the brain to probe network structure and determine which synapses are redundant. I will introduce a simple, local, unsupervised plasticity rule that either strengthens or prunes synapses using only synaptic weight and the noise-driven covariance of the neighboring neurons. For a subset of linear and rectified-linear networks, this rule provably preserves the spectrum of the original matrix and hence preserves network dynamics even when the fraction of pruned synapses asymptotically approaches 1. The plasticity rule is biologically-plausible and may suggest a new role for noise in neural computation. Time permitting, I will then turn to the problem of extracting structure from neural population data sets using dimensionality reduction methods. I will argue that nonlinear structures naturally arise in neural data and show how these nonlinearities cause linear methods of dimensionality reduction, such as Principal Components Analysis, to fail dramatically in identifying low-dimensional structure.
Disentangling the roles of dimensionality and cell categories in neural computations
The description of neural computations currently relies on two competing views: (i) a classical single-cell view that aims to relate the activity of individual neurons to sensory or behavioural variables, and organize them into functional classes; (ii) a more recent population view that instead characterises computations in terms of collective neural trajectories, and focuses on the dimensionality of these trajectories as animals perform tasks. How the two key concepts of functional cell classes and low-dimensional trajectories interact to shape neural computations is however at present not understood. Here I will address this question by combining machine-learning tools for training recurrent neural networks with reverse-engineering and theoretical analyses of network dynamics.