Metastability, Criticality and Phase Transitions in brain and its Models

This essay extends the previously deposited paper "Oscillations, Metastability and Phase Transitions" to incorporate the theory of Self-organizing Criticality. The twin concepts of Scaling and Universality of the theory of nonequilibrium phase transitions is applied to the role of reentrant activity in neural circuits of cerebral cortex and subcortical neural structures

Excitable Media Seminar

The simulation data presented here, and the conceptual framework developed for their interpretation are, both, in need of substantial refinement and extension. However, granting that they are initial pointers of some merit, and elementary indicators of general principles, several implications follow: the activity patterns of neurons and their assemblies are\ud interdependent with the extracellular milieu in which they are embedded, and to whose time varying composition they contribute. The complexity of this interdependence in the temporal dimension forecloses any time and context invariant relation between what the experimenter may consider stimulus input and its representation in neural activity. Hence, ideas of coding by (quasi)-digital neurons are called in question by the mutual interdependence of neurons and their\ud humoral milieu. Instead, concepts of 'mass action' in the Nervous system gain a new perspective: this time augmented by including the chemical medium surrounding neurons as part of the dynamics of the system as a whole. Accordingly, a meaningful way to describe activity in a neuron assembly would be in terms of a state space in which it can move along an infinite number of trajectories.\u

Brain Dynamics across levels of Organization

After presenting evidence that the electrical activity recorded from the brain surface can reflect metastable state transitions of neuronal configurations at the mesoscopic level, I will suggest that their patterns may correspond to the distinctive spatio-temporal activity in the Dynamic Core (DC) and the Global Neuronal Workspace (GNW), respectively, in the models of the Edelman group on the one hand, and of Dehaene-Changeux, on the other. In both cases, the recursively reentrant activity flow in intra-cortical and cortical-subcortical neuron loops plays an essential and distinct role. Reasons will be given for viewing the temporal characteristics of this activity flow as signature of Self-Organized Criticality (SOC), notably in reference to the dynamics of neuronal avalanches. This point of view enables the use of statistical Physics approaches for exploring phase transitions, scaling and universality properties of DC and GNW, with relevance to the macroscopic electrical activity in EEG and EMG

Brain rhythms of pain

Pain is an integrative phenomenon that results from dynamic interactions between sensory and contextual (i.e., cognitive, emotional, and motivational) processes. In the brain the experience of pain is associated with neuronal oscillations and synchrony at different frequencies. However, an overarching framework for the significance of oscillations for pain remains lacking. Recent concepts relate oscillations at different frequencies to the routing of information flow in the brain and the signaling of predictions and prediction errors. The application of these concepts to pain promises insights into how flexible routing of information flow coordinates diverse processes that merge into the experience of pain. Such insights might have implications for the understanding and treatment of chronic pain

Oscillations, metastability and phase transitions in brain and models of cognition

Neuroscience is being practiced in many different forms and at many different organizational levels of the Nervous System. Which of these levels and associated conceptual frameworks is most informative for elucidating the association of neural processes with processes of Cognition is an empirical question and subject to pragmatic validation. In this essay, I select the framework of Dynamic System Theory. Several investigators have applied in recent years tools and concepts of this theory to interpretation of observational data, and for designing neuronal models of cognitive functions. I will first trace the essentials of conceptual development and hypotheses separately for discerning observational tests and criteria for functional realism and conceptual plausibility of the alternatives they offer. I will then show that the statistical mechanics of phase transitions in brain activity, and some of its models, provides a new and possibly revealing perspective on brain events in cognition

Geometric Analysis of Synchronization in Neuronal Networks with Global Inhibition and Coupling Delays

We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled and interact with each other. The excitatory population is uncoupled, while the inhibitory population is tightly coupled. A geometric singular perturbation analysis yields existence and stability conditions for synchronization states under different firing patterns between the two populations, along with formulas for the periods of such synchronous solutions. Our results demonstrate that the presence of coupling delays in the network promotes synchronization. Numerical simulations are conducted to supplement and validate analytical results. We show the results carry over to a model for spindle sleep rhythms in thalamocortical networks, one of the biological systems which motivated our study. The analysis helps to explain how coupling delays in either excitatory or inhibitory synapses contribute to producing synchronized rhythms.Comment: 43 pages, 12 figure

Repeating Spatial-Temporal Motifs of CA3 Activity Dependent on Engineered Inputs from Dentate Gyrus Neurons in Live Hippocampal Networks.

Anatomical and behavioral studies, and in vivo and slice electrophysiology of the hippocampus suggest specific functions of the dentate gyrus (DG) and the CA3 subregions, but the underlying activity dynamics and repeatability of information processing remains poorly understood. To approach this problem, we engineered separate living networks of the DG and CA3 neurons that develop connections through 51 tunnels for axonal communication. Growing these networks on top of an electrode array enabled us to determine whether the subregion dynamics were separable and repeatable. We found spontaneous development of polarized propagation of 80% of the activity in the native direction from DG to CA3 and different spike and burst dynamics for these subregions. Spatial-temporal differences emerged when the relationships of target CA3 activity were categorized with to the number and timing of inputs from the apposing network. Compared to times of CA3 activity when there was no recorded tunnel input, DG input led to CA3 activity bursts that were 7× more frequent, increased in amplitude and extended in temporal envelope. Logistic regression indicated that a high number of tunnel inputs predict CA3 activity with 90% sensitivity and 70% specificity. Compared to no tunnel input, patterns of >80% tunnel inputs from DG specified different patterns of first-to-fire neurons in the CA3 target well. Clustering dendrograms revealed repeating motifs of three or more patterns at up to 17 sites in CA3 that were importantly associated with specific spatial-temporal patterns of tunnel activity. The number of these motifs recorded in 3 min was significantly higher than shuffled spike activity and not seen above chance in control networks in which CA3 was apposed to CA3 or DG to DG. Together, these results demonstrate spontaneous input-dependent repeatable coding of distributed activity in CA3 networks driven by engineered inputs from DG networks. These functional configurations at measured times of activation (motifs) emerge from anatomically accurate feed-forward connections from DG through tunnels to CA3

Traveling waves of excitation in neural field models

Field models provide an elegant mathematical framework to analyze large-scale patterns of neural activity. On the microscopic level, these models are usually based on either a firing-rate picture or integrate-and-fire dynamics. This article shows that in spite of the large conceptual differences between the two types of dynamics, both generate closely related plane-wave solutions. Furthermore, for a large group of models, estimates about the network connectivity derived from the speed of these plane waves only marginally depend on the assumed class of microscopic dynamics. We derive quantitative results about this phenomenon and discuss consequences for the interpretation of experimental data