scholarly journals Resilience through diversity: Loss of neuronal heterogeneity in epileptogenic human tissue renders neural networks more susceptible to sudden changes in synchrony

2021 ◽  
Author(s):  
Scott Rich ◽  
Homeira Moradi Chameh ◽  
Jeremie Lefebvre ◽  
Taufik A Valiante
Keyword(s):  
Cortical Neurons ◽  
Neural Circuits ◽  
Mean Field Theory ◽  
Mean Field ◽  
Cellular Heterogeneity ◽  
Dynamical Structure ◽  
Activation Functions ◽  
Pathological Changes ◽  
Mathematical Analyses

AbstractA myriad of pathological changes associated with epilepsy can be recast as decreases in cell and circuit heterogeneity. We propose that epileptogenesis can be recontextualized as a process where reduction in cellular heterogeneity renders neural circuits less resilient to transitions into information-poor, over-correlated seizure states. We provide in vitro, in silico, and mathematical support for this hypothesis. Patch clamp recordings from human layer 5 (L5) cortical neurons demonstrate significantly decreased biophysical heterogeneity of excitatory neurons in seizure generating areas (epilepetogenic zone). This decreased heterogeneity renders model neural circuits prone to sudden dynamical transitions into synchronous, hyperactive states (paralleling ictogenesis) while also explaining counter-intuitive differences in population activation functions (i.e., FI curves) between epileptogenic and non-epileptogenic tissue. Mathematical analyses based in mean-field theory reveal clear distinctions in the dynamical structure of networks with low and high heterogeneity, providing the theoretical undergird for how ictogenic dynamics accompany a reduction in biophysical heterogeneity.

scholarly journals Hopf Bifurcation in Mean Field Explains Critical Avalanches in Excitation-Inhibition Balanced Neuronal Networks: A Mechanism for Multiscale Variability

2020 ◽  
Vol 14 ◽  
Author(s):  
Junhao Liang ◽  
Tianshou Zhou ◽  
Changsong Zhou
Keyword(s):  
Hopf Bifurcation ◽  
Large Scale ◽  
Neural Circuits ◽  
Mean Field Theory ◽  
Mean Field ◽  
Stable State ◽  
Population Level ◽  
Field Equations ◽  
Public Data

Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) balanced neuronal network with biologically realistic synaptic kinetics. It can maintain irregular spiking dynamics with different levels of synchrony and critical avalanches emerge near the synchronous transition point. We propose a novel semi-analytical mean-field theory to derive the field equations governing the network macroscopic dynamics. It reveals that the E-I balanced state of the network manifesting irregular individual spiking is characterized by a macroscopic stable state, which can be either a fixed point or a periodic motion and the transition is predicted by a Hopf bifurcation in the macroscopic field. Furthermore, by analyzing public data, we find the coexistence of irregular spiking and critical avalanches in the spontaneous spiking activities of mouse cortical slice in vitro, indicating the universality of the observed phenomena. Our theory unveils the mechanism that permits complex neural activities in different spatiotemporal scales to coexist and elucidates a possible origin of the criticality of neural systems. It also provides a novel tool for analyzing the macroscopic dynamics of E-I balanced networks and its relationship to the microscopic counterparts, which can be useful for large-scale modeling and computation of cortical dynamics.

scholarly journals Filament extensibility and shear stiffening control persistence of strain and loss of coherence in cross-linked motor-filament assemblies

2018 ◽  
Author(s):  
Arvind Gopinath ◽  
Raghunath Chelakkot ◽  
L. Mahadevan
Keyword(s):  
Collective Behavior ◽  
Molecular Motors ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spatial Coordination ◽  
Elastic Filaments ◽  
Mechanical Information ◽  
Loss Of Coherence ◽  
Elastic Strains

AbstractCross-linked flexible filaments deformed by active molecular motors occur in many natural and synthetic settings including eukaryotic flagella, the cytoskeleton and in vitro motor assays. In these systems, an important quantity that controls spatial coordination and emergent collective behavior is the length scale over which elastic strains persist. We estimate this quantity in the context of ordered composites comprised of cross-linked elastic filaments sheared by active motors. Combining a mean-field theory valid for negligibly noisy systems with discrete simulations for noisy systems, we show that the effect of localized strains – be they steady or oscillatory – persist over distances determined by motor kinetics, motor elasticity and filament extensibility. The cut-off length that emerges from these effects controls the transmission of mechanical information and determines the criterion for spatially separated motor groups to stay synchronized. Our results generalize the notion of persistence in passive, Brownian filaments to active, cross-linked filaments.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals Epothilone D alters normal growth, viability and microtubule dependent intracellular functions of cortical neurons in vitro

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
J. A. Clark ◽  
J. A. Chuckowree ◽  
M. S. Dyer ◽  
T. C. Dickson ◽  
C. A. Blizzard
Keyword(s):  
Cortical Neurons ◽  
Normal Growth ◽  
Epothilone D

scholarly journals Swarm shedding in networks of self-propelled agents

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jason Hindes ◽  
Victoria Edwards ◽  
Klimka Szwaykowska Kasraie ◽  
George Stantchev ◽  
Ira B. Schwartz
Keyword(s):  
Network Topology ◽  
Collective Motion ◽  
Mean Field Theory ◽  
Mean Field ◽  
Interaction Strength ◽  
Central Question ◽  
Agent Interaction ◽  
Sparse Networks ◽  
Swarm Pattern ◽  
Limited Sensing

AbstractUnderstanding swarm pattern formation is of great interest because it occurs naturally in many physical and biological systems, and has artificial applications in robotics. In both natural and engineered swarms, agent communication is typically local and sparse. This is because, over a limited sensing or communication range, the number of interactions an agent has is much smaller than the total possible number. A central question for self-organizing swarms interacting through sparse networks is whether or not collective motion states can emerge where all agents have coherent and stable dynamics. In this work we introduce the phenomenon of swarm shedding in which weakly-connected agents are ejected from stable milling patterns in self-propelled swarming networks with finite-range interactions. We show that swarm shedding can be localized around a few agents, or delocalized, and entail a simultaneous ejection of all agents in a network. Despite the complexity of milling motion in complex networks, we successfully build mean-field theory that accurately predicts both milling state dynamics and shedding transitions. The latter are described in terms of saddle-node bifurcations that depend on the range of communication, the inter-agent interaction strength, and the network topology.

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