Burst Synchronization Burst Synchronization transition in neuronal transition in neuronal network of networksnetwork of networks

Sun XiaojuanSun Xiaojuan

Tsinghua UniversityTsinghua University

ICCN2010, SuzhouICCN2010, Suzhou

2010-10-162010-10-16

OUTLINEOUTLINE

BackgroundBackground-- Importance of synchronization in neuronal systemsImportance of synchronization in neuronal systems

- Network of network structures of neuronal systems- Network of network structures of neuronal systems - Motivation of this work- Motivation of this work

Burst synchronization (BS) transition Burst synchronization (BS) transition in a neuronal network of networksin a neuronal network of networks- Mathematical Models- Mathematical Models

- Observed BS transition- Observed BS transition

ConclusionsConclusions

BackgroundBackground

Importance of synchronization in neuronal systems

Relationship between synchronization and cognitive behavior

Attention modulates synchronized neuronal firing in primate somatosensory cortex (Ref: Nature, 2000, 404: 187-190)

Attention modulates the firing rates of neurons in many parts of the visual system (Ref: Annu. Rev.Neurosci., 2000, 23, 315-341)

Expectation boosts synchrony in motor cortex: neurons in the primary motor cortex become transiently synchronized when a stimulus appears, or when it is expected to appear but it does not (Ref: Science, 1997, 278: 1950-1953)

Rivalry induces changes in synchrony in V1 (Ref: PNAS, 1997, 94: 12699-12704)

Importance of synchronization in neuronal systems

Relationship between synchronization and brain disorders

Disorder Neural synchrony Cognitive dysfunctions

Epilepsy Increase in local synchrony; evidence for a reduction in long-range synchronization

Perception, executive, processes, memory, attention, social cognitive

Alzheimer’s disease

Reduced neural synchrony during resting state; evidence for reduced functional connectivity

Working memory, perception, attention, executive process

Parkinson’s disease

Increase in neural synchrony in the basal ganglia, but also between subcortical-cortical structures

Especially motor functioning, but also perception, working memory ,attention, executive process

clustered structure (Ref. C.C. Hilgetag, Neuroinformatics, 2004, 2: 353-360)

Network of network structures of neuronal system

Bars indicate borders between nodes in separate clusters.

Not only clustered but also hierarchy (Ref. C.S. Zhou, et al. New J. Physics, 2007, 9: 178.)

Network of network structures of neuronal system

Neuronal system is complex and composed by network of networks

Motivation

Cited from Ref: Shen Yu et al., PRE, 2008, 77: 031920

BS transition in a neuronal BS transition in a neuronal

network of networksnetwork of networks

Mathematical Models

Equations of the discussed neuronal network

Mathematical Models

Neuronal Network structure:

BS transition in HR neuronal network

Two cases: M=2, consider the effects of inter- and intra-

coupling strength, the random link probability on synchronization of the clustered neuronal network

M>2, except for the above mentioned three factors, we will further consider the effects of cluster numbers on synchronization.

BS transition in HR neuronal network

M=2

BS transition in HR neuronal network

BS transition in HR neuronal network

BS transition in HR neuronal network

BS transition in HR neuronal network

BS transition in HR neuronal network

BS transition in HR neuronal network

Cited from PRE_77_031920

BS transition in HR neuronal network

We turn back to the first equation of Eq.(1) and rewrite it as

BS transition in HR neuronal network

M>2

BS transition in HR neuronal network

M>2

ConclusionsConclusions

Under some conditions, coupling strength inside or between subnetworks and the number of links can change the synchrony of a neuronal network, which has clustered structures.

The number of subnetworks inside a network also influence the synchrony.

Our results may give some implications for the importance of synaptic plasticity in neuronal systems.

Thanks for your attention!Thanks for your attention!Thanks Prof. Qishao Lu Thanks Prof. Qishao Lu and Prof. Guanrong and Prof. Guanrong

ChenChen