Metastability in the Brain J.A.S. Kelso E. Tognoli Human Brain and Behavior Laboratory Center for Complex Systems and Brain Sciences

What are the coordination laws at work in the brain to organize the activity of its numerous and heterogeneous components? Kelso’s approach: Coordination Dynamics transcends levels of behavior, brain and groups of brains (societies) Our essay today: The principle of metastability observed in the extended HKB model applies to brain dynamics (Kelso, 1995; Friston, 1997; Bressler and Kelso, 2001; Fingelkurts & Fingelkurts, 2004; Perez-Velazquez & Wennberg, 2004; Werner, 2006).

Metastability: from L. meta- beyond and -stabilis able to stand  =  - a sin  - 2b sin (2  ) +  Q  t Initial HKB model: Symmetry of the components Extended HKB model: Symmetry-breaking

2 stable fixed points, 2 unstable fixed points multistability 1 stable fixed point, 1 unstable fixed point Notice the transient inflexion at the ghost of the annihilated fixed point Metastability End of states, only transients and tendencies The control parameter did not change at predefined times to create a succession of states and transitions. This metastable regime corresponds to fixed parameters of the model. The tendency of the trajectory to bend to horizontal (tendency to integrate, reminiscent of state) or vertical (tendency to segregate, reminiscent of transition) is inherent.

segregation integration

segregation integration information Awake resting state Epilepsy Cognition Schizophrenia Autism Cn

Symmetry breaking. Heterogeneity of the coordinating elements. Disappearance of fixed points Dynamical exploration of various regions in the attractor landscape.. SymmetrySymmetry Broken Symmetry  =  - a sin  - 2b sin (2  )  = - a sin  - 2b sin (2  )

Metastability in the Brain empirical evidence - predictions

Measuring metastability in the brain

Segregation

Integration

Metastability Dwell time Escape time

“Coordination in the brain is like a Balanchine ballet. Neural groups briefly couple, some join as others leave, new groups form and dissolve, creating fleeting dynamical coordination patterns of mind that are always meaningful but don’t stick around for very long.” Kelso & Engstrøm (2006) The Complementary Nature.

 0 -  -2  How to recognize metastability? Associated signs Level of coordinating elements: -Frequency altered by the coupling: shift/broadening of the spectrum Level of the system: -Increased phase coherence between the coordinating elements Collective variable proper -Relative phase between the coordinating elements Dwell time  0 -  -2  Escape time Provided the ability to measure accurately the oscillations of the coordinating elements (spatial resolution, identification of stationary segments, idling vs active coupling…)

metastabilitystate/transition How to distinguish metastability from state/transition Bressler & Kelso, TICS, 2001 [LFP, Coherence] Rodriguez et al, Nature, 1999 [EEG, PLV] Phase scattering Phase scattering  0 -  -2   0 -  -2  Stationarity not met Dwell and escape times

Advantages arising from a metastable regime 1.Coordination extended to a larger range of applicable systems: broken symmetry, heterogeneity of the components 2.Speed: no need for a disengagement mechanism (phase scattering) to leave the attractor( ’ s ghost) 3.Flexibility: a series of attracting tendencies can be visited dynamically over the time course of the Coordination Variable 4. Balance integration~segregation: situates the system in the range of maximal information 1.Coordination extended to a larger range of applicable systems: broken symmetry, heterogeneity of the components 2.Speed: no need for a disengagement mechanism (phase scattering) to leave the attractor( ’ s ghost) 3.Flexibility: a series of attracting tendencies can be visited dynamically over the time course of the Coordination Variable 4. Balance integration~segregation: situates the system in the range of maximal information

Metastability in the Brain Acknowledgments: GC. De Guzman Gautam Vallabha