Metastability in the Brain J.A.S. Kelso E. Tognoli

1. Human Brain and Behavior Laboratory Metastability in the BrainJ.A.S. Kelso E. Tognoli Center for Complex Systems and Brain Sciences kelso@ccs.fau.edu tognoli@ccs.fau.eduhttp://www.ccs.fau.edu/section_links/HBBLv2/

2. 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).

3. f = dw - a sinf - 2b sin (2f) + Qxt Metastability: from L. meta- beyond and -stabilis able to stand Initial HKB model: Symmetry of the components Extended HKB model: Symmetry-breaking

4. Metastability 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. End of states, only transients and tendencies 1 stable fixed point, 1 unstable fixed point Notice the transient inflexion at the ghost of the annihilated fixed point 2 stable fixed points, 2 unstable fixed points multistability

5. segregation integration

6. Cn information Cognition Awake resting state Schizophrenia Autism Epilepsy segregation integration

7. Symmetry f = - a sinf - 2b sin (2f) BrokenSymmetry f = dw - a sinf - 2b sin (2f) • Symmetry breaking. Heterogeneity of the coordinating elements. • Disappearance of fixed points • Dynamical exploration of various regions in the attractor landscape.

8. Metastability in the Brainempirical evidence - predictions

9. Measuring metastability in the brain

10. Segregation

11. Integration

12. Metastability Dwell time Escape time Escape time

13. “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.

14. p 0 -p -2p p 0 -p -2p How to recognize metastability? Provided the ability to measure accurately the oscillations of the coordinating elements (spatial resolution, identification of stationary segments, idling vs active coupling…) 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 Escape time Dwell time

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

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

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