Self-Regulated Complexity of Bio-Networks Activity

1. Self-Regulated Complexity of Bio-Networks Activity Phys Rev Lett in press Eshel Ben Jacob Eyal Hulata Itay Baruchi Ronen Segev Yoash Shapira Complexity is still a blurred intuitive notion with no agreed upon definition Inspired by the recorded activity of cultured neural networks We try to make sense out of the mess By looking for two quantified observables: Regularity and Complexity associated with the intuitive notion

2. On the Agenda Cultured networks and their activity Hints about self-regulation The requirements from the new observables Looking at the time-frequency plane The best tilling The sequence regularity The structure factor and structural complexity Results Looking ahead

3. frequency time Our approach: Relative information in both time and frequency: Tiling of the time-frequency plane

7. V. What do we expect from a measure of Structural complexity? [Hubberman and Hogg, Physica D 86, Gellmann “The Quark and the Jaguar”]

8. Comparison of the Time-frequency domains shuffled recorded New clue Local and global variations

9. Neuronal cell cultures • Dissociated cell culture from the cortex of one-day-old rats. • 10,000 neurons/mm2.

10. Multi Electrode Array 50µm

11. Non-Invasive Recording of the Activity (Capacitive Coupling between neurons and electrodes) 30micro Polymer one action potential of one neuron 20 milliseconds …….

12. Formation of Bursting Events Time

13. Tracking a WOOZLE Information-bearing templates in the Temporal ordering of the Recorded spontaneous activity

14. CONCISE HISTORICAL PERSPECTIVE Neurons are binary elements Localized information storage Distributed information storage Currently: a Dynamic Networks picture RATE CODING vs. PULSE CODING Guiding Questions 1. Is the spontaneous activity arbitrary or regulated ? 2. Can it provide clues about coding, storage and retrieval of information ?

15. Statistical scaling properties of the SBE sequences I(i) DifI(i) Interval distribution Increment distribution

16.  0 0  2 1/ The sequence's plasticity 1/ The sequence's regularity Probablity density function (pdf) Increment length (sec/τbin) Lévy distribution =2

17. Comparison between networks of various sizes 1. Similar most probable interval ~10 sec 2. DifI(i) can be approximated with zero-means symmetric Levy distributions (higher density) Smallmedium large 50 20,000 1000,000

18. This feature can be simulated in modeled networks if the neurons have two degrees of freedom and the synapses are dynamical Experimental Model 0.1 sec 100 sec 0.1 sec 100 sec

19. Interfacing Real and Modeled Networks Volman et al., Phys Rev E 1.Feeding the modeled network from regulating neurons 2.Testing the effect of synaptic strengths conclusion To show the same rate of activity as the similar networks the large networks have to be composed of coupled sub-networks

20. Hints about Self-Regulation Controlled large variations vs. arbitrary large fluctuations 2 < [DifI(i)] > recorded shuffled model network

21. x10 another hint : hierarchical temporal ordering Bursts of SBEs , bursts of bursts of SBEs … Time cascade 1ms 100ms 5-10sec 500-100sec SBE width Inter-SBEs Inter bursts of SBEs Spike width

22. Third hint :LONG-TIME CORRELATIONS OVER a DAY !!! [Hz]

23. THE OBSERVATIONS IMPLY THAT Both the PULSE CODING and the RATE CODING do not provide the proper template A new picture is needed

24. A DEDUCED CLUE The recorded sequences should be mapped (via wavelet packet decomposition) into time-frequency domains Local and Global variations “energy” frequency resolution frequency time resolution time

25. Structural complexity What have we seen so far? • Local features in segments of time series. • Temporal ordering and local rates. • Variation among segments.

26. Detour - Time-Frequency analysisA. Wavelet Transform

27. Detour - Time-Frequency analysisA. Wavelet Transform

28. Time bins Frequency bands Time bins Time-Frequency Plane of the Wavelet Transform

29. Detour - Time-Frequency analysisB. Wavelet Packets Decomposition Coifman & Wicherhauser, 1993

30. How do we choose packets?

32. Phase I: Level 0 Level 1 Level 2 The best tiling: Phase Ia: or ? Phase Ic: or ? Phase Id: or ? Phase II: Level 0 Level 1 Phase Ib: or ? Phase IIa: or ? The Best Tiling Algorithm Thiele & Villemous, A.C.H.A., 1996

33. Back to Structural complexity…

34. Physical Intuition - magnetization

36. Regularity Measure

37. Structure factor

38. Structural complexity

39. Our results:

40. The Regularity-Complexity Plane Studied using artificial sequences with Levy distribution

41. frequency frequency time time Applying to neuronal data: Neuronal time series of SBEs Shuffled Neuronal time series

42. Zoom: shuffling of neuronal data

44. Finding a characteristic time scale x10

45. Testing the Generality of Motives Investigating cultured networks made of neurons taken from the frontal ganglion.

46. In vivo frontal ganglion In vitro Ex vivo

47. RATIONALE This ganglion has a specific role (feeding). We will compare recordings from the ganglion inside the animal while feeding and while “thinking”, and when on the plate. Looking for “function-follow-form” in action

48. The Statistical Scaling Parameters of Ex-vivo In-vitro 3 different neurons In-situ In-vivo digesting “thinking”

49. 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 Culture complexity In-vivo 1.4 Culture 1.6 2.0 1.8 alpha 2.1 gama 6.0 In-vivo (f) Ex-vivo Self-regulated complexity of neural activity Hulata et al., PRL Ayali et al., ? regularity In vitro In situ In vivo (thinking) Ex vivo

50. Spikes, 4 days 10sec Alternation between active and non-active phases. 5-6 days 20sec Burst organization 9-10 days 100sec Hierarchical structure Burst of bursts, 14 days 100sec Looking at Networks Development