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

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

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 recorded shuffled New clue Local and global variations

9. Neuronal cell cultures Dissociated cell culture from the cortex of one-day-old rats. 10,000 neurons/ mm 2.

10. 50µm Multi Electrode Array

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

12. Time Formation of Bursting Events

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 RATE CODING vs. PULSE CODING Currently: a Dynamic Networks picture 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) Interval distribution Increment distribution DifI(i)

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

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 Small medium large 5020,0001000,000 (higher density)

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

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 recorded shuffled model network

21. another hint : hierarchical temporal ordering Bursts of SBEs, bursts of bursts of SBEs … x10 Time cascade 1ms 100ms 5-10sec500-100sec Spike width SBE widthInter-SBEsInter bursts of SBEs

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

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 time frequency “energy” time resolution frequency resolution Local and Global variations

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 analysis A. Wavelet Transform

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

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

30. How do we choose packets?

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

33. Back to Structural complexity…

34. Physical Intuition - magnetization

36. Regularity Measure

37. Structure factor

38. Structural complexity

39. Our results:

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

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

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 In vitro frontal ganglion 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 In-vitroEx-vivo In-vivoIn-situ “thinking”digesting 3 different neurons

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

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

51. 100msec10msec Electrical activity Recorded from 14 days network

52. Probability density function of increments distribution APs time series T 1 … T n-1, T n, T n+1 … Inter-spikes Intervals ISI n = T n -T n-1 Increments of ISI  (ISI) n = ISI n - ISI n-1 4 days5-6 days9 days 10 4 10 6 10 2 10 0 msec 10 0 10 2 10 4 msec 10 4 10 6 10 2 10 0 msec

53. log-log scale linear scale Inter burst intervals (IBI) distribution parameters “young” networks “mature” networks γ  2γ  2 5 < δ < 10 α  1.6 “young” network Pdf parameters γ  5γ  5 5 < δ < 10 α  1.2 “mature” network Pdf parameters Most probable interval Decay slope

54. t=0.002 Structural complexity of burst time series complexity regularity “young” networks “mature” networks “young” networks

55. Structural complexity of spike sequence during 4-6 days 0918361215 0918361215 time (hours) Complexity Regularity

56. 306121824 0 time (hours) 306121824 0 time (hours) Complexity Regularity Developments of the Bursts Regularity-Complexity

57. γ  5γ  5 5 < δ < 10 α  1.2 “mature” network Pdf parameters γ  2γ  2 5 < δ < 10 α  1.6 “young” network Pdf parameters α 1/ α; SC γ 1/ γ ; RM 0=δ 20=δ random periodic

58. Conclusions We have defined a new set of structural measures: Regularity Measure, Structure Factor, Structural Complexity. The measures fulfill both intuitive and quantitative requirements. The measures reveal new features of the neuro-informatic template of in-vitro neural networks. Future work: 1. comparison of in-vitro vs. in-vivo networks. 2. study the effects of chemical substances, coupling between networks, stimulations etc.

65. Regularity Measure