Form single neurons in culture to the behaving animal;

1. From 1.5 kilograms of flaccid matter, convoluted folds, about 100 billion neuronal components, hundreds of trillions of interconnections, many thousand kilometers of cabling, and a short cultural history emerged calculus, Swan Lake, Kind of Blue, the Macintosh, and The Master and Margarita. The brain is often casually described as the most complex system in the universe. What could this mean? …….. Our task as neuroscientists is to assess how complexity - the concept or the science - can help us better understand the workings of nervous systems. Complexity and the Nervous System Christof Koch and Gilles Laurent SCIENCE, April 1999, VOL 96, 284

2. Form single neurons in culture to the behaving animal; A quest for general motifs in neuronal systems’ form and function

3. The ultimate goal of our work is shedding light on some of the most fundamental principles responsible for the superior information processing capabilities and elevated plasticity of our brain.

4. The rationale behind this study is that roots or basic precursors of these much quested principles might already be recognizable in the dynamical activity of simple invertebrate ganglia and spontaneously constructed networks composed of dissociated ganglion cells

5. Morphological characterization of cultured neuronal networks – optimization principles Optimization & constraints in neural branching: - Anchors based flexibility - Two strategies ofoptimization Functional characterizations: from stand-alone cultures to task-performing animals

6. Morphological characterization of cultured neuronal networks – optimization principles

7. Optimization & constraints in neural branching: - Anchors based flexibility - Two strategies ofoptimization

8. Morphological characterization of cultured neuronal networks – optimization principles Optimization & constraints in neural branching: - Anchors based flexibility - Two strategies ofoptimization

9. Functional characterizations: from stand-alone cultures to task-performing animals

10. Morphological characterization of cultured neuronal networks – optimization principles Optimization & constraints in neural branching: - Anchors based flexibility - Two strategies ofoptimization Functional characterizations: from stand-alone cultures to task-performing animals

11. The in vitro culture enables easy access for optical observation. Insect neurons offer an attractive model due to their large size, and the ease of culturing them in various conditions. It enables a comparison between networks originated from different sources.

14. After 24 h in culture about 50% of the cells survive. Around 25% of these already develop processes (neurites). Culture Development During dissociation the neurons lose their original neurites, leaving only the soma or the soma with a short stump.

15. 50m

16. 7 days after plating:

18. 100 microns After 14 days: highly clustered network

19. Morphological characterization of the whole network

20. Collective dynamics of 'small-world' networks D. J. Watts & S. H. Strogatz , Nature (1998) • Clustering coefficient • Path length

21. 1. C>>Crandom (Crandom~k/n), that is, a Small World Network is much more highly clustered than the corresponding random graph. 2. l regular>> l>lrandom, that is, the characteristic free path of a Small World Network is close to that of a random graph, and much smaller than that of a regular graph. Small-World Network requires:

23. Analyzing the networks as graphs: set of vertices connected via edges • All vertices are identical • All edges are identical • ignoring edge length, • edges directionality • We ignored edge multiplicity 4 5 3 2 6 1 #vertices (nodes, n) =240, # edges=290 Average node connectivity <k>=2.38, L=17.6, C=0.11

24. Lreg =n/2k Lrand=ln(n)/ln<k> Path Length:

25. Our networks Clustering coefficient: Albert and Barabasi, 2002

26. Our networks fall into the category of small world networks First example of in vitro neuronal network • A consequence of two opposing forces: • Maximum interconnected networks • Minimum energetic cost: • minimum wiring length / volume FUNCTION FORM Next, we will zoom in and look for mechanisms - leading to that optimized organization

27. Branching (I): Anchors Based Flexibility

28. 10 *

29. Looking for rules governing neuronal branching angles

30. T2 T1 T0 Structural constrains: Tension (Bray, 1979) 2 1 1

31. Minimizing a cost function: Volume optimization (Murray, 1926)

33. 10 SEM: Single neuron

34. Mechanical Manipulation: Junction points act as anchors, adds a degree of freedom in order to achieve flexibility, doing so, satisfying functional requirements.

35. Branching (II) Two optimization phases: Minimum time ; Minimum Length

37. Isolated Connected

38. % of angles % of angles angle [degree] angle [degree] Isolated Connected

39. Simulation: Total Length Growth time

40. Time Length 120 360 40 280 120 360 200 40 280 200 angle angle X

41. Two phases in neuronal and network development: before and after neuron-neuron contact Two optimization strategies Minimum Time Minimum Length Function Form

42. Morphological characterization of cultured neuronal networks – optimization principles Optimization & constraints in neural branching: - Anchors based flexibility - Two strategies ofoptimization Functional characterizations: from stand-alone cultures to task-performing animals

44. How do we quantify temporal structure? • Local features in segments of time series. • Temporal ordering and local rates. • Variation among segments.

46. Action potentials Bursts of action potentials IBI(n-1) IBI(n) IBI(n+1) Inter Burst Intervals (IBI)

47. Action potentials Bursts of action potentials Increments: IBI (n)– IBI (n-1) =ΔIBI IBI(n-1) IBI(n) IBI(n+1) Inter Burst Intervals (IBI)

48. Where and how is information stored?

49. Qualitative intuition

50. Structural complexity within sequence Amount of information Where and how is information stored?