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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
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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
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
frequency time Our approach: Relative information in both time and frequency: Tiling of the time-frequency plane
V. What do we expect from a measure of Structural complexity? [Hubberman and Hogg, Physica D 86, Gellmann “The Quark and the Jaguar”]
Comparison of the Time-frequency domains shuffled recorded New clue Local and global variations
Neuronal cell cultures • Dissociated cell culture from the cortex of one-day-old rats. • 10,000 neurons/mm2.
Non-Invasive Recording of the Activity (Capacitive Coupling between neurons and electrodes) 30micro Polymer one action potential of one neuron 20 milliseconds …….
Tracking a WOOZLE Information-bearing templates in the Temporal ordering of the Recorded spontaneous activity
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 ?
Statistical scaling properties of the SBE sequences I(i) DifI(i) Interval distribution Increment distribution
0 0 2 1/ The sequence's plasticity 1/ The sequence's regularity Probablity density function (pdf) Increment length (sec/τbin) Lévy distribution =2
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
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
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
Hints about Self-Regulation Controlled large variations vs. arbitrary large fluctuations 2 < [DifI(i)] > recorded shuffled model network
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
Third hint :LONG-TIME CORRELATIONS OVER a DAY !!! [Hz]
THE OBSERVATIONS IMPLY THAT Both the PULSE CODING and the RATE CODING do not provide the proper template A new picture is needed
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
Structural complexity What have we seen so far? • Local features in segments of time series. • Temporal ordering and local rates. • Variation among segments.
Time bins Frequency bands Time bins Time-Frequency Plane of the Wavelet Transform
Detour - Time-Frequency analysisB. Wavelet Packets Decomposition Coifman & Wicherhauser, 1993
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
The Regularity-Complexity Plane Studied using artificial sequences with Levy distribution
frequency frequency time time Applying to neuronal data: Neuronal time series of SBEs Shuffled Neuronal time series
Testing the Generality of Motives Investigating cultured networks made of neurons taken from the frontal ganglion.
In vivo frontal ganglion In vitro Ex vivo
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
The Statistical Scaling Parameters of Ex-vivo In-vitro 3 different neurons In-situ In-vivo digesting “thinking”
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
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