Visits since 21 sepember 1998

A.M. SELVAM

Indian Institute of Tropical Meteorology, Pune 411008, India Fax : (0212) 347825 Telephone: (0212) 330846 E-mail: [email protected] Website : http://www.geocities.com/CapeCanaveral/Lab/5833

The neural networks of the human brain act as very efficient parallel processing computers co-ordinating memory related responses to a multitude of input signals from sensory organs. Information storage, update and appropriate retrieval are controlled at the molecular level by the neuronal cytoskeleton which serves as the internal communication network within neurons. Information flow in the highly ordered parallel networks of the filamentous protein polymers which make up the cytoskeleton may be compared to atmospheric flows which exhibit long-range spatiotemporal correlations, i.e. long-term memory. Such long-range spatiotemporal correlations are ubiquitous to real world dynamical systems and is recently identified as signature of self-organized criticality or chaos. The signatures of self-organized criticality i.e. long-range temporal correlations have recently been identified in the electrical activity of the brain. The physics of self-organized criticality or chaos is not yet identified. A recently developed non-deterministic cell dynamical system model for atmospheric flows predicts the observed long-range spatiotemporal correlations as intrinsic to quantum-like mechanics governing flow dynamics. The model visualises large scale circulations to form as the result of spatial integration of enclosed small scale perturbations with intrinsic two-way ordered energy flow between the scales. Such a concept maybe applied for the collection and integration of a multitude of signals at the cytoskeletal level and manifested in activation of neurons in the macroscale. The cytoskeleton networks inside neurons may be the elementary units of a unified dynamic memory circulation network with intrinsic global response to local stimuli. A cell dynamical system model for human memory circulation network analogous to atmospheric circulations network is presented in this paper.

The neural network of the human brain responds as a unified whole memory bank to a multitude of input signals from the environment and functions with a high degree of robustness and stability. The three aspects of neural networks memory bank are, storage, real-time update and retrieval. The memory is believed to be embedded in the strength of the numerous connections or synapses in the network. Sensory inputs (electrical) produce particular patterns of activity in groups of neurons which then trigger optimal response to the input signal. The cooperative response of millions of neurons to a multitude of input signals has been compared to a very efficient parallel processing computer with neurons and their synaptic connections as fundamental units of information processing, like switches within computers. However, recent studies by Hameroff et al [1,2] and Rasmussen et al [3] show that neurons and synapses are extremely complex and resemble entire computers, rather than switches. The interiors of neurons (and other eucaryotic cells) are now known to contain highly ordered parallel networks of filamentous protein polymers collectively termed the cytoskeleton. Information storage, update and appropriate retrieval are controlled at the molecular level by the neuronal cytoskeleton which serves as the internal communication network within neuron. Organization of information at the molecular level in the cytoskeletal network contributes to the overall response of each neuron and the collective activity pattern of neurons then governs the response to the environmental stimuli.

The general awareness or consciousness of the individual to environment may also be governed by the overall background activity pattern of the neurons and their cytoskeletal networks. Coherent signal flow patterns in neural networks may form the basis for general consciousness and response to stimuli (external or internal). Inputs signals trigger spontaneous appropriate coherent pattern formation in the activity of the neurons with implicit spatial correlations in the activity pattern. The time variation of electrical activity of the brain as recorded by the Electro Encephalogram (*EEG*) exhibits fluctuations on all scales of time, i.e. a broadband spectrum of periodicities (frequencies) contribute to the observed fluctuations [4]. Power spectral analysis which is used to resolve the component frequencies (*f*) and their intensities, shows that the intensity (power) of the component frequencies follow the inverse power law form *1/f ^{B}* where

Atmospheric flows exhibit self-organized criticality or long-range spatiotemporal correlations manifested in the selfsimilar fractal geometry to the global cloud cover pattern concomitant with inverse power law form *1/f ^{B}* for power spectrum of temporal fluctuations in meteorological variables such as temperature, pressure, etc. documented by Tessier et al [22]. The co-operative existence of fluctuations ranging in size (duration) from the turbulence scale of millimetres (seconds) to the planetary scale of thousands of kilometres (years) contribute to coherent weather pattern in atmospheric flows. Townsend [23] postulated that large eddies (waves) form in atmospheric flows as a chance configuration (envelope) of enclosed turbulent (small scale) eddies. A hierarchical continuum of eddies is therefore generated with larger eddies enclosing smaller eddies. Since large eddy is but the integrated mean of enclosed turbulent eddies, atmospheric eddy energy (kinetic) distribution follows normal distribution characteristics according to the Central Limit Theorem in Statistics. The eddy kinetic energy represented by square of eddy amplitude then represents the probability density. Such a result that the additive amplitudes of eddies, when squared, represent probability densities is observed in the subatomic dynamics of quantum system such as the electron or photon. Atmospheric eddy energy spectrum therefore follows quantum-like mechanical laws [19,20,21]. Condensation of water vapour in updraft regions of large eddies give rise to cloud formation while adjacent downdraft regions are associated with evaporation and cloud dissipation, thereby accounting for the discrete cellular structure to cloud geometry.

Frohlich [24] had described analogous self-organization of vibrational modes of all frequencies triggering coherent activity in biological functions. Insinna [25] has summarized Frohlich’s coherent excitation concept as follows. More than 20 years ago Frohlich [24,26-28] introduced the concept of cooperative vibrational modes between proteins. Coherent oscillations in the range of 10^{10}- 10^{12} Hz involving cell membranes, *DNA* and cellular proteins could be generated by interaction between vibrating electric dipoles contained in the proteins as a result of nonlinear properties of the system. Through long-range effects proper to Frohlich’s nonlinear electrodynamics a temporospatial link, is, in fact, established between all molecules constituting the system. Single molecules may thus act in a synchronized fashion and can no longer be considered individual. New unexpected features arise from such a dynamic system, reacting as a unified whole entity [25]. Coherent Frohlich oscillations may be associated with the dynamical pattern formation of intraneuronal cytoskeletal architecture which coordinates and integrates information flow into the neuron and generates output signal. Hameroff and colleagues [1,29-31] have simulated such interaction in their cellular automata model.

Fractal architecture to information flow path results in spatiotemporal integration of signals so that the fractal system responds as a unified whole to a multitude of input signals. Two disparate examples for such self-organized information flow networks are atmospheric flows and the neural networks of the human brain.

*Acknowledgements*

The author is grateful to Dr. A. S. R. Murty for his keen interest and encouragement during the course of the study. The author is indebted to Professor M. S. El Naschie for inspiration and guidance in this field of study

Thanks are due to Mr .R. D. Nair for typing the manuscript.

2. Hameroff, S. R., Rasmussen, S., Mansson, B., Molecular automata in microtubules: basic computational logic of the living state? in *Artificial life : Proceedings of an interdisciplinary workshop on the simulation, origin and representation of living systems*, ed. Cl Langton, M. A : Addison Wesley,1989.

3. Rasmussen, S., Karampurwala, H., Vaidyanath, R., Jensen, K. S., Hameroff, S., Computational connectionism within neurons : A model of cytoskeletal automata subserving neural networks, *Physica D*, 1990, **42**, 428-449.

4. Holden, A. V., Hyde, J., Zhang, H., Computing with the unpredictable : Chaotic dynamics and fractal structures in the brain, In : *Applications of fractals and chaos, *eds. A.J. Crilly, R.A. Earnshaw and J. Jones, New York : Springer-Verlag, 1993.

5. Bak, P., Tang, C. Wiesenfeld, K., Self-organized criticality, *Phys. Rev.A.*, 1988, **38**, 364-374.

6. Mandelbrot, B.B., *Fractals : Form, Chance and Dimension , *San Francisco : W. A. Freeman,1977.

7. Gleick, J., *Chaos : Making a New Science*, New York, Viking, 1987.

8. Nottale, L., Fractals and the quantum theory of spacetime. *Int'l J. Mod. Phys. A*, 1989, **4(19)** , 5047-5117.

9. Ord, G. N., Fractal space-time : a geometric analogue of relativistic quantum mechanics .*J. Phys .A: Math. Gen.* ,1983, **16** , 1869-1884.

10. El Naschie, M. S., Penrose tiling, semi-conduction and cantorian *1/f*^{a} spectra in four and five dimensions. *Chaos, Solitons and Fractals* , 1993, **3(4)** , 489-491.

11. Koruga, D., Information physics: in search of scientific basis of consciousness. In *Toward a Scientific Basis for Consciousness* Ed. Hameroff, S. et al, MIT Press,1995.

12. Koruga, D., Molecular network as a sub-neural factor of neural network. *BioSystems* , 1990, **23** , 297-303.

13. Koruga, D., Andjelkovic, M. ,Jankovic, S. and Hameroff, S., Cytoskeleton as feed back control system in neuron,399-402 In: *Artificial Neural Networks 2*, edited by Aleksander,I. And Taylor,J., Amsterdam, Elsevier Science Publishers, 1992.

14. Goldberger, A. L., Rigney, D. R., West, B.J., Chaos and fractals in human physiology, *Scientific American*, 1990, **February** , 41-47.

15. Kaiser, F., Biophysical models related to Frohlich excitations, *Nanobiology*, 1992, **1**, 149-161.

16. Selvam, A. M., Deterministic chaos model for self-organised adaptive networks in atmospheric flows, Proc. 41st Nat'l. Aerospace and Electronics Conference.(NAECON 89) 22-28 May 1989, Dayton, Ohio, USA.

17.Selvam A. M., Deterministic chaos: A signature of quantum like mechanics in self-organized adaptive networks, Proc. NAECON 91, Dayton, May 20-24, 1991.

18. Selvam A. M.,Radhamani R., Vijayakumar R., Spontaneous organization of intelligent fuzzy logic networks in atmospheric flows, Proc. NAECON '93 (IEEE National Aerospace and Electronics Conference),Dayton, Ohio, May 24-28, 1993.

19. Selvam A. M. and Suvarna Fadnavis, Signatures of a universal spectrum for atmospheric interannual variability in some disparate climatic regimes*. Meteorology and Atmospheric Physics* , 1998, **66**, 87-112.

20. Selvam A. M. and Suvarna Fadnavis, Superstrings, Cantorian-fractal Space-time and Quantum-like Chaos in Atmosperic flows.* Chaos, Solitons and Fractals*, 1998 (in Press)

21. Selvam A. M. and Suvarna Fadnavis, Cantorian fractal spacetime, quantum-like chaos and scale relativity in atmospheric flows. *Chaos, Solitons and Fractals, *1998. (in Press)

22. Tessier, Y., Lovejoy, S., Schertzer, D., Universal multifractals : Theory and observations for rain and clouds, *J. Appl. Meteor*.,1993, **32**, 223-250.

23. Townsend, A .A. , *The structure of turbulent shear flow*, U.K. : Cambridge University Press, 1956.

24. Frohlich, H., Long-range coherence and energy storage in biological systems, *International Journal of Quantum Chemistry,* 1968, **2**, 641-649.

25. Insinna, E.M., Synchronicity and coherent excitations in microtubules, *Nanobiology,* 1992,* ***1**, 191-208.

26. Frohlich, H., ‘Long-range coherence and the action of enzymes’ *Nature*, 1970, **228**, 1023

27. Frohlich H., The extraordinary dielectric properties of biological materials and the action of enzymes, *Proceedings of the National Academy of Sciences, USA***,** 1975, **72**, 4211-4215.

28. Frohlich, H., Coherent oscillations in active biological systems, in *Modern Biochemistry* eds. F. Gutmann and H. Keyzer, New York: Plenum Press, 1986.

29. Hameroff, S. R., Smith, S. A., Watt, R. C., Nonlinear electrodynamics in cytoskeletal protein lattices, in *Nonlinear Electrodynamics in Biology and Medicine* edited by F.A. Lawrence and W.R. Adey, New York : Plenum,1984.

30. Smith, S. A., Watt, R. C., Hameroff, S. R., Cellular automata in cytoskeletal lattices, *Physica D* ,1984, **10**, 168-174.

31. Hameroff, S., Quantum coherence in microtubules : a neural basis for emergent consciousness? *Journal of Consciousness Studies*,1994, **1**,91-118.

** This page hosted by Get your own Free Home Page**