Cooperativity and Coherence

Collective effects manifest as diffuse reverberation, sustained oscillation, phase transitions, and deterministic chaos have been observed in computer simulation of parallel networks (Choi and Huberman, 1984). Collective mechanisms can exert long-range cooperativity and an executive level of organization within parallel arrays. Collective phase transitions in brain parallel arrays could be a fabric of consciousness, an "idea" emerging like the property of superconductivity from a large number of simple, "aligned" subunits. In most views the neuronal synapse is the brain's fundamental subunit, however synaptic activities are the net result of dynamic processes orchestrated by the cytoskeleton. Layers of cytoskeletal organization are evident within neurons, and their participation in cognitive functions appears unavoidable. Thus the highly branched cytoskeleton may be another dimension of brain organization, perhaps related to neuronal networks as a "fractal." Many natural processes manifest fractals, growth patterns in which local areas are scaled down images of the entire pattern. This occurs through some form of long range correlation in the pattern: components "know about each other over distances far in excess of the range of the forces between them" (Sander, 1986). Fractal relationships are one type of long range cooperativity (Figures 1.7 and 1.8). Densely parallel interconnected networks of cytoskeletal structures resemble larger scale networks of neurons, and may be viewed as fractal subdimensions of neural networks.

Long range cooperativity and collective mechanisms are favored by the property of coherence which means peak energy excitations within an area occur "in phase," or simultaneously as in a laser. How may coherence arise in distributed processes? DeCallatay (1986) proposes that coherence in the brain and AI need to be imparted from the top of a hierarchy downward, like the chief executive of a corporation setting goals and intentions. A different view is that of an underlying rhythm or beat to which all elements are tuned. Rhythmic coupling among neurons may be important, and some interpreters of brain electrical activity (EEG) believe regional brain wave entrainment leads to functional regions of mental representation. A more fundamental coherence at the level of protein assemblies may be universally important for biological cooperativity and communication.

Figure 1.7: Tree fractal in which branching patterns are the same at every scale, or dimension. Long range order is present. Computer generation by Conrad Schneiker.

Figure 1.8: Branching box fractal in which patterns are identical at every scale, or dimension. Long range order is present. Computer generation by Conrad Schneiker.

Proteins and their components oscillate among specific conformational states which exist transiently for durations ranging from femtoseconds (10-15 sec) to minutes or longer. As will be described in Chapter 6, functional conformational states appear coupled to nanosecond (10-9 sec) oscillations and more prolonged "metastable states." Herbert Fröhlich, an eminent physicist who helped develop the theory of superconductivity in the 1950's, has devoted recent efforts to the question of cooperativity in biological systems. Fröhlich (1970, 1975, 1984) argues that biochemical energy supplied to biomolecular assemblies can result in coherent elastic vibrations of individual subunits in the sub-nanosecond time range. The effect presupposes a voltage effect in the biomolecule (i.e. an "electret") and an organized spatial structure whose geometry favors coupling among subunits. Coherent oscillations in an appropriate medium like the cytoskeleton can lead to collective phenomena such as long range cooperativity, communication, and holography.

Another model can help explain long range cooperativity in biomolecules. Soviet biophysicist A. S. Davydov has considered almost lossless energy transfer in biomolecular chains or lattices as wave-like propagations of coupled conformational and electronic disturbances: "solitons." Davydov used the soliton concept to explain molecular level events in muscle contraction, however solitons in the cytoskeleton may do what electrons do in computers.

The Fröhlich and Davydov approaches may be seen as complementary (Tuszynski, Paul, Chatterjee, and Sreenivasan, 1984). Fröhlich's coherency model focuses on time-independent effects (stable states) leading to order whereas Davydov's model looks at time-dependent effects which propagate order through the system. These and other theories of collective effects applied to information processing in cytoskeletal lattices will be described in Chapters 6 and 8.

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