## Massless Bosons Cytoskeletal Self Focusing

The complexity of biological systems has attracted the interest of nonbiologists who possess mathematical tools useful for "many body problems." In addition to Fröhlich, these include a group of scientists from the University of Milan (Del Giudice, Doglia, Milani and Vitiello, 1986). Viewing living matter as a sea of electric dipoles, they have taken advantage of mathematical and computer tools used to keep track of the countless particles involved in nuclear reactions. Using a mathematical approach called quantum field theory, the Milan group considers electret states and the consequent ordering of water around biomolecules as sets of dipoles whose states, order and symmetry have collective properties. In a typical nonbiological system, component dipoles are random and disordered, resulting in an overall symmetry.

Such a system would look the same when viewed from any angle ("rotationally invariant"). In living systems, order is induced by reduction of tridimensional symmetry to a rotational alignment along filamentous electrets such as cytoskeletal structures. According to the Milan group quantum field theory and the "Goldstone theorem" require that the symmetry breaking ("Bose condensation") results in long range interactions among system components (dipoles) conveyed by massless particle/waves ("Goldstone bosons"). The Milan group argues that the energy required to generate massless bosons is invested in the electret states of biomolecules and correlated fluctuations of their surrounding water and ions.

Celaschi and Mascarenhas (1977) showed that electret activation energy of biomolecules (0.2-0.4 electron volts) is equivalent to the hydrolysis of one ATP or GTP molecule and what Davydov predicted for initiation of solitons. Consequently solitons, massless bosons, and Frolich's coherent polarization waves may be synonymous.

Pursuing their quantum field approach, Del Giudice and his colleagues came to an astounding concept of self-focusing of electromagnetic energy within cytoskeletal filaments. Electromagnetic energy exceeding a threshold and penetrating into cytoplasm would be confined inside filaments whose diameters depended on the original symmetry breaking ("Bose condensation") of ordered dipoles. Any electric disturbance produced by thermally fluctuating dipoles or by any other source would be confined inside filamentous regions. Ordering is preserved outside the filaments and is disrupted only inside where energy becomes concentrated (the "Meissner effect"). The diameter of the self focusing energy filaments depends on the polarization density, or ordering of biological water. Del Guidice's group calculated a self focusing diameter of about 15 nanometers, precisely the inner diameter of microtubules! Del Guidice and colleagues feel the cytoskeleton is the material consequence of dynamic self focusing of polarization waves in the cytoplasm. The observed diameters of self focused optical beams in simple nonbiological liquids are of the order of microns; correlation among components is created by propagation of waves rather than as a specific property of the material itself. The Milan group concludes that focusing occurs in cytoplasm of eukaryotic cells due to the spatial coherence and ordering imparted by cytoskeletal electret behavior.

The self-focusing predicted by the Milan group would have interesting capabilities. Energy is refracted into beams which become surrounded by cylindrical waveguides: the Indian rope trick. Coherency imparted to the refracted energy by either a Fröhlich-type mechanism or periodic structure of a cytoskeletal waveguide biomolecule could lead to holographic mechanisms. A rudimentary theory of waveguide/holographic behavior in microtubules has been described (Hameroff, 1974). Photorefractive crystals can be used to generate dynamic, real time holography (Gower, 1985) and MT could be projecting dynamic cytoplasmic holograms.

Models of cooperative protein dynamics described by Davydov solitons or Fröhlich coherent oscillations may be different perspectives of the same phenomena. Tuszynski and co-workers (1984) have compared the two approaches and their respective emphasis. They observed that Fröhlich's model concentrates on time-independent effects, or stable states, to explain the establishment of order, whereas Davydov's model highlights time dependent propagation of order via solitons.

The overlapping cooperative models of protein conformational dynamics (coherence, resonance, solitons, electrets, self focusing) are of interest when applied to specific structural elements with relevant properties. For example, Davydov's model of soliton propagation was originally applied to contractile coupling between actin and myosin. The cytoskeleton appears uniquely suited to take advantage of cooperative dynamics related to information processing. Chapter 8 reviews evidence and models of cytoskeletal information processing based on cooperative dynamics. The next chapter describes anesthesia-the result of inhibition of collective, cooperative protein conformational dynamics in the brain.

## Post a comment