ULTIMATE COMPUTING - Quantum Consciousness Studies

Protein Conformational Dynamics 141
alpha helix, and that the coupled excitation propagates as a localized and
dynamically self sufficient entity called a solitary wave, or “soliton.” Davydov
reasoned that amide 1 vibrations generate longitudinal sound waves which in turn
provide a potential well that prevent vibrational dispersion, thus the soliton “holds
itself together.”
Solitary waves were first described by nineteenth century naval engineer John
Scott-Russell in 1844. While conducting a series of force-speed experiments for
boats on a Scottish canal, an accident happened. A rope broke and a canal boat
suddenly stopped, but the bow wave which the barge caused kept on going.
Russell galloped alongside the canal and followed the wave for several miles. He
described the exceptional stability and automatic self-organization of this type of
wave. Mathematical expressions of solitary waves can be given as particular
solutions of some nonlinear equations describing propagation of excitations in
continuous media which have both dispersive and nonlinear properties. These
solitary wave solutions have “particle-like” characteristics such as conservation of
form and velocity. Such traits led Zabusky and Kruskal (1965) to describe them
as “solitons.” As an answer to the problem of spatial transfer of energy (and
information) in biological systems, Davydov applied the soliton concept to
biological systems in general, and amide 1 vibrations within alpha helices in
particular. For solitons to exist for useful periods of time and distance, certain
conditions must be met. The nonlinear coupling between amide 1 bond vibrations
and sound waves must be sufficiently strong and the amide 1 vibrations be
energetic enough for the retroactive interaction to take hold. Below this coupling
threshold, a soliton cannot form and the dynamic behavior will be essentially
linear; above the threshold the soliton is a possible mechanism for virtually
lossless energy transduction.
Computer simulation and calculation of solitons have led to assumptions
about the parameters necessary for nolinearity and soliton propagation. A critical
parameter is the “anharmonicity,” or nonlinearity of the coupling of intrapeptide
excitations with displacement from equilibrium positions (Figure 6.5).
Anharmonicity is the nonlinear quality which determines the self capturing of the
two components of the, soliton. The degree to which the electronic disturbance
nonlinearly couples to the mechanical conformational change of the protein
structure is the crux of the soliton question. If the two are coupled as a step-like
functioning switch (nonlinear) rather than a direct linear correlation, they can
provide a “grain” to represent discrete entities capable of representing and
transferring information. An index for soliton viability, the anharmonicity
parameter, is known as χ. For χ greater than 0.3 x 10 -11 newtons, solitons in
computer simulation do propagate through the spines of an alpha helix at a
velocity of about 1.3 x 10 3 meters per second. The distance of 170 nanometers
corresponding to the length of a myosin head in striated muscle would then be
traversed by a soliton in about 0.13 nanoseconds. Computer simulations by
Eilbeck and Scott (1979) demonstrate, for above threshold values for the coupling
parameter χ, soliton-like excitations propagating along alpha helix spines in the
form of a local impulse with a size of a few peptide groups. Experimental data
supporting such biological solitons is slowly emerging. Although results from
biomolecular light scattering (Webb, 1980) seemed to provide confirmation
(Lomdahl et al., 1982), follow up work (Layne, et al., 1985) indicated another
source of the experimental observations. Optical experiments on crystalline
acetanilide (a hydrogen bonded, polypeptide crystal) however, do provide an
unambiguous demonstration of a localized state similar to that discussed by
Davydov (Careri, et al., 1984; Eilbeck, et al., 1984; Scott, et al., 1985; Scott,