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Important biological events involve spatial transfer of energy along protein molecules. One well known example is the contractile curling of myosin heads in muscle contraction, fueled by the hydrolysis of ATP molecules. These quanta of biological energy are equivalent to 0.43 electron volts, only 20 times greater than background energy and insufficient to excite molecular electronic states. Consequently, under usual conditions biological systems do not emit photons. This implied to Davydov (1977) during the 1970's that ATP hydrolysis energy is transferred by vibrational excitations of certain atomic groups within proteins. Davydov focused on the alpha helix regions of proteins and identified the "amide 1" (carbon-oxygen double bond) stretch vibration of the peptide group as the most likely "basket" in which energy may be carried. His selection was based on the "quasi-periodic," or crystal-like arrangement of amide 1 bonds, their low vibrational energy (0.21 electron volts-half the energy of ATP hydrolysis) and their marked dipole moment (0.3 Debye). According to linear analysis, energy transported by this means should spread out from the effects of dispersion and rapidly become disorganized and lost as a source of biological action. However Davydov analyzed nonlinear aspects of the amide 1 stretch and concluded that amide 1 vibrations are retroactively coupled to longitudinal soundwaves of the 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 %. For % 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 103 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 %, 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,

1985). Definitive resolution of the existence of solitons in biological materials may await the imminent advent of nanotechnology (Chapter 10).

Davydov has considered other types of solitons such as those in solid three-dimensional crystals which have phase transitions. He contends that sufficient anharmonicity in these lattice structures will produce soliton type excitations representing themselves as local displacements of the equilibrium positions moving along the molecular chains. These are called acoustic solitons. Other, "topological" solitons are described as symmetry "kinks" which travel through an ordered medium.

Toda (1979) invoked the concept of solitons to describe local displacements from equilibrium positions of molecules in one dimensional lattices. He studied molecular chains and assumed that displacement of individual molecules within the chain interacted with neighboring molecules. Mathematical evaluation of Toda lattices by Davydov show localized excitations described by a bell shaped function characterizing a reduction in the distance between molecules in the excitation region of the lattice. These are called "supersound acoustic solitons," or "lattice solitons" and have been modeled in proteins by Bolterauer, Henkel and Opper (1986).

Davydov's work further suggests that excess electrons can be captured by supersound acoustic solitons and conveyed along with them, giving rise to "electrosolitons." Electron transfer between donor-acceptor pairs of proteins are found in photosynthesis, cell respiration (ATP generation) and the activity of certain enzymes. These arrangements of structures are often called electron transport chains. Davydov observes that electron transfer has traditionally been assumed to be accomplished by quantum mechanical tunneling as first proposed by Britton Chance and colleagues (Devault, Parkas, Chance, 1967). In these systems, electrons are generally transferred between centers spaced about 3-7 nanometers apart. Davydov argues that this electron transfer can be better explained by an electrosoliton.

Figure 6.5: Computer simulation showing energy (vertical axis) localization along distance (southwest to northeast axis) as function of anharmonicity (southeast to northwest axis). Over a specific range, energy becomes localized and travels as solitary wave, or soliton. With permission from Bolterauer, Henkel and Opper (1986).

Figure 6.5: Computer simulation showing energy (vertical axis) localization along distance (southwest to northeast axis) as function of anharmonicity (southeast to northwest axis). Over a specific range, energy becomes localized and travels as solitary wave, or soliton. With permission from Bolterauer, Henkel and Opper (1986).

Concrete evidence exists for solitons as giant waves in or underneath the ocean, as optical solitons in laser fiber optics and in other systems. Current technologies are incapable of proving or disproving biological solitons. If Davydov is correct about myosin heads, then solitons are responsible for the molecular level filamentous contractions that drive every move we make. Propagating solitons in the cytoskeleton could be the dynamic medium of biological information processing. If so, solitons would be to consciousness what electricity is to computers.

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