To understand how a soliton is instrumental in the process of catalysis, we have to understand a little of the quantum world. The common sense view, that we live in a world of 'objects' with rigidly defined boundaries, is not applicable when we begin to think about electrons, protons and the phenomena of the very small. Quantum mechanics is a statistical discipline that does not treat very small objects as exactly definable in space and time. The Uncertainty Principle portrays a world where a particle may inhabit a range of possible states. To handle this 'uncertainty,' quantum mechanics treats a particle as a wave function that encompasses its possible states. Nor is the wave function simply a convenient mathematical construct. The mathematics of probability wave functions can accurately describe the quantum world and demonstrate a high degree of consistency between the mathematics and empirical observation.

One of the surprising consequences of quantum theory is a phenomenon termed 'quantum tunneling.' In the classical world, there are limits to what is possible. If an object does not have enough momentum to traverse a barrier, then the barrier will not be traversed. However, in the quantum world there are circumstances when this rule is broken. Imagine a barrier in the quantum world. Because of the wave description of quantum phenomena a particle cannot exist near a barrier without its wave function extending, to a degree, into the barrier itself; then, if the barrier is narrow enough, the probability-wave function may actually extend through the barrier entirely. The consequence of this is that there is a chance that the particle will 'disappear' from one side of the barrier and appear on the other side.

Just like quantum particles, molecules are also probability wave functions. The forces that may prevent a reaction from occurring spontaneously correspond to energy barriers as described above. In biologically based reactions this usually equates to the energy required to transfer an electron and/or a hydrogen nucleus (a proton) from one state (or position) to another. The bonds or forces that bind a proton or electron must first be broken, which requires energy - hence - an energy barrier. Somehow, the enzyme is able to overcome this energy barrier. Recent theoretical work suggests that the mechanism that effects this is a soliton wave. It is thought that the enzyme 'vibrates' in a characteristic way. A characteristic of solitons is that they can travel long distances in space and/or time with very little loss of energy and structure. The effect of this is that it can transfer a coherent 'lump' of energy from one place in the enzyme to another. The effect of the soliton in the enzyme is to cause it to change shape. This change of shape causes movement among any molecules bound to the enzyme. It is theorised that the soliton causes a conformational (i.e. shape) change in the enzyme, such that the wave functions of the reagents bound to the enzyme overlap and thereby greatly increase the possibility of quantum tunneling.

Again, as a consequence of the uncertainty principle, just as the probability wave function of a molecule means that it can occupy many potential states simultaneously, so the reagents and products of a reaction may represent simultaneous states in the overall probability description. At one level of description, therefore, we may consider the reaction as resulting from the overlapping of the wave functions of the reagents. At another level of description, teh reaction occurs as a consequence of the overlapping of the potential energy surfaces of the reagents and products. Fig. 2 shows a simplified phase space diagram of the potential energy surfaces of the reagent(s) and product(s) of a reaction. Each point on the potential energy surface corresponds to a particular shape of the molecule (for reagent(s) and product(s)) and its associated potential energy.

In the simplified diagram, the distributions of nuclear configurations are plotted for both reactants and the products (depicted two dimensionally). Unusual configurations, which are less likely, have higher potential energy than more likely configurations. The two distributions, for reactants and products, may overlap as a consequence of a soliton. The transition state of the reaction occurs at the point that they intersect. The transition is thought to involve quantum tunnelling (Sataric, Ivic, Tuszynski & Zakula, 1991).

An early application of solitons in biology was proposed by Davydov (1982). He suggested that they may play a role in the process of muscle contraction and relaxation (Also Pang, 2001, dealing with the criticism that solitons may not be very robust at body temperature). This model also serves to introduce the concept that in living processes there exists a unique relationship between energy and structure.

The Davydov model of Muscle function

The basic principles of muscle contraction have been known for some time. However, the precise mechanism is still unknown or else the subject of theoretical investigation. Muscle is comprised of bundles of elongated cells called muscle fibers. At the sub-cellular level, muscle fibers contain bundles of elongated structures called myofilaments. There are two types of myofilament - actin and myosin. Two sets of actin fibers are attached to membranes and face each other in a similar way that we might observe if we placed two combs together such that their teeth faced each other. Threaded between the teeth are myosin filaments - these are not attached to the membranes at either end. The entire structure of myofilaments, including the membrane at each end (termed a z-disc), is called the sarcomere. The action of muscle contraction translates, at the sub-cellular level, to a contraction of the overall length of the sarcomere. It is generally agreed that this achieved as a result of the myosin and actin myofilaments overlapping to a greater extent.

In the Davydov model, energy released by the hydrolysis of ATP at the binding site on the myosin molecule is translated into kinetic energy. Normally, this energy would be expected to quickly dissipate. However, Davydov noted that the structure of myosin (an @-helix protein) was comprised of regularly spaced pairs of oxygen and carbon atoms that would give rise to a compressive force that would cancel out the dissipative tendency of the energy wave. Consequently, a highly concentrated 'lump' of energy in the form of a soliton wave would progress as a deformation of the myosin filament. This deformation would provide sufficient localized kinetic energy such that the myosin heads that protrude from the @-helix protein strands at their ends would slide and interlock (or 'ratchet') with the surrounding actin filaments causing the overall length of the sarcomere to decrease.

In addition to the above examples there are many other biological processes in which solitons have been suggested as mechanisms of function.