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For larger excitations, however, the system shows remarkable properties, the most important being the establishment of a metastable state characterized by a non-vanishing mean value P+ of P, that is, by a permanent mean displacement as it is found in ferroelectric materials. In the present case, however, this state is metastable; it has a higher energy than the undisplaced ground state though it is stable against small displacements. This metastable state is best reached through excitation of coherent modes which have very different characteristics from non-coherent ones. As a consequence of non-linear properties of the model, excitation of a certain amount of incoherent vibrations in the metastable state will lead as an immediate mechanical consequence to excitation of a coherent mode−quite apart from the further arguments for such excitation given in ref. 2.
Assume now that the model may be applicable to enzyme molecules which would possess metastable excited states in which polar groups are stretched so that the molecule may have a very large dipole moment resembling a ferroelectric case, and in which excitations above this state are partly transform ret into coherent vibrational modes. An enzyme molecule so excited will have strong long range interaction with other molecules. This interaction will tend to lift other enzyme molecules into the metastable state, the required energy to be provided from the coherently excited modes. The interaction will also lead to attraction of other types of molecules (substrates) to the excited enzyme molecule, especially when they possess a proper frequency close to that of the coherent modes. It is therefore likely that the total energy of the stretched enzyme and substrate is lower than it would be otherwise and this may facilitate the relevant chemical processes in the substrates.
Some of the properties of our model resemble Koshland's hypothesis of conformational changes 3 but they go much further because they imply a stretching of dipoles throughout the large enzyme molecule rather than a deformation near the active site. A principal consequence is the occurrence of the new long range forces which are likely to dominate the dynamic behavior.
We thus arrive at the following dynamic picture. Assume the first substrate-enzyme complexes to be formed by fluctuations. The energy liberated by the relevant chemical transformations leaves the enzyme molecules coherently excited near their metastable state; return to the ground state would take a relatively long time. Through the long range forces so established they will (a) assist other enzyme molecules to transfer to the meta-stable state and (b) attract further substrates. The energy liberated by the chemical processes so acts as a pumping device. At this first stage the number of activated enzyme molecules − and therefore chemical processes − will consequently increase at an accelerating rate, much as in a chain reaction. This will continue until most enzyme molecules are in the metastable state after which the process will continue in a normal way.
These proposals could be tested in three ways.
First, by investigation of the build-up of the reaction rate (first stage; chain-like process) as a function of the enzyme density.
Second, by direct observation of the excited coherent modes. These modes are optically inactive. Use of Raman effect would, therefore, be appropriate. Through surface effects weak coherent radiation might, however, be observable.
Third, by the detection of increase in the static dielectric constant as a result of the expected large increase in the dipole moment of the enzyme molecules when they are transferred to the metastable state.
H. Frohlich
Department of Theoretical Physics,
University of Liverpool.
Received June 15, 1070.
1. Frohlich, H., − in Theoretical Physics and Biology (edit, by Marois.M.), 13 (North-Holland, Amsterdam) 1969).
2. Frohich, H. − Intern. J. Quantum Сhem., 2, 641 (1968).
3. Koshland, D.E. and Neet, K. E., − Ann. Rev. Biochem., 87, 369, 380 (1968).
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