Synchronization factor

According a simplified theory (Alexandrov, 1976), a concerted reaction occurs as a result of the simultaneous transition (taking approximately 10 13 s) of a system of independent oscillators, with the mean displacement of nuclei p0, from the ground state, to the activated state in which this displacement exceeds for each nuclei a certain critical value (q cr). If pCr Po and the activation energy of the concerted process Esyn nRT, the theory gives the following expression for the synchronization factor which is the ratio of the pre-exponential factors of the synchronous and simple processes  

In fact, in the frame of the Alexandrov model, when the average thermal energy of the system (Eav = nRT) exceeds the energy of the activation barrier, the process can be considered as activationless. Analysis of Eqs. 2.44 and 2.45 provides a clear idea of the scale of the synchronization factor, and the dependence of this factor on the number of n and therefore on the number of broken bonds and the energy activation (Fig. 2.12). For example, at moderate energy activation 20-40 kJ/mole, typical for enzymatic reactions, the incorporation of each new nucleus into the transition state can lead to a ten-fold decrease in the rate of the process. 

Therefore, in the case of an effective concerted mechanism, the decrease of the synchronization probability (asyn) with increasing n must be compensated for by an appreciable decrease in the activation energy. 

The models of concerted processes discussed above are only a crude approximation of the motion of a complex system of nuclei along the reaction coordinate. However, such an approximation apparently permits one to choose between the possible reaction mechanisms. The reliability of such a choice increases through a comparative examination of alternative reaction coordinates. 

THE PRINCIPLE OF OPTIMUM MOTION IN ELEMENTARY ACTS OF CHEMICAL AND ENZYMATIC PROSESSES. 

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The question of how glycolytic oscillations synchronize in a population of yeast cells is of great current interest [51]. It has long been known that the oscillations disappear in a yeast suspension when the cell density decreases below a critical value. Acetaldehyde appears to act as synchronizing factor in such suspensions [52], and the way it allows cells to synchronize is being... 

Effective Synchronization of Nuclei in a Chemical Concerted Reaction. In a concerted process the transition from initial state to transition states occurs upon the motion of nuclei (taking about 10"13 s) in a certain direction, which is the only possible path that can lead to reaction products. Obviously, the statistic thermal nature of chemical processes limits the number of nuclei, which can be involved in a signal elementary step. In such cases, the value of synchronization factor (asyn) can be markedly less then 1. 

Figure 2.12 Theoretical dependences of the synchronization factor (asyn) on the number of degrees of freedom (n) of the nuclei involved in a concerted reaction. The curves have been constructed in accordance with Eqs 2.44 and 2.45. (Likhtenshtein, 1988a). Reproduced with permission...

In transition state theory, the rate of an adiabatic chemical reaction depends only on the difference between free energy in initial and transition states. From point of view of thermodynamics, formation of an intermediate complex can not give any preference to the process as compared with a collision complex. Nevertheless, the formation of a preliminary (pretransition) structure on the reaction coordinate can constrain the system of nuclear motions that do not lead to reaction products and, therefore, accelerate the process. It is necessary to stress that this acceleration is not caused by entropy reason, but by the optimization of the synchronization factor. 

Enzymatic reactions, despite the obvious energy preference of certain concerted mechanisms, may be inefficient because of a too low synchronization factor. In such cases, the sequential transformation of the system through a number of steps is favorable. Here, the role of a multi-functional catalyst, in reaching a pretransition state is to provide favorable energy and synchronization factors through the optical use of the corresponding functional groups at each step of the process. 

Another possible two-electron mechanism involves the direct transport of two electrons from a mononuclear transition metal complex to a substrate (S). Such a transport alters sharply the electrostatic states of the systems and obviously requires a substantial rearrangement of the nuclear configuration of ligands and polar solvent molecules. For instance, the estimation of the synchronization factor (asyn) for an octahedral complex, with Eq. 2.44 shows a very low value of asyn = 10 7to 10 8 and, therefore, a very low rate of reaction. The probability of two-electron processes, however, increases sharply if they take place in the coordination sphere of a transition metal, where the reverse compensating electronic shift from the substrate to metal occurs. Involvement of bi- and, especially, polynuclear transition metal complexes and clusters and synchronous proton transfer in the redox processes may essentially decrease the environment reorganization, and, therefore, provide a high rate for the two- electron reactions. 

The multi-electron nature of the energetically favorable process does not evidently impose any new, additional restriction on its velocity. Within a coordination sphere the orbital overlap is effective and, therefore the resonance integral V is high. The strong delocalization of electrons in clusters, polynuclear complexes in clusters and polynuclear complexes reduces to a minimum the reconstitution of the nuclear system during electronic transitions and, therefore, provides a high value for the synchronization factor. 

Similar analysis of the reactioncatalyzed by formate dehydrogenase (Fig. 2.15 gives value of the synchronization factor asyn 1 O 8... 

S-adenosyl-L methionine (ADO-Met) dependent DNA methyl transferase catalyzed the transfer of a methyl group from AdoMet to a specific nucleotide within the DNA helix (Cheng et al., 1993). In a concerted reaction in the enzyme active site (Fig X) with a simultaneous addition of methyl residue of AdoMet to the cytosine ring and with an elimination of the ring proton by a water molecule requires involving seven heavy nuclei (two ofCys 81, four of AdoMet and one of water. An estimation with aid of Eq. 2.44 leads to value of the reaction synchronization factor asyn 10 4, that does not rule out the concerted mechanism, if the activation energy is less than 10 kcal/mole Nevertheless, a... 

Likhtenshtein, G.I. (1977a) On the principle of optimum motion in elementary acts of chemical and biological processes, I. Estimation of the synchronization factor for model processes. Kinetika I Kataliz (Kinetics and Catalysis), 28 878-882. 

In the general case of second harmonic generation, it can be shown that the conversion efficiency Izo/lm is strongly dependent on the phase synchronization factor 1/2) where Ak = i 2o) respectively,... 

Betz Moore, 1967 Betz Sel kov, 1969 Hess et al, 1969) or following changes in pH (Hess et al., 1969 Hocker et al, 1994). Yeast cells undergoing glycolytic oscillations rapidly synchronize in stirred suspensions (Ghosh, Chance Pye, 1971). The synchronizing factor... 

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