Vibrationally enhanced tunneling

Bruno, W.J. and Bialek, W. (1992) Vibrational enhanced tunneling as a mechanism for enzymatic hydrogen transfer, Biophys. J. 63, 6890-699. 

Recent studies (see Refs. 4,127) have suggested that vibrationally enhanced tunneling (VET) plays a major role in enzyme catalysis. Some workers (e.g., Ref. 128)... 

Agrawal, N., Hong, B., Mihai, C. and Kohen, A. (2004). Vibrationally enhanced hydrogen tunneling in the Escherichia coli thymidylate synthase catalyzed reaction. Biochemistry 43, 1998-2006... 

Let us assume that a variable A(t) is coupled to the reaction coordinate and that (A) is its mean value. If a measurement of some property P depends on (A), but not on the particular details of the time dependence of A(t), then we will call it a statistical dependence. If the property P depends on particular details of the dynamics of A(t) we will call it a dynamical dependence. Note that in this definition it is not the mode A(t) alone that causes dynamical effects, but it also depends on the timescale of the measured property P. Promoting vibrations (to be discussed in Sections 2-4) are a dynamic effect in this sense, since their dynamics is coupled to the reaction coordinate and have similar timescales. Conformation fluctuations that enhance tunneling (to be discussed in Section 5) are a statistical effect the reaction rate is the sum of transition state theory (TST) rates for barriers corresponding to some configuration, weighted by the probability that the system reaches that configuration. This distinction between dynamic and statistical phenomena in proteins was first made in the classic paper of Agmon and Hopfield.4 We will discuss three kinds of motions ... 

Recently, a controversial debate has arisen about whether the optimization of enzyme catalysis may entail the evolutionary implementation of chemical strategies that increase the probability of tunneling and thereby accelerate reaction rates [7]. Kinetic isotope effect experiments have indicated that hydrogen tunneling plays an important role in many proton and hydride transfer reactions in enzymes [8, 9]. Enzyme catalysis of horse liver alcohol dehydrogenase may be understood by a model of vibrationally enhanced proton transfer tunneling [10]. Furthermore, the double proton transfer reaction in DNA base pairs has been studied in detail and even been hypothesized as a possible source of spontaneous mutation [11-13]. 

The fact that enzymes employ dynamics, should in no way be surprising -evolution knows nothing of quantum mechanics, classical mechanics, or vibration-ally enhanced tunneling. Rates of reaction are optimized for living systems using all physical and chemical mechanisms available. It is also important to point out that such protein dynamics are far from the only contributor to the catalytic effect. In fact in an enzyme such as alcohol dehydrogenase, transfer of a proton from the alcohol to the coordinated zinc atom is critical to the possibility of the reaction. The specific modulation of the chemical barrier to reaction via backbone protein dynamics is now seen to be part of the chemical armamentarium employed by enzymes to catalyze reactions. 

ABSTRACT. After reviewing the time dependent wavepacket method as applied to collision induced dissociation processes,we report accurate quantum results for reactive and non reactive collinear A+BC systems. Both systems display a vibrational enhancement effect in the low energy region. While the non reactive systems exhibit a vibrational inhibition effect at higher energies,a more complex behavior is observed in the reactive case. Below the classical dissociation threshold,the non reactive systems display tunnelling tails which decrease with the initial vibrational excitation of the diatomic molecule. The reactive system displays important quantum effects at energies well above the classical dissociation threshold. 

In the next subsection, we present the mechanism of driven enhanced tunneling by a resonant pulse using an effective three-state model. The Hamiltonian and the coordinates used in the MCTDH calculations are derived in Sect. 8.2.2. The range of parameters considered in this work is justified in Sect. 8.2.3. In Sect. 8.2.4, quantum dynamics simulations of the control scheme investigated in this work using the exact vibrational Hamiltonian are presented. Simulations are presented and discussed both for linearly and circularly polarized fields. Conclusions are given in Sect. 8.2.5. 

This quantum analysis was systematized within the vibrationally enhanced ground-state tunneling theory (VEGST) (Bruno Bialek, 1992), experimentally verified on reactions catalyzed by the bacterial enzyme methylamine dehydrogenase (Basran et al., 1999), despite some limitations for those enzyme in which the tunneling process acts so close... 

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