Quantum Enzyme Kinetics

Although in the first century from their discover the enzymes were mainly studied for elucidation of their kinetics (Schnell Maini, 2003), emphasizing on how their stmcture is changed with the chemical modifications of 

The solvent d5mamics, i.e., the in vitro and in vivo conditions, and natural breathing , i.e., the quantum fluctuations in the active site, of the enzyme molecule need to be counted in a more complete picture of enzymic catalysis. However, the quantum (fluctuating) nature of the enzymic reactions can be visualized by combining the relationship between the catalytic rate and temperature (7) (DeVault Chance, 1966) with that between the reaction rate and the turnover number or the effective time of reaction (Ar) via Heisenberg relation 

Nevertheless, relation (1.167) is the basis of rethinking upon the static character of the energetic barrier, recalling the so-called steady state 

Basically, when applied to enzymic reactions the recent developments suggest that the textbook TST is, at least in some situations, necessarily flawed. This because TST primarily treat the enzymes as being only particle-like entities, completely ignoring their electronic and protonic constitution when mediate chemical information-transfer when act on substrate. On contrary, as electrical insulators the proteins can transfer their electrons only by means of wave-like properties or tuimel-ing processes. 

Actually, the wave-particle duality of matter allows designing new pathway from reactants (enzyme E and substrate S) to products (enzyme and product P) in a Brownian enzymic reaction (Brown, 1902) 

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Gao J, Truhlar DG (2002) Quantum mechanical methods for enzyme kinetics. Annu Rev Phys Chem 53 467-505... 

Methods similar to those discussed in this chapter have been applied to determine free energies of activation in enzyme kinetics and quantum effects on proton transport. They hold promise to be coupled with QM/MM and ab initio simulations to compute accurate estimates of nulcear quantum effects on rate constants in TST and proton transport rates through membranes. 

It is of interest in this connection that Steam,26 in a discussion of enzyme kinetics from the point of view of statistical mechanics and quantum mechanics, regards interaction between a dipole (as part of the enzyme protein) and the reacting groups of the substrate, e.g., C—0, resulting in a redistribution of charge within the C—0 bond, as a more rational mechanism of activation than the loosening of the bond by distortion. 

We continue our study of chemical kinetics with a presentation of reaction mechanisms. As time permits, we complete this section of the course with a presentation of one or more of the topics Lindemann theory, free radical chain mechanism, enzyme kinetics, or surface chemistry. The study of chemical kinetics is unlike both thermodynamics and quantum mechanics in that the overarching goal is not to produce a formal mathematical structure. Instead, techniques are developed to help design, analyze, and interpret experiments and then to connect experimental results to the proposed mechanism. We devote the balance of the semester to a traditional treatment of classical thermodynamics. In Appendix 2 the reader will find a general outline of the course in place of further detailed descriptions. 

March Advanced Organic Chemistry Reactions, Mechanisms, and Structure Memory Quantum Theory of Magnetic Resonance Parameters Pitzer and Brewer (Revision of Lewis and Randall) Thermodynamics Plowman Enzyme Kinetics... 

Billeter, S.R., et al. (2001). Hydride transfer in liver alcohol dehydrogenase quantum dynamics, kinetic isotope effects, and role of enzyme motion. J. Am. Chem. Soc. 123, 11262-11272... 

Agarwal, P. K., Iordanov, T., Hammes-Schiffer, S., Hydride Transfer in Liver Alcohol Dehydrogenase Quantum Dynamics, Kinetic Isotope Effects, and Role of Enzyme Motion, J. Am Chem. Soc. 2001, 123, 11262-11272. 

The accurate prediction of enzyme kinetics from first principles is one of the central goals of theoretical biochemistry. Currently, there is considerable debate about the applicability of TST to compute rate constants of enzyme-catalyzed reactions. Classical TST is known to be insufficient in some cases, but corrections for dynamical recrossing and quantum mechanical tunneling can be included. Many effects go beyond the framework of TST, as those previously discussed, and the overall importance of these effects for the effective reaction rate is difficult (if not impossible) to determine experimentally. Efforts are presently oriented to compute the quasi-thermodynamic free energy of activation with chemical accuracy (i.e., 1 kcal mol-1), as a way to discern the importance of other effects from the comparison with the effective measured free energy of activation. 

Alhambra C, Corchado J, Sanchez M, Garcia-Viloca M, Gao J, Truhlar DG. Canonical variational theory for enzyme kinetics with the protein mean force and multidimensional quantum mechanical tunneling dynamics. Theory and application to liver alcohol dehydrogenase. J Phys Chem B 2001 105 11326-11340. 

In this chapter I first summarize the theoretical methods developed in my group for enzyme kinetics modeling, which include both electronic and nuclear quantum effects. Then the methods are illustrated through applications to three energy systems, namely, alanine racemase, nitroalkane oxidase and dihydrofolate reductase. 

In this chapter, quantum mechanical methods developed for enzyme kinetics modeling in our group have been presented, including the treatment of the potential energy surface for reactive system and the incorporation of nuclear quantum effects in dynamics simulations. Two aspects are emphasized ... 

The latter method, called the PI-FEP/UM approach, allows accurate primary and secondary kinetic isotope effects to be computed for enzymatic reactions. These methods are illustrated by applications to three enzyme systems, namely, the proton abstraction and reprotonation process catalyzed by alanine race-mase, the enhanced nuclear quantum effects in nitroalkane oxidase catalysis, and the temperature (in)dependence of the wild-type and the M42W/G121V double mutant of dihydrofolate dehydrogenase. These examples show that incorporation of quantum mechanical effects is essential for enzyme kinetics simulations and that the methods discussed in this chapter offer a great opportunity to more accurately model the mechanism and free energies of enzymatic reactions. 

Tmhlar DG, Gao J, Alhambra C, Garcia-Viloca M, Corchado J, Sanchez ML, Villa J (2002) The incorporation of quantum effects in enzyme kinetics modeling. Acc Chem Res 35 341... 

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