Enzyme catalysis: Transition structures and quantum dynamical aspects: Modeling rubisco's oxygenation and carboxylation mechanisms

Abstract

Quantum dynamics is introduced with the help of molecular states (MS) for systems decomposable into n electrons and N nuclei. These states, when projected onto the electronic and nuclear configuration spaces, r and R, respectively, are represented as products of electronic and nuclear wave functions of the type Φk(r;αk°)χkj(R;αk°). The 3N coordinates αk° are the positions of positive charges in real space that are equivalent to the nuclear charges. The stationary geometry is derived from quantum chemical analytical gradient optimization procedures. The set {Φk(r;αk°)χkj(R;αk°)} is assumed to contain all cluster partitioning including corresponding asymptotic states. These MSs provide a basis to represent a quantum state as a particular linear superposition. Quantum states are (row) vectors in a dual space whose components are the complex coefficients in the linear superposition of MSs. A reactive system is represented in the direct product space of the MS and surrounding medium: ∣MS〉⊗∣E〉. The surrounding basis states {∣E〉} may be other molecular state systems (protein, solvent) or electromagnetic fields. A chemical reaction is represented as a time evolution of vectors in the dual space driven by the interaction with an energy source or sink system. A theory of catalysis is constructed on this new basis for which the protein–substrate interaction operator drives the quantum change of state. The chemical reaction catalyzed by rubisco is examined and used to introduce the theoretical scheme. The mechanism of carboxylation and oxygenation expressed as sets of transition structures is discussed from this new quantum mechanical perspective. For a protein in thermal equilibrium with a thermal bath at absolute temperature T, in so far as time evolution in the reactant system is concerned, the protein may be replaced by a blackbody radiation field. In real situations, both the protein–substrate and electromagnetic field–substrate interactions provide mechanisms to favor particular time evolutions of the quantum system. A mapping to a unit hypersphere with the axis represented by (orthogonalized) MSs permits a simple “visualization” of all bound quantum states related to the system as points on the surface of the hypersphere. Time evolution of complex systems can be systematized in this new way. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002