Quantum tunneling in biological reactions: the interplay between theory and experiments

Abstract

Ricardo Ferreira foi o primeiro cientista brasileiro a compreender a necessidade de aproximações teóricas sólidas para explicar os mecanismos que governam as ciências da vida. Nesta edição em sua homenagem, descrevemos como modelos teóricos têm sido aplicados para guiar o entendimento do fenômeno de tunelamento de elétrons em biologia. Durante quase vinte anos, o nosso modelo de "Pathways" tem se mostrado o mais bem sucedido modelo teórico para descrever o mecanismo de tunelamento no processo de transferência de elétrons em sistemas biológicos, particularmente em proteínas. Recentemente, o modelo de Pathways foi generalizado para incluir o efeito da dinâmica de proteínas na modulação do Fator Franck-Condon e dos elementos de tunelamento da matriz. A interferência entre diferentes trajetórias modula as interações de tunelamento de elétrons em proteínas (particularmente interferências destrutivas), e efeitos resultantes da dinâmica de proteínas são de importância crítica. O tunelamento de elétrons pode ser controlado por conformações de equilíbrio da proteína, as quais parecem ser necessárias para minimizar os efeitos de interferência destrutiva. Em contraste, quando configurações de equilíbrio apresentam pouca interferência destrutiva, o tunelamento de elétrons é promovido por uma (ou algumas) etapa(s) construtivamente interferente e os efeitos dinâmicos são modestos. Este novo mecanismo resultou na previsão de várias constantes de velocidades para reações de transferência de elétrons que foram confirmadas experimentalmente.Ricardo Ferreira was the first Brazilian scientist to understand the need of solid theoretical approaches to obtain quantitative understanding mechanisms governing the life sciences. Therefore, in this issue in his honor, we decided to describe how theory has been able to guide the understanding of electron tunneling in biology. During almost twenth years, our Pathway model has been the most powerful model in terms of predicting the tunneling mechanism for electron transfer in biological systems, particularly proteins. Recently, we have generalized the conventional Pathway models to understand how protein dynamics modulate not only the Franck-Condon Factor but also the tunneling matrix element. The interference among pathways modulates the electron tunneling interactions in proteins (particularly destructive interference), and dynamical effects are of critical importance. Tunneling can be controlled by protein conformations from equilibrium, which may be needed to minimize the effect of destructive interference during tunneling. In contrast, when equilibrium configurations have small destructive interference, electron tunneling is mediated by one (or a few) constructively interfering pathway tubes and dynamical effects are modest. This new mechanism has predicted several experimental rates that were later confirmed by experiments.

DFT-based Green's function pathways model for prediction of bridge-mediated electronic coupling

“…The converged eigenvalues provide the energies of the poles of the non-adiabatic intersection, and at this point, the GFM elements, G ij , represent the tunneling probabilities of the electron through the atomic orbital (AO) space of the bridge states between D and A. [4][5][6][7][8]22 Larger absolute magnitudes of G ij indicate a higher probability of electronic propagation from the i-th orbital to the j-th orbital, and contribute to a more dominant orbital pathway for the tunneling electron. 4,7,8,31 Alternating numeric signs of Green's function elements along a pathway, which relate to alternating phases of the orbitals in the pathway, are indicative of constructive interference and/or dominance of this single pathway.…”

“…In our previous work, electron transfer pathways were analyzed in terms of GFM decay elements, by association of the first atom in the pathway to each atom down the pathway, 4,7,8 e j ¼ G i; jþ1 G ij ; ð j 4 iÞ…”

“…Of central interest are models based on quantum mechanical (QM) and density functional theory (DFT) schemes. [1][2][3][4][5][6][7][8][9][10] For bridgemediated ET reactions, tunneling can take place over large bridge (B) distances between donor (D) and acceptor (A), as a cooperativity of through-bond (TB) and/or through-space (TS) interactions ( Fig. 1).…”

“…In previous work, the pathways model was invoked to address questions of how tunneling through protein medium occurs. 4,5,7,8,20 The methodology combined computationally inexpensive semi-empirical methods with molecular dynamics, to address important issues of dynamic effects and multiple pathway tubes in large protein structures. In the present effort, we return primarily to ET reactions dominated by a single pathway tube, but now further develop the models to improve quantitative T DA predictions with QM and density functional theory (DFT) methods, with an emphasis on accuracy as a function of wavefunction type or density functional, basis set, and localization scheme.…”

Mechanically Controlled Electron Transfer in a Single-Polypeptide Transistor

“…The ET between the redox centers mediated by peptide bridges has been thought to involve two possible mechanisms: the superexchange model and electron hopping model2526272829. In the superexchange (or tunneling) mechanism, ET takes place via coupling between the virtual states of the bridging units and involves tunneling movement through the bridge part without a transient stay in the bridge state; in such circumstances the rate constant shows an exponential decaying function of the peptide length30. This mechanism can thus be described as having the decay parameter β that is dependent on the bridge length, the conformational rigidity and the electronic properties of the electron donor and acceptor31323334.…”