Charge transfer in dynamical biosystems, or the treachery of (static) images

Abstract

CONSPECTUS: The image is not the thing. Just as a pipe rendered in an oil painting cannot be smoked, quantum mechanical coupling pathways rendered on LCDs do not convey electrons. The aim of this Account is to examine some of our recent discoveries regarding biological electron transfer (ET) and transport mechanisms that emerge when one moves beyond treacherous static views to dynamical frameworks. Studies over the last two decades introduced both atomistic detail and macromolecule dynamics to the description of biological ET. The first model to move beyond the structureless square-barrier tunneling description is the Pathway model, which predicts how protein secondary motifs and folding-induced through-bond and through-space tunneling gaps influence kinetics. Explicit electronic structure theory is applied routinely now to elucidate ET mechanisms, to capture pathway interferences, and to treat redox cofactor electronic structure effects. Importantly, structural sampling of proteins provides an understanding of how dynamics may change the mechanisms of biological ET, as ET rates are exponentially sensitive to structure. Does protein motion average out tunneling pathways? Do conformational fluctuations gate biological ET? Are transient multistate resonances produced by energy gap fluctuations? These questions are becoming accessible as the static view of biological ET recedes and dynamical viewpoints take center stage. This Account introduces ET reactions at the core of bioenergetics, summarizes our team's progress toward arriving at an atomistic-level description, examines how thermal fluctuations influence ET, presents metrics that characterize dynamical effects on ET, and discusses applications in very long (micrometer scale) bacterial nanowires. The persistence of structural effects on the ET rates in the face of thermal fluctuations is considered. Finally, the flickering resonance (FR) view of charge transfer is presented to examine how fluctuations control low-barrier transport among multiple groups in van der Waals contact. FR produces exponential distance dependence in the absence of tunneling; the exponential character emerges from the probability of matching multiple vibronically broadened electronic energies within a tolerance defined by the rms coupling among interacting groups. FR thus produces band like coherent transport on the nanometer length scale, enabled by conformational fluctuations. Taken as a whole, the emerging context for ET in dynamical biomolecules provides a robust framework to design and interpret the inner workings of bioenergetics from the molecular to the cellular scale and beyond, with applications in biomedicine, biocatalysis, and energy science.

Figure 1

Donor–bridge–acceptor structural fluctuations cause coupling values, H_DA, to vary. When exchange among molecular conformations is much faster than the ET rate, ⟨H_DA²⟩ enters the nonadiabatic rate expression in place of a single coupling value. The probability density for couplings, P(H_DA), is determined by structures accessed.^,, In the regime of slow exchange among conformations (k_exch ≪ k_ET), nonexponential or gated kinetics may be measured.

Figure 2

Studies of charge recombination in the cytochrome c/Zn-cytochrome c peroxidase complexes indicate hopping transport via Trp191. The very long heme-to-heme distances (and weak couplings), combined with the redox potentials, favor hopping recombination. Reproduced with permission from ref (61). Copyright 2013 American Chemical Society.

Figure 3

A nanowire from a Shewanella oneidensis MR-1 cell bridges two platinum electrodes. Used with permission from ref (64). Copyright 2012 Royal Society of Chemistry.

Figure 4

(a) Representation of the hopping network used to model transport in bacterial nanowires. Star shapes represent hopping sites. (b) Rendering of the decaheme protein structure from the outer-membrane of Shewanella oneidensis.(65) Note the near van der Waals contact among cofactors. Used with permission from ref (66). Copyright 2012 Royal Society of Chemistry.

Figure 5

Site energies associated with a model DBBA system. (a) Assuming uncorrelated Gaussian fluctuations of site energies, each ET unit has an energy standard deviation of σ_E(i) = (2λ_ik_BT)^1/2. (b) Most static pictures for transport “freeze” the energy levels at their mean values and apply transport theories on this energy landscape. (c) Flickering resonance transport considers the subensemble of energy matched D, B_n, and A sites that support coherent transport (with rate k_D→A^band). Formation probabilities require that the coupling between groups (V) exceeds any energy mismatch (δE) among the sites energies. The probability of forming FR structures drops exponentially with distance (eq 1), as does the FR mechanism ET rate.

Figure 6

Prediction of distance-dependent transport rates for FR at low and high temperatures. Elevating the temperature grows the injection prefactor (e^{–E_B2/2σ_E2}) but also increases the distance decay exponent Φ (eq 1), assuming that V_RMS is weakly temperature dependent. Traditional nonadiabatic ET rates would produce parallel lines in this plot.