Fragment Orbital Based Description of Charge Transfer in Peptides Including Backbone Orbitals

Abstract

Charge transfer in peptides and proteins can occur on different pathways, depending on the energetic landscape as well as the coupling between the involved orbitals. Since details of the mechanism and pathways are difficult to access experimentally, different modeling strategies have been successfully applied to study these processes in the past. These can be based on a simple empirical pathway model, efficient tight binding type atomic orbital Hamiltonians or ab initio and density functional calculations. An interesting strategy, which allows an efficient calculations of charge transfer parameters, is based on a fragmentation of the system into functional units. While this works well for systems like DNA, where the charge transfer pathway is naturally divided into distinct molecular fragments, this is less obvious for charge transfer along peptide and protein backbones. In this work, we develop and access a strategy for an effective fragmentation approach, which allows one to compute electronic couplings for large systems along nanosecond time scale molecular dynamics trajectories. The new methodology is applied to a solvated peptide, for which charge transfer properties have been studied recently using an empirical pathway model. As could be expected, dynamical effects turn out to be important, which emphasizes the importance of using effective quantum approaches which allow for sufficient sampling. However, the computed rates are orders of magnitude smaller than experimentally determined, which indicates the shortcomings of present modeling approaches. ■ INTRODUCTIONCharge transfer (CT) in biomolecules is a fundamental process that has been subject of intense scientific study for more than 50 years.1−4 It is highly relevant in the understanding of functional as well as pathological cellular processes, ranging from respiration and photosynthesis to DNA damage and repair.5−7 Our theoretical understanding of molecular CT has increased tremendously since the pioneering studies by Marcus and others, 8−16 but a complete detailed description on the molecular level remains elusive.Several approaches exist to compute the electronic couplings, ranging from empirical pathway models, 17−19 over tight-binding based 20,21 to ab initio or density functional calculations. 22−25Most of these quantum approaches are based on an atomic orbital description to compute charge transfer parameters, which becomes very costly for large systems, even when using extended Huckel or tight-binding Hamiltonians, because the computer time scales cubic with the number of atomic orbitals involved. An additional computational challange is the need for sampling along MD trajectories. The biochemical transfer of electrons over many nanometers through large protein assemblies involves dynamical changes that occur on time scales ranging from subpicosecond changes in electronic structure to microsecond or even slower conformational changes. Especially the interplay between the atomic structural fluctuations and the electron dynamics has bec...

Functional role of an unusual tyrosine residue in the electron transfer chain of a prokaryotic (6–4) photolyase

“…To compute the electronic properties along the classical MD simulations, we use the semi-empirical Tight-Binding Density Functional theory (DFTB) method, 53 which is derived from density functional theory (DFT) but roughly 2–3 orders of magnitude faster than standard GGA-DFT methods with medium sized basis sets. Running a fragmentation of the QM region into several functional parts speeds up the calculation significantly and allows to systematically correct for errors well known in DFT-GGA, like self-interaction error (for a detailed discussion see ref. 54 and 55 ).…”

“…This FO-DFTB approach has been extensively evaluated and tested in previous publications 32 , 54 , 57 and has been so far successfully applied to describe the charge transfer in photolyase, 23 cryptochrome 24 and DNA 58 , 59 where the HOMO's of the fragments were used to calculate the evolution of electronic couplings and site energies.…”

“…In case of super-exchange tunnelling mechanism for a bridged charge transfer, the n fragments of the bridge B must be included in the electronic coupling T DA calculation. The system is thus divided into the donor/acceptor (D/A) and bridge subspace and an effective Hamiltonian is calculated in which off-diagonal elements correspond to T DA (for detailed discussions see ref. 54 and 61 ): where β DA describes the direct electronic interaction between D and A, β D i and β j A the electronic interactions between D or A and the i or j -th fragment of the bridge.…”

Electronic Coupling Calculations for Bridge-Mediated Charge Transfer Using Constrained Density Functional Theory (CDFT) and Effective Hamiltonian Approaches at the Density Functional Theory (DFT) and Fragment-Orbital Density Functional Tight Binding (FODFTB) Level

“…71 In FODFTB calculations, we apply fragment orbitals as localized states, which are straightforward to use when D, A and B are separated molecules. 51 By solving one linear equation for ! and substituting the result in the second equation we can reduce Eq 4 to an equivalent equation of the D/A subspace !…”

“…Hamiltonian strategy with DFT-based Green's function pathway. 45 Electronic coupling contributions to ET through diverse biomolecules, including DNA strands, 46-49 polypeptide [50][51][52][53] , heme-to-heme ET 54 or cryptochrome/photolyases, 55,56 and to organic semi-conductors 57 have been successfully calculated with these approaches. In addition to our recent works, Ando and co-workers demonstrate the utility of the fragment molecular orbital-linear combination of MOs (FMO-LCMO) for T DA predictions within various organic and biological molecules.…”