Quantum effects in ultrafast electron transfers within cryptochromes

Abstract

Cryptochromes and photolyases are flavoproteins that may undergo ultrafast charge separation upon electronic excitation of their flavin cofactors. Charge separation involves chains of three or four tryptophan residues depending on the protein of interest. The molecular mechanisms of these processes are not completely clear. In the present work we investigate the relevance of quantum effects like the occurrence of nuclear tunneling and of coherences upon charge transfer in Arabidopsis thaliana cryptochromes. The possible breakdown of the Condon approximation is also investigated. We have devised a simulation protocol based on the realization of molecular dynamics simulations on diabatic potential energy surfaces defined at the hybrid constrained density functional theory/molecular mechanics level. The outcomes of the simulations are analyzed through various dedicated kinetics schemes related to the Marcus theory that account for the aforementioned quantum effects. MD simulations also provide a basic material to define realistic model Hamiltonians for subsequent quantum dissipative dynamics. To carry out quantum simulations, we have implemented an algorithm based on the Hierarchical Equations of Motion. With this new tool in hand we have been able to model the electron transfer chain considering either two- or three-state models. Kinetic models and quantum simulations converge to the conclusion that quantum effects have a significant impact on the rate of charge separation. Nuclear tunneling involving atoms of the tryptophan redox cofactors as well as of the environment (protein atoms and water molecules) is significant. On the other hand non-Condon effects are negligible in most simulations. Taken together, the results of the present work provide new insights into the molecular mechanisms controlling charge separation in this family of flavoproteins.

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

“… 31 These studies highlighted the role of Trp in the classical triad 27 – 29 or of additional residues 30 , 31 at an atomistic level, as well as the crucial role of the environment 24 , 25 , 29 or the quantum effects in these ultrafast charge transfers. 26 In our group, we have established a quantum mechanics/classical mechanics (QM/MM) scheme based on fragment orbital tight-binding density functional theory (FODFTB) coupled to MM molecular dynamics (MD). 22 – 24 , 32 Our approach allows direct simulations of the charge propagation along a Trp triad.…”

Efficient Constrained Density Functional Theory Implementation for Simulation of Condensed Phase Electron Transfer Reactions

“…We have specifically opted to solve the two states in parallel to maximize throughput, although a serial mode modification of the algorithm is possible in future applications of the method in case parallel converge issues arise, which is a strategy that has enjoyed success in hybrid CDFT/MM simulations. 40,41 By adopting these design criteria, the implementation allows the characterization of all ET parameters directly from CDFT MD simulations, and at the same time remains sufficiently efficient in terms of computational cost to enable the usage of an accurate, electronic structure based description of the solvent. To demonstrate this capability, we studied the intramolecular ET reaction of Q-TTF-Q •− in ca.…”

“…This has facilitated for example the quantification of dynamical quantum effects in the ET within cryptochromes via hybrid CDFT/molecular mechanics (MM) simulations. 41 A similar strategy has, to our knowledge, thus far not been applied to MD simulations at the full CDFT level. We speculate that such calculations have not been attempted with current CDFT capable software [22][23][24]37,40,[42][43][44][45][46][47] mainly due to the high associated computational cost, which is ultimately governed by the underlying DFT implementation, in particular the choice of basis set and electronic structure solver.…”

Regulatory Impact of the C-Terminal Tail on Charge Transfer Pathways in Drosophila Cryptochrome

“…Reorganization energies and driving forces of CT reactions in the non-anisotropic protein environment were computed numerically with three different QM/MM approaches. In the first approach, the reorganization energy was computed from the variance of the energy gap fluctuations [ 48 ] along an MD trajectory performed in electronic state x . Here, denotes the variance.…”