Search

Bacterial cytochromes P450 BM3 (CYP450 BM3) catalyze reactions of industrial importance. Despite many successful biotransformations, robust (re)design for novel applications remains challenging. Rational design and evolutionary approaches are not always successful, highlighting a lack of complete understanding of the mechanisms of electron transfer (ET) modulations. Thus, the full potential of CYP450 reactions remains under-exploited. In this work, we report the first molecular dynamics (MD)-based explicit prediction of BM3 ET parameters (reorganization energies; λ and ET free energies; Δ G °), and log ET rates (log k ET ) using the Marcus theory. Overall, the calculated ET rates for the BM3 wild-type (WT), mutants (F393 and L86), ligand-bound state, and ion concentrations agree well with experimental data. In ligand-free (LF) BM3, mutations modulate k ET via ET Δ G °. Simulations show that the experimental ET rate enhancement is due to increased driving force (more negative Δ G °) upon ligation. This increase is related to the protein reorganization required to accommodate the ligand in the binding pocket rather than binding interactions with the ligand. Our methodology (CYPWare 1.0) automates all the stages of the MD simulation step-up, energy calculations, and estimation of ET parameters. CYPWare 1.0 and this work thus represent an important advancement in the CYP450 ET rate predictions, which has the potential to guide the redesign of ET enzymes. This program and a Web tool are available on GitHub for academic research.

It was recently suggested that cytochrome c operates in an ergodicity-breaking regime characterized by unusually large energy gap thermal fluctuations and associated reorganization free energies for heme oxidation of up to 3.0 eV. The large fluctuations were reported to lower activation free energy for oxidation of the heme cofactor by almost a factor of 2 compared to the case where ergodicity is maintained. Our group has recently investigated this claim computationally at several levels of theory and found no evidence for such large energy gap fluctuations. Here we address the points of our earlier work that have raised criticism and we also extend our previous investigation by considering a simple linear polarizability model for cytochrome c oxidation. We find very consistent results among all our computational approaches, ranging from classical molecular dynamics, to the linear polarizability model to QM(PMM)/MM to full QM(DFT)/MM electrostatic emdedding. None of them support the notion of very large energy gap fluctuations or ergodicity breaking. The deviation between our simulations and the ones reported in [ J. Phys. Chem. B 2017, 121, 4958] is traced back to rather large electric fields at the Fe site of the heme c cofactor in that study, not seen in our simulations, neither with the AMBER nor with the CHARMM force field. While ergodicity breaking effects may well occur in other biological ET, our numerical evidence suggests that this is not the case for cytochrome c.

It was recently suggested that certain redox proteins operate in an ergodicity-breaking regime to facilitate biological electron transfer (ET). A signature for this is a large variance reorganization free energy (several electronvolts) but a significantly smaller Stokes reorganization free energy due to incomplete protein relaxation on the time scale of the ET event. Here we investigate whether this picture holds for oxidation of cytochrome c in aqueous solution, at various levels of theory including classical molecular dynamics with two additive and one electronically polarizable force field, and QM/MM calculations with the QM region treated by full electrostatic DFT embedding and by the perturbed matrix method. Sampling the protein and energy gap dynamics over more than 250 ns, we find no evidence for ergodicity-breaking effects. In particular, the inclusion of electronic polarizability of the heme group at QM/MM levels did not induce nonergodic effects, contrary to previous reports by Matyushov et al. The well-known problem of overestimation of reorganization free energies with additive force fields is cured when the protein and solvent are treated as electronically polarizable. Ergodicity-breaking effects may occur in other redox proteins, and our results suggest that long simulations, ideally on the ET time scale, with electronically polarizable force fields are required to obtain strong numerical evidence for them.

Photoelectron spectroscopy measurements and density functional calculations are combined to determine the lowest electron binding energies of first-row transition-metal aqua ions, titanium through copper, with 3d(1) through 3d(9) electronic configurations, in their most common oxidation states. Vertical ionization energies are found to oscillate considerably between 6.76 and 9.65 eV for the dications and between 7.05 and 10.28 eV for the respective trivalent cations. The metal cations are modeled as [M(H2O)n](q+) clusters (q = 2, 3, and 4; n = 6 and 18) surrounded by continuum solvent. The performance of 10 exchange-correlation functionals, two GGAs, three MGGAs, two HGGAs and three HMGGAs, combined with the MDF10(ECP)/6-31+G(d,p) basis set is assessed for 11 M-O bond distances, 10 vertical ionization energies, 6 adiabatic ionization energies, and the associated reorganization free energies. We find that for divalent cations the HGGA and HMGGA functionals in combination with the 18 water model show the best agreement with experimental vertical ionization energies and geometries; for trivalent ions, the MGGA functionals perform best. The corresponding reorganization free energies (λo) of the oxidized ions are significantly underestimated with all DFT functionals and cluster models. This indicates that the structural reorganization of the solvation shell upon ionization is not adequately accounted for by the simple solvation models used, emphasizing the importance of extended sampling of thermally accessible solvation structures for an accurate computation of this quantity. The photoelectron spectroscopy measurements reported herein provide a comprehensive set of transition-metal redox energetic quantities for future electronic structure benchmarks.

Cytochrome c oxidase (cco) catalyzes the oxygen reduction reaction in most aerobically respiring organisms. Decades of research have uncovered many aspects relating to structure and function of this enzyme. However, the origin of the unusually fast terminal electron transfer step from heme a to heme a(3) in cco has been the subject of intense discussions over recent years. Yet, no satisfactory consensus has been achieved. Carrying out large-scale molecular dynamics simulation of the protein embedded in a solvated membrane, we obtain a reorganization free energy λ = 0.57 eV. Evaluation of the quantized single-mode rate equation using the experimental rate and the computed reorganization free energy gives a value of 1.5 meV for the average electronic coupling (H(ab)) between heme a and heme a(3). Thus, according to our calculations, the nanosecond electron transfer (ET) is due to a small but significant activation barrier (ΔG(‡) = 0.12 eV) in combination with effective electronic coupling between the two cofactors. The activation free energy is caused predominantly by collective reorganization of protein residues. We show that our results are consistent with the weak temperature dependence observed in experiment if one allows for very minor variations in the donor-acceptor distance as the temperature changes.

Aqueous solutions of ferrous and ferric iron (Fe(2+/3+)) and of the iron-hexacyano complexes [Fe(CN)(6)](4-/3-) are studied by photoelectron spectroscopy using a liquid microjet in conjunction with synchrotron soft X-rays for ionization. For Fe(2+)(aq) we observe two well-resolved peaks at 7.09 and 9.16 eV electron binding energy (BE) that can be assigned to the iron-hexaaquo complex. For Fe(3+)(aq) we observe only one peak above the highest valence band of liquid water, at 10.08 eV BE. Interpreting the spectra in terms of the one-electron levels of Kohn-Sham density functional theory, we find that the two peaks for Fe(2+)(aq) originate from the energy splitting between the highest occupied β (= minority) spin level (Fe d(t(2g))) and the five highest occupied α (= majority) spin levels (Fe d(t(2g)) and d(e(g))). The peak for Fe(3+)(aq) arises from d-levels that are strongly mixed with the solvent. The spectra of the aqueous hexacyano complexes show a single strong peak at 6.11 and 7.52 eV BE for [Fe(CN)(6)](4-) and [Fe(CN)(6)](3-), respectively, originating from the highest occupied Fe d(t(2g)) levels, and two further peaks at higher BE originating from the cyano ligands. The PE spectra of the reduced aquo and cyano ions are then used to obtain-solely on experimental grounds-values for the reorganization free energy of the oxidized ions. DFT/continuum calculations of this important parameter in the Marcus theory of oxidation reactions are in fairly good agreement with experiment.

Energy-resolved photoemission spectroscopy and density functional molecular dynamics simulations are combined to construct an energy level diagram for the Mn(2+/3+) redox reaction in aqueous solution. Two peaks centered at 8.88 and 10.26 eV electron binding energies can be assigned to the Mn2+ hexa-aquo complex with a peak area ratio of 2:2.83. Using the notation of crystal field theory, the peak at lower energies can be interpreted as arising from ionization from the e(g) levels (highest occupied molecular orbital, HOMO), and the peak at higher energies are from ionization of the t(2g) levels. The difference corresponds to the average crystal field splitting, 1.38 eV. From the position of the HOMO level and the absolute redox potential, an experimental value for the reorganization free energy of the aqueous Mn3+ hexa-aquo complex is estimated to be 2.98 eV. Density functional molecular dynamics simulations can reproduce the experimental vertical ionization energy, redox free energy, and reorganization free energies fairly well, provided that the absolute potential shift in periodic boundary conditions, finite size effects, and inaccuracies of the exchange correlation functional are taken into account. Most strikingly, in the simulations, we observe spontaneous and reversible deprotonation of the aqueous Mn3+ hexa-aquo complex to form MnOH(H2O)5(2+) + H+, in line with the low experimental pKa value of this ion. The interconversion between protonation states leads to interesting redox phenomena for aqueous Mn3+, culminating in a bimodal thermal distribution of the electron affinity.

A well-behaved (low spin) transition metal aqua ion, Ru(aq)(2+), is used as a model system in an ab initio molecular dynamics study of a redox half reaction to which the Marcus theory of electron transfer is assumed to apply. Using constraint methods, we show that aqueous Ru(2+) can be reversibly transformed to Ru(3+) under the control of the classical solvent electrostatic potential as order parameter. The mean force is found to vary linearly with the order parameter in accordance with the Marcus theory. As can be expected for a half reaction, the slope in the oxidized and reduced states are asymmetric differing by approximately a factor of two. As a further test, we verify that the corresponding quadratic potential of mean force is in excellent agreement with the free energy profile obtained from the Gaussian distribution of potential fluctuations sampled from free (unconstrained) runs of the reduced and oxidized system. Similar to experimental electrochemical methods, our simulation scheme enables us to manipulate the effective thermodynamic driving force and align the free energy minima of product and reactant state. The activation energy and reaction entropy computed under these conditions are discussed and analyzed from the Marcus perspective.