Theoretical estimation of redox potential of biological quinone cofactors

Abstract

Redox potentials are essential to understand biological cofactor reactivity and to predict their behavior in biological media. Experimental determination of redox potential in biological system is often difficult due to complexity of biological media but computational approaches can be used to estimate them. Nevertheless, the quality of the computational methodology remains a key issue to validate the results. Instead of looking to the best absolute results, we present here the calibration of theoretical redox potential for quinone derivatives in water coupling QM + MM or QM/MM scheme. Our approach allows using low computational cost theoretical level, ideal for long simulations in biological systems, and determination of the uncertainties linked to the calculations. © 2017 Wiley Periodicals, Inc.

Systematic High‐Accuracy Prediction of Electron Affinities for Biological Quinones

“…The EA determines the function of the quinone in electron transfer and also forms the basis for computing reduction potentials, for which additional energetic contributions need to be considered. The computational prediction of quinone electron affinities and reduction potentials has received much attention, usually in system‐specific studies . Although approaches such as the equations‐of‐motion (EOM) or Green's function methods provide a direct way to obtain electron affinities for multiple electron attached states in a single calculation, quinone EAs are typically computed through differences of energies obtained by separate quantum chemical calculations of the quinone and the semiquinone radical.…”

Machine Learning for Efficient Prediction of Protein Redox Potential: The Flavoproteins Case

“…Several other studies have also highlighted and disclosed the roles of specific hydrogen bonds and electrostatic, hydrophobic, and π–π stacking interactions, as well as conformational changes of the tricyclic ring or its environment on the flavin reduction potential. − However, the quantitative prediction of the effects of these interactions and features on the redox potential of flavoproteins is extremely difficult to predict because the contribution of these effects is expected to scale in a nonlinear fashion and is therefore particularly difficult to quantify only on the ground of structural analysis. The redox potentials of proteins can be computed using ab initio , semiempirical, or classical methods, − some of which were tested and used to predict the redox potential of flavoproteins. , Truhlar and collaborators reported a series of seminal density functional theory investigations about lumiflavin in different solvents and with different substituents, which were used as benchmarks for subsequent quantum mechanics/molecular mechanics (QM/MM) studies aimed at investigating the redox properties of small flavoproteins . However, even though QM and QM/MM studies allow one to estimate the flavin reduction potential with an average error of only 10–20 mV, the massive and systematic application of QM and QM/MM methods in virtual screening protocols is still hindered by the large computational cost of such calculations. − In parallel to QM and QM/MM studies, approaches based on a molecular mechanics description of flavoproteins have been reported.…”

“…The redox potentials of proteins can be computed using ab initio , semiempirical, or classical methods, 24 − 27 some of which were tested and used to predict the redox potential of flavoproteins. 28 , 29 Truhlar and collaborators reported a series of seminal density functional theory investigations about lumiflavin in different solvents and with different substituents, which were used as benchmarks for subsequent quantum mechanics/molecular mechanics (QM/MM) studies aimed at investigating the redox properties of small flavoproteins. 30 However, even though QM and QM/MM studies allow one to estimate the flavin reduction potential with an average error of only 10–20 mV, the massive and systematic application of QM and QM/MM methods in virtual screening protocols is still hindered by the large computational cost of such calculations.…”

Accurate Quantum Mechanical/Molecular Mechanical Calculations of Reduction Potentials in Azurin Variants

“…19,29,58–60 Even with the classical MM force field models for the outer-sphere and solvents, the quality of the conformational sampling on the whole system remains a key issue to validate the results because the expensive QM calculation is required at every step during direct QM/MM MD. Some alternative techniques were proposed to reduce the computational cost, for example, refitting MM point charges in the classical model to capture the polarization effect from both protein and solvents, 61 performing MD sampling with classical force field followed by QM evaluations on the active center from partial trajectories, 29,60 decoupling of the QM and MM regions, 49,62 or using semiempirical QM/MM models. 63 More rigorous approaches can be applied to describe the influence of the environment on the reduction properties of active site accurately, such as QM/MM free energy perturbation (QM/MM-FEP), 64 QM/MM thermodynamic cycle perturbation, 65,66 MD perturbation matrix method, 29,67 QM/MM adiabatic approximation, 68 and QM/MM minimum free-energy path (QM/MM-MFEP) method in which the geometry of the active site was minimized on the potential of mean force (PMF) surface of QM coordinates rather than the potential energy surface.…”

“…In addition, the uncertainty from finite system size effects and the challenges for DFT models lead to an error for reduction potentials about 200 mV. , The combined quantum mechanical and molecular mechanical (QM/MM) method, first developed by Warshel and Levitt, provides an accurate and computationally efficient tool to describe chemical and biological systems in a complex environment. − During the past decade, Yang and co-workers developed a series of QM/MM approaches to calculate oxidation free energies and reorganization energies. − Several QM/MM calculations on the reduction properties of copper protein systems have been also reported in the past few years. ,,− Even with the classical MM force field models for the outer-sphere and solvents, the quality of the conformational sampling on the whole system remains a key issue to validate the results because the expensive QM calculation is required at every step during direct QM/MM MD. Some alternative techniques were proposed to reduce the computational cost, for example, refitting MM point charges in the classical model to capture the polarization effect from both protein and solvents, performing MD sampling with classical force field followed by QM evaluations on the active center from partial trajectories, , decoupling of the QM and MM regions, , or using semiempirical QM/MM models . More rigorous approaches can be applied to describe the influence of the environment on the reduction properties of active site accurately, such as QM/MM free energy perturbation (QM/MM-FEP), QM/MM thermodynamic cycle perturbation, , MD perturbation matrix method, , QM/MM adiabatic approximation, and QM/MM minimum free-energy path (QM/MM-MFEP) method in which the geometry of the active site was minimized on the potential of mean force (PMF) surface of QM coordinates rather than the potential energy surface. , We further combined QM/MM-MFEP with the fractional number of electron (FNE) method to study redox reactions. , Because the direct QM/MM MD sampling is replaced by iterative optimizations on the active site, the combined QM/MM-MFEP and FNE method is an excellent approach to calculate protein reduction potentials with a good balance between computational accuracy and efficiency.…”