Density-Dependent Formulation of Dispersion-Repulsion Interactions in Hybrid Multiscale Quantum/Molecular Mechanics (QM/MM) Models.

Mixed multiscale quantum/molecular mechanics (QM/MM) models are widely used to explore the structure, reactivity, and electronic properties of complex chemical systems. Whereas such models typically include electrostatics and potentially polarization in so-called electrostatic and polarizable embedding approaches, respectively, nonelectrostatic dispersion and repulsion interactions are instead commonly described through classical potentials despite their quantum mechanical origin. Here we present an extension of the Tkatchenko-Scheffler semiempirical van der Waals (vdWTS) scheme aimed at describing dispersion and repulsion interactions between quantum and classical regions within a QM/MM polarizable embedding framework. Starting from the vdWTS expression, we define a dispersion and a repulsion term, both of them density-dependent and consistently based on a Lennard-Jones-like potential. We explore transferable atom type-based parametrization strategies for the MM parameters, based on either vdWTS calculations performed on isolated fragments or on a direct estimation of the parameters from atomic polarizabilities taken from a polarizable force field. We investigate the performance of the implementation by computing self-consistent interaction energies for the S22 benchmark set, designed to represent typical noncovalent interactions in biological systems, in both equilibrium and out-of-equilibrium geometries. Overall, our results suggest that the present implementation is a promising strategy to include dispersion and repulsion in multiscale QM/MM models incorporating their explicit dependence on the electronic density.

Open-ended formulation of self-consistent field response theory with the polarizable continuum model for solvation.

The study of high-order absorption properties of molecules is a field of growing importance. Quantum-chemical studies can help design chromophores with desirable characteristics. Given that most experiments are performed in solution, it is important to devise a cost-effective strategy to include solvation effects in quantum-chemical studies of these properties. We here present an open-ended formulation of self-consistent field (SCF) response theory for a molecular solute coupled to a polarizable continuum model (PCM) description of the solvent. Our formulation relies on the open-ended, density matrix-based quasienergy formulation of SCF response theory of Thorvaldsen, et al., [J. Chem. Phys., 2008, 129, 214108] and the variational formulation of the PCM, as presented by Lipparini et al., [J. Chem. Phys., 2010, 133, 014106]. Within the PCM approach to solvation, the mutual solute-solvent polarization is represented by means of an apparent surface charge (ASC) spread over the molecular cavity defining the solute-solvent boundary. In the variational formulation, the ASC is an independent, variational degree of freedom. This allows us to formulate response theory for molecular solutes in the fixed-cavity approximation up to arbitrary order and with arbitrary perturbation operators. For electric dipole perturbations, pole and residue analyses of the response functions naturally lead to the identification of excitation energies and transition moments. We document the implementation of this approach in the Dalton program package using a recently developed open-ended response code and the PCMSolver libraries and present results for one-, two-, three-, four- and five-photon absorption processes of three small molecules in solution.

Open-ended response theory with polarizable embedding: multiphoton absorption in biomolecular systems.

We present the theory and implementation of an open-ended framework for electric response properties at the level of Hartree-Fock and Kohn-Sham density functional theory that includes effects from the molecular environment modeled by the polarizable embedding (PE) model. With this new state-of-the-art multiscale functionality, electric response properties to any order can be calculated for molecules embedded in polarizable atomistic molecular environments ranging from solvents to complex heterogeneous macromolecules such as proteins. In addition, environmental effects on multiphoton absorption (MPA) properties can be studied by evaluating single residues of the response functions. The PE approach includes mutual polarization effects between the quantum and classical parts of the system through induced dipoles that are determined self-consistently with respect to the electronic density. The applicability of our approach is demonstrated by calculating MPA strengths up to four-photon absorption for the green fluorescent protein. We show how the size of the quantum region, as well as the treatment of the border between the quantum and classical regions, is crucial in order to obtain reliable MPA predictions.

Averaged Solvent Embedding Potential Parameters for Multiscale Modeling of Molecular Properties.

We derive and validate averaged solvent parameters for embedding potentials to be used in polarizable embedding quantum mechanics/molecular mechanics (QM/MM) molecular property calculations of solutes in organic solvents. The parameters are solvent-specific atom-centered partial charges and isotropic polarizabilities averaged over a large number of geometries of solvent molecules. The use of averaged parameters reduces the computational cost to obtain the embedding potential, which can otherwise be a rate-limiting step in calculations involving large environments. The parameters are evaluated by analyzing the quality of the resulting molecular electrostatic potentials with respect to full QM potentials. We show that a combination of geometry-specific parameters for solvent molecules close to the QM region and averaged parameters for solvent molecules further away allows for efficient polarizable embedding multiscale modeling without compromising the accuracy. The results are promising for the development of general embedding parameters for biomolecules, where the reduction in computational cost can be considerable.

Electronic circular dichroism of fluorescent proteins: a computational study.

The electronic circular dichroism (ECD) properties of the green fluorescent protein and other fluorescent proteins have been calculated with density functional theory. The influence of different embedding models on the ECD signal of the chromophore has been investigated by modeling the protein environment by the polarizable continuum model (QM/PCM), by the polarizable embedding model (PE-QM/MM), by treating the minimal environment quantum mechanically at the same footing as the chromophore (QM/QM), and by adding the remaining part of the protein by means of PCM (QM/QM/PCM). The rotatory strength is found to be more sensitive than the oscillatory strength to changes in the geometry of the chromophore and its surroundings and to the type of embedding model used. In general, explicit embedding of the surrounding protein (PE-QM/MM or QM/QM) induces an increase in the rotatory strength of the chromophore. Explicit inclusion of the whole protein through polarizable embedding is found to be an affordable embedding model that gives the correct sign of the rotatory strength for all fluorescent proteins. PCM is useful as a first approximation to protein environment effects, but as a rule seems to underestimate the rotatory strength.

A polarizable embedding DFT study of one-photon absorption in fluorescent proteins.

A theoretical study of the one-photon absorption of five fluorescent proteins (FPs) is presented. The absorption properties are calculated using a polarizable embedding approach combined with density functional theory (PE-DFT) on the wild-type green fluorescent protein (wtGFP) and several of its mutants (BFP, eGFP, YFP and eCFP). The observed trends in excitation energies among the FPs are reproduced by our approach when performing calculations directly on the crystal structures or when using structures extracted from molecular dynamics simulations. However, in the former case, QM/MM geometry optimization of the chromophores within a frozen protein environment is needed in order to reproduce the experimental trends. An explicit account of polarization in the force field is not needed to yield the correct trend between the different FPs, but it is necessary for reproducing the experimentally observed red shift from vacuum to protein. This is the first computational study of a range of fluorescent proteins using a polarizable embedding potential.

A combined quantum mechanics/molecular mechanics study of the one- and two-photon absorption in the green fluorescent protein.

We present for the first time a QM/MM study of the one- and two-photon absorption spectra of the GFP chromophore embedded in the full protein environment described by an advanced quantum mechanically derived polarizable force field. The calculations are performed on a crystal structure of the green fluorescent protein (GFP) using the polarizable embedding density functional theory (PE-DFT) scheme. The importance of treating the protein environment explicitly with a polarizable force field and higher-order multipoles is demonstrated, as well as the importance of including water molecules close to the chromophore in the protein barrel. For the most advanced description we achieve good agreement with experimental findings, with a peak at 405 nm for the neutral and a peak at 475 nm for the anionic form of the GFP chromophore. The presence of a dark OPA state, as suggested by other studies to explain the discrepancies between OPA and TPA spectra, is not supported by our calculations.

Density functional theory/molecular mechanics approach for electronic g-tensors of solvated molecules.

A general density functional theory/molecular mechanics approach for computation of electronic g-tensors of solvated molecules is presented. We apply the theory to the commonly studied di-tert-butyl nitroxide molecule, the simplest model compound for nitroxide spin labels, and explore the role of an aqueous environment and of various approximations for its treatment. It is found that successive improvements of the solvent shift of the g-tensor are obtained by going from the polarizable continuum model to discrete solvent models of various levels of sophistication. The study shows that an accurate parametrization of the electrostatic potential and polarizability of the solvent molecules in terms of distributed multipole expansions and anisotropic polarizabilities to a large degree relieves the need to explicitly include water molecules in the quantum region, which is the common case in density functional/continuum model approaches. It is also shown that the local dynamics of the solvent around the solute significantly influences the electronic g-tensor and should be included in benchmarking of exchange-correlation functionals for evaluation of solvent shifts of g-tensors. These findings can have important ramifications for the use of advanced hybrid density functional theory/molecular mechanics approaches for modeling spin labels in solvents, proteins, and membrane environments.

Excitation energies in solution: the fully polarizable QM/MM/PCM method.

We present the theory and an implementation of the combined quantum mechanics/molecular mechanics/polarizable dielectric continuum (QM/MM/PCM) method. This is a fully polarizable layered model designed for effective inclusion of a medium in a quantum-mechanical calculation. The short-range part of the solvent electrostatic potential is described by an atomistic model while the long-range part of this potential is described by a dielectric continuum. The QM/MM/PCM method has been implemented in combination with QM linear response techniques allowing for the assessment of, e.g., vertical electronic excitation energies and linear dipole-dipole polarizabilities, in all cases using a nonequilibrium formulation of the environmental response. The model is general, but is here implemented for the case of density functional theory. Numerical examples are given for solvatochromic shifts relating to a set of organic molecules in aqueous solution. We find in general the QM/MM/PCM interface to exhibit a faster convergence with respect to the system size as compared to the use of QM/MM only.

Density Functional Restricted-Unrestricted/Molecular Mechanics Theory for Hyperfine Coupling Constants of Molecules in Solution.

A density functional restricted-unrestricted approach, capable of evaluating hyperfine coupling constants with the inclusion of spin polarization effects in a spin-restricted Kohn-Sham method, has been extended to incorporate environmental effects. This is accomplished by means of a hybrid quantum mechanics/molecular mechanics formalism which allows for a granular representation of the polarization and electrostatic interactions with the classically described medium. By this technique, it is possible to trace the physical origin of hyperfine coupling constants in terms of spin polarization and spin density contributions and disentangle the dependence of these contributions on molecular geometry and solvent environment, something that increases the prospects for optimal design of spin labels for particular applications. A demonstration is given for the nitrogen isotropic hyperfine coupling constant in di-tert-butyl nitroxide solvated in water. The results indicate that the direct spin density contribution is about 5 times smaller than the spin polarization contribution to the nitrogen isotropic hyperfine coupling constant and that the latter contribution is solely responsible for the solvent shift of the constant. The developed approach is found capable of achieving satisfactory accuracy in prediction of the hyperfine coupling constants of solvated di-tert-butyl nitroxide and other similar nitroxides without the inclusion of solvent molecules in the quantum region provided polarizable force fields are used for the description of these molecules.

Development of different human skin colors: a review highlighting photobiological and photobiophysical aspects.

Skin color has changed during human evolution. These changes may result from adaptations to solar ultraviolet radiation (protection of sweat glands, sunburn, skin cancer, vitamin D deficiency, defence against microorganisms, etc.), and/or sexual selection. Migration to areas with high levels of UV is associated with skin darkening, while migration to areas with low levels has led to skin lightening. However, other factors may have played roles. Temperature and food have probably been secondary determinants: heat exchange with the environment is dependent on ambient temperature, and a high intake of food rich in vitamin D allows a dark skin color to persist even at latitudes of low UV levels, as exemplified by Inuit's living at high latitudes. Future studies of human migration will show if skin lightening is a faster process and has a higher evolutionary impact than skin darkening. Maybe due to that some American Indians have kept a relatively light skin although they live under the equator. The following hypotheses for skin darkening are reviewed: shielding of sweat glands and blood vessels in the skin, protection against skin cancer and overproduction of vitamin D, camouflage, adaptation to different ambient temperatures, defense against microorganisms, protection against folate photodestruction. Hypotheses for skin lightening are: sexual selection, adaptation to cold climates, enhancement of vitamin D photoproduction, and changing food habits leading to lower intake of vitamin D. The genetical processes behind some of the changes of skin color will be also briefly reviewed.

Photodegradation of 5-methyltetrahydrofolate in the presence of Uroporphyrin.

The main form of folate in human plasma is 5-methyltetrahydrofolate (5MTHF). The observation that folate in human serum is photosensitive supports the hypothesis that humans developed dark skin in high ultraviolet fluences areas in order to protect folate in the blood from UV radiation. However, folates alone are quite photostable. Therefore, in this study, we examined for the first time the photodegradation of 5MTHF in the presence of the endogenous photosensitizer uroporphyrin (Uro), which is sometimes present in low concentration in human serum, under UV and near-UV light exposure. We found strong indications that while 5MTHF alone is rather photostable, it is degraded quickly in the presence of Uro. Using deuterium oxide (D(2)O) as an enhancer of the lifetime of singlet oxygen and the singlet oxygen sensor green reagent (SOSG) as a scavenger of singlet oxygen, we have found that the photodegradation most likely proceeds via a type II photosensitization. Our results show that singlet oxygen is likely to be the main intermediate in the photodegradation of 5MTHF mediated by Uro. Our findings may be useful for further studies the evolution of human skin colours.

5-Methyltetrahydrofolate is photosensitive in the presence of riboflavin.

5-Methyltetrahydrofolate (5MTHF) is the main form of folate in human plasma, and an important vitamin for human health. Photodegradation of folates may have played a role in the development of different human skin colours. 5MTHF can be degraded directly by exposure to ultraviolet radiation or by exposure to visible light in the presence of endogenous sensitizers like riboflavin (RF). These photochemical reactions were studied by absorption spectroscopy. While 5MTHF is stable under UV and visible light exposure in pure aqueous media, it is quickly degraded in the presence of RF during UVA and blue light exposure. The degradation of 5MTHF is dependent on the concentration of RF, but not on the concentration of 5MTHF itself. UVA and blue light gave similar reactions. Further investigations are necessary to evaluate the consequences of large light exposures in vivo in humans. Our findings should be taken into the ongoing discussion about the development of human skin colours. Due to the presence of RF in human blood, folate can be significantly degraded during prolonged or intense blue light exposure. Thus, a dark skin colour may be favourable for prevention of folate degradation under high solar fluence rates, such as in equatorial areas.

Is the seasonal variation in cancer prognosis caused by sun-induced folate degradation?

Recently, we have documented that the season of diagnosis affects the prognosis of Hodgkin's lymphoma, colon-, breast- and prostate-cancer patients in Norway. The relative risk of death was lower for the patients diagnosed during summer and autumn when compared with the winter diagnosis. We here hypothesise that UV (ultraviolet) induced degradation of folate may be the reason for the observed seasonal variations in cancer prognosis. It is known that folic acid, a synthetic form of folate, is degraded by UV radiation. We have also found that the most common folate derivative in the human body, 5-methyltetrahydrofolate, is UV sensitive.

Photodegradation of 5-methyltetrahydrofolate: biophysical aspects.

5-methyltetrahydrofolate (5MTHF) absorbs UV radiation and has an absorption coefficient of 24250+/-1170 M(-1) cm(-1) at 290 nm. It has a weak fluorescence emission in the wavelength region around 360 nm. Our data demonstrated induction of 5-methyldihydrofolate by exposure to UVB and, after continues irradiation, p-aminobenzoyl-L-glutamic acid was found. The photodegradation of 5MTHF follows a first order kinetic with a degradation rate constant of 9.2 x 10(-3) min(-1) under our conditions (fluence rate of 2.15 mW cm(-2), exposure wavelengths from 280 to 350 nm). Our results indicate that a direct degradation of 5MTHF by UV exposure in humans in vivo is rather unlikely. 5MTHF mainly absorbs, and is degraded by, UVB and UVC, radiation that does not penetrate the earth's atmosphere and the human skin well.