Unexpectedly strong energy stabilization inside the hydrophobic core of small protein rubredoxin mediated by aromatic residues: correlated ab initio quantum chemical calculations

The formation of a hydrophobic core of globular proteins is believed to be the consequence of exterior hydrophobic forces of entropic nature. This, together with the low occurrence of hydrogen bonds in the protein core, leads to the opinion that the energy contribution of core formation to protein folding and stability is negligible. We show that stabilization inside the hydrophobic core of a small protein, rubredoxin, determined by means of high-level correlated ab initio calculations (complete basis set limit of MP2 stabilization energy + CCSD(T) correction term), amounted to approximately 50 kcal/mol. These results clearly demonstrate strong attraction inside a hydrophobic core. This finding may lead to substantial changes in the current view of protein folding. We also point out the inability of the DFT/B3LYP method to describe a strong attraction between studied amino acids.     

Aqueous solvation free energies of ions and ion-water clusters based on an accurate value for the absolute aqueous solvation free energy of the proton

Thermochemical cycles that involve pKa, gas-phase acidities, aqueous solvation free energies of neutral species, and gas-phase clustering free energies have been used with the cluster pair approximation to determine the absolute aqueous solvation free energy of the proton. The best value obtained in this work is in good agreement with the value reported by Tissandier et al. (Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. J.; Earhart, A. D.; Coe, J. V. J. Phys. Chem. A 1998, 102, 7787), who applied the cluster pair approximation to a less diverse and smaller data set of ions. We agree with previous workers who advocated the value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton. Considering the uncertainties associated with the experimental gas-phase free energies of ions that are required to use the cluster pair approximation as well as analyses of various subsets of data, we estimate an uncertainty for the absolute aqueous solvation free energy of the proton of no less than 2 kcal/mol. Using a value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton, we expand and update our previous compilation of absolute aqueous solvation free energies; this new data set contains conventional and absolute aqueous solvation free energies for 121 unclustered ions (not including the proton) and 147 conventional and absolute aqueous solvation free energies for 51 clustered ions containing from 1 to 6 water molecules. When tested against the same set of ions that was recently used to develop the SM6 continuum solvation model, SM6 retains its previously determined high accuracy; indeed, in most cases the mean unsigned error improves when it is tested against the more accurate reference data.     

Dispersion interactions govern the strong thermal stability of a protein

Rubredoxin from the hyperthermophile Pyrococcus furiosus (Pf Rd) is an extremely thermostable protein, which makes it an attractive subject of protein folding and stability studies. A fundamental question arises as to what the reason for such extreme stability is and how it can be elucidated from a complex set of interatomic interactions. We addressed this issue first theoretically through a computational analysis of the hydrophobic core of the protein and its mutants, including the interactions taking place inside the core. Here we show that a single mutation of one of phenylalanine's residues inside the protein's hydrophobic core results in a dramatic decrease in its thermal stability. The calculated unfolding Gibbs energy as well as the stabilization energy differences between a few core residues follows the same trend as the melting temperature of protein variants determined experimentally by microcalorimetry measurements. NMR spectroscopy experiments have shown that the only part of the protein affected by mutation is the reasonably rearranged hydrophobic core. It is hence concluded that stabilization energies, which are dominated by London dispersion, represent the main source of stability of this protein.     

The influence of hydrophobic amino acid side groups on the acidity of the aromatic imidazole ring of histidine: A theoretical study

In this study we have calculated the acidity constant (pKa) of imidazole ring in Histidine‐Hydrophobic amino acid dipeptides using the quantum chemistry and continuum solvation methods. Density functional theory calculations with the large basis sets are used to determine the Gibbs free energy of deprotonate in the gas and liquid phases. Based on our results ΔG_S values are located between ?69.38 and ?18.82 kcal mol^?1 which are related to His⁺–Gly and His forms, respectively. pKa of the dipeptides in the aqueous phase was obtained from the calculated gas‐phase and solvation free energies through a thermodynamic cycle and the solvation model chemistry of Martin Karplus et al. Solvation effects are treated using a self‐consistent reaction field formalism involving polarized continuum models. According to our calculations pKa values are between 5.50 and 8.19 that are belong to His⁺–ILe and His⁺–Ala forms, respectively. Natural bond orbital analysis of dipeptides reveals that the electron delocalization in imidazole ring is the most effective factor in determination of acidity order for these compounds. Structural analysis confirmed that the orientation of carbonyl group with respect to imidazole ring is an effective factor in imidazole ring stability. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Structures and aggregation states of fluoromethyllithium and chloromethyllithium carbenoids in the gas phase and in ethereal solvent

Using high-level quantum mechanical calculations and various models to account for solvation effects, monomers and dimers of fluoromethyllithium and chloromethyllithium carbenoids are studied in the gas phase and in dimethyl ether solvent. A combination of explicit microsolvation and a continuum reaction field is required to account fully for the structural and energetic effects of solvation. One important effect of solvent is the stabilization of charge-separated structures in which the lithium-halogen distance is much greater than in the gas-phase structures. At the most complete level of theory the 173 K standard-state free energy of dimerization of fluoromethyllithium in dimethyl ether is predicted to be -0.9 kcal mol(-)(1), while that for chloromethyllithium in the same solvent is predicted to be 3.7 kcal mol(-)(1). This suggests that, under typical experimental conditions, dimers of chloroalkyllithiums will not be observed, while dimers of fluoroalkyllithiums may contribute to the equilibrium population at a detectable level.     

Contribution of water dimer absorption to the millimeter and far infrared atmospheric water continuum

We present a rigorous calculation of the contribution of water dimers to the absorption coefficient alpha(nu,T) in the millimeter and far infrared domains, over a wide range (276-310 K) of temperatures. This calculation relies on the explicit consideration of all possible transitions within the entire rovibrational bound state manifold of the dimer. The water dimer is described by the flexible 12-dimensional potential energy surface previously fitted to far IR transitions [C. Leforestier et al., J. Chem. Phys. 117, 8710 (2002)], and which was recently further validated by the good agreement obtained for the calculated equilibrium constant Kp(T) with experimental data [Y. Scribano et al., J. Phys. Chem. A. 110, 5411 (2006)]. Transition dipole matrix elements were computed between all rovibrational states up to an excitation energy of 750 cm(-1), and J=K=5 rotational quantum numbers. It was shown by explicit calculations that these matrix elements could be extrapolated to much higher J values (J=30). Transitions to vibrational states located higher in energy were obtained from interpolation of computed matrix elements between a set of initial states spanning the 0-750 cm(-1) range and all vibrational states up to the dissociation limit (approximately 1200 cm(-1)). We compare our calculations with available experimental measurements of the water continuum absorption in the considered range. It appears that water dimers account for an important fraction of the observed continuum absorption in the millimeter region (0-10 cm(-1)). As frequency increases, their relative contribution decreases, becoming small (approximately 3%) at the highest frequency considered nu=944 cm(-1).     

Microsolvation effects on the electron capturing ability of thymine: thymine-water clusters

The effects of solvation on the stability of thymine and its negative ion have been investigated by explicitly considering the structures of complexes of thymine with up to five water molecules and the respective anions at the B3LYP/DZP++ level of theory. The vertical detachment energy of thymine was predicted to increase gradually with the hydration number, consistent with experimental observations from a photodetachment-photoelectron spectroscopy study J. Schiedt et al., [Chem. Phys. 239, 511 (1998)]. The adiabatic electron affinity of thymine was also found to increase with the hydration number, which implies that while the conventional valence anion of thymine is only marginally bound in the gas phase, it may form a stable anion in aqueous solution.     

Atomic decomposition of the protein solvation free energy and its application to amyloid-beta protein in water

We report the development of an atomic decomposition method of the protein solvation free energy in water, which ascribes global change in the solvation free energy to local changes in protein conformation as well as in hydration structure. So far, empirical decomposition analyses based on simple continuum solvation models have prevailed in the study of protein-protein interactions, protein-ligand interactions, as well as in developing scoring functions for computer-aided drug design. However, the use of continuum solvation model suffers serious drawbacks since it yields the protein free energy landscape which is quite different from that of the explicit solvent model and since it does not properly account for the non-polar hydrophobic effects which play a crucial role in biological processes in water. Herein, we develop an exact and general decomposition method of the solvation free energy that overcomes these hindrances. We then apply this method to elucidate the molecular origin for the solvation free energy change upon the conformational transitions of 42-residue amyloid-beta protein (Aβ42) in water, whose aggregation has been implicated as a primary cause of Alzheimer's disease. We address why Aβ42 protein exhibits a great propensity to aggregate when transferred from organic phase to aqueous phase.     

Ab initio procedure for aqueous-phase pKa calculation: the acidity of nitrous acid

We present an ab initio procedure for accurately calculating aqueous-phase pKa values and apply it to study the acidity of nitrous acid (HNO2, or HONO). The aqueous-phase pK(a) of nitrous acid was obtained from calculated gas-phase acidities and solvation free energies via a thermodynamic cycle and the solvation model chemistry of Barone et al. (J. Chem. Phys. 1997, 107, 3210). Solvation free energies were calculated at the HF/6-31G(d) level using the dielectric-polarizable continuum and the integral equation formalism-polarizable continuum solvent models (D-PCM and IEF-PCM, respectively), with the D-PCM model yielding the most accurate pKa values. For HF free energies of solvation, significant improvements in accuracy could be made by moving to the larger 6-311++G(3df,3pd) and aug-cc-pVQZ basis sets. Solvation free energies were also calculated using the density functional theory (DFT) methods B3LYP, TPSS, PBE0, B1B95, VSXC, B98 and O3LYP, with the most accurate methods being TPSS and VSXC, which provided average errors of less than 0.11 pKa units. Solvation free energies calculated with the different DFT methods were relatively insensitive to the basis set used. Our theoretical calculations are compared with experimental results obtained using stopped flow spectrophotometry. The pKa of nitrous acid was measured as 3.16 at 25 degrees C, and the enthalpy and entropy of nitrous acid dissociation were calculated from measurements as 6.7 kJ mol(-1) and -38.4 J mol(-1) K(-1), respectively, between 25 and 45 degrees C. The UV/visible absorption spectra of the nitrite ion and nitrous acid were also examined, and molar extinction coefficients were obtained for each.     

On the stability of glycine-water clusters with excess electron: implications for photoelectron spectroscopy

Calculations are presented for the glycine-(H(2)O)(n) (-) (n=0-2) anionic clusters with excess electron, with the glycine core in the canonical or zwitterion form. A variety of conformers are predicted, and their relative energy is examined to estimate thermodynamic stability. The dynamic (proton transfer) pathways between the anionic clusters with the canonical and the zwitterion glycine core are examined. Small barrier heights for isomerization from the zwitterion glycine-(H(2)O)(2) (-) anion to those with canonical glycine core suggest that the former conformers may be kinetically unstable and unfavorable for detection of neutral glycine zwitterion-(H(2)O)(n) (n=1,2) clusters by photodetachment, in accordance with the photoelectron spectroscopic experiments by Bowen and co-workers [Xu et al., J. Chem. Phys. 119, 10696 (2003)]. The calculated stability of the glycine-(H(2)O)(n) (-) anion clusters with canonical glycine core relative to those with zwitterion core indicates that the observation of the anionic conformers with the canonical glycine core would be much more feasible, as revealed by Johnson and co-workers [Diken et al. J. Chem. Phys. 120, 9902 (2004)].     

A study on orientation and absorption spectrum of interfacial molecules by using continuum model

In this work, a numerical procedure based on the continuum model is developed and applied to the solvation energy for ground state and the spectral shift against the position and the orientation of the interfacial molecule. The interface is described as a sharp boundary separating two bulk media. The polarizable continuum model (PCM) allows us to account for both electrostatic and nonelectrostatic solute-solvent interactions when we calculate the solvation energy. In this work we extend PCM to the interfacial system and the information about the position and orientation of the interfacial molecule can be obtained. Based on the developed expression of the electrostatic free energy of a nonequilibrium state, the numerical procedure has been implemented and used to deal with a series of test molecules. The time-dependent density functional theory (TDDFT) associated with PCM is used for the electron structure and the spectroscopy calculations of the test molecules in homogeneous solvents. With the charge distribution of the ground and excited states, the position- and orientation-dependencies of the solvation energy and the spectrum have been investigated for the interfacial systems, taking the electrostatic interaction, the cavitation energy, and the dispersion-repulsion interaction into account. The cavitation energy is paid particular attention, since the interface portion cut off by the occupation of the interfacial molecule contributes an extra part to the stabilization for the interfacial system. The embedding depth, the favorable orientational angle, and the spectral shift for the interfacial molecule have been investigated in detail. From the solvation energy calculations, an explanation has been given on why the interfacial molecule, even if symmetrical in structure, tends to take a tilting manner, rather than perpendicular to the interface.     

Role of hydration in determining the structure and vibrational spectra of L-alanine and N-acetyl L-alanine N′-methylamide in aqueous solution: a combined theoretical and experimental approach

In this work we have utilized recent density functional theory Born-Oppenheimer molecular dynamics simulations to determine the first principles locations of the water molecules in the first solvation shell which are responsible for stabilizing the zwitterionic structure of L-alanine. Previous works have used chemical intuition or classical molecular dynamics simulations to position the water molecules. In addition, a complete shell of water molecules was not previously used, only the water molecules which were thought to be strongly interacting (H-bonded) with the zwitterionic species. In a previous work by Tajkhorshid et al. (J Phys Chem B 102:5899) the L-alanine zwitterion was stabilized by 4 water molecules, and a subsequent work by Frimand et al. (Chem Phys 255:165) the number was increased to 9 water molecules. Here we found that 20 water molecules are necessary to fully encapsulate the zwitterionic species when the molecule is embedded within a droplet of water, while 11 water molecules are necessary to encapsulate the polar region with the methyl group exposed to the surface, where it migrates during the MD simulation. Here we present our vibrational absorption, vibrational circular dichroism and Raman and Raman optical activity simulations, which we compare to the previous simulations and experimental results. In addition, we report new VA, VCD, Raman and ROA measurements for L-alanine in aqueous solution with the latest commercially available FTIR VA/VCD instrument (Biotools, Jupiter, FL, USA) and Raman/ROA instrument (Biotools). The signal to noise of the spectra of L-alanine measured with these new instruments is significantly better than the previously reported spectra. Finally we reinvestigate the causes for the stability of the P_π structure of the alanine dipeptide, also called N-acetyl-L-alanine N′-methylamide, in aqueous solution. Previously we utilized the B3LYP/6-31G* + Onsager continuum level of theory to investigate the stability of the NALANMA4WC Han et al. (J Phys Chem B 102:2587) Here we use the B3PW91 and B3LYP hybrid exchange correlation functionals, the aug-cc-pVDZ basis set and the PCM and CPCM (COSMO) continuum solvent models, in addition to the Onsager and no continuum solvent model. Here by the comparison of the VA, VCD, Raman and ROA spectra we can confirm the stability of the NALANMA4WC due to the strong hydrogen bonding between the four water molecules and the peptide polar groups. Hence we advocate the use of explicit water molecules and continuum solvent treatment for all future spectral simulations of amino acids, peptides and proteins in aqueous solution, as even the structure (conformer) present cannot always be found without this level of theory. Festschift in Honor of Philip J. Stephens’ 65th Birthday. During the proof stage of this article a very relevant article has been published by M. Losada and Y. Xu titled “Chirality transfer through hydrogen-bonding: Experimental and ab initio analyses of vibrational circular dichroism spectra of methyl lactate in water” in Phys Chem Chem Phys 2007, 9: 3127–3135. In that work they confirm that the effects of water are seen in the VCD spectra and hence it is fundamental to include explicit water molecules in modeling studies of the vibrational spectra of biomolecules in aqueous solution.     

A multiscale coarse‐grained polarizable solvent model for handling long tail bulk electrostatics

A multiscale coarse‐grained approach able to handle efficiently the solvation of microscopic solutes in extended chemical environment is described. That approach is able to compute readily and efficiently very long‐range solute/solvent electrostatic microscopic interactions, up to the 1‐μm scale, by considering a reduced amount of computational resources. All the required parameters are assigned to reproduce available data concerning the solvation of single ions. Such a strategy makes it possible to reproduce with good accuracy the solvation properties concerning simple ion pairs in solution (in particular, the asymptotic behavior of the ion pair potentials of mean force). This new method represents an extension of the polarizable pseudoparticle solvent model, which has been recently improved to account for the main features of hydrophobic effects in liquid water (Masella et al., J. Comput. Chem. 2011 , 32, 2664). This multiscale approach is well suited to be used for computing the impact of charge changes in free energy computations, in terms of both accuracy and efficiency. © 2013 Wiley Periodicals, Inc.     

Performance of SM8 on a test to predict small-molecule solvation free energies

The SM8 quantum mechanical aqueous continuum solvation model is applied to a 17-molecule test set proposed by Nicholls et al. (J. Med. Chem. 2008, 51, 769) to predict free energies of solvation. With the M06-2X density functional, the 6-31G(d) basis set, and CM4M charge model, the root-mean-square error (RMSE) of SM8 is 1.08 kcal mol(-1) for aqueous geometries and 1.14 kcal mol(-1) for gas-phase geometries. These errors compare favorably with optimal explicit and continuum models reported by Nicholls et al., having RMSEs of 1.33 and 1.87 kcal mol(-1), respectively. Other models examined by these workers had RMSEs of 1.5-2.6 kcal mol(-1). We also explore the use of other density functionals and charge models with SM8 and the RMSE increases to 1.21 kcal mol(-1) for mPW1/CM4 with gas-phase geometries, to 1.50 kcal mol(-1) for M06-2X/CM4 with gas-phase geometries, and to 1.27-1.64 kcal mol(-1) with three different models at B3LYP gas-phase geometries.     

Revised self-consistent continuum solvation in electronic-structure calculations

The solvation model proposed by Fattebert and Gygi [J. Comput. Chem. 23, 662 (2002)] and Scherlis et al. [J. Chem. Phys. 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multigrid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the non-electrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett. 94, 145501 (2005)] of the solute. The resulting self-consistent continuum solvation model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the polarizable continuum model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.3-0.4 kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating species and strong hydrogen-bond-forming compounds.     

On the nature of DNA-duplex stability

The unwinding free energy of 128 DNA octamers was correlated with the sum of interaction energies among DNA bases and their solvation energies. The former energies were determined by using the recently developed density functional theory procedure augmented by London dispersion energy (RI-DFT-D) that provides accurate hydrogen-bonding and stacking energies highly comparable with CCSD(T)/complete basis set limit benchmark data. Efficient tight-binding DFT covering dispersion energy was also used and yielded satisfactory results. The latter method can be used for extended systems. The solvation energy was determined by using a C-PCM continuum solvent at HF level calculations. Various models were adopted to correlate theoretical energies with experimental unwinding free energies. Unless all energy components (hydrogen-bonding, intra- and interstrand-stacking, and solvation energies) were included and weighted individually, no satisfactory correlation resulted. The most advanced model yielded very close correlation (RMSE=0.32 kcal mol(-1)) fully comparable with the entirely empirical correlation introduced in the original paper. Analysis of the theoretical results shows the importance of inter- and intramolecular stacking energies, and especially the latter term plays a key role in determining DNA-duplex stabilization.     

Recoil frame photoelectron angular distributions of BF3: a sensitive probe of the shape resonance in the F 1s continuum

Recoil frame photoelectron angular distributions (RFPADs) of BF(3) molecules are presented over the energy region of the shape resonance in the F 1s continuum. Time-dependent density functional theory calculations are also given to understand the shape resonance dynamics. The RFPADs have been compared with the theoretical calculations. It is found that the RFPADs calculated by the localized core-hole model are in better agreement with the experimental, compared with those by the delocalized core hole. Dipole matrix elements and dipole prepared continuum wavefunctions show that the shape resonance in the F 1s ionization continuum of BF(3) is induced by p-partial waves as previously reported by Swanson et al. [J. Chem. Phys. 75, 619 (1981)]. However, due to the couplings with the other partial waves the feature characteristic of the p-partial waves has not been observed in the RFPADs.     

How ion properties determine the stability of a lipase enzyme in ionic liquids: a molecular dynamics study

The influence of eight different ionic liquid (IL) solvents on the stability of the lipase Candida antarctica lipase B (CAL-B) is investigated with molecular dynamics (MD) simulations. Considered ILs contain cations that are based either on imidazolium or guanidinium as well as nitrate, tetrafluoroborate or hexafluorophosphate anions. Partial unfolding of CAL-B is observed during high-temperature MD simulations and related changes of CAL-B regarding its radius of gyration, surface area, secondary structure, amount of solvent close to the backbone and interaction strength with the ILs are evaluated. CAL-B stability is influenced primarily by anions in the order NO(3)(-)? BF(4)(-) < PF(6)(-) of increasing stability, which agrees with experiments. Cations influence protein stability less than anions but still substantially. Long decyl side chains, polar methoxy groups and guanidinium-based cations destabilize CAL-B more than short methyl groups, other non-polar groups and imidazolium-based cations, respectively. Two distinct causes for CAL-B destabilization are identified: a destabilization of the protein surface is facilitated mostly by strong Coulomb interactions of CAL-B with anions that exhibit a localized charge and strong polarization as well as with polar cation groups. Surface instability is characterized by an unraveling of α-helices and an increase of surface area, radius of gyration and protein-IL total interaction strength of CAL-B, all of which describe a destabilization of the folded protein state. On the other hand, a destabilization of the protein core is facilitated when direct core-IL interactions are feasible. This is the case when long alkyl chains are involved or when particularly hydrophobic ILs induce major conformational changes that enable ILs direct access to the protein core. This core instability is characterized by a disintegration of β-sheets, diffusion of ions into CAL-B and increasing protein-IL van der Waals interactions. This process describes a stabilization of the unfolded protein state. Both of these processes reduce the folding free energy and thus destabilize CAL-B. The results of this work clarify the impact of ions on CAL-B stabilization. An extrapolation of the observed trends enables proposing novel ILs in which protein stability could be enhanced further.     

Molecular simulation of solvent-induced stokes shift in absorption/emission spectra of organic chromophores

The values of steady-state solvatochromic Stokes shifts (SS) in absorption/emission electronic spectra of organic chromophores are studied theoretically in the framework of the Hush-Marcus model. Charge distributions for chromophore solutes in their S0 and S1 states are found by means of conventional quantum-chemical methods combined with the continuum PCM approach for treating solvation effects. The solvent reorganization energies, which are expected to correlate with the solvent-induced part of 1/2 SS, are found in a molecular dynamics (MD) simulation which invokes a novel method for separation of the inertial piece of the electrostatic response (Vener, et al. J. Phys. Chem. B 2006, 110, 14950). Computations, performed in two solvents (acetonitrile and benzene), consider three organic dyes: coumarin 153 as a benchmark system and two other chromophores, for which experimental spectra are also reported. The results are found to be in reasonable agreement with the experiment. A consistent treatment of nonlinear effect in the solvent response, promoted by the polarizability of solutes and contributing to the solvent reorganization energies (Ingrosso, et al. J. Phys. Chem. B 2005, 109, 3553), improves the results of computations.