Experimental Free Energy Differences Research Articles

Data-guided Multi-Map variables for ensemble refinement of molecular movies.

Driving molecular dynamics simulations with data-guided collective variables offer a promising strategy to recover thermodynamic information from structure-centric experiments. Here, the three-dimensional electron density of a protein, as it would be determined by cryo-EM or x-ray crystallography, is used to achieve simultaneously free-energy costs of conformational transitions and refined atomic structures. Unlike previous density-driven molecular dynamics methodologies that determine only the best map-model fits, our work employs the recently developed Multi-Map methodology to monitor concerted movements within equilibrium, non-equilibrium, and enhanced sampling simulations. Construction of all-atom ensembles along the chosen values of the Multi-Map variable enables simultaneous estimation of average properties, as well as real-space refinement of the structures contributing to such averages. Using three proteins of increasing size, we demonstrate that biased simulation along the reaction coordinates derived from electron densities can capture conformational transitions between known intermediates. The simulated pathways appear reversible with minimal hysteresis and require only low-resolution density information to guide the transition. The induced transitions also produce estimates for free energy differences that can be directly compared to experimental observables and population distributions. The refined model quality is superior compared to those found in the Protein Data Bank. We find that the best quantitative agreement with experimental free-energy differences is obtained using medium resolution density information coupled to comparatively large structural transitions. Practical considerations for probing the transitions between multiple intermediate density states are also discussed.

DNA duplex stability: the role of preorganized electrostatics.

The insertion of a DNA base moiety at the end of a DNA duplex to form a Watson-Crick or wobble pair during DNA annealing or replication is a step of fundamental biological importance. Therefore, we investigated the energetics of a formation of the terminal G x C, G x T, and G x A base pairs in DNA containing a 5'-dangling G adjacent to the base insertion point using differential scanning calorimetry and computer simulations. The energies calculated along classical molecular dynamics trajectories in aqueous solution were analyzed in the framework of linear-response approximation (LRA) to obtain relative free energies for the base insertion and their electrostatic, van der Waals, and preorganization components. Using the generic set of LRA parameters, the calculated free energies disfavored the mispair formation by 2.5 (G x C --> G x T) and 1.7 (G x C --> G x A) kcal/mol, in reasonable agreement with the experimental free energy differences of 1.8 and 1.4 kcal/mol, respectively. The calculated preorganization components of these free energies of 0.6 (G x C --> G x T) and -0.1 (G x C --> G x A) kcal/mol show that electrostatic preorganization, which is an important source of DNA replication fidelity, plays a lesser role in the mispair destabilization in the absence of DNA polymerase.

Spectroscopic Characterization and Conformational Properties of S‐(Fluoroformyl)‐O‐(acetyl) Thioperoxide and S‐(Fluoroformyl)‐O‐(trifluoroacetyl) Thioperoxide

AbstractThe conformational properties of FC(O)SOC(O)CH3 and FC(O)SOC(O)CF3 were studied by vibrational spectroscopy [IR (gas phase, Ar matrix), Raman (liquid phase)] and quantum chemical calculations (B3LYP and MP2 methods). For both compounds the syn‐gauche‐syn conformer with synperiplanar orientation of both carbonyl C=O bonds with respect to the S–O bond, and gauche orientation around the S–O bond (C1 symmetry) is the most stable structure [73(5) % for FC(O)SOC(O)CH3 and 82(5) % for FC(O)SOC(O)CF3]. For FC(O)SOC(O)CH3 two more conformers are observed in the Ar‐matrix spectra, 18(5) % syn‐trans‐syn with trans orientation around the S–O bond [φ(C–S–O–C) = 180°, C2 symmetry] and 9(5) % anti‐gauche‐syn with the FC(O) group oriented anti with respect to the S–O bond. The experimental free energy differences for these most stable forms of FC(O)SOC(O)CH3 are ΔG° = G°(syn‐trans‐syn) – G°(syn‐gauche‐syn) = 0.83(17) kcal mol–1 and ΔG° = G°(anti‐gauche‐syn) – G°(syn‐gauche‐syn) = 1.27(35) kcal mol–1, respectively. These values are well reproduced by the B3YLP/aug‐cc‐pVTZ method (0.76 and 1.23 kcal mol–1), but not by the MP2 approximation (2.72 and 1.28 kcal mol–1) For FC(O)SOC(O)CF3 only one more stable conformer, 18(5) % anti‐gauche‐syn, is observed. The experimental free energy difference between both rotamers of FC(O)SOC(O)CF3, ΔG° = G°(anti‐gauche‐syn) – G°(syn‐gauche‐syn) = 0.90(17) kcal mol–1, is reproduced very well by the B3YLP/6‐311++G** method (0.82 kcal mol–1) and reasonably well by B3LYP/aug‐cc‐pVTZ (1.17 kcal mol–1) and MP2/6‐31G* (1.23 kcal mol–1) calculations. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2009)

Density functional theory calculations of novel Rh(I) diphosphinite catalysts

Novel Rh(I) diphosphinite catalysts [Rh(( R, R)-3,4-(bis( O-diphenylphosphino)-1,2,5,6-tetra- O-methyl- chiro-inositol)]+ ([Rh-CANDYPHOS]+) and [Rh(( R, R)-3,4-(bis( O-diphenylphosphino)-1,2,5,6-tetra- O-ethyl- chiro-inositol)]+ ([Rh-EtCP]+) have been prepared utilizing naturally-occurring resources. Potential energy surfaces for the catalyzed asymmetric hydrogenation of the prochiral enamides methyl-( Z)-α-acetamido cinnamate, methyl-( Z)-α-acetamido cinnamic acid and dimethyl itaconate have been surveyed using density function theory (DFT) methods. Key transition states were identified from previous [Rh(( R, R)-DUPHOS)]+ studies for the two diastereoisomeric manifolds [1,2]. Transition state energies were found starting from models based on (1) the X-ray structure of the active complex (CANDYPHOS)( η 4-( Z, Z)-cyclo-octa-1,5-diene)-rhodium(I) tetrafluoroborate CHCl 3 solvate [3] and (2) models in which the complex (without substrate) started with C2 molecular symmetry. The difficulties encountered in calculations of the transition state energies of large cations are outlined and limitations noted. Transition state enthalpy values are compared with the observed experimental free energy differences results and previous studies [1,2]. The predictive aspects of the calculations appear to be limited with the starting models playing an important part in the absolute value of the final energies.

CBS-QB3 computational examination of substituent effects on the interconversion of 1,3,5-cyclooctatriene and bicyclo[4.2.0]-2,4-octadiene

The position of equilibrium between 7-substituted and 7,8-disubstituted 1,3,5-cyclooctatrienes ( 1) and the corresponding valence isomeric bicyclo[4.2.0]-2,4-octadienes ( 2) is highly sensitive to the nature of substituents. In particular, the difference between trans and cis-7,8 isomers in this regard has never been explained. These differences have been clarified by computational means. The CBS-QB3 hybrid quantum chemical computational method reproduces the experimental free energy differences between a series of cyclooctatrienes ( 1) and the corresponding valence isomers ( 2) with excellent accuracy; the MAD and root mean square (rms) differences are 0.54 kcal/mol and 0.58 kcal/mol, respectively. The energy barriers between several derivatives of 1 and 2 were computed with good accuracy (MAD=1.3 kcal/mol and rms=1.5 kcal/mol) by the same procedure. The dihedral angle between the substituents increases upon electrocyclic conversion of trans-7,8-disubstituted cyclooctatrienes to the bicyclic isomer and decreases for the corresponding cis isomers. This differential effect explains both the higher bicyclic proportion at equilibrium and the faster rate of cyclization in the trans series compared to cis.

Synthesis, Structure and Conformational Properties of Fluoroformylchlorodifluoroacetyl Disulfide, FC(O)SSC(O)CF2Cl: Conformational Transferability in –C(O)SSC(O)– Compounds

AbstractPure fluoroformylchlorodifluoroacetyl disulfide, FC(O)SSC(O)CF2Cl, has been prepared by the reaction of FC(O)SCl and CF2ClC(O)SH in quantitative yield. The conformational properties of the novel molecule have been studied by vibrational spectroscopy (IR – gas phase, Raman – liquid phase) and quantum chemical calculations (B3LYP and MP2 methods). The gaseous compound exhibits a conformational equilibrium at room temperature where the most stable form adopts a C1 symmetry and a syn‐periplanar (sp) orientation of both carbonyl groups with respect to the disulfide bond. A second form, observed in the IR spectrum of the vapor, corresponds to a conformer in which the carbonyl bond of the FC(O) moiety adopts an anti‐periplanar (ap) position with respect to the S–S single bond, and gauche with respect to the ClC–C=O moiety in the chlorodifluoroacetyl group. The experimental free energy difference value ΔG0 = G0(ap–sp) – G0(sp–sp) = 1.4(3) kcal/mol (IR) is reproduced well by the B3YLP/6‐311+G(3df) (1.1 kcal/mol) and the MP2/6‐31G* (1.8 kcal/mol) methods. In addition, the structure of a single‐crystal, grown in situ, was determined by X‐ray diffraction analysis at low temperature. The crystalline solid [monoclinic, P21/n, a = 5.579(3) Å, b = 16.615(7), c = 8.455(4) Å, β = 106.876(8)°] consists exclusively of molecules with the (sp–sp) conformation and the usual gauche orientation around the disulfide bond [φ(CS–SC) = 84.2°]. Conformational transferability is thus demonstrated once again for species that contain the –C(O)SSC(O)– group as part of a systematic program designed to analyze the behavior of this class of molecules. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)

Chlorocarbonyl Trifluoromethanesulfonate, ClC(O)OSO2CF3: Structure and Conformational Properties in the Gaseous and Condensed Phases

Pure chlorocarbonyl trifluoromethanesulfonate, ClC(O)OSO(2)CF(3), has been prepared in about 58% yield by the ambient-temperature reaction between ClC(O)SCl and AgCF(3)SO(3). The conformational properties of the gaseous molecule have been studied by vibrational spectroscopy [IR(gas), IR(matrix), and Raman(liquid)] and quantum chemical calculations (HF and B3LYP with 6-31+G* basis sets); in addition, the solid-state structure has been determined by X-ray crystallography. ClC(O)OSO(2)CF(3) exists in the gas phase as a mixture of trans [ClC(O) group trans with respect to the CF(3) group] and gauche conformers, with the trans form being the more abundant [66(8)% from IR(matrix) measurements]. In both conformers, the C=O bond of the ClC(O) group is oriented synperiplanar with respect to the S-O single bond. The experimental free energy difference between the two forms, DeltaG degrees = 0.8(2) kcal mol(-1) (IR), is slightly smaller than the calculated value (1.0-1.5 kcal mol(-1)). The crystalline solid at 150 K [monoclinic, P2(1)/n, a = 7.3951(9) angstroms, b = 24.897(3) angstroms, c = 7.4812(9) angstroms, beta = 99.448(2) degrees, Z = 8] consists surprisingly of both trans and gauche forms. Whereas the more stable conformer for the more or less discrete molecules and the polarization effects would tend to favor the trans form, the packing effects would stabilize the gauche rotamer in the solid state.

Fluorocarbonyl trifluoromethanesulfonate, FC(O)OSO2CF3: structure and conformational properties in the gaseous and condensed phases.

Pure fluorocarbonyl trifluoromethanesulfonate, FC(O)OSO(2)CF(3), is prepared in about 70% yield by the ambient-temperature reaction between FC(O)SCl and AgCF(3)SO(3). The geometric structure and conformational properties of the gaseous molecule have been studied by gas electron diffraction (GED), vibrational spectroscopy [IR(gas), IR(matrix), and Raman(liquid)] and quantum chemical calculations (HF, MP2, and B3LYP with 6-311G basis sets); in addition, the solid-state structure has been determined by X-ray crystallography. FC(O)OSO(2)CF(3) exists in the gas phase as a mixture of trans [FC(O) group trans with respect to the CF(3) group] and gauche conformers with the trans form prevailing [67(8)% from GED and 59(5)% from IR(matrix) measurements]. In both conformers the C=O bond of the FC(O) group is oriented synperiplanar with respect to the S-O single bond. The experimental free energy difference between the two forms, DeltaG degrees = 0.49(13) kcal mol(-1) (GED) and 0.22(12) kcal mol(-1) (IR), is slightly smaller than the calculated value (0.74-0.94 kcal mol(-1)). The crystalline solid at 150 K [monoclinic, P2(1)/c, a = 10.983(1) A, b = 6.4613(6) A, c = 8.8508(8) A, beta = 104.786(2) degrees ] consists exclusively of the trans conformer.

Tautomeric and conformational equilibria of biologically important (hydroxyphenyl)alkylamines in the gas phase and in aqueous solution

Protonation macro- and microconstants have been determined experimentally for the 4-aminophenol molecule and five hydroxy-substituted 2-phenylethylamines: tyramine, octopamine, dopamine, norepinephrine and epinephrine. In aqueous solution, 4-aminophenol is in the form of the neutral zero-net-charge tautomer, whereas (hydroxyphenyl)ethylamines exhibit tautomeric and conformational equilibria between the zwitterionic (zw) and the neutral (n) forms. The zw/n ratio was measured in the range of 0.09–7.43. No evident correlation has been found between the structural changes and changes in the zw/n values for this set of compounds. Polarizable continuum solvent calculations in the SCIPCM and PCM approximations and explicit solvent Monte Carlo simulations have been performed for theoretical investigation of tautomeric/conformational equilibria for the 4-aminophenol, tyramine and dopamine. Gas-phase and in-solution geometry optimizations were carried out mostly at the DFT/B3LYP/6-31G* level followed by B3LYP/6-311++G** single point calculations. All calculations found the neutral form as the stable one for the 4-aminophenol molecule in aqueous solution with an aniline-type amino group. Continuum solvent calculations underestimate the stability of the zwitterion relative to the neutral form for glycine and tyramine with an aliphatic amine group in the molecule. The calculated values are subject to a large basis set effect for tyramine. For explicit solvent calculations, an atomic charge set has been proposed where the charges were fitted to the molecular electrostatic potential calculated by using the self-consistent in-solution wave function. Using PCM/B3LYP/6-31G*-based atomic charges in Monte Carlo simulations, the preference of the zwitterionic tyramine was demonstrated. For reaching a better accord with the experimental free energy difference, corrections including intermolecular solute–solvent vibrational entropies are to be considered. Theoretical studies for the trans dopamine zwitterion predict the preference of the 4-OH form over the 3-OH isomer.

Ground state isomerization of a model green fluorescent protein chromophore

The relationship between ground state cis– trans isomerization and protonation state is explored for a model green fluorescent protein chromophore, 4-hydroxybenzylidene-1,2-dimethylimidazolinone (HBDI). We find that the protonation state has only a modest effect on the free energy differences between cis and trans isomers and on the activation energies for isomerization. Specifically, the experimental free energy differences are 3.3, 8.8, and 9.6 kJ/mol for cationic, neutral, and anionic forms of HBDI, respectively, and the activation energies are 48.9, 54.8, and 54.8 kJ/mol for cationic, neutral, and anionic forms, respectively. Furthermore, these activation energies are much smaller than might be expected based on comparison with similar systems. These results suggest that there may be a sub-population of the chromophore, which is nearly equally accessible to all three protonation states, through which thermal isomerization may proceed.

Efficient calculation of two-dimensional adiabatic and free energy maps: Application to the isomerization of the C13?C14 and C15?N16 bonds in the retinal of bacteriorhodopsin

Accurate calculation of potential energy and free-energy profiles along reaction coordinates of biological processes such as enzymatic reactions or conformational changes is fundamental to the obtention of theoretical insight into protein function. We describe here the practical implementation of the Automatic Map Refinement Procedure (AMRP) and two-dimensional Weighted Histogram Analysis Method (WHAM) for efficient computation of adiabatic potential energy and free-energy maps, respectively. Methods for efficiently sampling configuration space with high-energy barriers and for removing hysteresis in the case of periodic reaction coordinates are presented. The application of these techniques to the isomerization of the C13C14 and C15N16 bonds in the retinal of bacteriorhodopsin is described. In dark-adapted bacteriorhodopsin (bR), the retinal moiety exists in two conformers, all-trans and (13,15)cis, with the latter making ≃67% of the population. This experimental free energy difference is reproduced here to within kBT. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1644–1658, 1999

Dependence of Protein Stability on the Structure of the Denatured State: Free Energy Calculations of I56V Mutation in Human Lysozyme

Free energy calculations were carried out to understand the effect of the I56V mutation of human lysozyme on its thermal stability. In the simulation of the denatured state, a short peptide including the mutation site in the middle is employed. To study the dependence of the stability on the denatured-state structure, five different initial conformations, native-like, extended, and three random-coil-like conformations, were examined. We found that the calculated free energy difference, ΔΔ G cal, depends significantly on the structure of the denatured state. When native-like structure is employed, ΔΔ G cal is in good agreement with the experimental free energy difference, ΔΔ G exp, whereas in the other four models, ΔΔ G cal differs sharply from ΔΔ G exp. It is therefore strongly suggested that the structure around the mutation site takes a native-like conformation rather than an extended or random-coil conformation. From the free energy component analysis, it has been shown that free energy components originating from Lennard-Jones and covalent interactions dominantly determine ΔΔ G cal. The contribution of protein-protein interactions to the nonbonded component of ΔΔ G cal is about the same as that from protein-water interactions. The residues that are located in a hydrophobic core (F3, L8, Y38, N39, T40, and I89) contribute significantly to the nonbonded free energy component of ΔΔ G cal. We also propose a general computational strategy for the study of protein stability that is equally conscious of the denatured and native states.

Differences between DNA Base Pair Stacking Energies Are Conserved over a Wide Range of Ionic Conditions

Base pair stacking free energy parameters in a low ionic strength solvent were determined from an analysis of DNA fragments using temperature gradient gel electrophoresis (TGGE). Transition midpoint temperatures (Tu) were determined for the first melting domain (52 +/- 4 bp) of 16, 339 bp DNAs that differed from each other by single base pair substitutions. The data were combined with previously obtained Tu data from 17 similar DNAs that had single base pair changes at different sites [Ke, S. H., and Wartell, R. M. (1995) Biochemistry 34, 4593-4599]. The Tu values were used to evaluate free energy differences (deltaDeltaG) between 31 pairs of DNAs. Linear equations relating the deltaDeltaG values to changes in base pair stacking were analyzed by singular value decomposition (SVD) to determine the 10 nearest neighbor free energy parameters. The order of stability of the parameters, TA < AT < AA < AG < GT approximately TC approximately TG < CC < GC approximately CG, was essentially the same as the hierarchy determined in 1 M Na+ [Allawi, H. T., and SantaLucia, J., Jr. (1997) Biochemistry 36, 10581-10594]. The experimental free energy differences were in good agreement with predictions made using nearest-neighbor parameters determined from several previous studies conducted in medium or high salt concentrations. Conversely the parameters determined in the current study produced good predictions of free energy differences previously determined from 59 DNA oligomers in 1 M Na+. The results indicate that differences between base pair stacking energies are conserved across a wide range of ionic conditions, and in both oligomer and polymer DNA contexts.

Estimation of stabilities of staphylococcal nuclease mutants (Met 32 → Ala and Met 32 → Leu) using molecular dynamics/free energy perturbation

We performed molecular dynamics (MD)/free energy perturbation (FEP) calculations to reproduce the experimental free energy difference of denaturation for staphylococcal nuclease mutant Met 32 → Ala (M32A) and to predict the stability of the mutant Met 32 → Leu (M32L). The calculated free energy difference for the M32A of −1.9 kcal/mol was in good agreement with the experimental value. In the M32A, a small hydrophobic core formed by three aromatic rings (Tyr-27, Phe-34, Phe-76) in a wild-type crumbled as a result of exposure to water. The van der Waals interactions in the native state of the M32A were weaker than those of the wild-type, which strongly suggests that the Met-32 is important for the stability of the enzyme. The M32L has not been able yet, but is expected to retain the small hydrophobic core. The free energy difference of denaturation for the M32L was calculated to be 1.6 kcal/mol. The MD/FEP simulation showed that the native state structure of the M32L was only slightly changed when compared with that of the wild-type. It was suggested that the M32L is more stable than the wild-type because the electrostatic interactions in the denatured state are more disadvantageous than those in the native state.

The Equilibrium Unfolding Parameters of Horse and Sperm Whale Myoglobin: EFFECTS OF GUANIDINE HYDROCHLORIDE, UREA, AND ACID

The urea and guanidine hydrochloride (GuHCl) unfolding of sperm whale ferrimyoglobin and of horse ferrimyoglobin has been studied under equilibrium conditions at both neutral and acid pH. Using two spectral parameters (the Soret absorbance and the molar ellipticity at 222 nm) to monitor conformational equilibria, and various thermodynamic treatments of the resulting data, it was found that the conformational free energy of unfolding, ΔG0 (i.e. the value in the absence of denaturant obtained using the two-state transition model), differs by about 20% in these two proteins. In particular, ΔG0 = 13.6 and 11.0 Cal per mole for sperm whale ferrimyoglobin and horse ferrimyoglobin, respectively. Based on the crystal structure of sperm whale ferrimyoglobin, an analysis of the 19 amino acid differences in the two proteins indicates that sperm whale ferrimyoglobin has a net of two additional arginyl-aspartyl side chain interactions that cannot be realized in horse ferrimyoglobin. Also, sperm whale ferrimyoglobin is predicted to be approximately 0.8 Cal per mole more stable than horse ferrimyoglobin due to an internal residue and several surface contact residues of higher hydrophobicity than the corresponding groups in horse ferrimyoglobin. Thus, the experimental free energy difference of 2.6 Cal per mole in the two proteins can be qualitatively explained, although minor conformation differences in localized regions of the native structures may exist. The acid unfolding of the two proteins can be described reasonably well in terms of six abnormal histidyl groups in each protein. These groups titrate with apparent pK values of 5.9 in the unfolded proteins and 3.0 and 3.7, respectively, in native sperm whale ferrimyoglobin and horse ferrimyoglobin. Corrections for the electrostatic free energy of the protein give an intrinsic pK of 6.6 for these groups in the unfolded state. A slightly better fit to the acid unfolding data could be achieved by considering two other classes, each containing 6 partially masked residues. The ΔG0 obtained from acid unfolding was in good agreement with that found from urea and GuHCl unfolding at neutral pH. These results show that conservative mutations can have pronounced effects on the conformational stability of phylogenetically similar globular proteins. However, in spite of the significant difference in ΔG0 of these two myoglobins, it is known that the oxygenation free energy differs by only a few per cent. Thus, these data demonstrate that in the myoglobins the evolutionary constraints are such that little variation is permitted in the biological function, but that appreciable variation is allowed in parts of the primary structure with concomitant changes in stability and perhaps small changes in conformation.