Is the large plasmid of 120 MDa in Shigella sonnei composed of two DNA segments—90 and 30 MDa?

Abstract The reversibility of adhesion of 3 representative strains of oral streptococci from a phosphate-buffered suspension onto 5 different solid substrata was studied.
Streptococcus mitis T9 (surface free energy γ_b= 39 mJ · m⁻²). Streptococcus sanguis CH3 (γ_b= 95 mJ · m⁻²) and Streptococcus mutans NS (γ_b= 117 mJ · m⁻²) were selected on basis of their surface free energy. Solid substrata were employed with a surface free energy γ_s ranging from 20 mJ · m⁻² for polytetrafluorethylene to 109 mJ · m⁻² for glass. Bacterial suspensions containing 2.5 × 10⁹ cells per ml were incubated with 2 samples of each substratum. After 1 h the number of adhering bacteria was evaluated on one sample, while the second sample was kept for another hour at a 10-fold lower bacterial concentration. Bacteria with a low surface free energy desorbed only from substrata with a high surface free energy, while bacteria with a high surface free energy desorbed from substrata with a low surface free energy. Thus low energy bacterial strains adhered reversibly to high energy substrata and vice versa. Similar observations were made with polystyrene particles. Calculation of the interfacial free energy of adhesion (Δ F _adh) for each bacterial strain as well as for the polystyrene particles showed that a reversible adhesion was associated with a positive Δ F _adh, denoting unfavourable adhesion conditions upon a thermodynamic basis.     

The calculated free energy effects of 5-methyl cytosine on the B to Z transition in DNA

We have examined the free energy effects of 5-methylation of cytosine on the B in equilibrium Z conformational equilibrium in DNA. Free energy differences were calculated using the free energy perturbation approach, which uses an easily derived equation from classical statistical mechanics to relate the free energy difference between two states to the ensemble average of the potential energy difference between the states. Calculations were carried both in explicit solvent and (for comparison) in vacuo. The free energy values obtained for the explicit solvent systems are total free energies, with contributions from all parts of the system (solvent + solute), and so are relevant to the B in equilibrium Z transitions observed under real (physiological) conditions. We calculate that in solution, methylation makes the B in equilibrium Z transition more favorable by about -0.4 kcal/mole base pair (bp) in free energy. This value compares well with approximate experimentally derived values of about -0.3 kcal/mole-bp. We also discuss a method for determining the free energy difference between conformational states poorly maintained by a potential energy model. Finally, the effects of methylation on the melting temperature of DNA are examined.     

Application of MM/PBSA colony free energy to loop decoy discrimination: toward correlation between energy and root mean square deviation

Accurate free energy estimation is needed in many predictive tasks. The molecular mechanics/Poisson-Boltzmann solvent accessible surface area (MM/PBSA) approach has proven to be accurate. However, the correlation between the estimated free energy and the distance (e.g., root mean square deviation [RMSD]) from the most stable conformation is hindered by the strong free energy dependence on minor conformational variations. In this paper, a protocol for MM/PBSA free energy estimation is designed and tested on several loop decoy sets. We show that further integration of MM/PBSA free energy estimator with the colony energy approach makes the correlation between the free energy and RMSD from the native structure apparent, for the test sets on which it could be applied. Our results suggest that (1) the MM/PBSA free energy estimator is able to detect native-like structures for most decoy sets, and (2) application of the colony energy approach greatly hampers the MM/energy strong dependence on minor conformational changes.     

Conformational Entropy of the RNA Phosphate Backbone and Its Contribution to the Folding Free Energy

While major contributors to the free energy of RNA tertiary structures such as basepairing, base-stacking, and charge and counterion interactions have been studied extensively, little is known about the intrinsic free energy of the backbone. To assess the magnitude of the entropic strains along the phosphate backbone and their impact on the folding free energy, we have formulated a mathematical treatment for computing the volume of the main-chain torsion-angle conformation space between every pair of nucleobases along any sequence to compute the corresponding backbone entropy. To validate this method, we have compared the computed conformational entropies against a statistical free energy analysis of structures in the crystallographic database from several-thousand backbone conformations between nearest-neighbor nucleobases as well as against extensive computer simulations. Using this calculation, we analyzed the backbone entropy of several ribozymes and riboswitches and found that their entropic strains are highly localized along their sequences. The total entropic penalty due to steric congestions in the backbone for the native fold can be as high as 2.4 cal/K/mol per nucleotide for these medium and large RNAs, producing a contribution to the overall free energy of up to 0.72 kcal/mol per nucleotide. For these RNAs, we found that low-entropy high-strain residues are predominantly located at loops with tight turns and at tertiary interaction platforms with unusual structural motifs.     

Conformational Entropy of the RNA Phosphate Backbone and Its Contribution to the Folding Free Energy

While major contributors to the free energy of RNA tertiary structures such as basepairing, base-stacking, and charge and counterion interactions have been studied extensively, little is known about the intrinsic free energy of the backbone. To assess the magnitude of the entropic strains along the phosphate backbone and their impact on the folding free energy, we have formulated a mathematical treatment for computing the volume of the main-chain torsion-angle conformation space between every pair of nucleobases along any sequence to compute the corresponding backbone entropy. To validate this method, we have compared the computed conformational entropies against a statistical free energy analysis of structures in the crystallographic database from several-thousand backbone conformations between nearest-neighbor nucleobases as well as against extensive computer simulations. Using this calculation, we analyzed the backbone entropy of several ribozymes and riboswitches and found that their entropic strains are highly localized along their sequences. The total entropic penalty due to steric congestions in the backbone for the native fold can be as high as 2.4 cal/K/mol per nucleotide for these medium and large RNAs, producing a contribution to the overall free energy of up to 0.72 kcal/mol per nucleotide. For these RNAs, we found that low-entropy high-strain residues are predominantly located at loops with tight turns and at tertiary interaction platforms with unusual structural motifs.     

Potentiometric titration of poly-L-lysine: the coil-to-beta transition

We have performed potentiometric titrations of poly-L -lysine. From these data we have calculated the free energy and enthalpy changes for the folding of the random coil to the α-helix in 10% ethanol (?120 and ?120 cal/mole) and from the random coil to the β-structure in water (?140 and 870 cal/mole) and in 10% ethanol (?180 and 980 cal mole). Comparison of these values with each other and with values for the coil → α- helix transition in water (?78 and ?880 cal/mole) led to the following conclusions. The stabilization by ethanol of ethanol of the α-helix with respect to the coil is that predicted from the known free energy of transfer of the peptide group from water to 10% ethanol. Similar data to explain the enthalpy difference are not available. The thermodynamic functions for the transition from α-helix to β-structure, obtained by subtracting those for the coil → α-helix and coil → β-structure transitions, are explained from a consideration of the structural differences: non bonded interactions of the polypeptide backbone are less favorable in the β-structure than in the α-helix, causing an increase in the energy, while hydrophobic contacts between side chains raise the entropy of the β-structure as compared with the α-helix, so that the free energy difference between the two structures is small, but enthalpy and entropy differences are large. The observation of only small differences in the free energy and enthalpy changes for the transition from coil β-structure upon going from water to 10% ethanol is expected by considering both the free energy of transfer of the peptide group (as for the α-helix) and the free energy and enthalpy of transfer of the apolar part of the side chain involved in hydrophobic bond formation.     

Molecular Dynamics/Free Energy Perturbation Studies of the Thermostable V74I Mutant of Ribonuclease HI

Abstract

Recent site-directed mutagenesis and thermodynamic studies have shown that the V74I mutant of Escherichia coli ribonuclease HI (RNase HI) is more stable than the wild type protein [Ishikawa et al., Biochemistry 32, 6171 (1993)]. In order to clarify the stabilization mechanism of this mutant, we calculated the free energy change due to the mutation Val 74→Ile in both the native and denatured states by free energy perturbations based on molecular dynamics (MD) simulations. We carried out inclusive MD simulations for the protein in water; i.e., fully solvated, no artificial constraints applied, and all long-range Coulomb interactions included. We found that the free energy of the mutant increased slightly relative to the wild type, in the native state by 1.60 kcal/mol, and in the denatured state by 2.25 kcal/mol. The unfolding free energy increment of the mutant (0.66 ± 0.19 kcal/mol) was in good agreement with the experimental value (0.6 kcal/mol). The hysteresis error in the free energy calculations, i.e., forward and reverse perturbations, was only ±0.19 kcal/mol. These results show that the V74I mutant is stabilized relative to the wild type by the increased free energy of the denatured state and not by a decrease in the free energy of the native state as had been proposed earlier based on the mutant X-ray structure. It was found that the stabilization was caused by a loss of solvation energy in the mutant denatured state and not by improved packing interactions inside the native protein.     

Statistically Estimated Free Energies of Chromosome Aberration Production from Frequency Data

Janardan and Schaeffer (1977) suggested that the Lagrangian Poisson Distribution (LPD) could be used to estimate the net free energy for the production of induced chromosome aberrations. Using a Markov-chain model, a formal link between the LPD and the thermodynamic free energy is now provided. It is estimated that the free energy required to produce isochromatid breaks or dicentrics is about 3.67 KJ/mole/aberration and 18.4 KJ/mole, in good agreement with free energy estimates on the formation of DNA.     

Stability of XGCGCp, GCGCYp, and XGCGCYp helixes: an empirical estimate of the energetics of hydrogen bonds in nucleic acids

The stabilizing effects of dangling ends and terminal base pairs on the core helix GCGC are reported. Enthalpy and entropy changes of helix formation were measured spectrophotometrically for AGCGCU, UGCGCA, GGCGCCp, CGCGCGp, and the corresponding pentamers XGCGCp and GCGCYp containing the GCGC core plus a dangling end. Each 5' dangling end increases helix stability at 37 degrees C roughly 0.2 kcal/mol and each 3' end from 0.8 to 1.7 kcal/mol. The free energy increments for dangling ends on GCGC are similar to the corresponding increments reported for the GGCC core [Freier, S. M., Alkema, D., Sinclair, A., Neilson, T., & Turner, D. H. (1985) Biochemistry 24, 4533-4539], indicating a nearest-neighbor model is adequate for prediction of stabilization due to dangling ends. Nearest-neighbor parameters for prediction of the free energy effects of adding dangling ends and terminal base pairs next to G.C pairs are presented. Comparison of these free energy changes is used to partition the free energy of base pair formation into contributions of "stacking" and "pairing". If pairing contributions are due to hydrogen bonding, the results suggest stacking and hydrogen bonding make roughly comparable favorable contributions to the stability of a terminal base pair. The free energy increment associated with forming a hydrogen bond is estimated to be -1 kcal/mol of hydrogen bond.     

Calculating the free energy of association of transmembrane helices

A large number of experimental studies have been devoted to quantifying the interaction between transmembrane (TM) helices in detergent micelles and, more recently, in bilayers. Theoretical calculation of association free energy of TM helices would be useful for predicting the propensity of given sequences to oligomerize and for understanding the difference between association in micelles and in bilayers. In this article, the theoretical foundation for calculating the standard association free energy of TM helices is laid out and is applied to glycophorin A in both micelles and bilayers. The standard association free energy is decomposed into the effective energy, translational, rotational, and conformational entropy terms. The effective energy of association is obtained by molecular dynamics simulations in an implicit membrane model. The translational and rotational entropy of association is calculated from the probability distribution of the translational and rotational degrees of freedom obtained from the molecular dynamics simulations. The side-chain conformational entropy of association is estimated from the probability distribution obtained by rigid rotation of all side-chain dihedral angles. The calculated standard association free energy of glycophorin A in N-dodecylphosphocholine micelles is in good agreement with the experimental value. The translational entropy cost is larger, whereas the rotational entropy cost is smaller in bilayers than in micelles. The standard association free energy in 1,2-dimyristoyl-sn-glycero-3-phosphocholine bilayers is calculated to be approximately 1.3 kcal/mol more favorable than in N-dodecylphosphocholine micelles, consistent with available experimental data.     

A computational protocol to probe the role of solvation effects on the reduction potential of azurin mutants

Semiquantitative relationships between thermodynamic parameters of Cu2+ reduction experimentally measured for a series of azurin mutants and the solvation free energy of the oxidized state of the proteins were derived. Solvation free energy calculations were carried out within an ONIOM/PCM scheme specifically adapted to this protein series. The method proved to be able to capture the main determinants of the measured reduction parameters, providing satisfactory predictions of the E degrees '.     

Membrane phospholipids as an energy source in the operation of the visual cycle

Biology depends on the coupling of the free energy of hydrolysis of phosphate esters, such as ATP, to drive processes which would otherwise be thermodynamically unfavorable. Carboxyl esters are like phosphate esters in their ability to hydrolyze with substantial negative free energies, enabling them to participate in group transfer processes as well. In particular, membrane phospholipids constitute an enormous store of potential energy that could be used to fuel energetically unfavorable processes. One such process involves the biosynthesis of 11-cis-retinal, the chromophore of rhodopsin, from all-trans-retinol (vitamin A). The difference in free energy between an all-trans retinoid and its corresponding 11-cis retinoid is approximately 4 kcal/mol. This energy is provided for in a minimally two-step process involving membrane phospholipids as the energy source. First, all-trans-retinol is esterified in the retinal pigment epithelium by lecithin retinol acyl transferase (LRAT) to produce an all-trans-retinyl ester. Second, this ester is transformed into 11-cis-retinol by an isomerohydrolase in a process that couples the negative free energy of hydrolysis of the acyl ester to the formation of the strained 11-cis-retinol.     

Free energy calculations for the relative binding affinity between DNA and lambda-repressor

The change in the binding free energy between DNA and lambda-repressor resulting from a base substitution, thymine (T)-->deoxyuracil (abbreviated as U), was evaluated by the free energy perturbation method on the basis of molecular dynamics simulations for the DNA-lambda-repressor complex in water with all degrees of freedom and including long-range Coulomb interactions. The binding free energy change that we calculated (1.47 +/- 0.40 kcal/mol) was in good agreement with an experimental value (1.8 kcal/mol). We clarified why the small difference between T and U (CH(3) in T is replaced with H in U) caused such a significant change in the binding free energy: The substitution of CH(3) in T with H in U lowered the dissociated-state free energy level due to the gain of the hydration free energy. Furthermore, the T-->U substitution raised the free energy level in the associated state due to the loss of the favored van der Waals (vdW) interactions with the lambda-repressor amino acid residues. In other words, the amino acid residues of lambda-repressor can recognize the CH(3) in T through the vdW interactions with the CH(3). This recognition is enhanced in a water environment, because the hydrophobic CH(3) prefers the amino acid residues of lambda-repressor to water molecules.     

Electrostatic fixed charge distribution in the RBC-glycocalyx and their influence upon the total free interaction energy

On the basis of a recently developed biophysical model of cell-cell interaction, including electrostatic, electrodynamic, steric and bonding/bridging interaction energies the influence of different fixed charge (dissociated groups of the glycocalyx) density distributions in red blood cell (RBC) glycocalyces on the total free interaction energy was investigated. An analytical equation of electrostatic free energy on the basis of the linear Poisson-Boltzmann approach taking into account arbitrary distributions of fixed glycocalyx charges was obtained and corresponding free electrostatic energies of three example distributions were calculated. The electrodynamic, steric and bonding/bridging energies were computed as usual. It was shown that the free energy as a function of interaction distances strongly depends on the charge distribution and, correspondingly, the "weight" of this energy term in the total free interaction energy balance equation. Generally, it can be stated that as more charges are assumed to be fixed in the outer layer of RBC glycocalyx as more important becomes the electrostatic energy in contrast to the remaining three terms.     

Study of the insulin dimerization: binding free energy calculations and per-residue free energy decomposition

A calculation of the binding free energy for the dimerization of insulin has been performed using the molecular mechanics-generalized Born surface area approach. The calculated absolute binding free energy is -11.9 kcal/mol, in approximate agreement with the experimental value of -7.2 kcal/mol. The results show that the dimerization is mainly due to nonpolar interactions. The role of the hydrogen bonds between the 2 monomers appears to give the direction of the interactions. A per-atom decomposition of the binding free energy has been performed to identify the residues contributing most to the self association free energy. Residues B24-B26 are found to make the largest favorable contributions to the dimerization. Other residues situated at the interface between the 2 monomers were found to make favorable but smaller contributions to the dimerization: Tyr B16, Val B12, and Pro B28, and to an even lesser extent, Gly B23. The energy decomposition on a per-residue basis is in agreement with experimental alanine scanning data. The results obtained from a single trajectory (i.e., the dimer trajectory is also used for the monomer analysis) and 2 trajectories (i.e., separate trajectories are used for the monomer and dimer) are similar.     

High free energy of lipid/protein interaction in biological membranes

The free energy of lipid/protein interaction in biological membranes is still unknown although extensive partitioning and modelling studies have revealed many partial energetic increments. Multiple site binding kinetics are now applied to four well-studied functional membrane proteins, and mean free energy values (+/-S.D.) of -4.23+/-0.49 kcal/mol for single lipid binding sites and of -89.7+/-35.4 kcal/mol for complete lipid substitution are obtained. These high free energy values point to an important bioenergetic role of lipid/protein interaction in membrane functions.     

Empirical calculation of the relative free energies of peptide binding to the molecular chaperone DnaK

We describe a methodology to calculate the relative free energies of protein-peptide complex formation. The interaction energy was decomposed into nonpolar, electrostatic and entropic contributions. A free energy-surface area relationship served to calculate the nonpolar free energy term. The electrostatic free energy was calculated with the finite difference Poisson-Boltzmann method and the entropic contribution was estimated from the loss in the conformational entropy of the peptide side chains. We applied this methodology to a series of DnaK*peptide complexes. On the basis of the single known crystal structure of the peptide-binding domain of DnaK with a bound heptapeptide, we modeled ten other DnaK*heptapeptide complexes with experimentally measured K(d) values from 0.06 microM to 11 microM, using molecular dynamics to refine the structures of the complexes. Molecular dynamic trajectories, after equilibration, were used for calculating the energies with greater accuracy. The calculated relative binding free energies were compared with the experimentally determined free energies. Linear scaling of the calculated terms was applied to fit them to the experimental values. The calculated binding free energies were between -7.1 kcal/mol and - 9.4 kcal/mol with a correlation coefficient of 0.86. The calculated nonpolar contributions are mainly due to the central hydrophobic binding pocket of DnaK for three amino acid residues. Negative electrostatic fields generated by the protein increase the binding affinity for basic residues flanking the hydrophobic core of the peptide ligand. Analysis of the individual energy contributions indicated that the nonpolar contributions are predominant compared to the other energy terms even for peptides with low affinity and that inclusion of the change in conformational entropy of the peptide side chains does not improve the discriminative power of the calculation. The method seems to be useful for predicting relative binding energies of peptide ligands of DnaK and might be applicable to other protein-peptide systems, particularly if only the structure of one protein-ligand complex is available.     

Insight into the binding modes and inhibition mechanisms of adamantyl-based 1,3-disubstituted urea inhibitors in the active site of the human soluble epoxide hydrolase

Soluble epoxide hydrolase (sEH) is a promising new target for treating hypertension and inflammation. Considerable efforts have been devoted to develop novel inhibitors. In this study, the binding modes and interaction mechanisms of a series of adamantyl-based 1,3-disubstituted urea inhibitors were investigated by molecular docking, molecular dynamics simulations, binding free energy calculations, and binding energy decomposition analysis. Based on binding affinity, the most favorable binding mode was determined for each inhibitor. The calculation results indicate that the total binding free energy (ΔG_TOT, the sum of enthalpy ΔG_MM-GB/SA, and entropy ?TΔS) presents a good correlation with the experimental inhibitory activity (IC₅₀, r²?=?.99). The van der Waals energy contributes most to the total binding free energy (ΔG_TOT). A detailed discussion on the interactions between inhibitors and those residues located in the active pocket is made based on hydrogen bond and binding modes analysis. According to binding energy decomposition, the residues Asp333 and Trp334 contribute the most to binding free energy in all systems. Furthermore, Hip523 plays a major role in determining this class of inhibitor-binding orientations. Combined with the results of hydrogen bond analysis and binding free energy, we believe that the conserved hydrogen bonds play a role only in anchoring the inhibitors to the exact site for binding and the number of hydrogen bonds may not directly relate to the binding free energy. The results we obtained will provide valuable information for the design of high potency sEH inhibitors.     

Free energy simulation to investigate the effect of amino acid sequence environment on the severity of osteogenesis imperfecta by glycine mutations in collagen

Molecular dynamics simulations were carried out to calculate the free energy change difference of two collagen-like peptide models for Gly --> Ser mutations causing two different osteogenesis imperfecta phenotypes. These simulations were performed to investigate the impact of local amino acid sequence environment adjacent to a mutation site on the stability of the collagen. The average free energy differences for a Gly --> Ser mutant relative to a wild type are 3.4 kcal/mol and 8.2 kcal/mol for a nonlethal site and a lethal site, respectively. The free energy change differences of mutant containing two Ser residues relative to the wild type at the nonlethal and lethal mutation sites are 4.6 and 9.8 kcal/mol, respectively. Although electrostatic interactions stabilize mutants containing one or two Ser residues at both mutation sites, van der Waals interactions are of sufficient magnitude to cause a net destabilization. The presence of Gln and Arg near the mutation site, which contain large and polar side chains, provide more destabilization than amino acids containing small and nonpolar side chains.