Ground‐state structures of polymers

Two‐ and three‐dimensional structures A_xB_y can be characterized by the numbers T₁ and T₂ of nearest and next‐nearest neighbors of the same kind. A small number of structures at the border of the T₁, T₂ structure map is stabilized by enthalpy compared to an increased number of entropy stabilized structures. About 60 three‐dimensional structures with T₁=2 nearest neighbors of all A atoms are suitable for infinite chains of polymers like (CH)_∞, (CHCH₂)_∞, or (CH₂)_∞. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1944–1955, 2001     

How Cations Change Peptide Structure

Specific interactions between cations and proteins have a strong impact on peptide and protein structure. Herein, we shed light on the nature of the underlying interactions, especially regarding effects on the polyamide backbone structure. This was done by comparing the conformational ensembles of model peptides in isolation and in the presence of either Li⁺ or Na⁺ by using state‐of‐the‐art density‐functional theory (including van der Waals effects) and gas‐phase infrared spectroscopy. These monovalent cations have a drastic effect on the local backbone conformation of turn‐forming peptides, by disruption of the hydrogen‐bonding networks, thus resulting in severe distortion of the backbone conformations. In fact, Li⁺ and Na⁺ can even have different conformational effects on the same peptide. We also assess the predictive power of current approximate density functionals for peptide–cation systems and compare to results with those of established protein force fields as well as high‐level quantum chemistry calculations (CCSD(T)).     

Binding Studies of a Schiff Base Compound Containing a 1,2,4-Triazole Ring with Bovine Serum Albumin Using Spectroscopic Methods

The binding interaction of a Schiff base compound containing a 1,2,4‐triazole ring [4‐(4‐chlorobenzyl‐ideneamino)‐5‐methyl‐1,2,4‐triazole‐3‐thiol, CTT] with bovine serum albumin (BSA) was studied by spectroscopy methods including fluorescence and circular dichroism spectrum under simulative physiological conditions. Fluorescence investigation revealed that the fluorescence quenching of BSA was induced by the formation of a relative stable CTT‐BSA complex. The corresponding binding constants (K_a) between CTT and BSA at three different temperatures were calculated according to the modified Stern‐Volmer equation. The enthalpy change (ΔH^⊖) and entropy change (ΔS^⊖) were calculated to be −15.78 kJ·mol⁻¹ and 49.23 J·mol⁻¹·K⁻¹, respectively, which suggested that hydrophobic forces and hydrogen bond played major roles in stabilizing the CTT‐BSA complex. Site marker competitive experiments indicated that the binding of CTT to BSA primarily took place in sub‐domain IIIA (site II) of BSA. The binding distance (r) between CTT and the tryptophan residue of BSA was obtained to be 4.3 nm based on F?rster theory of non‐radioactive energy transfer. The conformational investigation revealed that the presence of CTT decreased the α‐helix content of BSA (from 58.62% to 54.66%) and induced the slight unfolding of the polypeptides of protein, which confirmed some micro‐environmental and conformational changes of BSA molecules.     

Thermodynamic enthalpy–entropy compensation effects observed in the complexation of basic drug substrates with β-cyclodextrin

Measurement of the variation of inherent drug solubility (S _o) and 1:1 drug/cyclodextrin complex formation constants (K ₁₁) with temperature were used to estimate the thermodynamic parameters (ΔH ^o, ΔS ^o and ΔG^o). A plot of TΔS ^o against ΔH ^o indicates the extent of enthalpy–entropy compensation; that is, how much of the enthalpic gain is cancelled by entropy loss or vice versa (the slope indicates the fraction of conformational change contribution to enthalpy gain that is cancelled by an accompanying entropy loss). The remaining fraction of enthalpy gain contributes to complex formation. The intercept is the inherent contribution to complex stability, which is due to desovation. Extensive phase solubility studies combined with rigorous analysis were conducted in the temperature range 20–45°C for the following basic drugs complexing with β-cyclodextrin (β-CD): astemizole (Astm), cisapride (Cisp), dipyridamole (Dipy), ketotifen (Keto), pizotifen (Pizo), terfenadine (Terf), fexofenadine (Fexo), sildenafil (Sild), and celecoxib (Celox). The results indicate that inherent drug solubility is accompanied by unfavorable conformational changes to the extent of 86%, which are counterbalanced by opposite favorable entropy changes. Only 14% of the favorable enthalpy change contributes to drug solubility. The extent of solvation (hydration) accompanying solubility amounts to −30 kJ/mol, which retards solubility as an unfavorable entropy change. In contrast, 1:1 drug/β-CD complex formation is accompanied by favorable conformational changes to the extent of 94%, which are counterbalanced by unfavorable entropy changes. Only about 6% of enthalpy changes contribute to complex stability. However, the extent of favorable entropy change (desolvation) accompanying complex formation amounts to 26 kJ/mol.     

2‐Amino‐1,2,3,6‐tetrahydro‐6‐oxocyclopenta[c]fluorene‐2‐carboxylic Acid (FlAib), a Completely Rigidified,Fluoren‐9‐one‐Based α‐Amino Acid

The synthesis, optical resolution, determination of absolute configuration and conformational preference, and spectroscopic characteristics of terminally protected (blocked) derivatives and short peptides of 2‐amino‐1,2,3,6‐tetrahydro‐6‐oxocyclopenta[c]fluorene‐2‐carboxylic acid (FlAib), a novel, rigid, chiral, cyclized C^α,α‐disubstituted glycine are described.     

枯草杆菌α-淀粉酶在一些色谱体系中的热力学和超热力学研究

通过测定不同温度范围的热力学平衡常数、焓变、熵变、自由能变和补偿温度,研究了枯草杆菌α-淀粉酶在几种色谱介质上的热力学和超热力学。结果表明,在RP-C18反相介质、Zn2+螯合的Sepharose fast-flow亲和介质和WCX-1阳离子交换介质上,当温度分别在13-30和30-50℃范围时,它们的lnKSL分别随绝对温度的倒数线性变化;而在PEG-400和修饰的PEG-400疏水色谱介质上,当温度分别在13-40和13-30℃范围时,它们的lnKSL分别随绝对温度的倒数线性减小,但当温度分别高于40℃和30℃时,它们则随绝对温度的倒数剧烈减小。通过研究不同温度范围的焓变、熵变、自由能变和α-淀粉酶构象变化之间的关系,发现在RP-C18反相和Zn2+螯合的Sepharose fast-flow亲和介质上在30- 50 ℃温度范围内,在WCX-1阳离子交换介质上在13-30 ℃温度范围内,α-淀粉酶的吸附过程由焓变和熵变共同所支配,而在Zn2+螯合的Sepharose fast-flow亲和介质上在13- 30 ℃温度范围内,在WCX-1阳离子交换介质上在30-50 ℃温度范围和在PEG-400 和修饰的PEG-400疏水色谱介质上在13-65 ℃温度范围时,α-淀粉酶的吸附过程仅仅由熵变所控制。最后,通过α-淀粉酶在这些色谱体系中的补偿温度进一步发现,它们的焓变仅仅只能通过它们构象变化所引起的熵变所补偿。     

Localized impurity states in the Hartree-Fock,LCAO approximation II. The F Center in KCI

We apply the techniques of a previous paper (I) to the F center in KCl. Our purpose is to place the application of Hartree-Fock methods to the F center on a firm theoretical basis by calculating in a consistent manner the magnitude and effect of approximations commonly made in less complete treatments. It is shown that the familiar point-ion approximations and crystal-field approximations with partial consideration of exchange effects are special cases of our results. We compute wave functions and energies step by step for each of the various levels of approximation possible with our model. It is found that the functions resulting from the point-ion model are not good approximations to the final wave functions. Our results show that exchange effects with at least the first two shells of nearest neighbors should be considered since they are of the same order of magnitude as terms in the point-ion model. Overlaps of the F-center function with ion functions out to sixth neighbors are considered. The absorption energy for the F center is calculated to be 0.1619 Ry as compared with the experimentally observed energy of 0.170 Ry. The magnetic hyperfine structure contact terms are calculated for the first two shells of nearest neighbor ions, using approximate orthogonalized functions, and found to be 29.7 Mc/h for the nearest neighbor K⁺ ions and 10.9 Mc/h for the next nearest neighbor Cl^? ions. The experimentally observed values are 21.6 and 7.0, respectively. Given these differences and the excessively low values of the one-electron energies, it is concluded that electronic and ionic polarization effects in the ionized crystal states must be considered to calculate accurate F-center wave functions and absolute energy levels.     

Spectroscopic Studies on the Binding of Kaempferol‐3,7‐α‐L‐rhamnopyranoside to Bovine Serum Albumin

The binding of kaempferol‐3,7‐α‐L‐rhamnopyranoside (KRR) with bovine serum albumin (BSA) was investigated by different spectroscopic methods under simulative physiological conditions. Analysis of ?uorescence quenching data of BSA by KRR at different temperatures using Stern‐Volmer methods revealed the formation of a ground state KRR‐BSA complex with moderate binding constant of the order 10⁴ L·mol^?1. The existence of some metal ions could weaken the binding of KRR on BSA. The changes in the van't Hoff enthalpy (ΔH⁰) and entropy (ΔS⁰) of the interaction were estimated to be ?26.53 kJ·mol^?1 and 3.33 J·mol^?1·K^?1 and both hydrophobic and electrostatic forces contributed to stabilizing the BSA‐KRR complex. According to the F?ster theory of non‐radiation energy transfer, the distance r between the donor (BSA) and the acceptor (KRR) was obtained (r=2.83 nm). Site marker competitive experiments showed that KRR could bind to Site I of BSA. In addition, synchronous fluorescence, UV‐Vis absorption and circular dichroism (CD) results indicated that the KRR binding could cause conformational changes of BSA.     

Validation of the GROMOS 54A7 Force Field Regarding Mixed α/β‐Peptide Molecules

A molecular‐dynamics (MD) simulation study of two heptapeptides containing α‐ and β‐amino acid residues is presented. According to NMR experiments, the two peptides differ in dominant fold when solvated in MeOH: peptide 3 adopts predominantly β‐hairpin‐like conformations, while peptide 8 adopts a 14/15‐helical fold. The MD simulations largely reproduce the experimental data. Application of NOE atom? atom distance restraining improves the agreement with experimental data, but reduces the conformational sampling. Peptide 3 shows a variety of conformations, while still agreeing with the NOE and ³J‐coupling data, whereas the conformational ensemble of peptide 8 is dominated by one helical conformation. The results confirm the suitability of the GROMOS 54A7 force field for simulation or structure refinement of mixed α/β‐peptides in MeOH.     

Influence of variation of a side chain on the folding equilibrium of a β‐peptide: Limitations of one‐step perturbation

In a recent study (Lin et al., Helv. Chim. Acta 2011, 94 , 597), the one‐step perturbation method was applied to tackle a challenging computational problem, that is, the calculation of the folding free enthalpies ΔG_F,U of six hepta‐β‐peptides with different, Ala, Val, Leu, Ile, Ser, or Thr, side chains in the fifth residue. The ΔG_F,U values obtained using one‐step perturbation based on a single molecular dynamics simulation of a judiciously chosen reference state with soft‐core atoms in the side chain of the fifth residue showed an overall accuracy of about k_BT for the four peptides with nonpolar side chains, but twice as large deviations were observed for the peptides with polar side chains. Here, alternative reference‐state Hamiltonians that better cover the conformational space relevant to these peptides are investigated, and post simulation rotational sampling of the χ₁ and χ₂ torsional angles of the fifth residue is carried out to sample different orientations of the side chain. A reference state with rather soft atoms yields accurate ΔG_F,U values for the peptides with the Ser and Thr side chains, but it failed to correctly predict the folding free enthalpy for one peptide with a nonpolar side chain, that is, Leu. Based on the results and those of earlier studies, possible ways to improve the accuracy of the efficient one‐step perturbation technique to compute free enthalpies of folding are discussed. © 2013 Wiley Periodicals, Inc.     

NMR‐Solution Structures in Methanol of an α‐Heptapeptide,of a β3/β2‐Nonapeptide,and of an all‐β3‐Icosapeptide Carrying the 20 Proteinogenic Side Chains

The NMR‐solution structure of an α‐heptapeptide with a central Aib residue was investigated in order to verify that, in contrast to β‐peptides, short α‐peptides do not form a helical structures in MeOH. Although the central Aib residue was found to induce a bend in the experimentally determined structure, no secondary structure typical for longer α‐peptides or proteins was found. A β²/β³‐nonapeptide with polar, positively charged side chains was subjected to NMR analysis in MeOH and H₂O. Whereas, in MeOH, it folds into a 10/12‐helix very similar to the structure determined for a corresponding β²/β³‐nonapeptide with only aliphatic side chains, no dominant conformation could be determined in H₂O. Finally, the NMR analysis of a β³‐icosapeptide containing the side chains of all 20 proteinogenic amino acids in MeOH is described. It revealed that this 20mer folds into a 3₁₄‐helix over its whole length forming six full turns, the longest 3₁₄‐helix found so far. Together, our findings confirm that, in contrast to α‐peptides, β‐peptides not only form helices with just six residues, but also form helices that are longer than helical sections usually observed in proteins or natural peptides. The higher helix‐forming propensity of long β‐peptides is attributed to the conformation‐stabilizing effect of the staggered ethane sections in β‐peptides which outweighs the detrimental effect of the increasing macrodipole.     

Protein secondary structure preferencs

This paper addresses the question to what extent steric properties of sequence neighbors effect the preferences of an amino acid residue to assume the-helical or some other secondary structure conformation. We find that an amino acid has increased tendency to be in-helical conformation when its sequence neighbors are bulky. This result is an outcome of our automated method for finding conformational preferences as functions of physical parameters important for protein folding. The steric environment for a given residue in a protein is defined as an average of water-accessible surface areas of its primary structure neighbors in extended conformation for model tripeptides. For all amino acids, including non-helix formers like glycine and arginine, the preference for the helical structure increases if their primary structure neighbors form a larger steric environment.     

Molecular modeling of polymers: I. Correct and efficient enumeration of intrachain conformational energetics

Polymer conformational analyses can require being able to model the intramolecular energetics of a very long (infinite) chain employing calculations carried out on a relatively short chain sequence. A method to meet this need, based upon symmetry considerations and molecular mechanics energetics, has been developed. Given N equivalent degrees of freedom in a linear polymer chain, N unique molecular groups are determined within the chain. A molecular unit is defined as a group of atoms containing backbone rotational degrees of conformational freedom on each of its ends. The interaction of these N molecular groups, each with a finite number of nearest neighbors, properly describe the intramolecular energetics of a long (infinite) polymer chain. Thus, conformational energetics arising from arbitrarily distant neighbor interactions can be included in the estimation of statistical and thermodynamic properties of a linear polymeric system. This approach is called the polymer reduced interaction matrix method (PRIMM) and the results of applying it to isotactic polystyrene (I-PS) are presented by way of example.     

Are accurate computations of the 13C′ shielding feasible at the DFT level of theory?

The goal of this study is twofold. First, to investigate the relative influence of the main structural factors affecting the computation of the ¹³C′ shielding, namely, the conformation of the residue itself and the next nearest‐neighbor effects. Second, to determine whether calculation of the ¹³C′ shielding at the density functional level of theory (DFT), with an accuracy similar to that of the ¹³C^α shielding, is feasible with the existing computational resources. The DFT calculations, carried out for a large number of possible conformations of the tripeptide Ac‐G XY ‐NMe, with different combinations of X and Y residues, enable us to conclude that the accurate computation of the ¹³C′ shielding for a given residue X depends on the: (i) (?,ψ) backbone torsional angles of X ; (ii) side‐chain conformation of X ; (iii) (?,ψ) torsional angles of Y ; and (iv) identity of residue Y . Consequently, DFT‐based quantum mechanical calculations of the ¹³C′ shielding, with all these factors taken into account, are two orders of magnitude more CPU demanding than the computation, with similar accuracy, of the ¹³C^α shielding. Despite not considering the effect of the possible hydrogen bond interaction of the carbonyl oxygen, this work contributes to our general understanding of the main structural factors affecting the accurate computation of the ¹³C′ shielding in proteins and may spur significant progress in effort to develop new validation methods for protein structures. © 2013 Wiley Periodicals, Inc.     

The Structural Characterization of Folded Peptides Containing the Conformationally Constrained β‐Amino Acid Residue β2,2Ac6c

Backbone alkylation has been shown to result in a dramatic reduction in the conformational space that is sterically accessible to α‐amino acid residues in peptides. By extension, the presence of geminal dialkyl substituents at backbone atoms also restricts available conformational space for β and γ residues. Five peptides containing the achiral β^2,2‐disubstituted β‐amino acid residue, 1‐(aminomethyl)cyclohexanecarboxylic acid (β^2,2Ac₆c), have been structurally characterized in crystals by X‐ray diffraction. The tripeptide Boc‐Aib‐β^2,2Ac₆c‐Aib‐OMe ( 1 ) adopts a novel fold stabilized by two intramolecular H‐bonds (C₁₁ and C₉) of opposite directionality. The tetrapeptide Boc‐[Aib‐β^2,2Ac₆c]₂‐OMe ( 2 ) and pentapeptide Boc‐[Aib‐β^2,2Ac₆c]₂‐Aib‐OMe ( 3 ) form short stretches of a hybrid αβ C₁₁ helix stabilized by two and three intramolecular H‐bonds, respectively. The structure of the dipeptide Boc‐Aib‐β^2,2Ac₆c‐OMe ( 5 ) does not reveal any intramolecular H‐bond. The aggregation pattern in the crystal provides an example of an extended conformation of the β^2,2Ac₆c residue, forming a ‘polar sheet’ like H‐bond. The protected derivative Ac‐β^2,2Ac₆c‐NHMe ( 4 ) adopts a locally folded gauche conformation about the C_β? C_α bonds (θ=?55.7°). Of the seven examples of β^2,2Ac₆c residues reported here, six adopt gauche conformations, a feature which promotes local folding when incorporated into peptides. A comparison between the conformational properties of β^2,2Ac₆c and β^3,3Ac₆c residues, in peptides, is presented. Backbone torsional parameters of H‐bonded αβ/βα turns are derived from the structures presented in this study and earlier reports.     

The Dependence of Amyloid‐β Dynamics on Protein Force Fields and Water Models

We studied the dynamics of Aβ₄₀, involved in Alzheimer's disease, by using 21 methods combined from Amber03, Amber99sb‐ILDN, Charmm27, Charmm22*, OPLS‐2001, OPLS‐2006, OPLS‐2008, Gromos96‐43a1, Gromos96‐53a6, Gromos96‐54a7, and the water models SPC, TIP3P, TIP4P. Major differences in the structural ensembles were systematized: Amber03, Charmm27, and Gromos96‐54a7 stabilize the helices; Gromos96‐43a1 and Gromos53a6 favor the β‐strands (with Charmm22* and Amber99sb‐ILDN in between), and OPLS produces unstructured ensembles. The accuracy of the NMR chemical shifts was in the order: Charmm22*>Amber99sb‐ILDN>OPLS‐2008≈Gromos96‐43a1>Gromos96‐54a7≈OPLS‐2001>OPLS‐2006>Gromos96‐53a6>Charmm27>Amber03. The computed ³J_HNHα‐coupling constants were sensitive to experiment type and Karplus parameterization. Overall, the ensembles of Charmm22* and Amber99sb‐ILDN provided the best agreement with experimental NMR and circular dichroism data, providing a model for the real Aβ monomer ensemble. Also, the polar water model TIP3P significantly favored helix and compact conformations.     

Conformationally Constrained Peptidomimetics as Inhibitors of the Protein Arginine Methyl Transferases

Protein arginine N‐methyl transferases (PRMTs) belong to a family of enzymes that modulate the epigenetic code through modifications of histones. In the present study, peptides emerging from a phage display screening were modified in the search for PRMT inhibitors through substitution with non‐proteinogenic amino acids, N‐alkylation of the peptide backbone, and incorporation of constrained dipeptide mimics. One of the modified peptides ( 23 ) showed an increased inhibitory activity towards several PRMTs in the low μm range and the conformational preference of this peptide was investigated and compared with the original hit using circular dichroism and NMR spectroscopy. Introducing two constrained tryptophan residue mimics (l ‐Aia) spaced by a single amino acid was found to induce a unique turn structure stabilized by a hydrogen bond and aromatic π‐stacking interaction between the two l ‐Aia residues.     

(Thermo)dynamic Role of Receptor Flexibility,Entropy, and Motional Correlation in Protein–Ligand Binding

The binding of 2‐amino‐5‐methylthiazole to the W191G cavity mutant of cytochrome c peroxidase is an ideal test case to investigate the entropic contribution to the binding free energy due to changes in receptor flexibility. The dynamic and thermodynamic role of receptor flexibility are studied by 50 ns‐long explicit‐solvent molecular dynamics simulations of three separate receptor ensembles: W191G binding a K⁺ ion, W191G–2a5mt complex with a closed 190–195 gating loop, and apo with an open loop. We employ a method recently proposed to estimate accurate absolute single‐molecule configurational entropies and their differences for systems undergoing conformational transitions. We find that receptor flexibility plays a generally underestimated role in protein–ligand binding (thermo)dynamics and that changes of receptor motional correlation determine such large entropy contributions.     

W2466.48 Opens a Gate for a Continuous Intrinsic Water Pathway during Activation of the Adenosine A2A Receptor

The question how G‐protein‐coupled receptors transduce an extracellular signal by a sequence of transmembrane conformational transitions into an intracellular response remains to be solved at molecular detail. Herein, we use molecular dynamics simulations to reveal distinct conformational transitions of the adenosine A_2A receptor, and we found that the conserved W246^6.48 residue in transmembrane helix TM6 performs a key rotamer toggle switch. Agonist binding induces the sidechain of W246^6.48 to fluctuate between two distinct conformations enabling the diffusion of water molecules from the bulk into the center of the receptor. After passing the W246^6.48 gate, the internal water molecules induce another conserved residue, Y288^7.53, to switch to a distinct rotamer conformation establishing a continuous transmembrane water pathway. Further, structural changes of TM6 and TM7 induce local structural changes of the adjacent lipid bilayer.     

A Method to Explore Protein Side Chain Conformational Variability Using Experimental Data

Experimentally measured values of molecular properties or observables of biomolecules such as proteins are generally averages over time and space, which do not contain su?cient information to determine the underlying conformational distribution of the molecules in solution. The relationship between experimentally measured NMR ³J‐coupling values and the corresponding dihedral angle values is a particularly complicated case due to its nonlinear, multiple‐valued nature. Molecular dynamics (MD) simulations at constant temperature can generate Boltzmann ensembles of molecular structures that are free from a priori assumptions about the nature of the underlying conformational distribution. They suffer, however, from limited sampling with respect to time and conformational space. Moreover, the quality of the obtained structures is dependent on the choice of force ?eld and solvation model. A recently proposed method that uses time‐averaging with local‐elevation (LE) biasing of the conformational search provides an elegant means of overcoming these three problems. Using a set of side chain ³J‐coupling values for the FK506 binding protein (FKBP), we ?rst investigate the uncertainty in the angle values predicted theoretically. We then propose a simple MD‐based technique to detect inconsistencies within an experimental data set and identify degrees of freedom for which conformational averaging takes place or for which force ?eld parameters may be de?cient. Finally, we show that LE MD is the best method for producing ensembles of structures that, on average, ?t the experimental data.