Theory of the cooperative transition between two ordered conformations of poly(L-proline). III. Molecular theory in the presence of solvent.

Phenomenological theories of the form I in equilibrium to form II interconversion in poly(L-proline) have been presented by Schwarz (using the parameters s, sigma, beta', and beta' in a 2 X 2 matrix formulation) and by the present authors (using the parameters s, sigma, betaC, and betaN in a 4 X 4 matrix formulation). In addition, a molecular theory was developed to compute s, sigma, beta', and beta' under vacuum. In this paper, we take into account the effect of solvent on the parameters s, sigma, beta', and beta' of the isothermal poly(L-proline) form I in equilibrium to form II interconversion. The growth parameter is sensitive to the binding of solvent molecules to the peptide CO groups, but the nucleation parameters sigma, beta', and beta' are not affected by this type of solvent effect. The calculated values of s and sigma under vacuum are in good agreement with the corresponding values derived from experimental data. By combining the theoretical values of s, sigma, beta', and beta' under vacuum with experimentally determined equilibrium constants for the binding of alcohols to the peptide CO groups (which differ in magnitude for form I and form II), it was possible to reproduce the experimental tranistion curves satisfactorily. Alternatively, the binding constants for alcohols, obtained by combining our theoretically computed parameters under vacuum with experimental equilibrium transition curves, are in a satisfactory agreement with those evaluated independently by infrared spectral measurements of the binding of alcohols to the peptide CO groups. It is pointed out that significant errors may arise in analyzing experimental data if short chains are included with long chains in the determination of s, sigma, beta', and beta' from the equilibrium transition curves. The transition of poly(L-proline) from form II to form I when n-butyl alcohol is added to a solution of the polymer in benzyl alcohol is brought about by the slight difference in the binding free energies of both alcohols to the carbonyl groups of form II. The different binding affinities of two alcohols, ROH, to form II may arise from (a) the different hydrogen-bond strength between the alcohol and the proline carbonyl group, and (b) possible differences in nonbonded and electrostatic interactions between the R group and the binding-site environment of the proline carbonyl group. The greater binding affinity of form II (compared to form I) for given alcohol is attributed to the more open and extended conformation of form II.     

Quantum mechanical study of the conformational behavior of proline and 4R-hydroxyproline dipeptide analogues in vacuum and in aqueous solution

The conformational behavior of the title compounds has been investigated by Hartree-Fock, MP2, and DFT computations on the most significant structures related to variations of the backbone dihedral angles, cis/trans isomerism around the peptide bond, and diastereoisomeric puckering of the pyrrolidine ring. In vacuum the reversed gamma turn (gammal), characterized by an intramolecular hydrogen bridge, corresponds to the absolute energy minimum for both puckerings (up and down) of the pyrrolidine ring. An additional energy minimum is found in the helix region, but only for an up puckering of the pyrrolidine ring. When solvent effects are included by means of the polarizable continuum model the conformer observed experimentally in condensed phases becomes the absolute minimum. The down puckering is always favored over its up counterpart, albeit by different amounts (0.4-0.5 kcal/mol for helical structures and about 2 kcal/mol for gammal structures). In helical structures cis arrangements of the peptide bond are only slightly less stable than their trans counterparts. This is no longer true for gammal structures, because the formation of an intramolecular hydrogen bond is possible only for trans peptide bonds. In most cases, proline and hydroxyproline show the same general trends; however, the electronegative 4(R) substituent of hydroxyproline leads to a strong preference for up puckerings irrespective of the backbone conformation.     

Understanding the role of stereoelectronic effects in determining collagen stability. 2. A quantum mechanical/molecular mechanical study of (Proline-Proline-Glycine)(n) polypeptides

The importance of vicinal and long-range interresidue effects in determining the stability of the collagen triple helix has been investigated by quantum mechanical (QM) and molecular mechanical (MM) computations on suitable model polypeptides, taking into account solvent effects by the polarizable continuum model (PCM). At the QM level, the PII conformation corresponds to an energy minimum for pentapeptide analogues incorporating the sequence Gly-Pro-Pro-Gly, irrespective of the down or up puckering of the pyrrolidine ring. However, our computations indicate that the alternation of down and up prolines characterizing collagen and collagen-like peptides is not due to an intrinsic preference of the Pro-Pro-Gly sequence. This result is confirmed by MM computations of longer polypeptides. Next, MM computations on model triple helices show that a better packing is obtained for specific values of backbone dihedrals, which, in turn, favor the alternation of down and up prolines along each chain.     

Theoretical determination of helix-coil parameter sigma from a model of partly helical polypeptide chain.

The Zimm and Bragg parameter sigma is calculated numerically for poly(L-alanine), polyglycine, and the copolymers of L-alanine and glycine using the molecular theory of s and sigma as developed by Go, Go, and Scheraga in a modified formulation. In this formulation, sigma is obtained from the partition function of the whole chain in the helix-coil transition region and represents therefore the contributions from the ends of helical and coil sequences and from the interactions between atoms in a coil sequence with those in the neighboring helical sequence. When the parameter sigma is calculated numerically from a hard-sphere potential, it appears that steric intractions between atoms in the coil sequence with atoms in the neighboring helical sequence, which have been neglected in previous calculations, contribute significantly to the value of sigma. Owing to these interactions the entropy of the coil sequence as well as sigma decrease, but the decrease of sigma is larger in poly(L-alanine) than in polyglycine, because of the higher flexibility of the monomer in polyglycine. The numerical value of sigma for polyglycine compared with that of poly(L-alanine) might be overestimated however by the model presented here due to approximations inherent in the hard-sphere treatment and because only regular helical sequences are considered.     

Puckering transition of proline residue in water

The puckering transition of the proline residue with trans and cis prolyl peptide bonds was explored by optimizations along the torsion angle chi1 of the prolyl ring using quantum-chemical methods in water. By analyzing the potential energy surfaces and local minima in water, it is observed that the puckering transition of the proline residue proceeds from a down-puckered conformation to an up-puckered one and vice versa through the transition state with an envelope form having the N atom at the top of the envelope and not a planar one, as seen in the gas phase, although the backbone conformations are different in the gas phase and in water. The barriers to the puckering transition DeltaGup-->down are estimated to be 3.12 and 3.00 kcal/mol for trans and cis conformers at the B3LYP/6-311++G(d,p) level of theory in water, respectively, which are about 1.7 kcal/mol higher than those in the gas phase. Out of 2197 prolines from the 241 high-resolution PDB chains, four transition-state-like structures with the envelope ring puckering are identified. Three of them have the trans prolyl peptide bonds and one has the cis one. The favorable or steric interactions by neighboring residues may be responsible for the stabilization of these transition-state-like ring structures in the proteins.     

Conformational studies of poly(cis-5-ethyl-D-proline)

Two possible conformations for poly(cis-5-ethyl-D -proline) have been identified and characterized by using combinations of ¹H- and ¹³C-NMR, CD, and ORD spectroscopic techniques. Both forms have helical conformations similar to those of poly(L -proline) characterized by different amide bonds (cis and trans). However, the carbonyl group of the amide in poly(cis-5-ethyl-D -proline) form II (trans) seems to be closer to perpendicular orientation with respect to the helical axis than in poly(L -proline) form II. The pyrrolidine ring conformation of form I (cis) is probably β⁺γ^?-puckered, whereas for form II it is probably β⁺-puckered in nature. The side-chain ethyl groups prefer to adopt anti conformations to the C₅? H bond, or prefer to have χ = 180°, regardless which of the two forms poly(cis-5-ethyl-D -proline) may like to assume. The experimental results agree well with our previous theoretical conformational energy calculations.     

Effect of included guest molecules on the normal state conductivity and superconductivity of beta''-(ET)(4)[(H(3)O)Ga(C(2)O(4))(3)].G (G = pyridine,nitrobenzene)

Normal state conductivity and superconductivity together with bulk magnetic susceptibility and magnetization measurements have been measured for two molecular charge-transfer salts: beta' '-(ET)4[(H3O)Ga(C2O4)3]G (ET = bis(ethylenedithio)tetrathiafulvalene, G = pyridine for compound I and nitrobenzene for compound II). With the exception of the included guest molecules (G) the crystal structures are almost identical. Both show minima in their electrical transport at 130 K for I and at 160 K for II, but at lower temperatures their behaviors differ markedly. The resistance of I reaches a maximum at 50 K with a further small peak at 2 K and possible superconductivity only below 2 K, whereas that of II increases continuously down to 7.5 K, where an abrupt transition to a superconducting state occurs.     

Recognition of the syndiotactic polypropylene polymorphs via dynamic-mechanical analysis

Three syndiotactic polypropylene samples were crystallized under different conditions in order to obtain different polymorphs. A first sample was crystallized at high temperature, obtaining the helical form I; a second was crystallized from the melt at 0°C for many days obtaining the trans-planar mesophase; a third sample was obtained by solvent induced crystallization followed by annaeling of the trans-planar mesophase, leading to a mixture of both the helical forms I and II. In the dynamic-mechanical analysis the helical form I showed only one peak of tan δ corresponding to the amorphous glass transition. The other polymorphs also showed this transition centered at about the same temperature. Beside the peak corresponding to the Tg, the trans-planar mesophase was characterized by a peak appearing at 70°C, and the helical form II by a peak at 100°C. These peaks, unambiguously associated to transitions of the different forms, can be considered a distinctive evidence for the polymorphs obtained in different processing conditions.     

Understanding the role of stereoelectronic effects in determining collagen stability. 1. A quantum mechanical study of proline, hydroxyproline, and fluoroproline dipeptide analogues in aqueous solution.

The importance of local (intraresidue) effects in determining the stability of the collagen triple helix has been investigated with special reference to the role played by hydroxyproline. To this end the dipeptide analogues of L-proline (ProDA), 4(R)-hydroxy-L-proline (HypDA), and 4(R)-fluoro-L-proline (FlpDA) have been studied by means of quantum mechanical ab initio calculations, taking into account solvent effects by the polarizable continuum model (PCM). Our results confirm that the relative stability of up puckerings of the pyrrolidine ring increases with the electronegativity of the 4(R) substituent (X), whereas down puckerings are favored by 4(S) electronegative substituents. Calculations on model compounds show that this effect is due to the interaction between vicinal C-H bonding and C-X antibonding orbitals. Electronegative substituents on the pyrrolidine ring affect cis-trans isomerism around the peptidic bond, with trans isomers stabilized by 4(R) substituents and cis isomers by 4(S) substituents. Also the hydrogen bonding power of the carbonyl moiety following the pyrrolidine ring is affected by 4(R) substituents, but this effect is tuned by the polarity of the embedding medium. Finally, up puckering favors smaller values of the backbone dihedrals phi and psi. All these results strongly support the proposal that the stability of triple helices containing fluorinated or hydroxylated prolines in Y positions is related to the necessity of having up puckerings in those positions.     

Solvent induced polymorphism of quenched syndiotactic polypropylene in different liquids

The solvent induced crystallization phenomenon (SINC) was studied for syndiotactic polypropylene quenched from the melt at 0 °C and kept at this temperature a for long time. In these conditions a mesophase having the chains in trans-planar conformation was formed. The interaction polymer-solvent with liquids having different solubility parameters, derived by both the swelling and the weight uptake, considerably varies among the different liquids, showing a maximum corresponding to carbon tetrachloride ('=8.6). A smaller maximum was found for chloroform ('=9.3). These two maxima were attributed to interaction either with the amorphous phase or with the trans-planar mesophase. Infrared analysis showed that all the liquids induce a conformational transition from trans-planar to helix, and only a small residual fraction of chains in trans-planar conformation was detected for the samples immersed in the liquids and vacuum dried for many hours. The X-ray analysis showed that the quenched sample undergoes in the solvents a complex transformation, partially crystallizing into the helical form I and partially into the helical form II. All the liquids induced the same transformation, in spite of very different levels of interaction.     

Thermodynamic Analysis of DSC Data for Acetaminophen Polymorphs

This article provides a thermodynamic analysis of DSC data for acetaminophen polymorphic forms I and II by measurement of heat capacity. Form I is found to have lower heat capacity and free energy and hence better stability than Form II down to at least –30°C. The transition temperature below which Form II becomes more stable was determined to be less than –120°C. Form I is more stable than Form II as a consequence of its higher entropy, since its crystallographic packing arrangement is of larger energy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spherulite growth rate and fold surface free energy of the form II mesophase in isotactic polybutene-1 and random butene-1/ethylene copolymers

The spherulite growth rate of isotactic polybutene-1 and random butene-1/ethylene copolymers has been measured in a wide range of temperatures between the glass transition and the melting temperature. The presence of ethylene co-units in the butene-1 chain leads to a distinct decrease of both the maximum spherulite growth rate and the temperature of fastest growth. The data were analyzed within the frame of the Hoffman–Lauritzen theory of crystallization to obtain form II mesophase surface free energies. The robust performed analysis revealed that the form II mesophase fold surface free energy in random copolymers of butene-1 with less than 5 mol% ethylene is 50–100 % higher than in the homopolymer. It is suggested that the increase of the fold surface free energy is related to the exclusion of ethylene chain defects from crystallization and their accumulation at the basal planes of the form II mesophase.     

Kinetics of helix-coil transition in all sizes of polypeptides.

The relaxation behavior of the helix-coil transition has been investigated for all sizes of polypeptides. Unlike previously reported results, regardless of the size of polypeptides, the first-order kinetics plays a principal role in the relaxation process when a helical state is relaxed to a half-coiled state [i.e. s(f) is congruent to 1, where s(f) is the helix stability parameter at the final state]. On the other hand, when a helical state is relaxed to a coiled state [i.e., s(f) is less than 1], the zeroth-order kinetics plays a major role. In addition, the range of the validity of a kinetic version of the zipper model has been investigated. We have found that when a helical state is relaxed to a state where s(f) is less than or equal to 1, the zipper model is valid for polypeptides with chain length N satisfying the relation N is less than 1/(sigmagammaC)1/2 where sigma is the cooperativity parameter and gammaC is the coil nucleation rate parameter.     

Theory of the cooperative transition between two ordered conformations of poly(L-proline). I. Phenomenological theory.

The states of three residues are correlated in a nearest-neighbor Ising model matrix treatment of a one-dimensional phase transition, in which nucleation is assumed to differ at each end of a regular sequence (asymmetric nucleation). The correlation of the states of three residues requires a 4 X 4 matrix, which cannot be reduced in size because of the asymmetric nature of the nucleation. Also, because of the asymmetry, at least four independent parameters for a homopolymer (rather than the two usually encountered in the helix-coil transition), ant at least five for a specific-sequence copolymer, are required to describe the transition behavior. The most important current interest in such a treatment (for a homopolymer) is its applicability to the poly(L-proline) form I in equilibrium form II interconversion.The earlier treatment of Schwarz, using the nearest-neighbor Ising model (with correlation of only two residues), is identical with the above treatment, and requires only a 2 X 2 matrix which greatly simplifies numerical computations, which are presented in the next two papers of this series. However, the 4 X 4 matrix treatment is required in order to make the asymmetric nature of the nucleation explicit and physically understandable, for a homopolymer; for a specific-sequence copolymer, such as a protein, it is essential in order to show how the asymmetric nature of helix nucleation differs from one amino acid to another.     

Sulfide and sulfoxide oxidations by mono- and diperoxo complexes of molybdenum. A density functional study

The molecular mechanism for the oxidation of sulfides to sulfoxides and subsequent oxidation to sulfones by diperoxo, MoO(O(2))(2)(OPH(3)) (I), and monoperoxo, MoO(2)(O(2))(OPH(3)) (II), complexes of molybdenum was studied using density functional calculations at the b3lyp level and the transition state theory. Complexes I and II were both found to be active species. Sulfide oxidation by I or II shows similar activation free energy values of 18.5 and 20.9 kcal/mol, respectively, whereas sulfoxides are oxidized by I (deltaG = 20.6 kcal/mol) rather than by II (deltaG = 30.3 kcal/mol). Calculated kinetic and thermodynamic parameters account for the spontaneous overoxidation of sulfides to sulfones as has been experimentally observed. The charge decomposition analysis (CDA) of the calculated transition structures of sulfide and sulfoxide oxidations revealed that I and II are stronger electrophilic oxidants toward sulfides than they are toward sulfoxides.     

Locked conformations for proline pyrrolidine ring: synthesis and conformational analysis of cis- and trans-4-tert-butylprolines

The motional restrictions of the proline pyrrolidine ring allow this secondary amine amino acid to act as a turn inducer in many peptides and proteins. The pyrrolidine ring is known to exhibit two predominant pucker modes (i.e., C-4 (Cgamma) exo and endo envelope conformers whose ratio can be controlled by proper substituents in the ring). In nature, the exo puckered 4(R)-hydroxy-l-proline plays a crucial role as a building block in collagen and collagen-like structures. It has been previously concluded that the electronegativity of the 4-cis-substituent increases the endo puckering while the electronegativity of the 4-trans-substituent favors the exo puckering. Here, we have introduced a sterically demanding tert-butyl group at C-4 in trans- and cis-configurations. In the case of trans-substitution, the induced puckering effect on the pyrrolidine ring was studied with X-ray crystallography and 1H NMR spectral simulations. Both cis- and trans-4-tert-butyl groups strongly favor pseudoequatorial orientation, thereby causing opposite puckering effects for the pyrrolidine ring, cis-exo and trans-endo for l-prolines, in contrast to the effects observed in the case of electronegative C-4 substituents. The syntheses and structural analysis are presented for the conformationally constrained 4-tert-butylprolines. The prolines were synthesized from 4-hydroxy-l-proline, substitution with t-BuCuSPhLi being the key transformation. This reaction gave N-Boc-trans-4-tert-butyl-l-proline tert-butyl ester in 94% ee and 57% de. Enantioselectivity was increased to 99.2% ee by crystallization of N-Boc-trans-4-tert-butyl-l-proline in the final step of the synthesis.     

Self-diffusion coefficients and shear viscosity of inverse power fluids: from hard- to soft-spheres

Molecular dynamics computer simulation has been used to compute the self-diffusion coefficient, D, and shear viscosity, eta(s), of soft-sphere fluids, in which the particles interact through the soft-sphere or inverse power pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The simulations were carried out on monodisperse systems for a range of n values from the hard-sphere (n --> infinity) limit down to n = 4, and up to densities in excess of the fluid-solid co-existence value. A new analytical procedure is proposed which reproduces the transport coefficients at high densities, and can be used to extrapolate the data to densities higher than accurately accessible by simulation or experiment, and tending to the glass transition. This formula, DX(c-1) proportional, variant A/X + B, where c is an adjustable parameter, and X is either the packing fraction or the pressure, is a development of one proposed by Dymond. In the expression, -A/B is the value of X at the ideal glass transition (i.e., where D and eta(s)(-1) --> 0). Estimated values are presented for the packing fraction and the pressure at the glass transition for n values between the hard and soft particle limits. The above expression is also shown to reproduce the high density viscosity data of supercritical argon, krypton and nitrogen. Fits to the soft-sphere simulation transport coefficients close to solid-fluid co-existence are also made using the analytic form, ln(D) = alpha(X)X, and n-dependence of the alpha(X) is presented (X is either the packing fraction or the pressure).     

Helix--coil stability constants for the naturally occurring amino acids in water. X. Tyrosine parameters from random poly(hydroxypropylglutamine-co-L-tyrosine).

The synthesis and characterization of water-soluble random copolymers containing L-tyrosine with N2-(3-hydroxypropyl)-L-glutamine are described, and the thermally induced helix--coil transitions of these copolymers in water have been studied. The incorporation of L-tyrosine was found to increase the helix content of the polymers at all temperatures. The Zimm-Bragg parameters sigma and sigma for the helix--coil transition in poly(L-tyrosine) in water were deduced from an analysis of the melting curves of the copolymers in the manner described in earlier papers. The large value of sigma indicates that, in water, tyrosine has a tendency to promote helix--coil boundaries at all temperatures; the values of sigma indicate that this residue enhances helix growth at low temperature and reduces it at high temperature.     

Puckering transition of 4-substituted proline residues

The puckering transition of 4-substituted proline residues by electron-withdrawing groups, i.e., 4(R)-hydroxy-L-proline (Hyp) and 4(R)-fluoro-L-proline (Flp) residues, with trans and cis prolyl peptide bonds was studied by adiabatic optimizations along the torsion angle chi1 of the prolyl ring at the HF/6-31+G(d) level. By analyzing the potential energy surface and local minima, it is observed that the puckering transition of the prolyl ring for Hyp and Flp residues proceeds from a down-puckered conformation to an up-puckered one through the transition state with an envelope form having the N atom at the top of envelope and not a planar one for both trans and cis conformers, which is the same as found for the unsubstituted proline residue. At HF/6-31+G(d) and B3LYP/6-311++G(d,p) levels, the structures of the backbone and prolyl ring for local minima of Ac-Hyp-NHMe and Ac-Flp-NHMe are quite similar to those of Ac-Pro-NHMe. However, the relative stability of the up-puckered conformation to the down-puckered one is increased for Ac-Hyp-NHMe with the cis imide bond and for Ac-Flp-NHMe with the trans and cis imide bonds. In particular, the 4(R)-substitution by hydroxy and fluorine groups has brought some structural changes in the prolyl ring of the transition states and the changes in barriers for the puckering transition. The puckering transitions for Ac-Hyp-NHMe and Ac-Flp-NHMe are proven to be predominantly electronically driven by analyzing the electronic and enthalpic contributions to the barriers, as seen for Ac-Pro-NHMe.     

Inherent flexibility and protein function: The open/closed conformational transition in the N-terminal domain of calmodulin

The key to understand a protein's function often lies in its conformational dynamics. We develop a coarse-grained variational model to investigate the interplay between structural transitions, conformational flexibility, and function of the N-terminal calmodulin domain (nCaM). In this model, two energy basins corresponding to the "closed" apo conformation and "open" holo conformation of nCaM are coupled by a uniform interpolation parameter. The resulting detailed transition route from our model is largely consistent with the recently proposed EFbeta-scaffold mechanism in EF-hand family proteins. We find that the N-terminal parts of the calcium binding loops shows higher flexibility than the C-terminal parts which form this EFbeta-scaffold structure. The structural transition of binding loops I and II are compared in detail. Our model predicts that binding loop II, with higher flexibility and earlier structural change than binding loop I, dominates the open/closed conformational transition in nCaM.