Origin of intrinsic 3(10)-helix versus strand stability in homopolypeptides and its implications for the accuracy of the Amber force field

Current all-atom force fields often fail to recognize the native structure of a protein as the lowest free energy minimum. One possible cause could be the mathematical form of the potential based on the assumption that the conformation of a residue is independent of its neighbors. Here, using quantum mechanical (QM) methods (MP2/6-31g**//HF/6-31g** and MP2/cc-pVDZ//cc-pVDZ//HF/cc-pVDZ), the intrinsic correctness of the gas phase terms (without solvation) of the Amber ff03 and ff99 potentials are examined by testing their ability to reproduce the relative 3(10)-helix versus extended structure stabilities in the gas phase for 1-7-residue alanine, valine, leucine, and isoleucine homopolypeptides. The 3(10)-helix versus extended state stability strongly depends on chain length and less on the amino acid identity. The helical conformation becomes lower in energy than the extended conformation for all tested peptides longer than two residues, and its stability increases with the increase of chain length. The ff03 potential better describes the 3(10)-helix versus extended state energy than ff99 and also reproduces the curvature of the relative helix-extended state energies. Therefore, the mathematical form of the Amber potential is sufficient to describe the local effect of 3(10)-helix versus extended structure stabilization in the gas phase. However, the energy curves are shifted and the backbone geometries differ compared with the QM results. This may cause significant geometric discrepancies between native and predicted structures. Therefore, extant molecular mechanics force fields, such as Amber, need refinement of their parameters to correctly describe helix-extended state energetics and geometry of major conformations.     

Implementation and application of helix-helix distance and crossing angle restraint potentials

Based on the definition of helix-helix distance and crossing angle introduced by Chothia et al. (J Mol Biol 1981, 145, 215), we have developed the restraint potentials by which the distance and crossing angle of two selected helices can be maintained around target values during molecular dynamics simulations. A series of assessments show that calculated restraint forces are numerically accurate. Since the restraint forces are only exerted on atoms which define the helical principal axes, each helix can rotate along its helical axis, depending on the helix-helix intermolecular interactions. Such a restraint potential enables us to characterize the helix-helix interactions at atomic details by sampling their conformational space around specific distance and crossing angle with (restraint) force-dependent fluctuations. Its efficacy is illustrated by calculating the potential of mean force as a function of helix-helix distance between two transmembrane helical peptides in an implicit membrane model.     

Effects of external electromagnetic fields on the conformational sampling of a short alanine peptide

Non‐equilibrium molecular dynamics simulations of a solvated 21‐residue polyalanine (A21) peptide, featuring a high propensity for helix formation, have been performed at 300 K and 1 bar in the presence of external electromagnetic (e/m) fields in the microwave region (2.45 GHz) and an r.m.s. electric field intensity range of 0.01–0.05 V/Å. To investigate how the field presence affects transitions between the conformational states of a protein, we report 16 independent 40 ns‐trajectories of A21 starting from both extended and fully folded states. We observe folding‐behavior of the peptide consistent with prior simulation and experimental studies. The peptide displays a natural tendency to form stable elements of secondary structure which are stabilized by tertiary interactions with proximate regions of the peptide. Consistent with our earlier work, the presence of external e/m fields disrupts this behavior, involving a mechanism of localized dipolar alignment which serves to enhance intra‐protein perturbations in hydrogen bonds (English, et al., J. Chem. Phys. 2010 , 133, 091105), leading to more frequent transitions between shorter‐lifetime states. © 2012 Wiley Periodicals, Inc.     

A new version of Bishop frame and an application to spherical images

In this work, we introduce a new version of Bishop frame using a common vector field as binormal vector field of a regular curve and call this frame as “Type-2 Bishop Frame”. Thereafter, by translating type-2 Bishop frame vectors to the center of unit sphere of three-dimensional Euclidean space, we introduce new spherical images and call them as type-2 Bishop spherical images. Frenet-Serret apparatus of these new spherical images are obtained in terms of base curve's type-2 Bishop invariants. Additionally, we express some interesting relations and illustrate two examples of our main results.     

四氢呋喃的糖环不是平面而是螺旋面

基于分子的群理论和量子力学计算,本文首次证明：四氢呋喃[THF]的平衡构型是C1 对称性,其糖环不是平面而是螺旋面。     

On Darboux helices in Euclidean 4‐space

The notion of Darboux helix in Euclidean 3‐space was introduced and studied by Yayl? et al. 2012. They show that the class of Darboux helices coincide with the class of slant helices. In a special case, if the curvature functions satisfy the equality κ² + τ² = constant, then these curves are curve of the constant precession. In this paper, we study Darboux helices in Euclidean 4‐space, and we give a characterization for a curve to be a Darboux helix. We also prove that Darboux helices coincide with the general helices. In a special case, if the first and third curvatures of the curve are equal, then Darboux helix, general helix, and V₄‐slant helix are the same concepts.     

Helicity induction on a poly(phenylacetylene) bearing a phosphonate residue by chiral dendrons

A series of optically active dendrons with a primary amino group at the terminal were prepared from L - or D -glutamic acid, and their helicity induction abilities for a poly(phenylacetylene) bearing a phosphonate pendant were characterized with ultraviolet–visible and circular dichroism spectroscopy. The magnitude of the Cotton effects of the polymer induced by the dendrons significantly increased upon complexation with a higher generation dendron. The effect of the chirality of the glutamate residues (L and D ) on the helicity induction was also studied. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4580–4586, 2004     

Solution properties of exocellular polysaccharides of rhizobium leguminosarum. Static and dynamic light-scattering: Characterization in dilute solution

Three polysaccharides, Rhizobium leguminosarum 8002 EPS(I), Rhizobium trifolii TA1-EPS (II), Rhizobium leguminosarum 127K87 EPS (III), produced by bacteria of Rhizobium genus have been investigated by static and dynamic light scattering combined with chirooptical measurements. All three polymers have the same backbone but differ in the length of the side chains and in the content of minor substituents. An isothermal conformational transition coil → helix was observed with I and II by adding salt (NaCl). The molecular parameters of the polysaccharides in the ordered state were determined by light-scattering data. Increasing the ionic strength a shrinking of the helix was observed accompanied by a corresponding decrease in the radius of gyration. An extraordinary chain stiffness in terms of Kuhn segment lengths was found in both cases, similar to that already observed for other microbial polysaccharides. In the case of III no disorder → order transition was induced by the salt, and the scattering behavior corresponds to that of a rather flexible polymer with a characteristic ratio C_∞ = 24. The incapability of III to form a helical structure is attributed to the effect of the very long side chain. The analysis of the time correlation functions revealed typical flexible chain behavior for all three polysaccharides. This behavior for the two ordered polymers is in agreement with a recent theory by Maggs and is due to bending modes of the rods. ©1995 John Wiley & Sons, Inc.     

Wave Properties of A Free Elliptical Helix Slow-Wave Structure with Arbitrary Eccentricity

This paper gives the investigations of the fundamental wave of a free elliptical helix slow-wave structure (SWS) with arbitrary eccentricity. The wave properties including the phase velocity characteristics, interaction impedance and the longitudinal electric field distribution of this mode has been fully studied. It is found that, when the eccentricity increases, the interaction impedance and the operating frequency of such SWS will be improved, which allows to have a higher gain and operating in a higher frequency band. Furthermore, the field configuration is different from that of a round helix; the azimuthal distribution of the E-field follows with the angular Mathieu function of the first kind, even with mode of zero. In radial, E-field is elliptical surface wave. When the eccentricity tends to zero, all the characteristics will be smoothly degenerates to the case of round helix correspondingly.