Conformational mapping and energetics of saccharide-aromatic residue interactions: implications for the discrimination of anomers and epimers and in protein engineering

Aromatic residues play a key role in saccharide-binding sites. Experimental studies have given an estimate of the energetics of saccharide-aromatic residue interactions. In this study, dependence of the energetics on the mutual position-orientation (PO) of saccharide and aromatic residue has been investigated by geometry optimization of a very large number (164) of complexes at MP2/6-31G(d,p) level of theory. The complexes are of Tyr and Phe analogs with α/β-D-Glc, β-D-Gal, α-D-Man and α/β-L-Fuc. A number of iso-energy POs are found for the complexes of all six saccharides. Stacking and non-stacking modes of binding are found to be of comparable strengths. In general, complexes of p-OHTol are stronger than those of Tol, and those dominated by OH···O interactions are more stable than ones dominated by CH···π interactions. The strengths of OH···O/π interactions, but not those of CH···π, show large variations. Even though an aromatic residue has a large variety of POs to interact with a saccharide, distinct preferences are found due to anomeric and epimeric differences. An aromatic residue can interact from either the a- or b-face of Glc, but only through the b-face with Gal, its C4-epimer. In contrast, stacking interaction with Man (C2-epimer of Glc) requires the participation of the -CH(2)OH group and free rotation of this group, as is observed in solution, precludes all modes of stacking interactions. It is also found that an aromatic residue can be strategically placed either to discriminate or to accommodate (i) anomers of Glc and of Fuc and (ii) Gal/Fuc. Thus, analysis of the optimized geometries of by far the largest number of complexes, and with six different saccharides, at this level of theory has given insights into how Nature cleverly uses aromatic residues to fine tune saccharide specificities of proteins. These are of immense utility for protein engineering and protein design studies.     

Convergence Analysis of Weighted Difference Approximations on Piecewise Uniform Grids to a Class of Singularly Perturbed Functional Differential Equations

We consider the numerical approximation of a singularly perturbed time delayed convection diffusion problem on a rectangular domain. Assuming that the coefficients of the differential equation be smooth, we construct and analyze a higher order accurate finite difference method that converges uniformly with respect to the singular perturbation parameter. The method presented is a combination of the central difference spatial discretization on a Shishkin mesh and a weighted difference time discretization on a uniform mesh. A?priori explicit bounds on the solution of the problem are established. These bounds on the solution and its derivatives are obtained using a suitable decomposition of the solution into regular and layer components. It is shown that the proposed method is $L_{2}^{h}$ -stable. The analysis done permits its extension to the case of adaptive meshes which may be used to improve the solution. Numerical examples are presented to demonstrate the effectiveness of the method. The convergence obtained in practical satisfies the theoretical predictions.     

Breakdown of the Stokes-Einstein relationship: role of interactions in the size dependence of self-diffusivity

Einstein and others derived the reciprocal dependence of the self-diffusivity D on the solute radius r(u) for large solutes based on kinetic theory. We examine here (a) the range of r(u) over which Stokes-Einstein (SE) dependence is valid and (b) the precise dependence for small solutes outside of the SE regime. We show through molecular dynamics simulations that there are two distinct regimes for smaller solutes: (i) the interaction or Levitation effect (LE) regime for solutes of intermediate size and (ii) the D proportional, variant 1/r(u)(2) for still smaller solutes. We show that as the solute-solvent size ratio decreases, the breakdown in the Stokes-Einstein relationship leading to the LE regime has its origin in dispersion interaction between the solute and the solvent. These results explain reports of enhanced solute diffusion in solvents existing in the literature seen for small solutes for which no explanation exists.     

Conformational specificity of non-canonical base pairs and higher order structures in nucleic acids: crystal structure database analysis

Non-canonical base pairs contribute immensely to the structural and functional variability of RNA, which calls for a detailed characterization of their spatial conformation. Intra-base pair parameters, namely propeller, buckle, open-angle, stagger, shear and stretch describe structure of base pairs indicating planarity and proximity of association between the two bases. In order to study the conformational specificities of non-canonical base pairs occurring in RNA crystal structures, we have upgraded NUPARM software to calculate these intra-base pair parameters using a new base pairing edge specific axis system. Analysis of base pairs and base triples with the new edge specific axis system indicate the presence of specific structural signatures for different classes of non-canonical pairs and triples. Differentiating features could be identified for pairs in cis or trans orientation, as well as those involving sugar edges or C-H-mediated hydrogen bonds. It was seen that propeller for all types of base pairs in cis orientation are generally negative, while those for trans base pairs do not have any preference. Formation of a base triple is seen to reduce propeller of the associated base pair along with reduction of overall flexibility of the pairs. We noticed that base pairs involving sugar edge are generally more non-planar, with large propeller or buckle values, presumably to avoid steric clash between the bulky sugar moieties. These specific conformational signatures often provide an insight into their role in the structural and functional context of RNA.     

Busy period analysis of queue: Lattice path approach

In this paper, we find the busy period density of queues in explicit computational form, through lattice path (LP) approach. Both the arrival and service time distributions are approximated by 2-phase Cox distribution C₂, which has a Markovian property enabling us to use LP combinatorics. Since any distribution with rational Laplace–Stieltjes transform (LST) and square coefficient of variation (CV²) lying in [1/2,∞) can be approximated by a C₂([M. Agarwal, K. Sen, B. Borkakaty, Busy period density of queueing system C₃/M/1, Journal of Combinatorics, Information and Systems Sciences 31 (1–4) (2006) 127–161]), the results obtained would be applicable to a very wide class of distributions occurring in real life.     

Modeling Disorder in the Crystal Structure of the α Polymorph of Alq<Subscript>3</Subscript>

Abstract  

Alq₃, tris(quinolin-8-olato)aluminum(III) is used in the electron transport and/or electron-injecting layer in multilayer organic light-emitting diode device structures. In recent years, five crystalline phases (α, β, γ, δ, and ε) of Alq₃ have been identified. A structure of the α form, containing the meridional isomer, has been reported in literature based on powder XRD data. Single crystals of α Alq₃ have been found to have essentially the same unit cell parameters [triclinic, space group P [`1]P \bar {1}, a = 6.2455(10) ?, b = 12.8710(18) ?, c = 14.739(3) ?, α = 69.890(6)°, β = 89.464(5)°, and γ = 82.520(13)°] as reported previously from powder XRD: triclinic, space group P [`1]P \bar {1}, a = 6.2586(8) ?, b = 12.914(2) ?, c = 14.743(2) ?, α = 109.66(1)°, β = 89.66(1)°, and γ = 97.68(1)°. The single-crystal XRD structure for α Alq₃, however, appeared to be present mostly as the facial isomer, with a high degree of disorder. Although the structure obtained by single-crystal XRD appears to be predominantly or entirely facial, various spectroscopy results (particularly NMR) are more consistent with a meridional composition. To resolve the α Alq₃ isomerism contradiction, we have reconsidered the structural conclusions that were drawn from the single crystal XRD. Based on modeling results, the hypothesis is that α Alq₃ could be a disordered analog of ε Alq_3, with meridional conformation.