Transition from disc to rod-like shape of 16-3-16 dimeric micelles in aqueous solutions

Small-angle neutron scattering (SANS) measurements from bis-cationic C16H33N+(CH3)(2)-(CH2)(3)-N+ (CH3)(2)C16H33 2Br(-) dimeric surfactant, referred to as 16-3-16, at different concentrations and temperatures, are reported. It is seen that micelles are disc-like for concentrations C = 2.5 and 10 mM at temperature T = 30 degrees C. At low concentration C = 0.5 mM micelles are rod-like. Similarly, there is a disc to rod-like transition of micelles on increasing the temperature. For C = 2.5 mM, micelles are rod-like at T = 45 and 70 degrees C.

Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

The structure of monopotassium phosphoenolpyruvate

CaH406P-.K +, M r = 206.10, is orthorhombic, space group Pbca (from systematic absences), a = 14.538(4), b = 13.364(5), c = 6.880 (6)A, U = 1383.9 A 3, D x = 2.07 Mg m -a, Z = 8, ~.(Mo Ka) = 0.7107/~, p(MO Ka) = 1.015 mm -1. The final R value is 0.042 for a total of 1397 reflections. The high energy P-O(13) and the enolic C(1)-O(13) bonds are 1.612 and 1.374 A respectively. The enolpyruvate moiety is essentially planar. The orientation of the phosphate with respect to the pyruvate group in PEP.K is distinctly different from that in the PEP-cyclohexylammonium salt, the torsion angle C (2)-C (1)-O(13)- P being -209.1 in the former and -90 ° in the latter. The K + ion binds simultaneously to both the phosphate and carboxyl ends of the same PEP molecule. The ester O(13) is also a binding site for the cation. The K + ion is coplanar with the pyruvate moiety and binds to 0(22) and O(13) almost along their lone-pair directions. The carbonyl 0(22) prefers to bind to the K + ion rather than take part in the formation of hydrogen bonds usually observed in carboxylic acid structures.

The modes of binding methyl-alpha (and beta)-D-glucopyranosides and some of their derivatives to concanavalin A--a theoretical approach

The probable modes of binding of Methyl--alpha (and beta)-D-glucopyranosides and some of their derivatives to concanavalin A have been proposed from theoretical studies. Theory predicts that beta-MeGlcP can bind to ConA in three different modes whereas alpha-MeGlcP can bind only in one mode. beta-MeGlcP in its most favourable mode of binding differs from alpha-MeGlcP in its alignment in the active-site of the lectin where it binds in a flipped or inverted orientation. Methyl substitution at the C-2 atom of the alpha-MeGlcP does not significantly affect the possible orientations of the sugar in the active-site of the lectin. Methyl substitution at C-3 or C-4, however, affects the allowed orientations drastically leading to the poor inhibiting power of Methyl-3-O-methyl-alpha-D-glucopyranoside and the inactivity of Methyl-4-O-methyl-alpha-D-glycopyranoside. These studies suggest that the increased activity of the alpha-MeGlcP over beta-MeGlcP may be due to the possibility of formation of better hydrogen bonds and to hydrophobic interactions rather than to steric factors as suggested by earlier workers. These models explain the available NMR and other binding studies.

Binding of N-dansylgalactosamine to winged-bean tuber lectin: studies by fluorescence quenching titrations

The winged-bean tuber lectin binds to N-dansyl(5-dimethylaminonaphthalene-1-sulphonic acid)galactosamine, leading to a 12.5-fold increase in dansyl fluorescence with a concomitant 25 nm blue-shift in the emission maximum. The enhancement of fluorescence intensity was completely reversed by the addition of methyl α-galactopyranoside. The lectin has two binding sites per molecule for this fluorescent sugar and an association constant of 2.59 · 105 M−1 at 25° C. The binding of N-dansylgalactosamine to the lectin shows that it can accommodate a large hydrophobic substituent on the C-2 carbon of d-galactose. Studies with other sugars indicate that a hydrophobic substituent with α-conformation at the anomeric position increases the affinity of binding. The C-4 and C-6 hydroxyl groups are also critical for sugar binding to this lectin.

Thermodynamic and kinetic studies on saccharide binding to soya-bean agglutinin.

The fluorescence of N-dansylgalactosamine [N-(5-dimethylaminonaphthalene-1-sulphonyl)galactosamine] was enhanced 11-fold with a 25 nm blue-shift in the emission maximum upon binding to soya-bean agglutinin (SBA). This change was used to determine the association constants and thermodynamic parameters for this interaction. The association constant of 1.51 X 10(6) M-1 at 20 degrees C indicated a very strong binding, which is mainly due to a relatively small entropy value, as revealed by the thermodynamic parameters: delta G = -34.7 kJ X mol-1, delta H = -37.9 kJ X mol-1 and delta S = -10.9 J X mol-1 X K-1. The specific binding of this sugar to SBA shows that the lectin can accommodate a large hydrophobic substituent on the C-2 of galactose. Binding of non-fluorescent ligands, studied by monitoring the fluorescence changes when they are added to a mixture of SBA and N-dansylgalactosamine, indicates that a hydrophobic substituent at the anomeric position increases the affinity of the interaction. The C-6 hydroxy group also stabilizes the binding considerably. Kinetics of binding of N-dansylgalactosamine to SBA studied by stopped-flow spectrofluorimetry are consistent with a single-step mechanism and yielded k+1 = 2.4 X 10(5) M-1 X s-1 and k-1 = 0.2 s-1 at 20 degrees C. The activation parameters indicate an enthalpicly controlled association process.

Thermodynamic and kinetic analysis of carbohydrate binding to the basic lectin from winged bean (Psophocarpus tetragonolobus)

A basic lectin (pI approximately 10.0) was purified to homogeneity from the seeds of winged bean (Psophocarpus tetragonolobus) by affinity chromatography on Sepharose 6-aminocaproyl-D-galactosamine. The lectin agglutinated trypsinized rabbit erythrocytes and had a relative molecular mass of 58,000 consisting of two subunits of Mr 29,000. The lectin binds to N-dansylgalactosamine, leading to a 15-fold increase in dansyl fluorescence with a concomitant 25-nm blue shift in the emission maximum. The lectin has two binding sites/dimer for this sugar and an association constant of 4.17 X 10(5) M-1 at 25 degrees C. The strong binding to N-dansylgalactosamine is due to a relatively positive entropic contribution as revealed by the thermodynamic parameters: delta H = -33.62 kJ mol-1 and delta S0 = -5.24 J mol-1 K-1. Binding of this sugar to the lectin shows that it can accommodate a large hydrophobic substituent on the C-2 carbon of D-galactose. Studies with other sugars indicate that a hydrophobic substituent in alpha- conformation at the anomeric position increases the affinity of binding. The C-4 and C-6 hydroxyl groups are critical for sugar binding to this lectin. Lectin difference absorption spectra in the presence of N-acetylgalactosamine indicate perturbation of tryptophan residues on sugar binding. The results of stopped flow kinetics with N- dansylgalactosamine and the lectin are consistent with a simple one- step mechanism for which k+1 = 1.33 X 10(4) M-1 s-1 and k-1 = 3.2 X 10(- 2) s-1 at 25 degrees C. This k-1 is slower than any reported for a lectin-monosaccharide complex so far. The activation parameters indicate an enthalpically controlled association process.

Is 3'-nucleotide rigid?

Conformational analysis of nucleic acids and polynucleotides is far more complex than that of proteins and polypeptides, due to five single bond rotations in addition to the sugar puckerings in the monomer. Sundaralingam1 proposed the concept of the 'rigid' nucleotides from analysis of crystal structure data, with the flexibility allowed only about the phosphodiester bonds. However, the crystal structure of deoxyguanosine-5'−phosphate2,3 indicates at gt conformation about the C-4'−C-5' bond against gg in a conformationally rigid nudeotide1. Jack et al. 4 considered the flexibility of nucleotides in tRNA about the C-4'−C-5' bond, thereby introducing the concept of 'non-rigid' ribonucleotides. Conformational flexibility of the f uranose ring in DNA and RNA and their energetics using classical and quantum chemical methods have been reported5−8. We have examined the flexibility of 3'-nucleotides. alpha, the most important of the conformational parameters defining the 3'-end of a nucleotide unit9, has a value in the range 195°−270° in all the 3'-nucleotides, dinucleoside monophosphates and higher oligomers which have been surveyed. A survey of the proposed structures of polyribonudeotides10,11 also shows the values of a to be greater than 200°. However, the structures proposed for B-DNA by Arnott and Hukins12,13 and D-DNA by Arnott et al. 14 have values of alpha of 155° and 141° respectively, much lower than the lowest observed value. The structure for B-DNA has two strong, short contacts (C-2'...OP-1 = 2.64 Å and HC-2"...OP-1 = 1.79 Å) which lead to an energetically unfavourable conformation. Hence, it is of interest to investigate whether, by allowing flexibility to the sugar moiety in the nucleotide unit, it is possible to make the structure energetically favourable. Here, conformational energy calculations were carried out to determine the range of alpha which would give rise to energetically favoured conformations with different sugar puckerings. Our analysis has shown that the theoretically obtained range is nearly the same as the preferred range in crystals, indicating the flexibility of the 3'-nucleotides.

The structure of the monobarium salt of glucose 6-phosphate heptahydrate

C6H11o9P2-.Ba2+.7H2o, M, = 521.5, is monoclinic, space group P21, a = 11.881 (4), b = 8.616 (5), c = 8.350 (4) A,B = 102.95 (3)0, Z = 2, U = 833.0 A 3, d m = 2.09, d c = 2.08 Mg m -3, F(000) = 516. Mo Ka (u = 0.034 mm -1) intensity data. R is 0.068 for 1603 reflections. Of the two endocyclic C-O bonds in the glucose ring, C(5)-O(5) [1.463 (23)] is longer than C(1)-O(5) [1.395 (23)A]. The pyranose sugar ring takes a 4C1 chair conformation. The Cremer-Pople puckering parameters are, 0 = 6.69 o, Q = 0.619 A and 0 = 263.7o. The conformation about the exocyclic C(5)-C(6) bond is gauche-gauche, in contrast to gauche-trans observed in the structure of glucose 1-phosphate. The phosphate ester bond, P-O(6), is 1.61 (1)A. It is similar in length to the 'high-energy' P~O bond in phosphoenolpyruvate. The Ba 2÷ ion is surrounded by nine O atoms within a distance of 2.95 A, of which seven are from water molecules. There is an intramolecular hydrogen bond between the sugar hydroxyl 0(4) and phosphate oxygen O(12).

A theory of the upper critical field in antiferromagnetic superconductors

A generalized Ginzburg-Landau approach is used to study the nonmonotonic temperature dependence of the upper critical field H c 2(T) in antiferromagnetic superconductors RE(Mo)6S8; RE = Dy, Tb, Gd. It is found that electrodynamic effects incorporated through screening and indirect coupling between the staggered magnetization M Q (T) and superconducting order parameter psgr cannot explain the observed nonmonotonicity. This suggests that the direct coupling between the two order parameters should be considered to understand the experimental results, a finding which is consistent with recent microscopic calculations.

The Structure of the Monosodium Salt of Cytidine(5')diphosphoethanolamine

CI1H19N4OIIP2.Na+.TH2 O, Mr = 594.08, is orthorhombic, space group P21212 l, with a = 6.946 (2), b = 12.503 (4), c = 28.264 (8)/k, U = 2454.6 A, a, D x = 1.61 Mg m -a, Z = 4, ~t(CuKa) = 2.612 mm -1, F(000) = 1244. Final R = 0.101 for 1454 observed reflections. The cytosine base is in the anti conformation with respect to the sugar (ZCN = 62"60) . The ribose exhibits an uncommon C(l')exo-C(2')endo puckering. The pyrophosphate has a characteristic staggered geometry. The conformation about P(2)-O(7') is trans (-103.4°). This makes CDPethanolamine more extended compared to the folded geometry of CDP-choline, which has a gauche conformation (71.3 o). The molecular interactions in the extended crystal structure, however, are similar to those found in CDP-choline, with the CMP-5' portions tightly bound by metal ligation and the phosphorylethanolamine parts only loosely held by water molecules.

The Structure of Monosodium Phosphoenolpyruvate

CDH406P-.Na +.H20 , M r = 208.0, is monoclinic, Cc, a = 11.423 (2), b = 23.253 (5), c - 6.604 (1) A, fl = 123.63 (1) °, U = 1460.6 A 3, D x =. 1.89 Mg m -a, Z = 8, 2(Mo Ka) = 0.7107 A, p(Mo Ka) = 0.44 mm -~, F(000) = 840. Final R = 0.063 for 1697 reflections.The two crystallographically independent molecules of phosphoenolpyruvate (PEP) (A and B) are almost mirror images of each other, the mirror being the planar enolpyruvate group. The torsion angle C(3)-C(2)- O(1)-P(1) is 122.6 in A and -112.0 ° in B, in contrast to -209.1 ° in PEP.K. The enolic C(2)-O(1) has a partial double-bond character [1.401 (A), 1.386A (B)]. The high-energy P~O bond (1.595 and 1.610A) is comparable to that in PEP.K (1.612 A). Na(1) has six nearest neighbours while Na(2) has only five. The Na + ions are involved in binding only the phosphates of different molecules, in contrast to the K ÷ ion in PEP. K, which binds to both the phosphate and carboxyl ends of the same molecule. The planar carboxyl groups stack on each other at an average distance of 3.2 A instead of forming hydrogen-bonded dimers usually found in carboxylate structures.

Structural Crystallography and Crystal Chemistry

CaH406P-.K +, M r = 206.10, is orthorhombic, space group Pbca (from systematic absences), a = 14.538(4), b = 13.364(5), c = 6.880 (6)A, U = 1383.9 A 3, D x = 2.07 Mg m -a, Z = 8, ~.(Mo Ka) = 0.7107/~, p(MO Ka) = 1.015 mm -1. The final R value is 0.042 for a total of 1397 reflections. The high energy P-O(13) and the enolic C(1)-O(13) bonds are 1.612 and 1.374 A respectively. The enolpyruvate moiety is essentially planar. The orientation of the phosphate with respect to the pyruvate group in PEP.K is distinctly different from that in the PEP-cyclohexylammonium salt, the torsion angle C (2)-C (1)-O(13)- P being -209.1 in the former and -90 ° in the latter. The K + ion binds simultaneously to both the phosphate and carboxyl ends of the same PEP molecule. The ester O(13) is also a binding site for the cation. The K + ion is coplanar with the pyruvate moiety and binds to 0(22) and O(13) almost along their lone-pair directions. The carbonyl 0(22) prefers to bind to the K + ion rather than take part in the formation of hydrogen bonds usually observed in carboxylic acid structures.

Structure of disodium deoxyuridine 5'-phosphate pentahydrate

Disodium deoxyuridine 5'-nhosDhate pentahvdrate, Na2(C9H l INEOsP). 5 H20, Call 11N208 P2-. 2Na +. 5 H20, crystallizes in the monoclinic space group P2: with a = 7.250 (4), b = 35.45 (2), c = 7.132 (4)/~, fl = 102.2 (4) °, Z = 4. The Cu Ka intensity data were collected photographically and estimated visually. The structure was obtained by the minimum-function method and difference syntheses and refined to an R of 0.089. In both molecules the uracil base has an anti conformation (2cN = 57.1 and 59.9 °) with respect to the sugar. The deoxyribose moiety of molecule B shows a typical C(l')-exo puckering, with C(I') displaced by 0.52 /k from the best plane. The furanose ring conformation of molecule A can be described as C(2')-endo,C(l')-exo. Both the molecules have an unusual trans-gauche conformation about the exocyclic C(4')-C(5') bond with (~0oo = 171.1, 172.2°; ~0oc = -64.7, -65.9°).

On the growth of the Bergman kernel near an infinite-type point

We study diagonal estimates for the Bergman kernels of certain model domains in C-2 near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as well. Thisn condition quantifies, in some sense, how flat a domain is at an infinite-type boundary point. In this scheme of quantification, the model domains considered below range-roughly speaking-from being mildly infinite-type'' to very flat at the infinite-type points.