Curvature based mobility analysis and form closure of smooth planar curves with multiple contacts

This paper presents a simple second-order, curvature based mobility analysis of planar curves in contact. The underlying theory deals with penetration and separation of curves with multiple contacts, based on relative configuration of osculating circles at points of contact for a second-order rotation about each point of the plane. Geometric and analytical treatment of mobility analysis is presented for generic as well as special contact geometries. For objects with a single contact, partitioning of the plane into four types of mobility regions has been shown. Using point based composition operations based on dual-number matrices, analysis has been extended to computationally handle multiple contacts scenario. A novel color coded directed line has been proposed to capture the contact scenario. Multiple contacts mobility is obtained through intersection of the mobility half-spaces. It is derived that mobility region comprises a pair of unbounded or a single bounded convex polygon. The theory has been used for analysis and synthesis of form closure configurations, revolute and prismatic kinematic pairs. (C) 2013 Elsevier Ltd. All rights reserved.

Homology between jacalin and artocarpin from jackfruit (Artocarpus integrifolia) seeds. Partial sequence and preliminary crystallographic studies of artocarpin

Jacalin and artocarpin, the two lectins from jackfruit (Artocarpus integrifolia) seeds, have different physicochemical properties and carbohydrate-binding specificities. However, comparison of the partial amino-acid sequence of artocarpin with the known sequence of jacalin indicates close to 50% sequence identity. Artocarpin crystallizes in two forms, both monoclinic P2(1), with one and two tetramic molecules, respectively, in the asymmetric units of form I (a = 69.9, b = 73.7, c = 60.6 Angstrom and beta = 95.1 degrees) and form II (a = 87.6, b = 72.2, c = 92.6 Angstrom and beta = 101.1 degrees). Both the crystal structures have been solved by the molecular replacement method using the known structure of jacalin as the search model and ope of them partially refined, confirming that the two lectins are indeed homologous.

Left-Handed DNA in Synthetic and Topologically Constrained Form V-DNA

We have investigated structural transitions in Poly(dG-dC) and Poly(dG-Me5dC) in order to understand the exact role of cations in stabilizing left-handed helical structures in specific sequences andthe biological role, if any, of these structures. From a novel temperature dependent transition it has been shown that a minor fluctuation in Na+ concentration at ambient temperature can bring about Β to Ζ transition. Forthe first time, wehave observed a novel double transition in poly(dG-Me5dC) as the Na+ concentration is gradually increased. This suggests that a minor fluctuation in Na+ concentration in conjunction with methylation may transform small stretches of CG sequences from one conformational state to another. These stretches could probably serve as sites for regulation. Supercoiled formV DNA reconstituted from pBR322 and pßG plasmids have been studied as model systems, in order to understand the nature and role of left-handed helical conformation in natural sequences. A large portion of DNA in form V, obtained by reannealing the two complementary singlestranded circles is forced to adopt left-handed double helical structure due to topological constraints (Lk = 0). Binding studies with Z-DNA specific antibody and spectroscopic studies confirm the presence of left-handed Z-structure in the pßG and pßR322 form V DNA. Cobalt hexamine chloride, which induces Z-form in Poly(dG-dC) stabilizes the Z-conformation in form V DNA even in the non-alternating purine-pyrimidine sequences. A reverse effect is observed with ethidium bromide. Interestingly, both topoisomerase I and II (from wheat germ) act effectively on form V DNA to give rise to a species having an electrophoretic mobility on agarose gel similar to that of open circular (form II) DNA. Whether this molecule is formed as a result of the left-handed helical segments of form V DNA undergoing a transition to the right-handed B-form during the topoisomerase action remains to be solved.

Annealing Behavior of Isotactic Polybutene-1

The annealing behavior of isotactic polybutene-1 (PB-1) has been studied by differential scanning calorimetry and wide-angle x-ray diffraction. On annealing at 110°C, PB-1 yields thick crystals melting at -140°C which are mainly of Form I. An increase in the heat of fusion (ΔHf) and crystallinity is found for annealing times up to 12 h at 110°C; at longer times these properties decrease with increasing annealing time. The increases in ΔHf and crystallinity are attributed to increases in the lamellar thickness in the chain direction and in crystal perfection, and subsequent decreases to degradation of the polymer.

Substrate specificity plays an important role in uncoupling the catalytic and scaffolding activities of rat testis DNA topoisomerase IIalpha

Topoisomerase II (topo II) is a dyadic enzyme found in all eukaryotic cells. Topo II is involved in a number of cellular processes related to DNA metabolism, including DNA replication, recombination and the maintenance of genomic stability. We discovered a correlation between the development of postnatal testis and increased binding of topo IIalpha to the chromatin fraction. We used this observation to characterize DNA-binding specificity and catalytic properties of purified testis topo IIalpha. The results indicate that topo IIalpha binds a substrate containing the preferred site with greater affinity and, consequently, catalyzes the conversion of form I to form IV DNA more efficiently in contrast to substrates lacking such a site. Interestingly, topo IIalpha displayed high-affinity and cooperativity in binding to the scaffold associated region. In contrast to the preferred site, however, high-affinity binding of topo IIalpha to the scaffold-associated region failed to result in enhanced catalytic activity. Intriguingly, competition assays involving scaffold-associated region revealed an additional DNA-binding site within the dyadic topo IIalpha. These results implicate a dual role for topo IIalpha in vivo consistent with the notion that its sequestration to the chromatin might play a role in chromosome condensation and decondensation during spermatogenesis.

Structural and mechanistic investigations on Salmonella typhimurium acetate kinase (AckA): identification of a putative ligand binding pocket at the dimeric interface

Background: Bacteria such as Escherichia coli and Salmonella typhimurium can utilize acetate as the sole source of carbon and energy. Acetate kinase (AckA) and phosphotransacetylase (Pta), key enzymes of acetate utilization pathway, regulate flux of metabolites in glycolysis, gluconeogenesis, TCA cycle, glyoxylate bypass and fatty acid metabolism. Results: Here we report kinetic characterization of S. typhimurium AckA (StAckA) and structures of its unliganded (Form-I, 2.70 angstrom resolution) and citrate-bound (Form-II, 1.90 angstrom resolution) forms. The enzyme showed broad substrate specificity with k(cat)/K-m in the order of acetate > propionate > formate. Further, the K-m for acetyl-phosphate was significantly lower than for acetate and the enzyme could catalyze the reverse reaction (i.e. ATP synthesis) more efficiently. ATP and Mg2+ could be substituted by other nucleoside 5'-triphosphates (GTP, UTP and CTP) and divalent cations (Mn2+ and Co2+), respectively. Form-I StAckA represents the first structural report of an unliganded AckA. StAckA protomer consists of two domains with characteristic beta beta beta alpha beta alpha beta alpha topology of ASKHA superfamily of proteins. These domains adopt an intermediate conformation compared to that of open and closed forms of ligand-bound Methanosarcina thermophila AckA (MtAckA). Spectroscopic and structural analyses of StAckA further suggested occurrence of inter-domain motion upon ligand-binding. Unexpectedly, Form-II StAckA structure showed a drastic change in the conformation of residues 230-300 compared to that of Form-I. Further investigation revealed electron density corresponding to a citrate molecule in a pocket located at the dimeric interface of Form-II StAckA. Interestingly, a similar dimeric interface pocket lined with largely conserved residues could be identified in Form-I StAckA as well as in other enzymes homologous to AckA suggesting that ligand binding at this pocket may influence the function of these enzymes. Conclusions: The biochemical and structural characterization of StAckA reported here provides insights into the biochemical specificity, overall fold, thermal stability, molecular basis of ligand binding and inter-domain motion in AckA family of enzymes. Dramatic conformational differences observed between unliganded and citrate-bound forms of StAckA led to identification of a putative ligand-binding pocket at the dimeric interface of StAckA with implications for enzymatic function.

Polymorphs and hydrates of Etoricoxib, a selective COX-2 inhibitor

The crystal structures of two polymorphs and two polymorphic hemihydrates of Etoricoxib are reported. Etoricoxib is a non-steroidal anti-inflammatory drug (NSAID) that is a selective inhibitor of COX-2. It is used in the treatment of various types of inflammation, pain and fever. Clas et al. have reported four polymorphs (labeled I through IV) and two solvates (hemi-and sesquihydrate) of the API in US patent 6,441,002 (Clas et al, US patent 6,441,002, 2002). However, no crystal structures have been reported for any of these forms. A comparison was made between the PXRD patterns reported in patent `002 and the powder spectra simulated from single crystal data. The two polymorphs characterized here correspond to form I and form IV of the patent. Form II of the patent could not be obtained by us with a variety of experimental conditions. Form III of the patent corresponds to hemihydrate II of this study. Form III is therefore not a polymorph of form I and form IV. What we have termed hemihydrate I in this study is obtained under a wide variety of conditions and it is also the only hemihydrate reported as such in the patent. Because the Etoricoxib molecule contains no conventional hydrogen bond donors, there cannot be any strong hydrogen bonds in the crystal structures of forms I and IV. The packing is accordingly characterized by weak hydrogen bonds of the C-H center dot center dot center dot O=S and C-H center dot center dot center dot N type. Thermal data were collected for form I, form IV and hemihydrate I to shed some light on relative stabilities. PXRD diffractograms show the transformation of form IV to form I at elevated temperature, indicating that form I is more stable than form IV. However, this transformation occurs only in samples of form IV that contain some form I; it does not occur in pure form IV. The formation of the two hemihydrates could follow from the known tendency of an acceptor-rich molecule to crystallize as a hydrate.

The Role of Weak Interactions in the Phase Transition and Distinct Mechanical Behavior of Two Structurally Similar Caffeine Co-crystal Polymorphs Studied by Nanoindentation

Although weak interactions, such as C-H center dot center dot center dot O and pi-stacking, are generally considered to be insignificant, it is their reorganization that holds the key for many a solid-state phenomenon, such as phase transitions, plastic deformation, elastic flexibility, and mechanochromic luminescence in solid-state fluorophores. Despite this, the role of weak interactions in these dynamic phenomena is poorly understood. In this study, we investigate two co-crystal polymorphs of caffeine:4-chloro-3-nitrobenzoic acid, which have close structural similarity (2D layered structures), but surprisingly show distinct mechanical behavior. Form I is brittle, but shows shear-induced phase instability and, upon grinding, converts to Form II, which is soft and plastically shearable. This observation is in contrast to those reported in earlier studies on aspirin, wherein the metastable drug forms are softer and convert to stable and harder forms upon stressing To establish a molecular level understanding, have investigated the two co-crystal polymorphs I and II by single crystal X-ray diffraction, nanoindentation to quantify mechanical properties, and theoretical calculations. The lower hardness (from nanoindentation) and smooth potential surfaces (from theoretical studies) for shearing of layers in Form II allowed us to rationalize the role of stronger intralayer (sp(2))C-H center dot center dot center dot O and nonspecific interlayer pi-stacking interactions in the structure of II. Although the Form I also possesses the same type of interactions, its strength is clearly opposite, that is, weaker intralayer (sp(3))C-H center dot center dot center dot O and specific interlayer pi-stacking interactions. Hence, Form I is harder than Form IL Theoretical calculations and indentation on (111) of Form I suggested the low resistance of this face to mechanical stress; thus, Form I converts to II upon mechanical action. Hence, our approach demonstrates the usefulness of multiple techniques for establishing the role of weak noncovalent interactions in solid-state dynamic phenomena, such as stress induced phase transformation, and hence is important in the context of solid-state pharmaceutical chemistry and crystal engineering.

Structural Investigations on Poly(4-hydroxy-L-proline). 1. Theoretical Studies

Model building studies on poly(hydroxypro1ine) indicate that in addition to the well-known helical structure of form A, a left-handed helical structure with trans peptide units and with h = 2.86 A and n = 2.67 (i.e., 8 residues in 3 turns) is also possible. In this structure which is shown to be in agreement with X-ray data of the form B in the next paper, the y-hydroxyl group of an (i + 1)th Hyp residue is hydrogen bonded to the carbonyl oxygen of an (i - 1)th residue. The possibility of a structure with cis peptide units is ruled out. It is shown that both forms A and B are equally favorable from considerations of intramolecular energies. Since form B is further stabilized by intrachain hydrogen bonds, we believe that this is likely to be the ordered conformation for poly(hydroxypro1ine) in water.

Preliminary X-ray crystallographic studies on acetate kinase (AckA) from Salmonella typhimurium in two crystal forms

Acetate kinase (AckA) catalyzes the reversible transfer of a phosphate group from acetyl phosphate to ADP, generating acetate and ATP, and plays a central role in carbon metabolism. In the present work, the gene corresponding to AckA from Salmonella typhimurium (StAckA) was cloned in the IPTG-inducible pRSET C vector, resulting in the attachment of a hexahistidine tag to the N-terminus of the expressed enzyme. The recombinant protein was overexpressed, purified and crystallized in two different crystal forms using the microbatch-under-oil method. Form I crystals diffracted to 2.70 angstrom resolution when examined using X-rays from a rotating-anode X-ray generator and belonged to the monoclinic space group C2, with unit-cell parameters a = 283.16, b = 62.17, c = 91.69 angstrom, beta = 93.57 degrees. Form II crystals, which diffracted to a higher resolution of 2.35 angstrom on the rotating-anode X-ray generator and to 1.90 angstrom on beamline BM14 of the ESRF, Grenoble, also belonged to space group C2 but with smaller unit-cell parameters (a = 151.01, b = 78.50, c = 97.48 angstrom, beta = 116.37 degrees). Calculation of Matthews coefficients for the two crystal forms suggested the presence of four and two protomers of StAckA in the asymmetric units of forms I and II, respectively. Initial phases for the form I diffraction data were obtained by molecular replacement using the coordinates of Thermotoga maritima AckA (TmAckA) as the search model. The form II structure was phased using a monomer of form I as the phasing model. Inspection of the initial electron-density maps suggests dramatic conformational differences between residues 230 and 300 of the two crystal forms and warrants further investigation.

Shock propagation in gas dynamics: explicit form of higher order compatibility conditions

With the use of tensor analysis and the method of singular surfaces, an infinite system of equations can be derived to study the propagation of curved shocks of arbitrary strength in gas dynamics. The first three of these have been explicitly given here. This system is further reduced to one involving scalars only. The choice of dependent variables in the infinite system is quite important, it leads to coefficients free from singularities for all values of the shock strength.

Constraining the low-energy pion electromagnetic form factor with space-like and phase of time-like data

The Taylor coefficients c and d of the EM form factor of the pion are constrained using analyticity, knowledge of the phase of the form factor in the time-like region, 4m(pi)(2) <= t <= t(in) and its value at one space-like point, using as input the (g - 2) of the muon. This is achieved using the technique of Lagrange multipliers, which gives a transparent expression for the corresponding bounds. We present a detailed study of the sensitivity of the bounds to the choice of time-like phase and errors present in the space-like data, taken from recent experiments. We find that our results constrain c stringently. We compare our results with those in the literature and find agreement with the chiral perturbation-theory results for c. We obtain d similar to O(10) GeV-6 when c is set to the chiral perturbation-theory values.

A thermal molecular migration in the solid-state - structures of isomeric 5-amino-4-(2,6-dichlorophenyl)-1-(2-nitrophenyl)-1h-1,2,3-triazole (yellow form i) and 4-(2,6-dichlorophenyl)-5-(2-nitroanilino)-2h-1,2,3-triazole (red form-ii), c14h9cl2n5o2

Yellow form (I): Mr= 350.09, monoclinic, P2Jn, Z--4, a=9.525(1), b=14.762(1), c= 11.268(1),/t, fl= 107.82 (1) o , V= 1508.3 A 3 , Din(flotation in aqueous KI)= 1.539 (2), D x= 1.541 (2) g cm -3, #(Cu Ka, 2 = 1.5418 A) = 40.58 cm -~, F(000) = 712, T= 293 K, R = 8.8% for 2054 significant refections. Red form (II): Mr= 350.09, triclinic, Pi, Z=2, a=9.796(2), b= 10.750 (2), c= 7.421 (1)A, a= 95.29 (2), fl= 0108-2701/84/111901-05501.50 70.18 (1), y = 92-.76 (2) °, V= 731.9 A 3, Din(flotation in KI) = 1.585 (3), D x = 1.588 (3) g cm -3, ~t(Cu Ka, 2 = 1.5418/~) = 40.58 cm -1, F(000) = 356, T=293 K, R = 5.8% for 1866 significant reflections. There are no unusual bond distances or angles. The triazole and two phenyl rings are planar. On the basis of packing considerations the possibility of intermolecular interactions playing a role in the reactivity of the starting material is ruled out.

Conformational flexibility in androgenic steroids - the structure of a new form of (+)-17-beta-hydroxy-19-nor-4-androsten-3-one (19-nortestosterone), c18h26o2

The structure and conformation of a second crystalline modification of 19-nortestosterone has been determined by X-ray methods. M r = 274, monoclinic P2 l, a=9.755(2), b= 11.467(3), c= 14.196(3)/L fl=101.07(2) ° , V=1558.4 (8) A 3, Z=4, Ox= I. 168 g cm -3, Mo Ka, 2 = 0.7107 ,/k, ~ = 0.80 cm -l, F(000) = 600, T= 300 K. R = 0.060 for 2158 observed reflections. The two molecules in the asymmetric unit show significant differences in the A-ring conformation from that of the previously reported form of the title compound [Precigoux, Busetta, Courseille & Hospital (1975). Acta Cryst. B31, 1527-1532]. The l a,2fl-half-chair conformation of the A ring increases its conformational freedom compared with testosterone.