Mersenne numbers

These notes have been issued on a small scale in 1983 and 1987 and on request at other times. This issue follows two items of news. First, WaIter Colquitt and Luther Welsh found the 'missed' Mersenne prime M110503 and advanced the frontier of complete Mp-testing to 139,267. In so doing, they terminated Slowinski's significant string of four consecutive Mersenne primes. Secondly, a team of five established a non-Mersenne number as the largest known prime. This result terminated the 1952-89 reign of Mersenne primes. All the original Mersenne numbers with p < 258 were factorised some time ago. The Sandia Laboratories team of Davis, Holdridge & Simmons with some little assistance from a CRAY machine cracked M211 in 1983 and M251 in 1984. They contributed their results to the 'Cunningham Project', care of Sam Wagstaff. That project is now moving apace thanks to developments in technology, factorisation and primality testing. New levels of computer power and new computer architectures motivated by the open-ended promise of parallelism are now available. Once again, the suppliers may be offering free buildings with the computer. However, the Sandia '84 CRAY-l implementation of the quadratic-sieve method is now outpowered by the number-field sieve technique. This is deployed on either purpose-built hardware or large syndicates, even distributed world-wide, of collaborating standard processors. New factorisation techniques of both special and general applicability have been defined and deployed. The elliptic-curve method finds large factors with helpful properties while the number-field sieve approach is breaking down composites with over one hundred digits. The material is updated on an occasional basis to follow the latest developments in primality-testing large Mp and factorising smaller Mp; all dates derive from the published literature or referenced private communications. Minor corrections, additions and changes merely advance the issue number after the decimal point. The reader is invited to report any errors and omissions that have escaped the proof-reading, to answer the unresolved questions noted and to suggest additional material associated with this subject.

The structure of crystallisable copolymers of L-lactide, epsilon-caprolactone and glycolide

We apply a new X-ray scattering approach to the study of melt-spun filaments of tri-block and random terpolymers prepared from lactide, caprolactone and glycolide. Both terpolymers contain random sequences, in both cases the overall fraction of lactide units is similar to 0.7 and C-13 and H-1 NMR shows the lactide sequence length to be similar to 9-10. A novel representation of the X-ray fibre pattern as series of spherical harmonic functions considerably facilitates the comparison of the scattering from the minority crystalline phase with hot drawn fibres prepared from the poly(L-lactide) homopolymer. Although the fibres exhibit rather disordered structures we show that the crystal structure is equivalent to that displayed by poly(L-lactide) for both the block and random terpolymers. There are variations in the development of a two-phase structure which reflect the differences in the chain architectures. There is evidence that the random terpolymer includes non-lactide units in to the crystal interfaces to achieve a well defined two-phase structure. (c) 2005 Published by Elsevier Ltd.

A hierarchical distributed approach for mining molecular fragments

Recently, two approaches have been introduced that distribute the molecular fragment mining problem. The first approach applies a master/worker topology, the second approach, a completely distributed peer-to-peer system, solves the scalability problem due to the bottleneck at the master node. However, in many real world scenarios the participating computing nodes cannot communicate directly due to administrative policies such as security restrictions. Thus, potential computing power is not accessible to accelerate the mining run. To solve this shortcoming, this work introduces a hierarchical topology of computing resources, which distributes the management over several levels and adapts to the natural structure of those multi-domain architectures. The most important aspect is the load balancing scheme, which has been designed and optimized for the hierarchical structure. The approach allows dynamic aggregation of heterogenous computing resources and is applied to wide area network scenarios.

Interference and communications among active network applications

This paper focuses on active networks applications and in particular on the possible interactions among these applications. Active networking is a very promising research field which has been developed recently, and which poses several interesting challenges to network designers. A number of proposals for e±cient active network architectures are already to be found in the literature. However, how two or more active network applications may interact has not being investigated so far. In this work, we consider a number of applications that have been designed to exploit the main features of active networks and we discuss what are the main benefits that these applications may derive from them. Then, we introduce some forms of interaction including interference and communications among applications, and identify the components of an active network architecture that are needed to support these forms of interaction. We conclude by presenting a brief example of an active network application exploiting the concept of interaction.

Adaptive routing in active networks

New conceptual ideas on network architectures have been proposed in the recent past. Current store-andforward routers are replaced by active intermediate systems, which are able to perform computations on transient packets, in a way that results very helpful for developing and deploying new protocols in a short time. This paper introduces a new routing algorithm, based on a congestion metric, and inspired by the behavior of ants in nature. The use of the Active Networks paradigm associated with a cooperative learning environment produces a robust, decentralized algorithm capable of adapting quickly to changing conditions.

Microbe-associated molecular pattern (MAMP) signatures, synergy, size and charge: influences on perception or mobility and host defence responses

Triggering of defences by microbes has mainly been investigated using single elicitors or microbe-associated molecular patterns (MAMPs), but MAMPs are released in planta as complex mixtures together with endogenous oligogalacturonan (OGA) elicitor. We investigated the early responses in Arabidopsis of calcium influx and oxidative burst induced by non-saturating concentrations of bacterial MAMPs, used singly and in combination: flagellin peptide (flg22), elongation factor peptide (elf18), peptidoglycan (PGN) and component muropeptides, lipo-oligosaccharide (LOS) and core oligosaccharides. This revealed that some MAMPs have additive (e.g. flg22 with elf18) and even synergistic (flg22 and LOS) effects, whereas others mutually interfere (flg22 with OGA). OGA suppression of flg22-induced defences was not a result of the interference with the binding of flg22 to its receptor flagellin-sensitive 2 (FLS2). MAMPs induce different calcium influx signatures, but these are concentration dependent and unlikely to explain the differential induction of defence genes [pathogenesis-related gene 1 (PR1), plant defensin gene 1.2 (PDF1.2) and phenylalanine ammonia lyase gene 1 (PAL1)] by flg22, elf18 and OGA. The peptide MAMPs are potent elicitors at subnanomolar levels, whereas PGN and LOS at high concentrations induce low and late host responses. This difference might be a result of the restricted access by plant cell walls of MAMPs to their putative cellular receptors. flg22 is restricted by ionic effects, yet rapidly permeates a cell wall matrix, whereas LOS, which forms supramolecular aggregates, is severely constrained, presumably by molecular sieving. Thus, MAMPs can interact with each other, whether directly or indirectly, and with the host wall matrix. These phenomena, which have not been considered in detail previously, are likely to influence the speed, magnitude, versatility and composition of plant defences.

Burkholderia Hep_Hag autotransporter (BuHA) proteins elicit a strong antibody response during experimental glanders but not human melioidosis

BACKGROUND: The bacterial biothreat agents Burkholderia mallei and Burkholderia pseudomallei are the cause of glanders and melioidosis, respectively. Genomic and epidemiological studies have shown that B. mallei is a recently emerged, host restricted clone of B. pseudomallei. RESULTS: Using bacteriophage-mediated immunoscreening we identified genes expressed in vivo during experimental equine glanders infection. A family of immunodominant antigens were identified that share protein domain architectures with hemagglutinins and invasins. These have been designated Burkholderia Hep_Hag autotransporter (BuHA) proteins. A total of 110/207 positive clones (53%) of a B. mallei expression library screened with sera from two infected horses belonged to this family. This contrasted with 6/189 positive clones (3%) of a B. pseudomallei expression library screened with serum from 21 patients with culture-proven melioidosis. CONCLUSION: Members of the BuHA proteins are found in other Gram-negative bacteria and have been shown to have important roles related to virulence. Compared with other bacterial species, the genomes of both B. mallei and B. pseudomallei contain a relative abundance of this family of proteins. The domain structures of these proteins suggest that they function as multimeric surface proteins that modulate interactions of the cell with the host and environment. Their effect on the cellular immune response to B. mallei and their potential as diagnostics for glanders requires further study.

Dendrimers: a new class of nanoscopic containers and delivery devices

Dendrimers and hyperbranched polymers are a relatively new class of materials with unique molecular architectures and dimensions in comparison to traditional linear polymers. This review details recent notable advances in the application of these new polymers in terms of the development of new polymeric delivery systems. Although comparatively young, the developing field of hyperbranched drug delivery devices is a rapidly maturing area and the key discoveries in drug-conjugate systems amongst others are highlighted. As a consequence of their ideal hyperbranched architectures, the utilisation of host-guest chemistries in dendrimers has been included within the scope of this review. (C) 2003 Elsevier Ltd. All rights reserved.

Segregated self-assembly and pillaring action of aliphatic dicarboxylic acids in the super structure of Cu-picolinate complexes

Three new supramolecular assemblies of co-crystallized metal complexes and aliphatic dicarboxylic acids, {[Cu(pic)(2)(H2O)(2)](H(2)mal)}(n) (1), {[Cu(pic)(2)(H2O)(2)](H(2)mal)(2)(H2O)(2)}(n) (2) and {[Cu(pic)(2)(MeOH)](H(2)succ)}(n) (3) {Hpic = 2-picolinic acid, H(2)mal = malonic acid and H(2)succ = succinic acid} have been synthesized and characterized by X-ray single-crystal structure determination. The crystal packings of the complexes reveal that supramolecular associations of the monomeric complex units lead to the formation of layers through hydrogen bonding. In all the complexes, the dicarboxylic acid units connect the 2-D layers to act as pillars. The interaction between water molecules and the dicarboxylic acid plays an important role in the overall supramolecular assembly. (C) 2008 Elsevier Ltd. All rights reserved.

Binding studies of a protonated dioxatetraazamacrocycle with carboxylate substrates

The tetraprotonated form of the dioxatetraazamacrocycle, 6,19-dioxa-3,9,16,22-tetraaza[22.2.2.2(11,14)]-triaconta-1(26),11,13,24, 27,29-hexaene, (H4L1)(4+), was used as the receptor for binding studies with carboxylate anionic substrates of different shapes, sizes, and charges [succinate (suc(2-)), cyclo- hexanetricarboxylate (cta(3-)), phthalate (ph(2-)), isophthalate (iph(2-)), terephthalate (tph(2-)), and benezenetricarboxylate (btc(3-))]. Association constants were determined by potentiometry in aqueous solution at 298.2 K and 0.10 M KCl and by H-1 NMR titration in D2O. The strongest association was found for the btc3- anion at 5-7 pH region. From both techniques it was possible to establish the binding preference trend of the receptor for the different substrates, and the H-1 NMR spectroscopy gave important suggestions about the type of interactions between partners and the location of the substrates in the supramolecular entities formed. The effective binding constants at pH 6 follow the order: btc(3-)>iph(2-)>cta(3-) =ph(2-)>tph(2-)>suc(2-). All the studies suggest that the anionic substrates bind to the receptor via N-H center dot center dot center dot O = C hydrogen bonds and electrostatic interactions, and the aromatic substrates can also establish pi-pi stacking interactions. The crystal structures of (H4L1)(4+) and its supramolecular assemblies with ph(2-) and tph(2-) were determined by X-ray diffraction. The last two structures showed that the association process in solid state occurs via multiple N-H center dot center dot center dot O = C hydrogen bonds with the anionic substrate located outside the macrocyclic cavity of the receptor. Molecular dynamics simulations carried out for the association of (H4L1)(4+) with tph(2-) and btC(3-) in water solution established at atomic level the existence of all interactions suggested by the experimental studies, which act cooperatively in the binding process. Furthermore, the binding free energies were estimated and the values are in agreement with the experimental ones, indicating that the binding of these two anionic substrates occurs into the receptor cavity. However, the tph(2-) has also propensity to leave the macrocyclic cavity and its molecular recognition can also happen at the top of the receptor. (C) 2008 Elsevier Ltd. All rights reserved.

Recognition of sequence-information in synthetic copolymer chains by a conformationally-constrained tweezer molecule

A novel type of tweezer molecule containing electron-rich 2-pyrenyloxy arms has been designed to exploit intramolecular hydrogen bonding in stabilising a preferred conformation for supramolecular complexation to complementary sequences in aromatic copolyimides. This tweezer-conformation is demonstrated by single-crystal X-ray analyses of the tweezer molecule itself and of its complex with an aromatic diimide model-compound. In terms of its ability to bind selectively to polyimide chains, the new tweezer molecule shows very high sensitivity to sequence effects. Thus, even low concentrations of tweezer relative to diimide units (<2.5 mol%) are sufficient to produce dramatic, sequence-related splittings of the pyromellitimide proton NMR resonances. These induced resonance-shifts arise from ring-current shielding of pyromellitimide protons by the pyrenyloxy arms of the tweezer-molecule, and the magnitude of such shielding is a function of the tweezer-binding constant for any particular monomer sequence. Recognition of both short-range and long-range sequences is observed, the latter arising from cumulative ring-current shielding of diimide protons by tweezer molecules binding at multiple adjacent sites on the copolymer chain.

Carboxylate anions binding and sensing by a novel tetraazamacrocycle containing ferrocene as receptor

A tetraazamacrocycle containing ferrocene moieties has been synthesized and characterized. The tetraprotonated form of this compound was evaluated as a receptor (R) for anion recognition of several substrates (S), Cl-, PF6-, HSO4-, H2PO4- and carboxylates, such as p-nitrobenzoate (p-nbz(-)), phthalate (ph(2-)), isophthalate (iph(2-)) and dipicolinate (dipic(2-)). H-1 NMR titrations in CD3OD indicated that this receptor is not suitable for recognizing HSO4- and H2PO4-, but weakly binds p-nbz(-), and strongly interacts with ph(2-), dipic(2-), and iph(2-) anions forming 1 : 2 assembled species. The largest beta(2) binding constant was determined for ph(2-), followed by dipic(2-) and finally iph(2-). The effect of the anionic substrates on the electron-transfer process of the ferrocene units of R was evaluated using cyclic voltammetry (CV) and square wave voltammetry (SWV) in methanol solution and 0.1 mol dm(-3) (CH3)(4)NCl as the supporting electrolyte. Titrations of the receptor were undertaken by addition of anion solutions in their tetrabutylammonium or tetramethylammonium forms. The protonated ligand exhibits a reversible voltammogram, which shifts cathodically in the presence of the substrates. The data revealed kinetic constraints in the formation of the receptor/substrate entity for dipic(2-), ph(2-) and iph(2-) anions, but not for p-nbz(-). In spite of the slow kinetics of assembled species formation with the ph(2-) substrate, this anion provides the largest redox-response when the supramolecular entity is formed, followed by dipic(2-), iph(2-) and finally p-nbz(-) anions. This trend is in agreement with the H-1 NMR results and the values of the binding constants. Single crystal X-ray structures of the receptor with PF6-, ph(2-), iph(2-) and p-nbz(-) were carried out and showed that supermolecules with a RS2 stoichiometry are formed with the first three anions, but RS4 with p-nbz(-). In all cases the binding occurs outside the macrocyclic cavity via N-H center dot center dot center dot O=C hydrogen bonds for carboxylate anions and N - H center dot center dot center dot F hydrogen bonds for the PF6- anion, which is in agreement with the solution results. The macrocyclic framework adopts different conformations in order to interact with each substrate having Fe center dot center dot center dot Fe intramolecular distances ranging from 10.125(14) to 12.783(15) angstrom.

Low molecular weight organogelators from self-assembling synthetic tripeptides with coded amino acids: morphological, structural, thermodynamic and spectroscopic investigations

A series of self-assembling terminally blocked tripeptides (containing coded amino acids) form gels in various aromatic solvents including benzene, toluene, xylenes at low concentrations. However these tripeptides do not form gels in aliphatic hydrocarbons like n-hexane, cyclohexane, n-decane etc. Morphological studies of the dried gel indicate the presence of an entangled fibrous network, which is responsible for gelation. Differential scanning calorimetric (DSC) studies of the gels produced by peptide 1 clearly demonstrates thermoreversible nature of the gel and tripeptide-solvent complex may be produced during gel formation. FT-IR and H-1 NMR studies of the gels demonstrate that an intermolecular hydrogen-bonding network is formed during gelation. Single crystal X-ray diffraction studies for peptides 1, 2 and 3 have been performed to investigate the molecular arrangement that might be responsible for forming the fibrous network of these self-assembling peptide gelators. It has been found that the morph responsible for gelation of peptides 1, 2 and 3 in benzene is somewhat different from that of its xerogel.

Conformational and self-assembly studies of helix forming hexapeptides containing two alpha-amino isobutyric acids

Single crystal X-ray diffraction studies reveal that three hexapeptides with general formula Boc-Ile-Aib-Xx-Ile-Aib-Yy-OMe, where Xx and Yy are Leu in peptide I, Len and Phe in peptide II, and Phe and Leu in peptide III, respectively, adopt equivalent conformations that can be described as mixed 3(10)/alpha-helice with two 4 -> 1 and two 5 -> 1 intramolecular N-H center dot center dot center dot O=C H-bonds. The peptides do not generate any helixterminating Schellman motif despite having Aib at the penultimate position from C-terminus. In the crystalline state, the helices are packed in head-to-tail fashion through intermolecular hydrogen bonds to create supramolecular helical structures. The CD Studies of the three hexapeptides in acetonitrile indicate that they are folded in well-developed 3(10)-helical structures. NMR studies of peptide I in CDCl3 also suggest the formation of a homogeneous 3 m-helical structure. The field emission scanning electron microscopic (FE-SEM) images of peptide 11 in the solid state reveal a non-twisted ribbon-like morphology, which is formed through lateral association of non-twisted filaments. (c) 2007 Elsevier Ltd. All rights reserved.

Stabilization of two smallest possible diastereomeric beta-hairpins in a water soluble tetrapeptide containing non-coded alpha-amino isobutyric acid (Aib) and m-amino benzoic acid

Single crystal X-ray diffraction study reveals that the water soluble tetrapeptide H2N-Ile-Aib-Leu-m-ABA-CO2H, containing non-coded Aib (alpha-amino isobutyric acid) and m-ABA (meta-amino benzoic acid), crystallizes with two smallest possible diastereomeric beta-hairpin molecules in the asymmetric unit. Although in both of the molecules the chiralities at Ile(1) and Leu(3) are S, a conformational reversal in the back bone chain is observed to produce the beta-hairpins with beta-turn conformations of type II and II'. Interestingly Aib which is known to adopt helical conformation, adopts unusual semi-extended conformation with phi: -49.5(5)degrees, psi: 135.2(5)degrees in type II and phi: 50.6(6)degrees. psi: -137.0(4)degrees in type II' for occupying the i + 1 position of the beta-turns. The two hairpin molecules are further interlocked through intermolecular hydrogen bonds and electrostatic interactions between CO2- and -+NH3 groups to form dimeric supramolecular beta-hairpin aggregate in the crystal state. The CD measurement and 2D NMR study of the peptide in aqueous medium support the existence of beta-hairpin structure in water. (C) 2009 Elsevier B.V. All rights reserved.