Spatial organization in two-species annihilation

The spatial structure of reactants in the two-species annihilation reaction A+B0 is described. In one dimension, we investigate the distribution of domain sizes and the distributions of nearest-neighbor distances between particles of the same and of opposite species. The latter two quantities are characterized by a new length scale which is intermediate to the domain size t^1/2 and the typical interparticle spacing t^1/4. A scaling argument suggests that the typical distance between particles of opposite species, or equivalently the gaps between domains, grows ast , with = 3/8 and 1/3, respectively, in spatial dimensiond=1 and 2. The average density profile of a single domain is spatially nonuniform, with the density decaying to zero linearly as the domain edge is approached. This behavior permits a determination of the distribution of nearest-neighbor distances of same-species reactants. The corresponding moments of this distribution exhibit multiscaling which involves geometric averages of different powers of the domain size and the interparticle spacing.     

Canonical conjugate momentum of discrete label operators in quantum mechanics I: formalism

We discuss the inadequacy of the standard definition of canonical conjugation for a quantum operator having adiscrete spectrum. A different definition is proposed, based on the analogy betweencontinuous anddiscrete translations (or rotations). This definition can be applied to special operators which we calllabel operators. The general form of the conjugate momentum of a label operator is found and the resulting canonical commutation rules are discussed. It is shown that the canonical commutator acts like ac number in itsdomain _I , but the domain does not coincide with the whole Hilbert space. The properties of the subspace _I are also discussed.     

Modeling of enzyme–substrate complexes for the metalloproteases MMP-3, ADAM-9 and ADAM-10

The matrix metalloproteases (MMPs) and the ADAMs (A Disintegrin And Metalloprotease domain) are proteolytic enzyme families containing a catalytic zinc ion, that are implicated in a variety of normal and pathological processes involving tissue remodeling and cancer. Synthetic MMP inhibitors have been designed for applications in pathological situations. However, a greater understanding of substrate binding and the catalytic mechanism is required so that more effective and selective inhibitors may be developed for both experimental and clinical purposes. By modeling a natural substrate spanning P4-P4' in complex with the catalytic domains, we aim to compare substrate-specificities between Stromelysin-1 (MMP-3), ADAM-9 and ADAM-10, with the aid of molecular dynamics simulations. Our results show that the substrate retains a favourable antiparallel beta-sheet conformation on the P-side in addition to the well-known orientation of the P'-region of the scissile bond, and that the primary substrate selectivity is dominated by the sidechains in the S1' pocket and the S2/S3 region. ADAM-9 has a hydrophobic residue as the central determinant in the S1' pocket, while ADAM-10 has an amphiphilic residue, which suggests a different primary specificity. The S2/S3 pocket is largely hydrophobic in all three enzymes. Inspired by our molecular dynamics calculations and supported by a large body of literature, we propose a novel, hypothetical, catalytic mechanism where the Zn-ion polarizes the oxygens from the catalytic glutamate to form a nucleophile, leading to a tetrahedral oxyanion anhydride transition state.     

Identifying the inhibition of TIR proteins involved in TLR signalling as an anti-inflammatory strategy

Toll/IL1 receptor (TIR) adaptor proteins continue to be an integral part of Toll-like receptors’ (TLR) signalling involved in inflammation. Signalling is likely to be initiated by these TIR adaptors when they are recruited to a TIR–TIR interface formed by TLR dimerization. Among these, myeloid differentiation factor-88 (MyD88), MyD88 adapter-like protein (Mal), TIR domain-containing adaptor protein inducing interferon-β (TRIF) and TRIF-related adaptor molecule (TRAM) play pivotal roles at many steps in the signalling events leading to inflammation. The presence of the conserved BB loop residues in the TIR domain of all these important adaptor proteins make them possible targets for inhibition by synthetic compounds. We have designed compounds based on an already known MyD88 TIR dimerization inhibitor, T6167923, which binds well not only to the original target but also to the TIR domains of Mal, TRIF and TRAM. The designed inhibitors are based on modifications of the bromophenyl-sulphonyl-thiophenyl-piperazine-carboxamide series of compounds. We have further suggested modifications in these high-affinity compounds for efficient absorption inside the body. Further, a pharmacophore model highlighting important structural interaction features has been developed. The screened compounds are better in binding to the TIR proteins then the parent compound and hence are good starting points for multi-TIR inhibition.     

Zero Problems of the Bergman Kernel Function on the First Type of Cartan-Hartogs Domain*

The authors give the condition that the Bergman kernel function on the first type of Cartan-Hartogs domain exists zeros. If the Bergman kernel function of this type of domain has zeros, the zero set is composed of several path-connected branches, and there exists a continuous curve to connect any two points in the non-zero set.     

Obtaining a family of high-affinity,high-specificity protein inhibitors of plasmin and plasma kallikrein

Summary Human lipoprotein-associated coagulation inhibitor (LACI) is a serum protein containing three Kunitz domains. We displayed the first domain (LACI-D1) on the III protein of phage M13 and made libraries of this domain. We iteratively varied 13 residues in the region corresponding to the BPTI-trypsin interface and selected for binding to human plasmin (PLA) and human plasma kallikrein (pKAL). For PLA, our first-round best binder, EPI-P211, had K_D=2 nM. Using information from the first selection, we made a PLA-biased library containing 500 000 proteins and selected from these a protein, EPI-P302, having a K_D for PLA of 87 pM. EPI-P302 inhibits pKAL with K_D=250 nM (2800-fold higher than for PLA) and K_D values for other proteases are higher yet. From the same initial LACI-D1 library, we selected an inhibitor of pKAL, EPI-K401, with a K_D for pKAL of 287 pM. We used information from this selection to construct a pKAL-biased library from which we selected EPI-K502, which has a K_D for pKAL of 40 pM. EPI-K502 inhibits PLA with K_D20 nM (500-fold higher than for pKAL); K_D values for other proteases are much higher. For both targets and for both selections, there are families of proteins having a few differences and a range of affinities for their targets. These proteins are candidate drugs and imaging agents for indications involving excess PLA or pKAL. Structure-activity relationships of PLA and pKAL binders will allow design of small molecules that are specific for these targets.Abbreviations APP-I-D1 Kunitz domain of amyloid precursor protein-I - BPTI bovine pancreatic trypsin inhibitor - F.VII_a Factor VII_a - F.XI_a Factor XI_a - FIR fraction of input recovered - hNE human neutrophil elastase - LACI-D1 lipoprotein-associated coagulation inhibitor, first Kunitz domain - pKAL human plasma kallikrein - PLA human plasmin - RT room temperature - THBN human thrombin - Vg variegated - w.t. wild-type - %RIA percent residual inhibitory activity - :: fusion (gene or protein)     

Faux-boolean algebras and classical models

A certain substructure of the lattice of projections on a Hilbert space is defined, and it is shown under what conditions such a structure can be said to have a classical model (in a sense made precise). The results have implications for the interpretation of quantum mechanics.     

Faux-boolean algebras,classical probability,and determinism

It is possible to define, for any quantum system, an algebra of definite-valued events—those events that are definitely occurrent or non-occurrent. It is shown that two different sets of constraints on the algebra of definite-valued events are each equivalent to the definition of that set as a certain pseudo-Boolean algebra.     

A renewal theorem in the finite-mean case

Let be a c.d.f. on such that is regularly varying with exponent . Then as , where is the renewal function associated with . Moreover similar estimates are given for distributions in the domain of attraction of the normal distribution and for the variance of The estimates improve earlier results of Teugels and Mohan.

     

下缘芳香取代结构对杯[4]芳烃Langmuir膜的影响

The Langmuir monolayer properties of lower rim aromatically substituted calix[4]arenes, 5,11,17,23-tetra-tert-butyl-25,27-bis（2-naphth-1＇-ylacetylaminoethoxy）-26,28-dihydroxylcalix[4]arene （BNAEC）, 5,11,17,23-tetra-tert- butyl-25,27-bis（2-benzoylamino ethoxy）-26,28-dihydroxylcalix[4]arene （BBAEC） and 5,11,17,23-tetra-tert-butyl- 25,27-bis（2-cinnamoylaminoethoxy）-26,28-dihydroxylcalix[4]arene （BCAEC）, have been studied. Film balance measurements and Brewster angle microscopy （BAM） observation demonstrate that all the compounds can form Langmuir monolayers with different molecular limiting areas. BNAEC or BBAEC monolayer is able to form condensed domains during compression, while BCAEC monolayer can never form condensed domain. BNAEC monolayer is more readily to form condensed domain than BBAEC monolayer. Moreover, BNAEC monolayer can form the total condensed phase during compression even when T=28℃, while BBAEC monolayer can not when T 〉 10 ℃. The results imply that different lower rim aromatic substitutions affect essentially the intermolecular interaction and molecular packing in the monolayer at air/water interface.