Bifurcation analysis of bacteria and bacteriophage coexistence in the presence of bacterial debris

The dynamics of bacteria and bacteriophage coexistence in the presence of bacterial debris, in a marine environment, was studied using a system of delay differential equations (DDE). The system exhibits a rich variety of behavior in terms of two control parameters values: the bacteriophage burst size β, and the lysing time delay τ. Limit cycles of various periodicity, quasiperiodicity, period doubling, chaotic bands and toroidal chaos were identified using basic tools of non-linear dynamics analysis: first return maps, Poincaré sections, Fourier spectrum, and largest Lyapunov exponents.     

Rapidity renormalization group

We introduce a systematic approach for the resummation of perturbative series which involves large logarithms not only due to large invariant mass ratios but large rapidities as well. A series of this form can appear in a variety of gauge theory observables. The formalism is utilized to calculate the jet broadening event shape in a systematic fashion to next-to-leading logarithmic order. An operator definition of the factorized cross section as well as a closed form of the next-to-leading-log cross section are presented. The result agrees with the data to within errors.     

Regioselective placement of alkanethiolate domains on tetrahedral and octahedral gold nanocrystals

Electrostatically stabilized monolayer shells of metal-oxide cluster anions (polyoxometalates, or POMs) on the surfaces of ca. 8 nm tetrahedral and octahedral gold nanocrystals regioselectively direct water-soluble alkanethiolate ligands to the corners and edges of the gold polyhedra.     

A Vanishing Theorem for Operators in Fock Space

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space, we show that rotation invariance implies the absence of terms which either create or annihilate only a single particle. We outline an application of this result in an operator theoretic renormalization analysis of Hamilton operators, which occur in non-relativistic qed.     

Reduction of O2 to superoxide anion (O2.-) in water by heteropolytungstate cluster-anions

Fundamental information concerning the mechanism of electron transfer from reduced heteropolytungstates (POM(red)) to O2, and the effect of donor-ion charge on reduction of O2 to superoxide anion (O2.-), is obtained using an isostructural series of 1e--reduced donors: alpha-X(n+)W12O40(9-n)-, X(n+) = Al3+, Si4+, P5+. For all three, a single rate expression is observed: -d[POM(red)]/dt = 2k12[POM(red)][O2], where k12 is for the rate-limiting electron transfer from POM(red) to O2. At pH 2 (175 mM ionic strength), k12 increases from 1.4 +/- 0.2 to 8.5 +/- 1 to 24 +/- 2 M-1s-1 as Xn+ is varied from P5+ (3red) to Si4+ (2red) to Al3+ (1red). Variable-pH data (for 1red) and solvent-kinetic isotope (KIE = kH/kD) data (all three ions) indicate that protonated superoxide (HO2.) is formed in two steps--electron transfer, followed by proton transfer (ET-PT mechanism--rather than via simultaneous proton-coupled electron transfer (PCET). Support for an outersphere mechanism is provided by agreement between experimental k12 values and those calculated using the Marcus cross relation. Further evidence is provided by the small variation in k12 observed when Xn+ is changed from P5+ to Si4+ to Al3+, and the driving force for formation of O2.- (aq), which increases as cluster-anion charge becomes more negative, increases by nearly +0.4 V (a decrease of >9 kcal mol-1 in DeltaG degrees ). The weak dependence of k12 on POM reduction potentials reflects the outersphere ET-PT mechanism: as the anions become more negatively charged, the "successor-complex" ion pairs are subject to larger anion-anion repulsions, in the order [(3(ox)3-)(O2.-)]4- < [(2(ox)4-)(O2.-)]5- < [(1(ox)5-)(O2.-)]6-. This reveals an inherent limitation to the use of heteropolytungstate charge and reduction potential to control rates of electron transfer to O2 under turnover conditions in catalysis.     

Parallel synthesis of diarylureas and their evaluation as inhibitors of insulin-like growth factor receptor

Diarylurea (DAU) compounds, particularly species composed of a heteroaryl ring system conjugated through a urea linkage to a substituted arene, were previously identified by the screening of a diverse chemical library to be active against the insulin growth factor receptor (IGF-1R). DAU compounds 4{a,b} were synthesized in parallel by the coupling of aryl amines 2{a} with aryl isocyanates 3{b}. Preparative RP-HPLC purification was found necessary to remove an impurity 5{b}, the symmetric urea resulting from the hydrolytic degradation of aryl isocyanates. Two libraries of DAU compounds were prepared to perform preliminary optimization of the two-ring systems for inhibitory activity against IGF-1R. In the first library, we explored a series of heteroaryl ring systems and found the 4-aminoquinaldine ring system to be optimal among those evaluated. The second library fixed the 4-aminoquinaldine ring system and we evaluated a series of substituted arenes conjugated to it. Overall, eight compounds based on the 4-aminoquinaldine heteroaryl system were found to have moderate activity against IGF-1R with IC(50) values better than 40 microM.     

2,4‐Disila‐1,3,5‐oxadiazin,Cyclodisilazan‐Carbonsäure‐silylamid und ‐silylester

The lithium salts of the Me₃Si‐ as well as Me₃Si‐ and Me₂SiF‐substituted Cyclotrisilazanes I and II react with tert‐butylacylchloride under ring contraction and formation of the cyclodisilazane‐silylester, Me₃SiN(SiMe₂–N)₂SiMe₂–O–CO–CMe₃ ( 1 ). The lithium salt of the fluorodi‐methylsilyl‐substituted cyclotrisilazan III forms with benzoylchloride primarily in the analogous reaction the carboxy‐silyl‐amide, Me₂SiF(N–SiMe₂)₂SiMe₂–NH–CO–C₆H₅⁺ ( 2 ), which can be converted with III and benzoylchloride into the cyclodisilazane‐silylester, Me₂SiF(NSiMe₂)₂SiMe₂–O–CO–C₆H₅, ( 3 ). A silylester substituted six‐membered disila‐oxadiazine ( 4 ) is the result of the reaction of the lithiated cyclotrisilazane, (Me₂SiNH)₂, (Me₂SiNLi) with tert‐butyl‐acylchloride. The reaction includes anionic ring contraction and can be rationilized by a process analogous to keto‐enol‐tautomerism. Dilithiated octamethyl‐cyclotetrasilazane, (Me₂SiNHMe₂SiNLi)₂, reacts with tert‐butyl‐acylchloride or benzoylchloride in a molar ratio 1:2 to yield symmetrically acylestersubstituted cyclodisilazanes, (RCO–O–SiMe₂–NSiMe₂)₂, R = C₆H₅ ( 5 ), CMe₃ ( 6 ). The reaction mechanisms are discussed and the crystal structures of 2 and 6 are reported.     

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