A Note on Euler Approximations for Stochastic Differential Equations with Delay

An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure convergence is obtained under local Lipschitz and also under monotonicity conditions.     

Cyclodextrin knowledgebase a web-based service managing CD-ligand complexation data

Cyclodextrins are cyclic oligosaccharides that are able to form water-soluble inclusion complexes with small molecules. Because of their complexing ability, they are widely applied in food, pharmaceutical and chemical industries. In this paper we describe the development of a free web-service, Cyclodextrin KnowledgeBase: (http://www.cyclodextrin.net). The database contains four modules: the Publication, Interaction, Chirality and Analysis Modules. In the Publication Module, almost 50,000 publication details are collected that can be retrieved by text search. In the Interaction and Chirality Modules relevant literature data on cyclodextrin complexation and chiral recognition are collected that can be retrieved by both text and structural searches. Moreover, in the Analysis Module, the geometries of small molecule-cyclodextrin complexes can be predicted using molecular docking tools in order to explore the structures and interaction energies of the inclusion complexes. Complex geometry prediction is made possible by the built-in database of 95 cyclodextrin derivatives, where the 3D structures as well as the partial charges are calculated and stored for further utilization. The use of the database is demonstrated by several examples.     

Syntheses of vinca alkaloids and related compounds. 104. A concise synthesis of (-)-vincapusine

beta-Iodo-enamines with an eburnane skeleton (5a and 5c) were obtained with the aid of iodine from compounds 2a and 2c and were then transformed into hydroxyl lactams (6a and 6c) with CuSO4.5H2O in a mixture of DMF and water. Lactams (6a and 6c) were reduced selectively with BH3.SMe2 to result in the first synthesis of (-)-vincapusine (4a) as well as its natural 14-decarbomethoxy analogue (4c).     

Method for the synthesis of multi-epitopic Streptococcus pyogenes lipopeptide vaccines using native chemical ligation

The aim of this study was to investigate methods for the synthesis of highly pure, well-characterized analogues of the lipid core peptide (LCP) system. Difficulties synthesizing and purifying conventional LCP systems have led to the requirement for a technique to produce highly pure, LCP-based vaccines for potential use in human clinical trials. The current study describes methods for the attachment of lipophilic adjuvants onto multi-epitopic peptide vaccines. Described is the synthesis, using native chemical ligation, of a highly pure, tri-epitopic, group A streptococcal (GAS) lipopeptide vaccine candidate. Intranasal immunization of the described tri-epitopic GAS lipopeptide with the mucosal adjuvant cholera toxin B subunit induced high serum IgG antibody titers specific for each of the incorporated peptide epitopes.     

The Effects of Octanol on the Late Photointermediates of Rhodopsin

Membrane suspensions of unperturbed rhodopsin and rhodopsin perturbed with 2.5 niM octanol were photo-lyzed with 477 nm laser pulses at 20^OC and 35°C. Changes in absorbance were monitored at times ranging from 1 u-s to 80 ms after excitation. The data were analyzed using singular value decomposition, global exponential fitting and kinetic modeling. A recently proposed model involving the photointermediate Meta-I₃₈₀ (T. E. Thorgeirsson, J. W. Lewis, S. E. Wallace-Williams, and D. S. Kliger, Biochemistry 32,13861–13872, 1993) fits data for samples with and without octanol. Comparison of the microscopic rates shows this alcohol accelerates the formation of Meta-II via Meta-I₃₈₀. Activation and equilibrium thermodynamic parameters obtained from Ar-rhenius plots suggest that octanol reduces the entropy increase in forming both Meta-I_3g0 and Meta-II. It also lowers the enthalpy of Meta-1, _SI, relative to Lumi and of Meta-II relative to Meta-I₄₈₀. To help determine whether octanol affects the protein directly or indirectly through the lipid bilayer, similar experiments were conducted using rhodopsin solubilized in 0.13% dodecyl maltoside with and without octanol. Spectral shifts in the presence of octanol suggest that a direct protein interaction exists in addition to previously reported effects dependent on membrane free volume.     

Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering

Experiments on chaotically oscillating arrays of 64 nickel electrodes in sulfuric acid were carried out. External resistors in parallel and series are added to vary the extent of global coupling among the oscillators without changing the other properties of the system. The array is heterogeneous due to small variations in the properties of the electrodes and there is also a small amount of noise. The addition of global coupling transforms a system of independent elements to a state of complete synchronization. At intermediate coupling strengths stable clusters, or condensates of elements, form. All the elements in a cluster follow the same chaotic trajectory but each cluster has its own dynamics; the system is thus temporally chaotic but spatially ordered. Many cluster configurations occur under the same conditions and transitions among them can be produced. For values of the coupling parameter on either side of the stable cluster region a non-stationary behavior occurs in which clustered and synchronized states alternately form and break up. Some statistical properties of the cluster states are determined. (c) 2000 American Institute of Physics.     

Chaotic advection,diffusion, and reactions in open flows

We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics.     

On Stochastic Differential Equations with Locally Unbounded Drift

We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift.