The mean square error of a randomly discounted sequence of uncertain payments

Expressions are developed for the mean square deviation between a discounted sequence of uncertain payments and the estimated present value. These formulas incorporate random variation from four sources: (1) from the fact that expected values of individual payments are estimated, (2) from the fact that future discount factors are estimated, (3) random variation in the events that give rise to future payments, and (4) random variation in future discount rates. The results extend and encompass existing expressions based on the assumed constancy of one or more of the random vectors.     

Comparison of three sequential extraction procedures to describe metal fractionation in anaerobic granular sludges

In the last few decades, several sequential extraction procedures have been developed to quantify the chemical status of metals in the solid phase. In this study, three extraction techniques (modified [A. Tessier, P.G.C. Campbell, M. Bisson, Anal. Chem. 51 (1979) 844]; [R.C. Stover, L.E. Sommers, D.J. Silvera, J. Water Pollut. Con. F. 48 (1976) 2165]; and the Bureau Communautaire de Reference (BCR) [K.F. Mossop, C.M. Davidson, Anal. Chim. Acta 478 (2003) 111]) were applied to study the distribution of trace (Co, Ni, Zn and Cu) and major (Mn and Fe) elements in two different anaerobic granular sludges from full-scale methanogenic wastewater treatment plants. The Stover scheme displayed a higher number of fractions that induces a poor recovery compared to the other schemes. The sequential extraction scheme recommended by BCR and the modified Tessier scheme gave similar trends and are sufficiently repeatable and reproducible for application in fractionation studies. However, the BCR scheme seems to be of limited utilisation to study anaerobic matrixes because the extraction stage for its reducible fraction may release substantial amounts of trace elements bound to the organic/sulfides fraction, and consequently, the recovery of trace elements in the oxide fraction may be overestimated at the expense of the oxidisable fraction. As a final conclusion, the modified Tessier scheme seems to be the most suitable scheme to study the metal partitioning in anaerobic granular sludges.     

Characterization of a new tailoring domain in polyketide biogenesis: the amine transferase domain of MycA in the mycosubtilin gene cluster

We report the expression and characterization of a truncated form of MycA from the Mycosubtilin gene cluster from Bacillus subtilis. The MycA fragment contains a new amino transferase (AMT) tailoring domain, allowing the first detailed study of a PLP-dependent enzyme operating in cis within the PKS and NRPS biosynthetic paradigm. As the AMT domain acts on covalently bound beta-ketothioesters, and is therefore a single-turnover system, electrospray ionization-Fourier transform mass spectrometry (ESI-FTMS) was used to observe the amine-transfer reaction both for amine donor substrate specificity and to regiospecifically determine enzyme-bound intermediates. We confirm the function of the AMT domain, dissect the mechanistic steps of amine transfer, identify the preferred amine source, and localize the beta-ketothioester substrate during amine transfer.     

Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space

We have developed a new numerical technique, called Green's-function reaction dynamics (GFRD), that makes it possible to simulate biochemical networks at the particle level and in both time and space. In this scheme, a maximum time step is chosen such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equation can be solved analytically using Green's functions. The main idea of GFRD is to exploit the exact solution of the Smoluchoswki equation to set up an event-driven algorithm, which combines in one step the propagation of the particles in space with the reactions between them. The event-driven nature allows GFRD to make large jumps in time and space when the particles are far apart from each other. Here, we apply the technique to a simple model of gene expression. The simulations reveal that spatial fluctuations can be a major source of noise in biochemical networks. The calculations also show that GFRD is highly efficient. Under biologically relevant conditions, GFRD is up to five orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space. GFRD is not limited to biochemical networks. It can also be applied to a large number of other reaction-diffusion problems.     

Synthesis of carbosilane dendritic wedges and their use for the construction of dendritic receptors

A divergent route for the synthesis of carbosilane wedges that contain either a bromine or amine as focal point has been developed. These new building blocks enable the construction of various core-functionalized carbosilane dendrimers. As a typical example carbosilane dendrimers up to the third generation containing a N,N',N'-1,3,5-benzenetricarboxamide core (G1-G3) have been synthesized. This new class of molecules has been studied as host molecules and they have been found to bind protected amino acids as guest molecules via hydrogen bonding interactions. A decrease in the association constants was observed for the higher generation dendritic hosts, which is attributed to the increased steric hindrance around the core where the binding site is located. The binding properties of the dendritic host molecules can be tuned by modifying the binding motif at the core of the carbosilane dendrimers. A higher association constant for N-CBZ-protected glutamic acid 1-methyl ester (5) was observed when the third generation N,N',N'-1,3,5-tris(L-alaninyl)benzenetricarboxamide core-functionalized carbosilane dendrimer (G3') was used as the host molecule compared to G3. Different association constants for the formation of the diastereomeric G3'.L-5(K=295 M(-1)) and G3'.(D-5)(2) (K=236 M(-1)) host-guest complexes were observed, pointing to a small enantioselective recognition effect. The difference between the association constants for the formation of the G3'.(L-5)(2) and G3'.(D-5)(2) host-guest complexes was much more pronounced, K=37 M(-1)versus K=10 M(-1), respectively.     

Unusual coordination behavior of Cr3+ in microporous aluminophosphates

A CrAPO-5 molecular sieve has been investigated with X-ray absorption spectroscopy (EXAFS-XANES) as dehydrated material and after loading with water and ammonia to unravel the coordination geometries of Cr3+ in the framework of a microporous crystalline aluminophosphate, more particularly of the AFI-type. A comparison of the XANES data, a preedge analysis with crystal field multiplet calculations and EXAFS data, pointed toward the presence of framework Cr3+ which, on dehydration, takes on a distorted tetrahedral coordination state. Due to the 3d3 configuration of Cr3+, this unusual tetrahedral coordination environment strongly tends to transform into the more stable 6-fold coordination geometry by binding two extraframework water molecules during hydration. In the presence of ammonia, tetrahedral Cr3+ readily transforms into a 5-fold coordination geometry by binding one ammonia molecule. Therefore, depending on the environmental conditions, the Cr3+ ions can occur in a 4-, 5-, or 6-fold coordination. This observation underlines the flexibility of transition metal ions, such as Cr3+, to cope with unusual coordination geometries in inorganic hosts, making them interesting as potential active sites in heterogeneous catalysis.