Theoretical study of the importance of the spectator groups on the hydrolysis of phosphate triesters

The spontaneous hydrolysis of a series of five triaryl and two dialkyl aryl phosphate triesters, previously studied experimentally, is examined theoretically using two different hybrid density functional methods, B3LYP and M06; two basic sets, 6-31+G(d) and 6-311++G(d,p); and the Gaussian 09 program. The B3LYP/6-31+G(d) methodology combined excellent accuracy with minor computational cost. The calculations show excellent quantitative agreement with experiment, which is best in the presence of three discrete water molecules. The results support a two-step mechanism involving a pentacovalent addition intermediate, with a lifetime of tenths of a millisecond. The rate-determining formation of this intermediate involves general base catalysis, defined by concerted proton transfers in a six-membered cyclic activated complex (TS1), which involves two hydrogen-bonded water molecules supporting a well-developed H(2)O···P bond (mean % evolution 77.83 ± 0.97). The third water molecule is hydrogen-bonded to P═O and subsequently involved in product formation via TS2. The effects on reactivity of all the groups attached to phosphorus in TS1 are examined in detail: the two non-leaving groups in particular are found to play an important role, accounting for the substantial difference in reactivity between triaryl and dialkyl aryl phosphate triesters.     

The Uniform Schanuel Conjecture Over the Real Numbers

We prove that Schanuel's conjecture for the reals is equivalentto a uniform version of itself. 2000 Mathematics Subject Classification11J81, 11U09, 03C64.     

Architecture of intracellular networks in plant matrices

Pectin is an integral component of plant cell walls. It is believed to form an interconnected network structure independent of the cellulose–xyloglucan network structure. Pectin gels are often used as a model for the pectin network structure within the plant cell wall. The middle lamella pectin can be extracted with chelating agents and is believed to be associated through cooperative binding of calcium ions in the so-called egg-box junction zones. Although a great deal is known about the nature of the junction zones in pectin gels, less is known about the long-range structure within calcium-set gels. Two plausible alternative models for long-range order in these gels are a pseudo rubber-like structure and a fibrous network structure. Atomic force microscopy studies of calcium-induced gel precursors, and fragments released from gels, suggest that association leads to a branched fibrous structure within the gels. Enzymatic de-esterification of high methoxy pectin in the presence of calcium ions can induce gelation of the pectin. Thus pectin gel networks may provide a model for a self-assembled network structure within the middle lamella region of the plant cell wall.