Discrete multistep

Yuan W, Serron SC, Haddican MM, Cawley GE, Eyer CS, Backes WL (1997) Ethylbenzene modulates the expression of different cytochrome P-450 isozymes by discrete multistep processes. Biochim Biophys Acta 1334 361-372... 

Interpretation of pubhshed data is often comphcated by the fact that rather complex catalytic materials are utilized, namely, poly disperse nonuniform metal particles, highly porous supports, etc., where various secondary effects may influence or even submerge PSEs. These include mass transport and discrete particle distribution effects in porous layers, as confirmed by Gloaguen, Antoine, and co-workers [Gloaguen et al., 1994, 1998 Antoine et al., 1998], and diffusion-readsorption effects, as shown by Jusys and co-workers for the MOR and by Chen and Kucemak for the ORR [Jusys et al., 2003 Chen and Kucemak, 2004a, b]. Novel approaches to the design of ordered nanoparticle arrays where nanoparticle size and interparticle distances can be varied independently are expected to shed hght on PSEs in complex multistep multielectron processes such as the MOR and the ORR. 

The multistep radical elimination may involve the generation of discrete intermediates, which for instance could be formed by a cyclization process7) such as 15- 16- 17e). Alternatively, there may be no intermediate involved in the elimination sequence, but the actual transition states 19, 22 are substantially lower in energy due to the anchimeric assistance of suitable functional groups9,10) (4). 

For simultaneous solution of (16), however, the equivalent set of DAEs (and the problem index) changes over the time domain as different constraints are active. Therefore, reformulation strategies cannot be applied since the active sets are unknown a priori. Instead, we need to determine a maximum index for (16) and apply a suitable discretization, if it exists. Moreover, BDF and other linear multistep methods are also not appropriate for (16), since they are not self-starting. Therefore, implicit Runge-Kutta (IRK) methods, including orthogonal collocation, need to be considered. 

Despite closely reasoned counter-arguments (DeMore and Benson, 1964), the commonly held view, due to Skell, is that singlet carbenes add to olefins in a stereospecific cia-manner, whereas attack by triplet carbenes leads to non-stereospecific addition (Skell and Woodworth, 1956). The rationale of this view is that a singlet carbene should react with the olefin to form a cyclopropane in a one-step, concerted process because in this way it could occur with conservation of spin (equation 23) the addition would thus be stereospecifically cis. On the other hand, a concerted addition of a triplet carbene would violate the rule of spin conservation in consequence, a multistep reaction, in which spin inversion of an intermediate 1,3-diradical constitutes a discrete process... 

Some simple relationships giving an estimate of the discretization error in the case of multistep formulae have been proposed. Very often, the difference between the values deduced from predictor and corrector equations is used as an error estimate. 

The macromolecular silyl chloride reacts with sodium in a two-electron-transfer reaction to form macromolecular silyl anion. The two-electron-trans-fer process consists of two (or three) discrete steps formation of radical anion, precipitation of sodium chloride and generation of the macromolecular silyl radical (whose presence was proved by trapping experiments), and the very rapid second electron transfer, that is, reduction to the macromolecular silyl anion. Some preliminary kinetic results indicate that the monomer is consumed with an internal first-order-reaction rate. This result supports the theory that a monomer participates in the rate-limiting step. Thus, the slowest step should be a nucleophilic displacement at a monomer by macromolecular silyl anion. This anion will react faster with the more electrophilic dichlorosilane than with a macromolecular silyl chloride. Therefore, polymerization would resemble a chain growth process with a slow initiation step and a rapid multistep propagation (the first and rate-limiting step is the reaction of an anion with degree of polymerization n[DP ] to form macromolecular silyl chloride [DP +J, and the chloride is reduced subsequently to the anion). 

In the simplest model of [PS7] metabolism, de novo conversion from the [psi to the PS/+ state involves two discrete steps initiation and propagation. During initiation, the first replicon (e.g., seed or nucleus) is formed. During propagation, newly synthesized protein is influenced by the replicon to convert to the [PS7+] state. Since the [PS7+] read-out is a colony-based assay (reversion to prototrophy), these steps are nearly impossible to separate. However, recent studies of [PS7+] interaction with other proteins, chemical agents, and prions have provided our first glimpses into the multistep process of prion induction (Fig. 1). 

We will start with classical solution-phase combinatorial chemistry with two examples, one of discretes and one of pools, describing the application of homogeneous phase library synthesis to multistep reaction sequences. The ex-... 

The library synthetic steps were carefully adjusted to avoid complex purification procedures, but even the simple washing/drying/extraction procedures made this library synthesis rather laborious and time requiring. The authors, in fact, synthesised only 600 discrete compounds of the 3078 which were planned in the library design. This either calls for simpler and effective work-up procedures for multistep solution libraries, which are very difficult to identify, or new automated techniques to overcome the purification/work-up bottleneck (see some of the following paragraphs). 

Nonequilibrium phenomena are distinguished by two principal features. First, they occur on a time scale much shorter than the typical equilibration time for statistical decay of a compound nucleus (t 10 s). Second, they produce multiparticle final states that are subsequently followed by statistical decay of the excited heavy product. In normal kinematics (Ap < At), the energetic light particles or clusters are forward-peaked and form a distinct exponential tail (area B in Fig. 3.41) on the Maxwellian spectra produced in later evaporation stages (area A in O Fig. 3.41). The preequilibrium component for the nucleon channels is as in by early stage emissions of the multistep compound model, as in by the FKK model for example. At the extreme of nonequilibrium emissions are the discrete peaks (labeled C), which correspond to direct reactions, or the first step in a multistep compound model. 

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