Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

What determines the size frequency distribution of β-amyloid (Aβ) deposits in Alzheimer's disease patients?

The factors determining the size of individual β-amyloid (A,8) deposits and their size frequency distribution in tissue from Alzheimer's disease (AD) patients have not been established. In 23/25 cortical tissues from 10 AD patients, the frequency of Aβ deposits declined exponentially with increasing size. In a random sample of 400 Aβ deposits, 88% were closely associated with one or more neuronal cell bodies. The frequency distribution of (Aβ) deposits which were associated with 0,1,2,...,n neuronal cell bodies deviated significantly from a Poisson distribution, suggesting a degree of clustering of the neuronal cell bodies. In addition, the frequency of Aβ deposits declined exponentially as the number of associated neuronal cell bodies increased. Aβ deposit area was positively correlated with the frequency of associated neuronal cell bodies, the degree of correlation being greater for pyramidal cells than smaller neurons. These data suggested: (1) the number of closely adjacent neuronal cell bodies which simultaneously secrete Aβ was an important factor determining the size of an Aβ deposit and (2) the exponential decline in larger Aβ deposits reflects the low probability that larger numbers of adjacent neurons will secrete Aβ simultaneously to form a deposit. © 1995.

Highly selective Pd/titanate nanotube catalysts for the double-bond migration reaction

Pd(II) and Pd(0) catalysts supported onto titanate nanotubes (H2Ti3O7) were prepared by an ion-exchange technique. The catalysts are characterised by narrow size distribution of metal nanoparticles on the external surface of the nanotubes. Pd(II) catalysts show high selectivity toward double-bond migration reaction versus hydrogenation in linear olefins. The catalytic activity exhibits a volcano-type dependence on the metal loading, with the maximum activity observed at ca. 8 wt%. The Pd(II) was shown to be rapidly reduced to Pd(0) by appropriate choice of solvent. Prereduced Pd(0) catalysts were found to be less active toward double-bond migration and more selective toward hydrogenation. The DBM reaction was faster in protic solvents, such as methanol or ethanol. © 2006 Elsevier Inc. All rights reserved.

Laminar distribution of β-amyloid (Aβ) peptide deposits in the frontal lobe in familial and sporadic Alzheimer's disease

To determine whether genetic factors influence frontal lobe degeneration in Alzheimer's disease (AD), the laminar distributions of diffuse, primitive, and classic β-amyloid (Aβ) peptide deposits were compared in early-onset familial AD (EO-FAD) linked to mutations of the amyloid precursor protein (APP) or presenilin 1 (PSEN1) gene, late-onset familial AD (LO-FAD), and sporadic AD (SAD). The influence of apolipoprotein E (Apo E) genotype on laminar distribution was also studied. In the majority of FAD and SAD cases, maximum density of the diffuse and primitive Aβ deposits occurred in the upper cortical layers, whereas the distribution of the classic Aβ deposits was more variable, either occurring in the lower layers, or a double-peaked (bimodal) distribution was present, density peaks occurring in upper and lower layers. The cortical layer at which maximum density of Aβ deposits occurred and maximum density were similar in EO-FAD, LO-FAD and SAD. In addition, there were no significant differences in distributions in cases expressing Apo E ε4 alleles compared with cases expressing the ε2 or ε3 alleles. These results suggest that gene expression had relatively little effect on the laminar distribution of Aβ deposits in the frontal lobe of the AD cases studied. Hence, the pattern of frontal lobe degeneration in AD is similar regardless of whether it is associated with APP and PSEN1, mutation, allelic variation in Apo E, or with SAD.