Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

A randomised interventional trial of ω-3-polyunsaturated fatty acids on endothelial function and disease activity in systemic lupus erythematosus

Objective: To determine the clinical effect of dietary supplementation with low-dose ?-3-polyunsaturated fatty acids on disease activity and endothelial function in patients with systemic lupus erythematosus. Methods: A 24-week randomised double-blind placebo-controlled parallel trial of the effect of 3 g of ?-3-polyunsaturated fatty acids on 60 patients with systemic lupus erythematosus was performed. Serial measurements of disease activity using the revised Systemic Lupus Activity Measure (SLAM-R) and British Isles Lupus Assessment Group index of disease activity for systemic lupus erythematosus (BILAG), endothelial function using flow-mediated dilation (FMD) of the brachial artery, oxidative stress using platelet 8-isoprostanes and analysis of platelet membrane fatty acids were taken at baseline, 12 and 24 weeks. Results: In the fish oil group there was a significant improvement at 24 weeks in SLAM-R (from 9.4 (SD 3.0) to 6.3 (2.5), p

Structure and function of sedoheptulose-7-phosphate isomerase, a critical enzyme for lipopolysaccharide biosynthesis and a target for antibiotic adjuvants

The barrier imposed by lipopolysaccharide (LPS) in the outer membrane of Gram-negative bacteria presents a significant challenge in treatment of these organisms with otherwise effective hydrophobic antibiotics. The absence of L-glycero-D-manno-heptose in the LPS molecule is associated with a dramatically increased bacterial susceptibility to hydrophobic antibiotics and thus enzymes in the ADP-heptose biosynthesis pathway are of significant interest. GmhA catalyzes the isomerization of D-sedoheptulose 7-phosphate into D-glycero-D-manno-heptose 7-phosphate, the first committed step in the formation of ADP-heptose. Here we report structures of GmhA from Escherichia coli and Pseudomonas aeruginosa in apo, substrate, and product-bound forms, which together suggest that GmhA adopts two distinct conformations during isomerization through reorganization of quaternary structure. Biochemical characterization of GmhA mutants, combined with in vivo analysis of LPS biosynthesis and novobiocin susceptibility, identifies key catalytic residues. We postulate GmhA acts through an enediol-intermediate isomerase mechanism.

Corpus callosum size and inter-hemispheric function in schizophrenia

We studied the relationship between corpus callosum area and both inter-hemispheric facilitation and interference in schizophrenics and controls. Mid-sagittal sections through the corpus callosum were measured using structural magnetic resonance imaging on 42 patients and 43 normal controls, along with symptom profiles. In a sub-sample, a modified version of the Stroop Test was also performed (27 patients and 29 controls) to assess inter-hemispheric facilitation and interference of colour naming. In the larger sample (total subjects, n=85), there were no significant differences between patients and controls in CC area but a trend towards smaller values in patients in all but the posterior segment. In the sub-sample, bilateral facilitation was greater, and interference, less in schizophrenics compared with controls. There was a positive correlation between facilitation and posterior CC area, parallelled by a negative correlation between interference and posterior CC area, in both patients and controls, which only reached statistical significance when both groups were combined. These findings suggest that the link, between CC size and neuropsychological processes involving inter-hemispheric transfer of information, is common to both schizophrenics and normal controls. There were significant negative correlations between anterior CC area and psychomotor poverty (avolition, anhedonia and affective flattening), and a suggestion that the negative correlation between age and CC size in controls was not present in patients.