Difference in the homocysteine-lowering effect of folic acid in haemodialysis patients with and without occlusive vascular disease.

BACKGROUND: Hyperhomocysteinaemia has been identified as an independent cardiovascular risk factor and is found in more than 85% of patients on maintenance haemodialysis. Previous studies have shown that folic acid can lower circulating homocysteine in dialysis patients. We evaluated prospectively the effect of increasing the folic acid dosage from 1 to 6 mg per dialysis on plasma total homocysteine levels of haemodialysis patients with and without a history of occlusive vascular artery disease (OVD). METHODS: Thirty-nine stable patients on high-flux dialysis were studied. Their mean age was 63 +/-11 years and 17 (43%) had a history of OVD, either coronary and/or cerebral and/or peripheral occlusive disease. For several years prior to the study, the patients had received an oral post-dialysis multivitamin supplement including 1 mg of folic acid per dialysis. After baseline determinations, the folic acid dose was increased from 1 to 6 mg/dialysis for 3 months. RESULTS: After 3 months, plasma homocysteine had decreased significantly by approximately 23% from 31.1 +/- 12.7 to 24.5 +/- 9 micromol/l (P = 0.0005), while folic acid concentrations had increased from 6.5 +/- 2.5 to 14.4+/-2.5 microg/l (P < 0.0001). However, the decrease of homocysteine was quite different in patients with and in those without OVD. In patients with OVD, homocysteine decreased only marginally by approximately 2.5% (from 29.0 +/- 10.3 to 28.3 +/- 8.4 micromol/l, P = 0.74), whereas in patients without OVD there was a significant reduction of approximately 34% (from 32.7+/-14.4 to 21.6+/-8.6 micromol/l, P = 0.0008). Plasma homocysteine levels were reduced by > 15% in three patients (18%) in the group with OVD compared with 19 (86%) in the group without OVD (P = 0.001), and by > 30% in none of the patients (0%) in the former group compared with 13 (59%) in the latter (P = 0.001). CONCLUSIONS: These results indicate that the homocysteine-lowering effect of folic acid administration appears to be less effective in haemodialysis patients having occlusive vascular disease than in those without evidence of such disease.

The spike trains of inhibited pacemaker neurons seen through the magnifying glass of nonlinear analyses.

This communication describes the new information that may be obtained by applying nonlinear analytical techniques to neurobiological time-series. Specifically, we consider the sequence of interspike intervals Ti (the "timing") of trains recorded from synaptically inhibited crayfish pacemaker neurons. As reported earlier, different postsynaptic spike train forms (sets of timings with shared properties) are generated by varying the average rate and/or pattern (implying interval dispersions and sequences) of presynaptic spike trains. When the presynaptic train is Poisson (independent exponentially distributed intervals), the form is "Poisson-driven" (unperturbed and lengthened intervals succeed each other irregularly). When presynaptic trains are pacemaker (intervals practically equal), forms are either "p:q locked" (intervals repeat periodically), "intermittent" (mostly almost locked but disrupted irregularly), "phase walk throughs" (intermittencies with briefer regular portions), or "messy" (difficult to predict or describe succinctly). Messy trains are either "erratic" (some intervals natural and others lengthened irregularly) or "stammerings" (intervals are integral multiples of presynaptic intervals). The individual spike train forms were analysed using attractor reconstruction methods based on the lagged coordinates provided by successive intervals from the time-series Ti. Numerous models were evaluated in terms of their predictive performance by a trial-and-error procedure: the most successful model was taken as best reflecting the true nature of the system's attractor. Each form was characterized in terms of its dimensionality, nonlinearity and predictability. (1) The dimensionality of the underlying dynamical attractor was estimated by the minimum number of variables (coordinates Ti) required to model acceptably the system's dynamics, i.e. by the system's degrees of freedom. Each model tested was based on a different number of Ti; the smallest number whose predictions were judged successful provided the best integer approximation of the attractor's true dimension (not necessarily an integer). Dimensionalities from three to five provided acceptable fits. (2) The degree of nonlinearity was estimated by: (i) comparing the correlations between experimental results and data from linear and nonlinear models, and (ii) tuning model nonlinearity via a distance-weighting function and identifying the either local or global neighborhood size. Lockings were compatible with linear models and stammerings were marginal; nonlinear models were best for Poisson-driven, intermittent and erratic forms. (3) Finally, prediction accuracy was plotted against increasingly long sequences of intervals forecast: the accuracies for Poisson-driven, locked and stammering forms were invariant, revealing irregularities due to uncorrelated noise, but those of intermittent and messy erratic forms decayed rapidly, indicating an underlying deterministic process. The excellent reconstructions possible for messy erratic and for some intermittent forms are especially significant because of their relatively low dimensionality (around 4), high degree of nonlinearity and prediction decay with time. This is characteristic of chaotic systems, and provides evidence that nonlinear couplings between relatively few variables are the major source of the apparent complexity seen in these cases. This demonstration of different dimensions, degrees of nonlinearity and predictabilities provides rigorous support for the categorization of different synaptically driven discharge forms proposed earlier on the basis of more heuristic criteria. This has significant implications. (1) It demonstrates that heterogeneous postsynaptic forms can indeed be induced by manipulating a few presynaptic variables. (2) Each presynaptic timing induces a form with characteristic dimensionality, thus breaking up the preparation into subsystems such that the physical variables in each operate as one

Scaling regions for food web properties.

The robustness of eight common food web properties is examined with respect to web size. We show that the current controversy concerning the scale dependence or scale invariance of these properties can be resolved by accounting for scaling constraints introduced by webs of very small size. We demonstrate statistically that the most robust way to view these properties is not to lump webs of all sizes, but to divide them into two distinct categories. For the present data set, small webs containing 12 or fewer species exhibit scale dependence, and larger webs containing more than 12 species exhibit scale invariance.

Effects of taxonomic and trophic aggregation on food web properties.

Historically, ecologists have been more interested in organisms feeding at the tops of food chains than in organisms feeding at or near the bottom. The problem of taxonomic and trophic inconsistency within and among described food webs is central to criticisms of contemporary food web research. To study the effects of taxonomic and trophic aggregation on food web properties, 38 published food webs, each containing a large fraction of investigator-defined biological species, were systematically aggregated by taxonomy and trophic (functional) group similarity. During each step of taxonomic and trophic aggregation, eight food web properties (MIN, MAX, mean chain lengths; the fractions of basal, intermediate and top species; the ratio of all links by the total number of species, L/S; and rigid circuits) were calculated and their departures from the original, unaggregated version were recorded. We found only two␣properties showing wide systematic departure from initial values after both taxonomic and trophic group aggregation: the fraction of basal species and L/S. One reason for the relative `constancy' of the six other properties was due in part to large numbers of trophically equivalent species (species with identical sets of prey and predators) found in these and other published webs. In the 38 webs, the average number of trophically equivalent species was 45% and ranged from a low of 13% in aquatic webs to a high of 71% in certain terrestrial systems (i.e., carrion webs). Six of the eight properties (MIN, MAX and mean chain lengths, the fractions of top and basal species, and the L/S ratio) were found to be more sensitive to taxonomic than to trophic aggregation. The relatively smaller variations observed in trophically lumped versions suggest that food web properties more aptly reflect functional, rather than taxonomic, attributes of real food webs. These findings parallel earlier trophic-based results, and bolster the conclusion that uneven lumping of taxonomic and trophic groups in published food web reports do not modify markedly the scaling behaviour of most of their descriptive properties.