Mathematical interpretation of dose-response curves

The dose-response of an individual organism can be described by a step functions if the organism survives when the dose is below a certain lethal level and dies when this level is exceeded. If, in a population of organism, the lethal dose for an individual has a unimodal distribution, the latter's properties will determine the shape of the population's response in the following manner. If the distribution is symmetric the dose-response curve has a symmetric sigmoid shape when plotted on linear coordinates. The location of the inflection point and the curve's slope around it are determined by the distribution's mode and variance. When the distribution is skewed, the dose-response curve has an asymmetric sigmoid shape which becomes reminiscent of an exponential decay when the distribution is strongly skewed to the right. The population's dose-response curve can be constructed by integration of the step changes over the distribution range. The step function representing the dose-response of an individual organism can be approximate by a Fermi function, and the distribution of an lethal doses can be represented by the Weibull distribution function. When the two functions are combined, the resulting dose-response of the populationS(X)), which is the fraction of survivors after exposure to a doseX, is given by:S(X)=∫ ₀ ¹ [1/{+exp{(X-X _c (φ))/a _i ]}]dω whereX _c (ω)={(1/b)[-ln(1-ω)]}^(1/n),n andb being the constants of the Weibull distribution anda _i an arbitrarily small number, i.e.a _i ≪[X−X _c (ϕ)], whose actual magnitude is of little significance. This model can be used to determine the underlying distributions of experimental dose-response relationship. It was applied to published survival data of microorganisms exposed to pulsed electric field, X-ray radiation and ozone to show that the different observed shapes of the dose-response curve, and shifts between them, can be expressed in terms of the correponding distribution parameters, namely the mode, variance and skewness.     

Genetic complementation of rhizobial nod mutants with Frankia DNA: artifact or reality?

Two divergent reports have been published on the genetic complementation of rhizobial nod mutants using Frankia DNA. In 1991 putative Frankia cosmid library clones were reported to restore normal nodulation properties to Rhizobium leguminosarum biovar viciaenodD::Tn5, but no supporting sequence data were published. In 1992 a second group reported a failure to find any evidence of functional complementation of various rhizobial nod mutants by Frankia DNA (nodA, nodB and nodC). Complementation tests of nine Nod⁻ R. leguminosarum bv. viciae or Sinorhizobium meliloti Tn5 mutants (nodA ⁻ , nodB ⁻ , nodC ⁻ , nodD ⁻ , nodF  ⁻ , nodL ⁻ , nodH ⁻ ) were thus performed using a Frankia gene library in pLAFR3 to clarify this situation. Rhizobial transconjugants obtained by tri-parental matings were screened for restoration of the nodulation phenotype on their host plants, Vicia sativa subsp. nigra or Medicago sativa. Nodulation was observed on plants inoculated with transconjugants of the R. leguminosarum bv. viciaenodC::Tn5 mutant. The Nod⁺ rhizobial transconjugants were isolated and analysed. The Nod⁺ phenotype of these transconjugants was found to be due to Tn5 excision/transposition. No functional complementation was found with any of the mutants used, suggesting that rhizobial complementation of nod mutants with Frankia DNA is unlikely to occur. Received: 17 April 1998 / Accepted: 22 July 1998     

Natural cell-mediated cytotoxicity in normal human peripheral blood lymphocytes and its in vitro boosting with BCG

Summary Natural cell-mediated cytotoxicity (NCMC) against K-562 human erythroleukemic cells was monitored in an overnight chromium release assay using normal human peripheral blood lymphocytes (PBL) as effector cells. Two hundred and ten normal individuals were tested from 3 to 24 times over a period of 3 years. The level of NCMC was shown to vary from 4% to 46% lysis at an effector-to-target cell ratio of 5/1; males had higher levels of activity than females (P<0.001). A group of individuals with low natural killer (NK) cell activity (below the 90% tolerance limit) was identified in replicate experiments and 60% of them were young women (ages 20–39). In vitro boosting of NK activity with Bacillus Calmette-Guérin (BCG) was also studied; overall, 56% of normal individuals responded positively to BCG. There was a significant (P<0.0001) correlation between the unstimulated level of NCMC and the in vitro boosting with BCG, as 63% of individuals with a normal level of NK activity could be boosted as against only 19% of persons with low NK activity. We have also established the in vivo relevance of this in vitro test by determining the degree of correlation between responses to in vitro boosting with BCG and a positive or negative reaction in a hypersensitivity skin test using 5 IU of PPD (purified protein derivative of BCG). Our results indicate that NCMC is an individual trait that varies little under physiological conditions, and that the response to BCG is a characteristic property of the effector lymphocyte, depending primarily on the unstimulated level of NCMC.     

Crystal structure of a recombinant form of the maltodextrin-binding protein carrying an inserted sequence of a B-cell epitope from the preS2 region of hepatitis B virus

We report the crystal structure of MalE-B133, a recombinant form of the maltodextrin-binding protein (MBP) of Escherichia coli carrying an inserted amino-acid sequence of a B-cell epitope from the preS2 region of the hepatitis B virus (HBV). The structure was determined by molecular replacement methods and refined to 2.7 Å resolution. MalE-B133 is an insertion/deletion mutant of MBP in which residues from positions 134 to 142, an external α helix in the wild-type structure, are replaced by a foreign peptide segment of 19 amino acids. The inserted residues correspond to the preS2 sequence from positions 132 to 145 and five flanking residues that arise from the creation of restriction sites. The conformation of the recombinant protein, excluding the inserted segment, closely resembles that of wild-type MBP in the closed maltose-bound form. MalE-B133 was shown by previous studies to display certain immunogenic and antigenic properties of the hepatitis B surface antigen (HBsAg), which contains the preS2 region. The crystal structure reveals the conformation of the first nine epitope residues (preS2 positions 132 to 140) exposed on the surface of the molecule. The remaining five epitope residues (preS2 positions 141 to 145) are not visible in electron density maps. The path of the polypeptide chain in the visible portion of the insert differs from that of the deleted segment in the structure of wild-type MBP, displaying a helical conformation at positions 134 to 140 (preS2 sequence numbering). A tripeptide (Asp-Pro-Arg) at the N terminus of the helix forms a stable structural motif that may be implicated in the cross-reactivity of anti-HBsAg antibodies with the hybrid protein. Proteins 27:1–8 © 1997 Wiley-Liss, Inc.     

Plant community composition and species richness in the High Arctic tundra: From the present to the future

Arctic plant communities are altered by climate changes. The magnitude of these alterations depends on whether species distributions are determined by macroclimatic conditions, by factors related to local topography, or by biotic interactions. Our current understanding of the relative importance of these conditions is limited due to the scarcity of studies, especially in the High Arctic. We investigated variations in vascular plant community composition and species richness based on 288 plots distributed on three sites along a coast‐inland gradient in Northeast Greenland using a stratified random design. We used an information theoretic approach to determine whether variations in species richness were best explained by macroclimate, by factors related to local topography (including soil water) or by plant‐plant interactions. Latent variable models were used to explain patterns in plant community composition. Species richness was mainly determined by variations in soil water content, which explained 35% of the variation, and to a minor degree by other variables related to topography. Species richness was not directly related to macroclimate. Latent variable models showed that 23.0% of the variation in community composition was explained by variables related to topography, while distance to the inland ice explained an additional 6.4 %. This indicates that some species are associated with environmental conditions found in only some parts of the coast–inland gradient. Inclusion of macroclimatic variation increased the model's explanatory power by 4.2%. Our results suggest that the main impact of climate changes in the High Arctic will be mediated by their influence on local soil water conditions. Increasing temperatures are likely to cause higher evaporation rates and alter the distribution of late‐melting snow patches. This will have little impact on landscape‐scale diversity if plants are able to redistribute locally to remain in areas with sufficient soil water.     

Fragment-based discovery of hepatitis C virus NS5b RNA polymerase inhibitors

Non-nucleoside inhibitors of HCV NS5b RNA polymerase were discovered by a fragment-based lead discovery approach, beginning with crystallographic fragment screening. The NS5b binding affinity and biochemical activity of fragment hits and inhibitors was determined by surface plasmon resonance (Biacore) and an enzyme inhibition assay, respectively. Crystallographic fragment screening hits with 1–10 mM binding affinity (K_D) were iteratively optimized to give leads with 200 nM biochemical activity and low μM cellular activity in a Replicon assay.