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 interaction between the nip1 mutation and genes affecting integration and excision in phage P2

Summary The excision of prophage P2 is controlled by two genes, int and cox. (The cox gene discussed in this report is defined by the cox class II mutants, defined by Six and Lindqvist, 1978). The combined activity of these two genes is rather inefficient, however, since only about 1% of the lysogens carrying an int ⁺ cox ⁺ prophage actually produce phage when derepressed. The efficiency of phage production (and presumably excision) can be increased 100-fold by an additional mutation called nip1 (Calendar et al., 1972), which is dominant and is located in or near the int gene.The nip1 mutation was mapped between c5, a mutation in the C gene, and an amber int mutation, int150. Phages carrying nip1 and either int150 or a cox mutation, cox3, were prepared by recombination. The nip1 mutation was found to increase excision only when it was located on the same chromosome as an active int ⁺ gene and only if cox ⁺ gene product was also available. The cox gene, known to be located between genes B and C (Lindahl and Sunshine, 1972), was further localized to a region between 77.2 to 78.1% from the conventional left end of the P2 chromosome by comparing the ability of phages with overlapping deletions to promote excision of the prophage in a P2 nip1 c5 cox3 lysogen.Other features of the integration-excision system in P2 are discussed.     

Using CFD simulations and statistical analysis to correlate oxygen mass transfer coefficient to both geometrical parameters and operating conditions in a stirred-tank bioreactor

Optimization of a bioreactor design can be an especially challenging process. For instance, testing different bioreactor vessel geometries and different impeller and sparger types, locations, and dimensions can lead to an exceedingly large number of configurations and necessary experiments. Computational fluid dynamics (CFD), therefore, has been widely used to model multiphase flow in stirred-tank bioreactors to minimize the number of optimization experiments. In this study, a multiphase CFD model with population balance equations are used to model gas–liquid mixing, as well as gas bubble distribution, in a 50 L single-use bioreactor vessel. The vessel is the larger chamber in an early prototype of a multichamber bioreactor for mammalian cell culture. The model results are validated with oxygen mass transfer coefficient (k_La) measurements within the prototype. The validated model is projected to predict the effect of using ring or pipe spargers of different sizes and the effect of varying the impeller diameter on k_La. The simulations show that ring spargers result in a superior k_La compared to pipe spargers, with an optimum sparger-to-impeller diameter ratio of 0.8. In addition, larger impellers are shown to improve k_La. A correlation of k_La is presented as a function of both the reactor geometry (i.e., sparger-to-impeller diameter ratio and impeller-to-vessel diameter ratio) and operating conditions (i.e., Reynolds number and gas flow rate). The resulting correlation can be used to predict k_La in a bioreactor and to optimize its design, geometry, and operating conditions.     

A plasmid-based vector system for the cloning and expression of Helicobacter pylori genes encoding outer membrane proteins

Helicobacter pylori produces a number of proteins associated with the outer membrane, including adhesins and the vacuolating cytotoxin. We observed that the functional expression of such proteins is deleterious to Escherichia coli, the host bacterium used for gene cloning. Therefore, a general method was developed for the functional expression of such genes on a shuttle vector in H. pylori, which has been termed SOMPES (Shuttle vector-based Outer Membrane Protein Expression System). The intact, active gene is reconstituted by recombination in H. pylori from partial gene sequences cloned on an E. coli-H. pylori shuttle vector. This system was established in an H. pylori strain carrying a precise, unmarked chromosomal deletion of the vacA gene, which was constructed by adapting the streptomycin sensitivity system to H. pylori. It is based on the expression of the H. pylori rpsL gene as a counterselectable marker in the genetic background of an rpsL mutant. The utility of this approach is demonstrated by the expression of a recombinant gene encoding vacuolating cytotoxin (vacA) and a recombinant gene encoding an adherence-associated outer membrane protein (alpA) in H. pylori. Received: 10 May 1999 / Accepted: 7 July 1999     

Empirical regression as a conditional expected value of a special distribution-mixture for a modelfree quantitative recording of stochastical relations

An “empirical” distribution function F?(x, y) is estimated from measured points (xi, yi), i =1(1)n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y). The density function F?(x, y) of F?(x, y) is a mixture of n two-dimensional normal densities. The first order moments of F?(x, y) are the sample means x and y, whilst the second order moments are only proportional to the sample variances and the sample covariance. This “empirical” distribution F?(x, y) is used for evaluation of an empirical regression curve where a free parameter has to be fixed by an optimality criterion. The procedure is demonstrated by an example from morphometrical research.     

An Alternative Approach for the Assessment of Bioequivalence Between Two Formulations of a Drug

The problem of the assessment of bioequivalence between a test formulation (T) and a reference formulation (R) of a drug using a two-way crossover experiment is considered. To claim bioequivalence between two formulations, it is required by the United States Food and Drug Administration (FDA) to demonstrate that the true ratio of means μT/μR of pharmacokinetic parameters of concern falls within some reasonable limits (e.g., (80%, 120%)) with certain assurance. A commonly used approach is to construct an approximate 90% confidence interval for μT/μR and compare it with (80%, 120%). In this paper, an exact approach according to the FDA's criteria is proposed. The proposed procedure is derived by constructing an exact confidence region (an ellipse) for (μR, μT) and comparing it with the region bounded by μT = 0.8 μR and μT = 1.2 μR. Bioequivalence is concluded if the ellipse is within the critical region.     

Identification and functional characterization of <Emphasis Type="Italic">Candida albicans CDC4</Emphasis>

Summary The CDC4 gene of Saccharomyces cerevisiae encodes an essential function that is required for G1-S and G2-M transitions during mitosis and at various stages during meiosis. We have isolated a functional homologue of CDC4 (CaCDC4) from the pathogenic yeast Candida albicans by complementing the S. cerevisiae cdc4-3 mutation with CaCDC4 expressed from its own promoter on a single-copy vector. The predicted product of CaCDC4 has 37% overall identity to the S. cerevisiae Cdc4 protein, although this identity is biased towards the C-terminal region of the two proteins which contains eight copies of the degenerate WD-40 motif, an element found in proteins that regulate diverse biological processes and an F-box domain proximal to the first iteration of the WD-40 motif. Both the F-box domain and WD-40 motifs appear necessary for the mitotic functions of Cdc4 in both yeasts. In contrast to its conserved role in mitosis, C. albicans CDC4 is unable to rescue the meiotic deficiency in a S. cerevisiae cdc4 homozygous diploid under restrictive conditions, even when expressed from an efficient S. cerevisiae promoter. In opposition to S. cerevisiae CDC4 being essential, C. albicans CDC4 appears to be nonessential and in its absence is critical for filamentous growth in C. albicans.     

Cloning and characterisation of the Neisseria gonorrhoeaearoB gene

The gene coding for the 3-dehydroquinate synthetase (aroB) of Neisseria gonorrhoeae has been cloned by functional complementation of an Escherichia coli aroB mutant. The aroB gene isolated from a gonococcal plasmid library encodes a 359 amino acid protein with a molecular mass of 38.6 kDa. Alignment of different prokaryotic and eukaryotic aroB gene products reveals an overall identity ranging from 33 to 55%. An open reading frame coding for an aroK homologue is located immediately upstream of aroB. Downstream of aroB a region of inverted repeats and a gene showing high homology to yafJ of E. coli has been identified. Disruption of aroB generates a gonococcal mutant that is unable to grow in the absence of aromatic compounds. Complementation of the mutant with the intact aroB gene intrans indicates that the gene is responsible for the auxotrophic phenotype. In infection assays with AroB-deficient gonococcal strains, binding, entry and short-term survival in epithelial cells is not affected. The aroB gene might be useful as a selectable marker and target for attenuation of a gonococcal live vaccine strain or as a biosafe laboratory strain. Received: 23 September 1997 / Accepted: 19 November 1997     

The Mean of the Inverse of a Punctured Normal Distribution and Its Application

The fundamental properties of a punctured normal distribution are studied. The results are applied to three issues concerning X/Y where X and Y are independent normal random variables with means μ_X and μ_Y respectively. First, estimation of μ_X/μ_Y as a surrogate for E(X/Y) is justified, then the reason for preference of a weighted average, over an arithmetic average, as an estimator of μ_X/μ_Y is given. Finally, an approximate confidence interval for μ_X/μ_Y is provided. A grain yield data set is used to illustrate the results. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Autonomy of the wingless mutation in Drosophila melanogaster

Summary T(Y;2) translocations were used to cytologically localise the wingless locus of Drosophila melanogaster. We found that an existing T(Y;2), which is an insertion of a segment of 2L into the Y chromosome, has wg ⁺ within this insert. This Y chromosome was used to generate an attached XY chromosome containing wg ⁺. The mutation claret-nondisjunctional (ca ^nd) was used to induce the loss of this XY chromosome and thus generate gynandromorphs with wg ¹/wg ¹ male tissue and wg ⁺/wg ¹/wg ¹ female tissue. Analysis of these gynanders demonstrated that a genotypically wingless mutant hemithorax is usually also phenotypically mutant in these half body mosaics; thus wg ¹ is discautonomous. This observation is of interest as it is known that wg is not cell autonomous.     

Phylogenetic reconstruction of Chirita and allies (Gesneriaceae) with taxonomic treatments

Abstract Chirita D. Don, a large genus in the subfamily Cyrtandroideae of Gesneriaceae, has been the subject of much debate whether it is a natural group or not. In addition, the highly heterogeneous Chirita has also been very problematic with regard to delimitation and subdivision. Here we used the nrDNA internal transcribed spacer and cpDNA trnL‐F for molecular phylogenetic analaysis, combined with morphological data. Our results suggest that Chirita is an artificial, polyphyletic genus. The most important character that defines Chirita, the dorso‐ventrally oblique and bilamellar stigma, has evolved convergently in different clades of diandrous Cyrtandroideae. Chirita sensu stricto only includes the species of Chirita sect. Chirita, whereas Chirita sect. Microchirita is an independent clade located at the basal node of the phylogenetic tree. Chirita sect. Liebigia is closely related to Didymocarpus with an entire stigma unlike other species of Chirita. The species of Chirita sect. Gibbosaccus, Chiritopsis, Primulina, and Wentsaiboea form a monophyletic group that is sister to a strongly supported clade comprising four monotypic genera Paralagarosolen, Calcareoboea, Petrocodon, and Tengia. We further analyzed the morphological evolution of Chirita and identified a series of morphological synapomorphies for the monophyletic groups revealed herein, and thereby provide a taxonomic treatment in this study.     

Effectors of metabolic depression in an estivating pulmonate snail (Helix aspersa): whole animal and in vitro tissue studies

 We have examined metabolic depression in the land snail (Helix aspersa) during estivation, and have developed a tissue model of metabolic depression using an in vitro mantle preparation. The metabolic rate of H. aspersa is depressed by 84% in vivo within 4 weeks of onset of estivation, and this metabolic depression is accompanied by a decrease in haemolymph PO₂ and pH, and an increase in haemolymph PCO₂. The in vitro mantle preparation has a stable O₂ consumption and energy charge, and an energy charge similar to that of mantle in vivo. The in vitro mantle is an O₂-conforming tissue, with VO₂ varying curvilinearly with PO₂. Consequently, we have developed a mathematical method of calculating tissue VO₂ at any PO₂. These calculations show that under appropriate incubation conditions of pH and PO₂, the mantle from estivating animals shows a stable in vitro metabolic depression of 48% compared to mantle from control snails. The extrinsic effects of PO₂ and pH account for 70% of the total in vitro metabolic depression of mantle tissue; intrinsic effectors contribute a further 30%. Accepted April 26, 1996     

Characterization of a regulatory gene, <Emphasis Type="Italic">aveR</Emphasis>, for the biosynthesis of avermectin in <Emphasis Type="Italic">Streptomyces avermitilis</Emphasis>

Avermectin is an important macrocyclic polyketide produced by Streptomyces avermitilis and widely used as an anthelmintic agent in the medical, veterinary, and agricultural fields. The avermectin biosynthetic gene cluster contains aveR, which belongs to the LAL-family of regulatory genes. In this study, aveR was inactivated by gene replacement in the chromosome of S. avermitilis, resulting in the complete loss of avermectin production. The aveR mutant was unable to convert an avermectin intermediate to any avermectin derivatives, and complementation by intact aveR and its proper upstream region restored avermectin production in the mutant, suggesting that AveR is a positive regulator controlling the expression of both polyketide biosynthetic genes and postpolyketide modification genes in avermectin biosynthesis. Despite the general concept that an increased amount of a positive pathway-specific regulator leads to higher production, a higher amount of aveR resulted in complete loss of avermectin, indicating that there is a maximum threshold concentration of aveR for the production of avermectin.     

An external substrate-free blue/white screening system in Escherichia coli

Since the lacZα-based blue/white screening system was introduced to molecular biology, several different visual reporter systems were developed and used for various purposes in Escherichia coli. A common limit to the existent visual reporter systems is that an extracellular chromogenic substrate has to be added for the visible pigment production. In this study, we developed a new blue/white screening system based on a non-ribosomal peptide synthetase encoded by idgS from Streptomyces and a phosphopantetheinyl transferase encoded by sfp from Bacillus. When IdgS is activated from an apo-form to a holo-form via a posttranslational modification catalyzed by Sfp, it can synthesize a blue pigment indigoidine using L-glutamine, the amino acid abundant in cells, as a substrate. The new blue/white screening system contains a recipient E. coli strain with an optimized idgS gene cassette and a cloning vector harboring an sfp gene with an in-frame insertion of a multiple cloning site close to its N-terminal. We demonstrated that the IdgS/Sfp-based blue/white screening system is a powerful alternative to the lacZα-based screening system, which does not require any external substrate addition.

     

p-SINE1-like intron of the CatA catalase homologs and phylogenetic relationships among AA-genome Oryza and related species

 Intron-2 of the Oryza sativa CatA catalase gene is similar in nucleotide sequence to p-SINE1, a retroposon, and seems to have been added to the ancestral genome of rice. To examine when the p-SINE1-like intron was inserted into CatA during the evolutionary divergence of Oryza species, and to elucidate the evolutionary relationships among Oryza species using the sequence of the intron as a marker, we performed polymerase chain reaction (PCR) analyses of 32 accessions of 17 Oryza species with various genome types. Agarose-gel electrophoresis of the PCR products revealed that all the Oryza species with an AA genome have the CatA homolog with the intron, whereas other Oryza species have the CatA homolog without the intron. These results indicate that intron-2 of CatA is a good marker for distinguishing species with an AA genome among Oryza species. Sequencing of the PCR products showed that all the introns are similar to p-SINE1, though with slight variations in length. We also performed PCR analyses using four accessions of three species in genera related to Oryza, and found that there is an intron in the CatA homolog of Leersia perrieri. On the other hand, the CatA homolog of Porteresia coarctata has no intron. Sequence data showed that the L. perrieri homolog has a p-SINE1-like intron similar to that in Oryza species with an AA genome. These results suggest that the p-SINE1-like intron was already present in the common ancestor of Oryza and L. perrieri and was then lost in the ancestors of P. coarctata and of the Oryza species other than those with an AA genome. The phylogenetic tree of Oryza species with an AA genome based on the nucleotide sequences of the introns leads us to propose that Oryza species with an AA genome evolved from an ancestor of Oryza longistaminata. Received: 29 August 1998 / Accepted: 2 November 1998