Statistical prediction of the number of cells surviving infection by an autointerfering virus using the Poisson distribution

A method for estimating the number of defective interfering virus particles in a virus sample is presented. It can be used whenever the interference results in the survival of the “interfered” cell. The analysis assumes only that the infectious virus and defective interfering particles are distributed randomly and independently to cells. Thus the proportion of cells receiving X = x virus and Y = y particles is the product of the two independent Poisson distribution terms. The two dimensional matrix (X values × Y values) that can be constructed encompasses all of the possible (cellular) outcomes of viral infection. By comparing the actual number of surviving cells with the number predicted by various models of interference, it is possible to determine whether defective interfering particles are dominant (completely or partially) to infectious virus, and to estimate their number in the virus sample. This is accomplished by determining the experimental survival curve (% survival vs. input infectious virus/cell) and then constructing theoretical curves to fit the data.     

Chloroplast translocations in Lemna trisulca L. induced by continuous irradiation and by light pulses

The analytical model describing the steady state position of chloroplasts in dependence of fluence rate as well as the chloroplast response to single strong light pulses has been proposed. The model is based on the following assumptions: 1. Irradiation of the cell generates the state X in the cell membrane region, proportional to the local fluence rate. After switching on the light, the value of X increases exponentially with the time constant of about 3 min. The dark decay of X is also exponential with the same time constant. The level of X controls all kinds of chloroplast arrangements. 2. The state X generates two further states: Y ₁ and Y ₂, the first of them representing attraction forces for chloroplasts and the second representing repulsion forces. Empirical equations have been found for both Y states. The fluence rate response curve can be described with the use of functions Y ₁ and Y ₂. 3. The kinetic analysis requires the introduction of two additional functions Z in order to account for delays and time dispersion of the chloroplast movement in response to driving and resistance factors. The computer program for the proposed model was developed and the results of calculations were compared with experimental data (fluence rate response curve and pulse effects) with satisfactory agreement. Initially no attempt was made to ascribe any physical meaning to the postulated states. Some suggestions in this respect are mentioned in the discussion.     

Mitotic Recombination in the Heterochromatin of the Sex Chromosomes of DROSOPHILA MELANOGASTER

The frequency of spontaneous and X-ray-induced mitotic recombination involving the Y chromosome has been studied in individuals with a marked Y chromosome arm and different XY compound chromosomes. The genotypes used include X chromosomes with different amounts of X heterochromatin and either or both arms of the Y chromosome attached to either side of the centromere. Individuals with two Y chromosomes have also been studied. The results show that the bulk of mitotic recombination takes place between homologous regions.     

X-Y Exchange and the Coevolution of the X and Y Rdna Arrays in Drosophila melanogaster

The nucleolus organizers on the X and Y chromosomes of Drosophila melanogaster are the sites of 200-250 tandemly repeated genes for ribosomal RNA. As there is no meiotic crossing over in male Drosophila, the X and Y chromosomal rDNA arrays should be evolutionarily independent, and therefore divergent. The rRNAs produced by X and Y are, however, very similar, if not identical. Molecular, genetic and cytological analyses of a series of X chromosome rDNA deletions (bb alleles) showed that they arose by unequal exchange through the nucleolus organizers of the X and Y chromosomes. Three separate exchange events generated compound X·Y ^L chromosomes carrying mainly Y-specific rDNA. This led to the hypothesis that X-Y exchange is responsible for the coevolution of X and Y chromosomal rDNA. We have tested and confirmed several of the predictions of this hypothesis: First, X· Y^L chromosomes must be found in wild populations. We have found such a chromosome. Second, the X·Y^L chromosome must lose the Y^L arm, and/or be at a selective disadvantage to normal X⁺ chromosomes, to retain the normal morphology of the X chromosome. Six of seventeen sublines founded from homozygous X·Y^Lbb stocks have become fixed for chromosomes with spontaneous loss of part or all of the appended Y^L. Third, rDNA variants on the X chromosome are expected to be clustered within the X⁺ nucleolus organizer, recently donated (" Y") forms being proximal, and X-specific forms distal. We present evidence for clustering of rRNA genes containing Type 1 insertions. Consequently, X-Y exchange is probably responsible for the coevolution of X and Y rDNA arrays.     

Probability density functions for axial ratios of sectioning profiles of anisotropically arranged elliptical microvessels

The article theoretically regards probability density functions (PDFs) for axial ratio (X/Y) of sectioning profiles of elliptical microvessels (MVs) arranged with anisotropy in a biological tissue volume. A technique for the PDF_X/Y calculations in anisotropy of the elliptical MVs is described. The essence of this technique is introducing anisotropy in PDF(α,φ), i.e. the function of the joint distribution of the polar and planar angles α and φ, which define mutual orientation of the elliptical MVs and sectioning planes. With the aid of this technique, the anisotropy cases are studied with PDF(α,φ) given by pair combinations of the following distributions: (i) a uniform distribution of the angles α and/or φ, (ii) the angle α distribution with , and (iii) Gaussian distributions of the α or φ values. Specifically, PDF_X/Y curves are obtained for MVs with the true, or three-dimensional, axial ratio X₀/Y₀=2.0, and the anisotropy effects on the X/Y expected frequencies are analysed. Conclusions of this analysis, the PDF_X/Y calculation technique, and the PDF_X/Y curves obtained are useful for stereological reconstruction of anisotropically organised microcirculatory networks, with an ellipticity of their MVs being taken into consideration.     

An analysis of the influence of age and school-attendance status on the spread of variola minor.

Definitions are proposed for the independent and joint contributions that the chemical groups A and B make to the free energy of association of the ligand A?B with a receptor. The definitions are independent of the choice of the standard state and are consistent with the basic thermodynamic cycle relating the association of the ligands A?B, A?Y and X?B to the receptor Rappaport 1976. The basic idea is the use of the excess free energy of association of the ligand A?Y over the free energy of association of the reference ligand X?Y as the measure of the “independent” contribution of the group A to the binding. This definition allows the free energy of association of the ligand A?B to be written as the sum of the independent contributions of the groups A and B, their joint contribution, and an invariant free energy of association of the reference ligand with any receptor. With the appropriate definition of the receptor-reference ligand complex, water can be chosen as the reference ligand. Using ΔG(A?OH)?AG(HOH), ΔG(H?B?H)?ΔG(HOH) and ΔG(HO?C)?ΔG(HOH) as the definitions of the “independent” contributions of the chemical groups A, B and C to the binding of the ligand A?B?C, the joint contribution of the groups A and C to the binding is ΔG(A?B?C) ? ΔG(A?B?H) ? ΔG(H-B-C) + ΔG(H?B?H).     

Discovering General Multidimensional Associations

When two variables are related by a known function, the coefficient of determination (denoted R²) measures the proportion of the total variance in the observations explained by that function. For linear relationships, this is equal to the square of the correlation coefficient, ρ. When the parametric form of the relationship is unknown, however, it is unclear how to estimate the proportion of explained variance equitably—assigning similar values to equally noisy relationships. Here we demonstrate how to directly estimate a generalised R² when the form of the relationship is unknown, and we consider the performance of the Maximal Information Coefficient (MIC)—a recently proposed information theoretic measure of dependence. We show that our approach behaves equitably, has more power than MIC to detect association between variables, and converges faster with increasing sample size. Most importantly, our approach generalises to higher dimensions, estimating the strength of multivariate relationships (Y against A, B, …) as well as measuring association while controlling for covariates (Y against X controlling for C). An R package named matie (“Measuring Association and Testing Independence Efficiently”) is available (http://cran.r-project.org/web/packages/matie/).     

The precision of results from nonlinear regression analysis of data following a three-parameter one-exponential equation

Simulated experimental data were generated from error-free data following the equation y = A ? Be^?k1 where A, B, and k are constants and were analyzed by iterative nonlinear regression using one of two basic published computer programs. The effect of the simulated experimental error in y on the precision of the computed constants A, B, and k was evaluated. The errors were either independent of y (simple errors) or proportional to y (relative errors) and outliers were sometimes introduced. Other factors investigated were the number of data points per regression, the range of values of y, and the effect of weighting the data. The results show that the errors in the computed constants, and particularly the rate constant k, may be considerably magnified with respect to the errors in the experimental data. The quantitative relationships that are presented are useful aids in the design of biochemical experiments in which the above equation is applicable.     

Die Cytogenetik zweier norddeutscher Populationen von Nosopsyllus fasciatus Bosc (Aphaniptera)

Specimens of the populations Hamburg and Wilhelmshaven of the ratflea N. fasciatus exhibit variation of the chromosome number in the range of 2n=20–23 and 2n=20–27 respectively, resulting from individual differences in the number of supernumerary chromosomes beyond the basic chromosome complement of 2n=20. The supernumerary chromosomes are mostly euchromatic and partly or completely homologous to each other and to the 10. pair of the basic complement. The numerical variation in the population Wilhelmshaven is produced by recurrent mitotic non-disjunction of the supernumerary chromosomes in anaphase II of spermatogenesis. Constant mitotic non-disjunction and preferential segregation of the supernumerary chromosomes towards the pronucleus leads to their accumulation in the population.—A multiple sex-chromosome mechanism of the type X₁ X₂ Y₁ Y₂ (male): X₁ X₁ X₂ X₂ (female) has been demonstrated for the population Wilhelmshaven of N. fasciatus. The X₁ X₂ Y₁ Y₂-chain of four is restricted to the male meiosis, in oogenesis two sex bivalents (X₁ X₁ and X₂ X₂) are formed. — The cytogenetic data presented do not support the concept of a closer phylogenetic relationship between the Aphaniptera and Nematocera, but do not preclude the possibility of a kinship of Aphaniptera and Neomecoptera.     

Phenotypic expression time of mutagen-induced 6-thioguanine resistance in Chinese hamster ovary cells (CHO/HGPRT system).

Mutation induction at the hypoxanthine-guanine phosphoribosyl transferase (HGPRT) locus in Chinese hamster ovary (CHO) cells (referred to as the CHO/HGPRT system) can be quantitated by selection for the phenotype of resistance to 6-thioguanine (TG) under stringently defined conditions. The phenotypic expression time, that is, the time interval after mutagen treatment which is necessary befor all mutant cells are able to express the TG-resistant phenotype, has been found to be 7–9 days in this CHO/HGPRT system when the cells are subcultured every 48 h. Subculture in medium with or without hypoxanthine (HX) utilizing trypsin, ethylenediaminetetraacetic acid (EDTA), or ethylene glycol bis(β-aminoethyl ether)-N,N,N′,N′-tetraacetic acid (EGTA) for cell removal yields identical results. When subculture at intervals greater than 48 h is employed, a slight lengthening of the expression time is observed. An alternative method to regular subculture has also been achieved by maintaining the cells in a viable, non-dividing state in serum-free medium. This procedure yields a similar time course of phenotypic expression and thus shows that continued cell division is not essential to this expression process. In addition, this observation offers methodology which can significantly reduce the investment of time and money for mutation induction determinations in this mammalian cell gene mutation assay.     

The sufficient-component discrete-cause model and its extension to several risk factors

This paper is concerned with Koopman's (1981) discussion of using the ICDR as a measure of deviation from an additive model of no interaction. This measure has been shown to be zero or slightly negative when the assumptions of no interaction hold in the sufficient-component discrete-cause model. The discussion centers around a theoretical structure of sufficient causes for juvenile-onset diabetes where there is a component cause common to all sufficient causes and two binary factors or risks X and Y are measured (X: Coxsackie B₄ infection; Y: HLA4). In this paper, we have extended Koopman's discussion to the case where three or more binary factors X, Y, Z,… are measured. We have considered interaction between factors in every subset and have proved that the ICDR is again either zero or negative when the assumptions of no interaction hold in the sufficient-component cause model. It is supposed that these factors in conjunction will inevitably result in beta-cell destruction together with a set of immunologic conditions that permit dissemination of the enterovirus infection and permit an autoimmune response.     

The use of Chinese hamster ovary cells to quantify specific locus mutation and to determine mutagenicity of chemicals: A report of the GENE-TOX program

The GENE-TOX Group on Specific Gene Mutations in Chinese Hamster Ovary (CHO) Cells has evaluated the use of mutational systems in these cells for identification of mutagenic chemicals from 261 references in the file of the Environmental Mutagen Information Center, Oak Ridge National Laboratory by February, 1979; 68 references were found to be relevant to the stated task. After establishing that the end-point of mutational measurement occurs at a specific locus and the determinations are quantifiable and reproducible, data from 21 references were found to fulfill such requirements. Among them, 14 were concerned with chemically-induced mutations to resistance to a purine analogue, 6-thioguanine, which selects for variants deficient in the enzyme hypoxanthine—guanine phosphoribosyl transferase (HGPRT). This mutational system is referred to as the CHO/HGPRT assay. Studies with other genetic markers offer promise for the development of quantitative specific genemutational assays, but these studies have not advanced thoroughly enough to assess their value.Several lines of genetic, physiological and biochemical evidence support the premise that the CHO/HGPRT system fulfills the criteria for measurement of specific gene mutations using CHO-K₁-BH₄ subclone and other appropriate CHO subclones. Based largely on published information, this Work Group has suggested a protocol for testing of chemical agents with consideration of the following: cells, media, culture conditions and their quality control, treatment with test compounds with and without an exogenous metabolic activation system, estimation of cytoxicity (cloning efficiency), optimum expression and selection of the mutant phenotype, calculation of mutation frequency, positive and negative controls, vehicles or solvents, spontaneous mutation frequency, dosage selection and number of doses, and collection of raw data.For interpretation of the mutagenesis data, this Work Group recommends various ways of presenting data, numerous criteria for acceptability of data, the need to use appropriate statistical procedures for data evaluation, and a potential applicability of results to hazard evaluation.Evaluation of test performances with 18 chemicals revealed that the correlation between mutagenicity in CHO/HGPRT assay and animal mutagenicity and carcinogenicity is high. Since the number of chemicals tested was small and 17 of the 18 compounds were direct-acting agents, the utility of the system for identification of various classes of potential mutagens and carcinogens cannot be adequately assessed until more chemical classes, especially promutagens, are tested. However, the assay has a sound genetic and biochemical basis for quantifying specific locus mutation reproducibly. The fact that CHO cells are also useful for determination of chemically-induced chromosome aberration and sister-chromatid exchange adds an additional strength to the assay. Future research should address the possible improvement of procedures for phenotypic expression and application for testing gaseous and volatile liquids, as well as such problems as appropriate metabolic activation system(s) and effective statistical procedures common to perhaps all short-term cellular assays. Recent rapid development of mutagen test systems like the CHO/HGPRT assay calls for a need to update and evaluate the data base generated.     

On Mohan's Property of the Poisson Distribution

Two interesting results encountered in the literature concerning the Poisson and the negative binomial distributions are due to Moran (1952) and Patil & Seshadri (1964), respectively. Morans result provided a fundamental property of the Poisson distribution. Roughly speaking, he has shown that if Y, Z are independent, non-negative, integer-valued random variables with X = Y | Z then, under some mild restrictions, the conditional distribution of Y | X is binomial if and only if Y, Z are Poisson random variables. Motivated by Morans result Patil & Seshadri obtained a general characterization. A special case of this characterization suggests that, with conditions similar to those imposed by Moran, Y | X is negative hypergeometric if and only if Y, Z are negative binomials. In this paper we examine the results of Moran and Patil & Seshadri in the case where the conditional distribution of Y | X is truncated at an arbitrary point k – 1 (k = 1, 2, …). In fact we attempt to answer the question as to whether Morans property of the Poisson distribution, and subsequently Patil & Seshadris property of the negative binomial distribution, can be extended, in one form or another, to the case where Y | X is binomial truncated at k – 1 and negative hypergeometric truncated at k – 1 respectively.     

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)     

A New Approach to Equivalence Assessment in Standard Comparative Bioavailability Trials by Means of the Mann-Whitney Statistic

By a suitable transformation of the pairs of observations obtained in the successive periods of the trial, bioequivalence assessment in a standard comparative bioavailability study reduces to testing for equivalence of two continuous distributions from which unrelated samples are available. Let the two distribution functions be given by F(x) = P[X ≤ x], G(y) = P[Y ≤ y] with (X, Y) denoting an independent pair of real-valued random variables. An intuitively appealing way of putting the notion of equivalence of F and G into nonparametric terms can be based on the distance of the functional P[X > Y] from the value it takes if F and G coincide. This leads to the problem of testing the null hypothesis H_o P[X > Y] ≤ 1/2 - ε₁ or P[X > Y] ≥ 1/2 + ε₂ versus H₁ : 1/2 ? ε₁ < P[X > Y] < 1/2 + ∈₂, with sufficiently small ε₁, ε₂ ∈ (0, 1/2). The testing procedure we derive for (₀, H₁) and propose to term Mann-Whitney test for equivalence, consists of carrying out in terms of the U-statistics estimator of P[X > Y] the uniformly most powerful level a test for an interval hypothesis about the mean of a Gaussian distribution with fixed variance. The test is shown to be asymptotically distribution-free with respect to the significance level. In addition, results of an extensive simulation study are presented which suggest that the new test controls the level even with sample sizes as small as 10. For normally distributed data, the loss in power as against the optimal parametric procedure is found to be almost as small as in comparisons between the Mann-Whitney and the t-statistic in the conventional one or two-sided setting, provided the power of the parametric test does not fall short of 80%.     

The utility and performance of near-infra red spectroscopy in simultaneous monitoring of multiple components in a high cell density recombinant Escherichiacoli production process

Bioprocess optimisation is often limited by an inability to measure biomass, nutrient and by-product concentrations in a time frame which allows process adjustments. Near-infrared (near-IR) spectroscopy can potentially be used to measure each of these components within 2 minutes of sampling, using an unprocessed whole broth sample. In the present study the use of near-IR spectroscopy for at-line (rapid off-line) monitoring of biomass, glycerol, ammonium, and acetate in a recombinant Escherichia coli fed batch process was investigated. The following robust correlation models were developed for these analytes using multiple least squares linear regression (MLR): [Glycerol],gl^?1 =15.957 ? 2219.270^* A(λ₂₂₇₄)?1705.041^* A(λ₂₁₇₂); [Acetate],gl^?1=27.683 ?1757.258^* A(λ₂₂₅₄)+296.903^* A(λ₂₃₄₀)?21.325^* A (λ₆₂₀); [Ammonium],gl^?1=?1310.502?47912.960^* A (λ₂₁₄₈)?135149.300^* A(λ₁₇₈₂)?27636.200^* A (λ₈₃₀); and [Biomass],gl^?1=14.034?3.548^* A(λ₆₀₂/λ₁₁₃₄) ?4286.050^* A(λ₉₂₈). Using these models permitted rapid simultaneous analysis of all four analytes. This improved monitoring capability was used to develop a high cell density recombinant E. coli fed-batch process in which ammonium and acetate accumulation were minimised leading to higher cell densities. By manipulation of the C?:?N ratio in the complex feed, the toxic effects of ammonium accumulation upon the organism were minimised, thereby facilitating the application of a carbon limited feeding strategy. The effect of these C?:?N ratio medium changes, upon the near-IR measurement capability, was investigated. In this process, near-IR spectroscopy has been shown to be a powerful, accurate and precise method for simultaneously measuring several key process variables. Its accuracy, precision and utility for at-line measurement and control are evaluated, particularly in reference to processes where the initial medium composition may vary, leading to changes in the chemical matrix. The potential of near-infra red for online analysis and control is discussed.     

A probabilistic and algebraic treatment of regular inbreeding systems

Summary A probabilistic and algebraic treatment of regular inbreeding systems is presented. Regular inbreeding systems can be thought of as graphs which have certain natural homogeneity properties. Random walks X_n and Y_n are introduced on the nodes of the graphs; the event {X_n = Y_n} is a renewal event by the homogeneity property. We show that in such regular inbreeding systems the population becomes genetically uniform if and only if the event {X_n = Y_n} is recurrent, which happens if 1/ A_n diverges, where A_n is the number of ancestors n generations into the past. We give two counterexamples to show the converse is false in general, but we verify the converse in the case of the graphs of certain finitely presented semigroups.An expended version of this paper was submitted as a doctoral thesis to Purdue University. This thesis was directed by Professor Stanley Sawyer.     

Variations in the Number of the Y Chromosomal Rrna Genes in DROSOPHILA HYDEI

The number of rRNA cistrons is measured by filter saturation hybridization in different stocks of D. hydei, where the wild-type X chromosome has one nucleolus organizer (NO) and the wild-type Y has two separated NO's. (see PDF) females having no X chromosomal NO show an rDNA content exceeding that of a Y chromosome. An even greater increase in the rRNA cistron number is measured in two translocation stocks where the (see PDF) is combined with one half of a Y and, therefore, each stock contains only one of the two Y chromosomal NO's. But when the same Y fragments are brought together with a wild-type X chromosome they lose about one-half of their rRNA cistrons within one generation. Males with two complementary Y fragments but having no X chromosomal NO show a considerably higher rDNA content than the (see PDF) females, although both are equal in respect of their NO number. Consideration is given to related phenomena in Drosophila melanogaster.     

Genotypes of the vitamin D-binding protein gene in patients with chronic obstructive pulmonary disease and in the healthy population of the Republic Bashkortostan

Allele and genotype frequency distributions of the vitamin D-binding protein gene (DBP) were studied in patients with chronic obstructive pulmonary disease (COPD, N = 298) and healthy individuals (N = 237) from two ethnic groups (Tatars and Russians) resident in the Republic Bashkortostan. The DBP genotype frequency distribution significantly differed between Tatars and Russians (X ² = 8.854, df = 5, P = 0.04). The DBP allele frequency distribution was similar in healthy subjects of both ethnic groups, with allele frequency decreasing as GC*1S > GC*1F > GC*2. The most common DBP genotype was GC*1F/1S in Tatars (36.79%) and GC*1S/2 in Russians (34.62%). It was demonstrated that, in Tatars, the genotype GC*1F/1S is protective against COPD, its frequency being significantly lower in COPD patients than in healthy subjects (19.85% vs. 36.79%; X ² = 7.622, P = 0.0067, P _cor = 0.0335; OR = 0.42, 95%CI 0.42–0.95). On the other hand, the genotype GC*1F/2 was more common among COPD patients than among healthy individuals (19.08% vs. 8.49%; X ² = 4.52, P = 0.033, P _cor = 0.165; OR = 2.54, 95%CI 1.067–6.20). No differences in DBP genotype and allele frequency distributions was found between COPD patients and healthy individuals in the Russian population.     

The Clinical Significance and Risk Factors of Solitary Lymph Node Metastasis in Gastric Cancer

Aims

To assess the clinical significance and risk factors of solitary lymph node metastasis (SLM) in gastric carcinoma and establish a more accurate method to evaluate the possibility of lymph node metastasis (LM).

Methods

A total of 385 patients with gastric carcinoma who underwent D2 lymphadenectomy at the Cancer Center of Sun Yat-Sen University were included in this research. Then we used a group of data from Sun Yat-sen University Gastrointestinal Hospital (SYSUGIH) to validate the accuracy of our developed method. The χ² test, Kaplan–Meier analysis, log-rank test, COX model, and discriminate analysis were used to analyze the data with SPSS13.0.

Results

We found that the LM number and pathological T staging were independent prognostic risk factors. CEA grading, LN status by CT, and T staging by CT were independent risk factors for LM in gastric carcinoma. In addition, we developed the equation Y = -5.0 + X ₁ + 1.8X ₃ + 0.7X ₄ (X ₁ = CEA grading, X ₃ = LN status by CT, X ₄ = T staging by CT) to evaluate the situation of LM. The data from SYSUGIH shows this equation has a better accuracy compared with CT.

Conclusions

SLM is an independent risk factor in gastric cancer. And there was no survival difference between the skip metastasis group and the other SLM group (P = 0.659). It is inappropriate for the patient with SLM doing a standard D2 lymphadenectomy, due to the fact that LM rarely occurs in the splenic artery, splenic hilum. The risk factors for LM include CEA grading, LN status by CT, and T staging by CT. And we can use Y = -5.0 + X ₁ + 1.8X ₃ + 0.7X ₄ (X ₁, CEA grading, X ₃ = LN status by CT, X ₄ = T staging by CT, the critical value is 0.3) to estimate the possibility of LM, which has a better accuracy compared with CT.