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An individual study of Ixodes persulcatus Schulze, 1930, established that the distribution of infected ticks differs from the normal distribution and it is most close to the Poisson distribution. There is a tendency to deviation from the uniform-random distribution associated with higher infected tick contact rates in some parts of the route.
Determining the degree of diversity in therapeutic sensitivity exhibited by a tumour population is of considerable clinical importance. In addition to being a contributor to radiation resistance, diversity is the basis for variation in sensitivity over the course of treatment. To study intrapopulation diversity in radiosensitivity following gamma-irradiation (2 Gy), distributions of the number of micronuclei/binucleate cell were obtained for human cervix carcinoma sandwich populations. Cell-to-cell diversity in radioresponse (micronucleus expression) was quantified using the overdispersion index ((variance/mean)--1). As measured by this index, the radioresponse diversity of sandwich cultures sharply increased after introduction of oxygen/nutrients to the cultures, mimicking tumour reperfusion. In addition, a strong correlation was found between this measure of diversity and the extent to which the fraction of cells without micronuclei exceeds that expected from a Poisson distribution. This correlation indicates that for a diverse population there can be a significant departure of the aggregate population sensitivity (determined, for instance, by log-survival in a clonogenic assay) from that inferable from simply averaging per-cell sensitivities (reflected, e.g. by mean number of chromosome aberrations/cell). Our experimental results suggest a model attributing diversity in a population to its being a mixture of distinct subpopulations, each biologically homogeneous with respect to micronucleus expression, and each contributing an individual Poisson-distributed micronucleus response. We demonstrate how such radiodiversity may be quantified and show that reoxygenation of a microenvironmentally heterogeneous population leads to an increase in its radiobiological diversity.
UNLABELLED: The aim of the study was to assess the share of positive correlation between speech disorders and tics, urination disorders and hyperkinetic behavior. The subjects were: E--experimental group with 700 children (459 boys and 241 girls) 6-14 years old, with speech pathology, C--a group of 510 (271 boys and 239 girls) healthy children from kindergartens and schools, aged 6-10. The transversal method along with clinical and statistical methods were used. RESULTS: correlation between speech discorders and ticks--this phenomenon was regarded as an infrequent event and checked by the Poisson Distribution A and B and the Chi-square test. The obtained results: X2 = 26. 83 P--0 showing that the difference is significant and that tics are more often found in the E than in the C group. Correlation between speech disorders and enuresis--it is necessary to determine features of the incidence of the phenomenon which also rarely occurs. These data were also checked by the Poisson distribution A and B, and Chi-square test. The obtained results: X2 = 59.91 P --> O indicating that in the E group the occurrence of enuresis was significantly higher than in the K group. The correlation between the speech function and hyperkinesis was checked by Chi-square test. Since X2 = 2.31 the difference was not statistically significant.
This paper demonstrates that when 'spot' specimens of sputum are cultured for tubercle bacilli on Löwenstein-Jensen medium, bacterial contamination occurs at random and follows a Poisson distribution. Over a period of 14 years, contamination rates with overnight 'collection' specimens (4.5 to 10.2%) were substantially higher than with spot specimens (1.3 to 4.0%), but the correlation between the two was very high (r = 0.98). In contrast to spot specimens, the incidence of contamination with collection specimens was significantly higher for females than for males, and significant variation was also found between patients of the same sex. In consequence, the Poisson distribution, which assumes a constant contamination rate for all patients, did not provide a satisfactory fit to the data on collection specimens. However, a negative binomial distribution, which incorporates individual variability in contamination rate, provided a good fit. The reasons for individual variability are discussed.
In a prospective drug-testing program, individuals whose job classifications have been defined as sensitive are placed in a selection pool. Periodically, individuals are chosen from this pool for drug testing. Random selection is a fair and impartial approach for this because each individual has an equal chance of being selected. Random selection also serves to reinforce the deterrent potential of a drug-testing program because individuals in the pool never know when or if they will be selected. This uncertainty discourages drug usage because of the risk involved in being selected and tested. A random selection process generates a Poisson distribution of probabilities that can be used to predict how many times an individual will be selected during a specific time interval. This information can be used to model the selection part of a drug-testing program to determine whether specific conditions of testing are met. For example, the probability of being selected a given number of times during the testing period can be minimized or maximized by varying the frequency of the sampling process. Consequently, the Poisson distribution and the mathematics governing it can be used to structure a drug-testing program to meet the needs of any given situation.
Long-term, HLA disparate, renal allograft recipients were assessed by a dose-dependent CML (cell-mediated lympholysis) assay for evidence of donor-specific CML hyporesponsiveness. The frequency of cytolytic T-cell (CTL) precursors capable of responding to donor alloantigen was also examined by a limiting-dilution assay and application of Poisson distribution statistics. Four recipients were found to have depressed CML responses against donor class I HLA antigens (mean 2-5% specific lysis), whereas significant responses against third party targets were noted (15-60% specific lysis). These data are consistent with an antigen-specific defect in the recipient CTL effector mechanism. To determine whether or not this may be due to a deletion of anti-donor alloreactive cells, a sensitive limiting-dilution assay was developed in conjunction with Poisson distribution statistics to obtain the frequency of both anti-donor and anti-third party CTLp present in recipient PBLs. A simultaneous reduction in the number of alloreactive clones and the presence of an active suppressor population were defined, suggesting that several mechanisms may operate concurrently in long-term renal allograft recipients with well-functioning grafts.
This study investigated the spatial distribution of Tetramicra brevifilum spores in the musculature of infected turbot Scophthalmus maximus, with the aim of identifying the most appropriate body locations for diagnostic assays. A PCR protocol optimized for the detection of T. brevifilum spores in turbot muscle is also described. In fish showing low- and moderate-intensity infection, the spatial distribution of spores was best fitted by a negative binomial distribution, indicating a clumped spatial pattern; the negative binomial coefficient k was lower for fish with low-intensity infection, indicating a more markedly clumped pattern in these fish. In fish with high-intensity infection, the spatial distribution of spores was best fitted by the Poisson distribution, indicating a random pattern. In both low- and moderate-intensity infection, spores were present at highest density in the musculature adjoining the dorsal fins. Samples for PCR were therefore obtained from this location. PCR amplification was of the small subunit ribosomal DNA (SSUrDNA), using a pair of species-specific primers that amplify the 1250 bp product. The PCR protocol developed showed better sensitivity than microscopical techniques (detection rate by microscopy 25%, versus 42% by PCR), suggesting that it may be useful for routine screening for Tetramicra brevifilum infection in cultured turbot.
OBJECTIVE: To develop a simple quantitative measure of dental health inequality. METHOD: Define equality based on statistical theory and construct a formula to compare actual and theoretical disease distributions. RESULT: A new index (DHII) is proposed, based on the ratio of the distribution of the actual disease to a (theoretical) Poisson distribution. An example using caries data is provided. CONCLUSION: Use of DHII will allow quantitative measurement of dental health inequality.
Chinese hamster cells (V79) were treated with ethylnitrosourea (ENU) and cis-diamminedichloroplatinum(II) (DDP) alone and in combination. Sister chromatid exchanges (SCEs) were quantified as measures of genotoxicity of the two agents. The combination experiment employed a factorial design in which cells were treated, in various concentration combinations, with both agents simultaneously. Response surface methodology, using a polynomial model based on a negative binomial distribution of SCE events, was employed for analysis of the interactions of the two genotoxic agents. The negative binomial distribution, a generalization of the Poisson distribution, is required since SCEs are discrete variables which, under the conditions of these experiments, have a distribution which exhibits extra-Poisson variability. The model of the ENU/DDP combinations indicated an increasingly less-than-additive effect resulting from increasing concentrations of each agent in the combination. The analysis of these experiments demonstrates the usefulness of a powerful statistical procedure for evaluating the biological effects resulting from exposure to multiple cytotoxic agents. The methodology can be used with many other types of endpoints and is not limited by the number of treatment agents.
Generalized linear models (GLM) are now widely used in analyzing data from clinical trials and in epidemiological studies. In Poisson regression, which fits in the framework of a GLM, the response variable is a count that follows the Poisson distribution. This article describes the basic methodology of Poisson regression analysis and its application to clinical research. Overdispersion, model diagnostics, and sample size issues are discussed. The methodology is illustrated on a data set from a clinical trial for the treatment of bladder cancer, using a new procedure (PROC GENMOD) in the statistical package SAS.
We have used random oligonucleotide mutagenesis (or saturation mutagenesis) to create a library of point mutations in the alpha 1 protein domain of a Major Histocompatibility Complex (MHC) molecule. This protein domain is critical for T cell and B cell recognition. We altered the MHC class I H-2DP gene sequence such that synthetic mutant alpha 1 exons (270 bp of coding sequence), which contain mutations identified by sequence analysis, can replace the wild type alpha 1 exon. The synthetic exons were constructed from twelve overlapping oligonucleotides which contained an average of 1.3 random point mutations per intact exon. DNA sequence analysis of mutant alpha 1 exons has shown a point mutant distribution that fits a Poisson distribution, and thus emphasizes the utility of this mutagenesis technique to "scan" a large protein sequence for important mutations. We report our use of saturation mutagenesis to scan an entire exon of the H-2DP gene, a cassette strategy to replace the wild type alpha 1 exon with individual mutant alpha 1 exons, and analysis of mutant molecules expressed on the surface of transfected mouse L cells.
The mitochondrial DNA (mtDNA) control region was sequenced in 37 sperm whales from a large part of the global range of the species. Nucleotide diversity was several-fold lower than that reported for control regions of abundant and outbred mammals, but similar to that for populations known to have experienced bottlenecks. Relative neck tests did not suggest that the low diversity is due to a lower substitution rate in sperm whale mtDNA. Rather, it is more likely that demographic factors have reduced diversity. The pattern of nucleotide substitutions was examined by cladistic methods, facilitated by the apparent monophyly of lineages from the Southern Hemisphere, as defined by a single base pair deletion. Substitutions were nonrandom in nature, confined to a few "hot spots," and parallel substitutions constituted a majority of the inferred changes. The substitution pattern fitted a negative binomial distribution better than a Poisson distribution, and the bias in number of substitutions among sites was considerably higher than previously reported for the mtDNA control region of any species. A novel method of estimating time since common ancestry was developed, which utilizes the transition/transversion ratio R and the number of substitutions inferred from a parsimony analysis. Using this method, we estimated the age of sperm whale mtDNA diversity to be about 6,000-25,000 years, and when the uncertainty of R was accounted for, a range of about 1,000-100,000 years was obtained.
The effect of mechanical agitation (blending) on the removal of F pili, type I pili, and flagella from Hfr (high-frequency recombinant) and resistance transfer factor (RTF) fi(+)Escherichia coli cells was studied by electron microscopy. The reduction in number and length of appendages was measured as a function of blendor speed under standard conditions of temperature, medium, cell density, and blendor configuration. F pili and flagella were removed within the same narrow range of blendor speeds. Type I pili were removed within a higher and broader range of speeds. The speed which reduced the average length of type I pili to 50% was 3.5 times the speed which reduced the average length of F pili to 50%. None of the speeds employed inhibited cell growth, viability, or the ability to produce cell appendages. The kinetics of reappearance of F pili and type I pili after removal by blending were also different. F pili grew out very rapidly, reaching 50% of their full length in 30 sec and their full length in 4 to 5 min. The number of attached F pili per cell also increased rapidly, reaching a constant value in 4 to 5 min. After 5 min, F pilus lengths were distributed around a modal value of about 1.2 mum, and the numbers of F pili per cell were distributed according to a Poisson distribution, with an average of 1.0 per cell. These reappearance kinetics, length distributions, and number distributions are consistent with a model of F-pilus outgrowth in which new F pili appear at random locations on the cell surface at an average rate of about once every 4 min, grow to their characteristic length in about 4 min, and then separate from the cell. F pili which had separated could absorb to the cells, leading to the presence of two classes of F pili on cells: those in the process of natural out-growth and those attached by absorption. Type I pili increased in length much more slowly than did F pili, although the fraction of cells having visible type I pili increased very rapidly after blending because of the large number of type I pili per cell. The fraction of flagellated cells increased even more slowly, reaching only 30% of the unblended fraction in 30 min. The application of blending spectra and reappearance kinetics to the identification of cell functions with surface structures is discussed.
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The frequency of chromosome aberrations per traversal of a nucleus by a charged particle at the low dose limit increases proportionally to the square of the linear energy transfer (LET), peaks at about 100 keV/micron and then decreases with further increase of LET. This has long been interpreted as an excessive energy deposition over the necessary energy required to produce a biologically effective event. Here, we present an alternative interpretation. Cell traversed by a charged particle has certain probability to receive lethal damage leading to direct death. Such events may increase with an increase of LET and the number of charged particles traversing the cell. Assuming that the lethal damage is distributed according to a Poisson distribution, the probability that a cell has no such damage is expressed by e-cLx, where c is a constant, L is LET, and x is the number of charged particles traversing the cell. From these assumptions, the frequency of chromosome aberration in surviving cells can be described by Y = alpha SD + beta S2D2 with the empirical relation Y = alpha D + beta D2 in the low LET region, where S = e-cL, alpha is a value proportional to LET, beta is a constant, and D is the absorbed dose. This model readily explains the empirically established relationship between LET and relative biological effectiveness (RBE). The model can also be applied to clonogenic survival. If cells can survive and they have neither unstable chromosome aberrations nor other lethal damage, the LET-RBE relationship for clonogenic survival forms a humped curve. The relationship between LET and inactivation cross-section becomes proportional to the square of LET in the low LET region when the frequency of a directly lethal events is sufficiently smaller than unity, and the inactivation cross-section saturates to the cell nucleus cross-sectional area with an increase in LET in the high LET region.
A quantitative analysis on homogeneity degree in distribution of proliferating parathyrocytes in the parathyroid glands under conditions of an acute stimulation of their function, produced by bilateral nephrectomy (12 rats, 50-70 h after the operation) and by hemiparathyroidectomy (12 rats, 2-3 days after the operation) have been performed. Six intact animals serve as the control. In order to reveal proliferating cells, 1 h before sacrifice 3H-thymidine (1 mc Ci/g) is injected intraperitoneally, and to some animals--colchicine (1 mg/kg) is injected 6 h before the sacrifice. By means of successive investigation of the glands serial sections along their whole area the amount of the microscope field of vision, having various content of proliferating cells are calculated; using the criterion chi 2, the correspondence of the empiric distributions obtained to the Poisson distribution are estimated. In the hyperfunctioning parathyroid glands the proliferating cells form foci of clusters and rarifaction. A similar clustering appears when a definite level of mitotic activity of the parathyrocytes is reached (1-1.2%), probably reflecting certain regional peculiarities of their functional state.
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