LOCALIZATION OF MACROMOLECULES IN ESCHERICHIA COLI : I. DNA and Proteins

If thin sections of Escherichia coli, labeled uniformly with tritium, are radioautographed calculations, based on the distribution of section sizes show that the number of H³ decays per section should be very close to a Poisson distribution. We might, therefore, expect that the distribution of radioautographic grain counts among random cross-sections should follow a Poisson distribution. It can then be inferred that a deviation from a Poisson indicates a high concentration of label in a preferred region. This region can then be identified by analysis of serial section and comparison with electron micrographs. Sections of cells labeled with leucine-H3 gave a Poisson distribution of grain counts, and it was concluded that proteins were distributed fairly uniformly throughout the cell. The situation was not changed if labeled cells were placed in chloramphenicol or if very short pulses of label were used. When Escherichia coli is grown in presence of chloramphenicol a major morphological change concerns the nuclear region: it becomes more regular in outline, nearly spherical, and occupies a smaller proportion of the cell length. The previously described association between DNA labeled with thymidine-H3 and the nuclear region was confirmed by showing that the distribution of the label in the cell followed exactly the morphological changes of the nuclear region. It was also shown that the concentration of DNA in the nuclear region was at least 45 times higher than that of the cytoplasm. Several morphological features of cells grown in chloramphenicol and examined in the electron microscope are discussed.     

Use of the 82Sr/82Rb Generator in Clinical PET Studies

The use of the ⁸²Sr/⁸²Rb generator in clinical positron emission tomography (PET) studies of myocardial perfusion has been described. An infusion pump is used to deliver the short-lived ⁸²Rb from the generator to the patient. Various characteristics of the generator and the infusion system are described. The ⁸²Rb yield was 69.8 ± 13.3% and the ⁸²Sr breakthrough was always less than the limit of 0.02 μCi/mCi ⁸²Rb. The yield of ⁸²Rb increased with the flow rate and the potency of the generator. Patients with coronary artery disease were studied for myocardial perfusion abnormalities by the ⁸²Rb PET technique and images of excellent diagnostic quality were obtained.     

Physiological imaging of the lung: single-photon-emission computed tomography (SPECT).

Emission tomography provides three-dimensional, quantitative images of the distribution of radiotracers used to mark physiological, metabolic, or pathological processes. Quantitative single photon emission computed tomography (SPECT) requires correction for the image-degrading effects due to photon attenuation and scatter. Phantom experiments have shown that radioactive concentrations can be assessed within some percentage of the true value when relevant corrections are applied. SPECT is widely spread, and radiotracers are available that are easy to use and comparably inexpensive. Compared with other methods, SPECT suffers from a lower spatial resolution, and the time required for image acquisition is longer than for some alternative methods. In contrast to some other methods, SPECT allows simultaneous imaging of more than one process, e.g., both regional blood flow and ventilation, for the whole lung. SPECT has been used to explore the influence of posture and clinical interventions on the spatial distribution of lung blood flow and ventilation. Lung blood flow is typically imaged using macroaggregates of albumin. Both radioactive gases and particulate aerosols labeled with radioactivity have been used for imaging of regional ventilation. However, all radiotracers are not equally suited for quantitative measurements; all have specific advantages and limitations. With SPECT, both blood flow and ventilation can be marked with radiotracers that remain fixed in the lung tissue, which allows tracer administration during conditions different from those at image registration. All SPECT methods have specific features that result from the used radiotracer, the manner in which it is administered, and how images are registered and analyzed.     

The lognormal distribution fits the decay profile of eukaryotic mRNA.

A general program was written which simulates radioactive labeling of RNA $\text{in vivo}$. The program was used to determine the effect that different distributions of half-lives would have on the composite decay curve observed in a pulse-chase experiment. Four biologically relevant points emerge: 1) The published, experimentally determined composite decay curves for eukaryotic mRNA are not compatible with a normal, uniform, or exponential distribution of decay times. 2) The experimental curves are compatible with a lognormal distribution of decay times as well as the two-component discrete distribution previously hypothesized. 3) If the lognormal or some similar distribution were correct, about half the mRNA species would decay faster than what is presently called the “fast component of decay”. This point is crucial to any argument about the fraction of poly (A) or other nuclear sequence that is transported to the cytoplasm. 4) If a $\text{particular}$ mRNA species is found to decay at a constant rate for 3 half-lives, that is not only consistent with 1 half-life for all the mRNA, but also consistent with 20 different half-lives which are normally or uniformly distributed.In addition to the decay of mRNA, the lognormal distribution is also compatible with data on the decay of poly(A)-containing nuclear RNA and total cellular protein.     

An urn model study of variability within a compartment

Formulas are derived for the mean and variance of the number of radioactive atoms present in a compartment (or urn). Initally,n ₁ radioactive atoms andb stable atoms are placed in the urn; and subsequently,r stable atoms are added and an equal number,r, of a random mixture of stable and radioactive atoms is removed per unit time. The expected number of radioactive atoms,E(t), present at timet is, as expected,n ₁ e^−λt where λ=(r/Δt)/(b+r+n ₁). The relative variance, σ²(t)/n ₁ ² , vanishes to zero forr=1, atoms per unit time and for a large number ofn ₁ radioactive atoms; but for a large number of bothr andn ₁ atoms the relative variance is ∼e ^−λt , equal to the fractional retention, fort>1/λ. Thus in studies where radionuclides are injected into animals and a single compartment represents the data, if a large variance is observed it might be due to the fact that large numbers of atoms are transferred out in unit time. When a small variance is observed, this is probably due to the fact that few atoms are transferred in smaller units of time (such that λ is the same in both cases). Research sponsored by the Energy Research and Development Administration under contract with Union Carbide Corporation.     

Interpretation of intramolecular stacking effect on the fluorescence intensity decay of 3-methylbenzimidazolyl(5′-5′)guanosine dinucleotides using a model of lifetime distribution

Time-resolved fluorescence of 3-methylbenzimidazole (m³B) was used to study stacking interaction between base moieties in di-, tri- and tetra-phosphate analogues of 3-methylbenzimidazolyl(5′-5′)guanosine (m³Bp _n G, n = 2, 3, 4), using 5′-triphosphate of 3-methylbenzimidazole riboside (m³BTP) as reference. Fluorescence intensity decays of all compounds cannot be satisfactory fitted with single-exponential function. Although an increase of a number of exponents led to better fits, interpretation of the individual exponential terms, i.e. pre-exponential amplitudes and fluorescence lifetimes, cannot be adequately characterized. We show that these fluorescence decays are best fitted by power-like function derived from physically justified distribution of the fluorescence lifetimes, and characterized by the mean value of the excited-state lifetime and relative variance of lifetime fluctuations around the mean value. The latter led to the parameter of heterogeneity and number of decay paths, which depend on the factors responsible for non-radiative decay of the excited state, including base–base stacking interaction. This was studied by means of changes of temperature and the number of phosphate groups in dinucleotides. It was shown that the strongest effect of stacking interactions, characterized by lowest values of both fluorescence mean decay time and relative variance, occurs in the case of m³Bp₃G containing the same number of phosphates as natural mRNA cap. The possible importance of these results for interpretation of the mechanism of function of the mRNA cap structure is discussed.     

Modeling Sage data with a truncated gamma-Poisson model

Background  

Serial Analysis of Gene Expressions (SAGE) produces gene expression measurements on a discrete scale, due to the finite number of molecules in the sample. This means that part of the variance in SAGE data should be understood as the sampling error in a binomial or Poisson distribution, whereas other variance sources, in particular biological variance, should be modeled using a continuous distribution function, i.e. a prior on the intensity of the Poisson distribution. One challenge is that such a model predicts a large number of genes with zero counts, which cannot be observed.     

A new bisphosphonate-containing <Superscript>99m</Superscript>Tc(I) tricarbonyl complex potentially useful as bone-seeking agent: synthesis and biological evaluation

Aiming to develop new bone-seeking radiotracers based on the organometallic core fac-[^99mTc(CO)₃]⁺ with improved radiochemical and biological properties, we have prepared new conjugates with phosphonate pendant groups. The conjugates comprise a chelating unit for metal coordination, which corresponds to a pyrazolyl-containing backbone (pz) with a N,N,N donor-atom set, and a pendant diethyl phosphonate (pz-MPOEt), phosphonic acid (pz-MPOH) or a bisphosphonic acid (pz-BPOH) group for bone targeting. Reactions of the conjugates with the precursor [^99mTc(H₂O)₃(CO)₃]⁺ yielded (mote than 95%) the single and well-defined radioactive species [^99mTc(CO)₃(κ³-pz-MPOEt)]⁺ (1a), [^99mTc(CO)₃(κ³-pz-MPOH]⁺ (2a) and [^99mTc(CO)₃(κ³-pz-BPOH)]⁺ (3a), which were characterized by reversed-phase high-performance liquid chromatography . The corresponding Re surrogates (1–3), characterized by the usual analytical techniques, including X-ray diffraction analysis in the case of 1, allowed for macroscopic identification of the radioactive conjugates. These radioactive complexes revealed high stability both in vitro (phosphate-buffered saline solution and human plasma) and in vivo, without any measurable decomposition. Biodistribution studies of the complexes in mice indicated a fast rate of blood clearance and high rate of total radioactivity excretion, occurring primarily through the renal–urinary pathway in the case of complex 3a. Despite presenting moderate bone uptake (3.04 ± 0.47% injected dose per gram of organ, 4 h after injection), the high stability presented by 3a and its adequate in vivo pharmacokinetics encourages the search for new ligands with the same chelating unit and different bisphosphonic acid pendant arms.     

Oviposition pattern of phytophagous insects: on the importance of host population heterogeneity

Frequency distributions of insect immatures per host are often fitted to contagious distributions, such as the negative binomial, to deduce oviposition pattern. However, different mechanisms can be involved for each theoretical distribution and additional biological information is needed to correctly interpret the fits. We chose the chestnut weevil Curculio elephas, a pest of the European chestnut Castanea sativa, as a model to illustrate the difficulties of inferring oviposition pattern from fits to theoretical distributions and from the variance/mean ratio. From field studies over 13–16 years, we show that 20 out of the 31 yearly distributions available fit a negative binomial and 25 a zero-inflated Poisson (ZIP). No distribution fits a Poisson distribution. The ZIP distribution assumes heterogeneity within the fruit population. There are two categories of host: the first comprises chestnuts unsuitable for weevil oviposition or in excess relative to the number of weevil females, and the second comprises suitable fruits in which oviposition behavior is random. Our results confirm this host heterogeneity. According to the ZIP distribution, the first category of hosts includes on average 74% of the chestnuts. A negative binomial distribution may be generated by either true or false contagion. We show that neither interference between weevil females, nor spatial variation in the infestation rate exist. Consequently, the observed distributions of immatures are not the result of false contagion. Nevertheless, we cannot totally exlude true contagion of immatures. In this paper we discuss the difficulty of testing true contagion in natural conditions. These results show that we cannot systematically conclude in favour of contagion when fitting a distribution such as the negative binomial or when a variance/mean ratio is higher than unity. Received: 22 September 1997 / Accepted: 15 December 1997     

Poisson,compound poisson and process approximations for testing statistical significance in sequence comparisons

DNA and protein sequence comparisons are performed by a number of computational algorithms. Most of these algorithms search for the alignment of two sequences that optimizes some alignment score. It is an important problem to assess the statistical significance of a given score. In this paper we use newly developed methods for Poisson approximation to derive estimates of the statistical significance ofk-word matches on a diagonal of a sequence comparison. We require at leastq of thek letters of the words to match where 0<q≤k. The distribution of the number of matches on a diagonal is approximated as well as the distribution of the order statistics of the sizes of clumps of matches on the diagonal. These methods provide an easily computed approximation of the distribution of the longest exact matching word between sequences. The methods are validated using comparisons of vertebrate andE. coli protein sequences. In addition, we compare two HLA class II transplantation antigens by this method and contrast the results with a dynamic programming approach. Several open problems are outlined in the last section. This work was supported by grants DMS 90-05833 from NSF and GM 36230 from NIH.     

Confidence limits of the probability of success in animal experiments and clinical studies: A Bayesian approach

PurposeTo determine from the number of trials, n, and the number of observed successes, k the most probable value, the variance and the confidence limits of the probability of success, p, in animal experiments and clinical studies subject to binomial statistics.MethodIn such experiments the probability of success is an unknown parameter. The Bayesian approach to the problem is advocated, based on constructed distribution of the probability of success.ResultsA simple Matlab code for the calculation of the confidence limits according to the proposed method is provided. The most probable, the mean, the variance and the confidence limits are calculated applying the usual definitions of these characteristics.ConclusionThe proposed method works for any number of trials – large and small and all possible values of the number of successes, including k = 0 and k = n, providing exact formulae for the calculation of the confidence limits in all cases.     

A probability distribution model of small -scale species richness in plant communities

We devised a probability distribution model that best expressed species richness per quadrat in grassland communities, and clarified the mechanism by which the mean richness per quadrat was always larger than the variance among quadrats. Our model will aid in the understanding of community structures, and allow comparisons among different communities. The model was constructed based on relatively simple theoretical assumptions about the mechanisms in play in target communities. We assumed in the model that the number of species occurring in an actual quadrat, j, is the sum of “the fundamental number of species”, k (constant), and “a fluctuating number of species”, i (a Poisson variate with the mean of μ); that is, j = k + i, where i, j and k are non-negative integers. The probability that j species occur in a quadrat is given by a Poisson-like distribution (extended Poisson), with two parameters k and μ. The mean species richness in the probability distribution is expressed by λ (= k + μ), and the variance is λ − k. The proposed model afforded a good fit for the observed frequency distribution of species richness per quadrat. If even one species is common among many quadrats, the mean number of species per quadrat is greater than the variance. The greater the number of common species among quadrats is, the larger is the value of k, and then the more pronounced is the difference between the mean and the variance (although the variance does not change). We fitted the model to 55 datasets collected by ourselves from grasslands in various locations (Tibet, Inner Mongolia, Slovakia, or Japan), with varying quadrat size (0.25, 0.0625, or 0.01 m²), and under differing management status (various stocking densities).     

Further evidence that ouabain-resistant variants induced by chemical carcinogens in transformable C3H/10T1/2 Cl 8 mouse fibroblasts are mutants

Ouabain-resistant (Oua^r) variants were induced in C3H/10T1/2 Cl 8 cells by the chemical carcinogens, N-methyl-N′-nitro-N-nitrosoguanidine (MNNG), N-acetoxy-N-2-acetylaminofluorene (N-AcO-AAF), and benzo[a]pyrene (BaP). The use of the Poisson calculation to determine Oua^r variant frequencies gave more linear dose-response curves than when variant frequencies were calculated from the observed number of Oua^r colonies. Increasing the Oua concentration from 3 to 6 mM decreased the frequency of Oua^r variants. When cloned Oua^r variants were mixed with wild-type cells, there was no metabolic cooperation and no loss of mutants when mock expression-time curves were determined. Oua^r variants remained Oua^r after prolonged cultivation in the absence of Oua. ⁸⁶Rubidium (⁸⁶Rb) uptake was at least 10-fold more resistant to inhibition by Oua in Oua^r variants than in wild-type cells. In one Oua^r clone, one-third of the ⁸⁶Rb uptake was not inhibited by Oua concentrations as high as 10 mM, indicating that C3H/10T1/2 Cl 8 cells might be triploid at the Oua^r locus. The relationship between the inhibition of ⁸⁶Rb uptake and the cytotoxicity caused by the same concentration of Oua was the same for 2 Oua^r clones and wild-type C3H/10T1/2 Cl 8 cells. Therefore, the Oua^r variants detected by this assay are most likely true mutants possessing an altered Na⁺K⁺ transport system, the Na⁺K⁺Mg²⁺-activated adenosine triphosphate (ATPase), that is more resistant to Oua inhibition than the ATPase in wild-type cells.     

No Significant Contribution of Arbuscular Mycorrhizal Fungi to Transfer of Radiocesium from Soil to Plants

The diffuse pollution by fission and activation products following nuclear accidents and weapons testing is of major public concern. Among the nuclides that pose a serious risk if they enter the human food chain are the cesium isotopes ¹³⁷Cs and ¹³⁴Cs (with half-lives of 30 and 2 years, respectively). The biogeochemical cycling of these isotopes in forest ecosystems is strongly affected by their preferential absorption in a range of ectomycorrhiza-forming basidiomycetes. An even more widely distributed group of symbiotic fungi are the arbuscular mycorrhizal fungi, which colonize most herbaceous plants, including many agricultural crops. These fungi are known to be more efficient than ectomycorrhizas in transporting mineral elements from soil to plants. Their role in the biogeochemical cycling of Cs is poorly known, in spite of the consequences that fungal Cs transport may have for transfer of Cs into the human food chain. This report presents the first data on transport of Cs by these fungi by use of radiotracers and compartmented growth systems where uptake by roots and mycorrhizal hyphae is distinguished. Independent experiments in three laboratories that used different combinations of fungi and host plants all demonstrated that these fungi do not contribute significantly to plant uptake of Cs. The implications of these findings for the bioavailability of radiocesium in different terrestrial ecosystems are discussed.     

Counting statistics of 1/f fluctuations in neuronal spike trains

The mesencephalic reticular formation (MRF) neurons are regarded as contributing to the activation of the celebral cortex. In this paper, the statistical features of single neuronal activities in MRF of cat during dream sleep are investigated; the neuronal spike train exhibits 1/f fluctuations. Counting statistics is applied to the neuronal spike train giving rise to a variance/mean curve which follows at -law. For an interpretation of these findings, the clustering Poisson process is applied which not only gives rise to at -law but also suggests a generation mechanism. The MRF neuronal activities are closely fitted by the clustering Poisson process and the underlying statistical parameters can be estimated. These findings strongly suggest that neuronal activities can be interpreted as superposition of randomly occuring clusters ( = bursts of spikes).     

Biophysical analysis of the dose-dependent overdispersion and the restricted linear energy transfer dependence expressed in dicentric chromosome data from alpha-irradiated human lymphocytes

Experimental data for the induction of dicentric chromosomes in phytohemagglutinin (PHA)-stimulated human T lymphocytes by ²⁴¹Am alpha-particles obtained by Schmid et al. have been analyzed in the light of biophysical theory. As usual in experiments with alpha-particles, the relative variance of the intercellular distribution of the number of aberrations per cell exceeds unity, and the multiplicity of the aberrations per particle traversal through the cell is understood as the basic effect causing this overdispersion. However, the clearly expressed dose dependence of the relative variance differs from the dose-independent relative variance predicted by the multiplicity effect alone. Since such dose dependence is often observed in experiments with alpha-particles, protons, and high-energy neutrons, the interpretation of the overdispersion needs to be supplemented. In a new, more general statistical model, the distribution function of the number of aberrations is interpreted as resulting from the convolution of a Poisson distribution for the spontaneous aberrations with the overdispersed distributions for the aberrations caused by intratrack or intertrack lesion interaction, and the fluctuation of the cross-sectional area of the cellular chromatin must also be considered. Using a suitable mathematical formulation of the resulting dose-dependent overdispersion, the mean number λ ₁ of the aberrations produced by a single particle traversal through the cell nucleus and the mean number λ ₂ of the aberrations per pairwise approach between two alpha-particle tracks could be estimated. Coefficient α of the dose-proportional yield component, when compared between ²⁴¹Am alpha-particle irradiation and ¹³⁷Cs gamma-ray exposure, is found to increase approximately in proportion to dose-mean restricted linear energy transfer, which indicates an underlying pairwise molecular lesion interaction on the nanometer scale. Received: 17 December 1996 / Accepted in revised form: 20 April 1997     

On the estimation of the number of antibody-forming cells

The variability of the number of antibody-forming cells (AbFC) on using the plaque method is discussed. In the first part of the study it is shown on the basis of experimental data that the number of AbFC in a standard number of spleen cells has approximately Poisson distribution in one animal if the number of AbFC in a suspension is small, but that as the number of AbFC rises (even if the number of test cells in the given volume remains the same), variance increases more rapidly than the mean value and negative binomial distribution is a better probability model. The maintenance of conditions for Poisson distribution is evidently also related to the absolute number of test cells in a given volume, however. If the number of spleen cells in a given volume is raised, it is impossible to maintain complete homogeneity of the suspension; the cells form agglomerates, resulting in greater variability of the number of cells in individual drops. Under certain conditions, however, negative binomal distribution tends to Poisson distribution. In the second part, the question of determination of the error of estimation of the number of AbFC, expressed as percentages of the true value, is studied. Presuming Poisson distribution, it is pointed out that it is impossible to predetermine a fixed limit of the experiment, i.e one which will ensure for a given confidence level that the empirically determined value will not differ from the true value by more than a predetermined percentage of the true value; for routine use, however, a nomogram for the approximate estimation of the degree of error with which we work is suggested. Alternatively, the sequential method can be employed for estimating the number of AbFC with a given degree of error, but this statistical method is more exacting as regards both the preparation and the execution of the experiment. Dedicated to Academician Ivan Málek on the occasion of his 60th birthday     

Brain PET imaging optimization with time of flight and point spread function modelling

PurposeTo assess the influence of reconstruction algorithms and parameters on the PET image quality of brain phantoms in order to optimize reconstruction for clinical PET brain studies in a new generation PET/CT.MethodsThe 3D Hoffman phantom that simulates ¹⁸F-fluorodeoxyglucose (FDG) distribution was imaged in a Siemens Biograph mCT TrueV PET/CT with Time of Flight (TOF) and Point Spread Function (PSF) modelling. Contrast-to-Noise Ratio (CNR), contrast and noise were studied for different reconstruction models: OSEM, OSEM + TOF, OSEM + PSF and OSEM + PSF + TOF.The 2D multi-compartment Hoffman phantom was filled to simulate 4 different tracers' spatial distribution: FDG, ¹¹C-flumazenil (FMZ), ¹¹C-Methionine (MET) and 6-¹⁸F-fluoro-l-dopa (FDOPA). The best algorithm for each tracer was selected by visual inspection. The maximization of CNR determined the optimal parameters for each reconstruction.ResultsIn the 3D Hoffman phantom, both noise and contrast increased with increasing number of iterations and decreased with increasing FWHM. OSEM + PSF + TOF reconstruction was generally superior to other reconstruction models. Visual analysis of the 2D Hoffman brain phantom suggested that OSEM + PSF + TOF is the optimum algorithm for tracers with focal uptake, such as MET or FDOPA, and OSEM + TOF for tracers with diffuse cortical uptake (i.e. FDG and FMZ). Optimization of CNR demonstrated that OSEM + TOF reconstruction must be performed with 2 iterations and a filter FWHM of 3 mm, and OSEM + PSF + TOF reconstruction with 4 iterations and 1 mm FWHM filter.ConclusionsOptimization of reconstruction algorithm and parameters has been performed to take particular advantage of the last generation PET scanner, recommending specific settings for different brain PET radiotracers.     

Assessing the exceptionality of network motifs.

Getting and analyzing biological interaction networks is at the core of systems biology. To help understanding these complex networks, many recent works have suggested to focus on motifs which occur more frequently than expected in random. To identify such exceptional motifs in a given network, we propose a statistical and analytical method which does not require any simulation. For this, we first provide an analytical expression of the mean and variance of the count under any exchangeable random graph model. Then we approximate the motif count distribution by a compound Poisson distribution whose parameters are derived from the mean and variance of the count. Thanks to simulations, we show that the compound Poisson approximation outperforms the Gaussian approximation. The compound Poisson distribution can then be used to get an approximate p-value and to decide if an observed count is significantly high or not. Our methodology is applied on protein-protein interaction (PPI) networks, and statistical issues related to exceptional motif detection are discussed.