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PubMed1994

Frailty selection in bivariate survival models: a cautionary note.

"One problem that researchers face in analyzing the survival times of groups of related individuals is selecting how the distribution of frailty--an unobserved (or not adequately observed) random factor--should be specified. Several distributions have received attention--for instance, the gamma distribution and a nonparametric N-point, discrete probability distribution. Researchers have selected these distributions more for mathematical convenience than for their ability to represent biological, social, or economic reality, and the implications of choosing one functional representation of frailty over alternative choices have not been studied extensively.... This research paper explores the association among survival times under gamma, inverse Gaussian, nonparametric N-point, and Poisson distributions. It shows that the pattern and strength of this association depends on how the distribution of frailty is specified." (SUMMARY IN FRE)

Demography↗
PubMed2004

Statistical characterization of the interchange-instability spectrum of a separable ideal-magnetohydrodynamic model system.

A Suydam-unstable circular cylinder of plasma with periodic boundary conditions in the axial direction is studied within the approximation of linearized ideal magnetohydrodynamics (MHD). The normal mode equations are completely separable, so both the toroidal Fourier harmonic index n and the poloidal index m are good quantum numbers. The full spectrum of eigenvalues in the range 1< or = m < or = m(max) is analyzed quantitatively, using asymptotics for large m, numerics for all m, and graphics for qualitative understanding. The density of eigenvalues scales like m(2)(max) as m(max) -->infinity . Because finite-m corrections scale as 1/ m(2)(max) , their inclusion is essential in order to obtain the correct statistics for the distribution of eigenvalues. Near the largest growth rate, only a single radial eigenmode contributes to the spectrum, so the eigenvalues there depend only on m and n as in a two-dimensional system. However, unlike the generic separable two-dimensional system, the statistics of the ideal-MHD spectrum departs somewhat from the Poisson distribution, even for arbitrarily large m(max) . This departure from Poissonian statistics may be understood qualitatively from the nature of the distribution of rational numbers in the rotational transform profile.

Journal Article↗
PubMed1976

Properties of the larval neuromuscular junction in Drosophila melanogaster.

The anatomy and physiology of the Drosophila larval neuromuscular junction were studied. 2. The dependence of muscle resting potentials on [K+]o and [Na+]o follows the Goldman-Hodgkin-Katz equation (PNa/PK=0-23). Chloride ions distribute passively across the membrane. 3. The mean specific membrane resistance of muscle fibres is 4-3 X 10(3) omega cm2, and the mean specific membrane capacitance is 7-1 muF/cm2. The muscle fibre is virtually isopotential. 4. Transmitter release is quantal. Both the miniature excitatory junctional potential and the evoked release follow the Poisson distribution. 5. Transmitter release depends on approximately the fourth power of [Ca2+]o. If Sr2+ replaces Ca2+, it depends on approximately the fourth power of [Sr2+]o. Mg2+ reduces transmitter release without altering the fourth power dependence on [Ca2+]o.

Animals↗
PubMed2005

Theory of photon statistics in single-molecule Förster resonance energy transfer.

We present the theory for the distribution of the number of donor and acceptor photons detected in a time bin and the corresponding energy-transfer efficiency distribution obtained from single-molecule Forster resonance energy-transfer measurements. Photon counts from both immobilized and freely diffusing molecules are considered. Our starting point is the joint distribution for the donor and acceptor photons for a system described by an arbitrary kinetic scheme. This is simplified by exploiting the time scale separation between fast fluorescent transitions and slow processes which include conformational dynamics, intersystem conversion to a dark state, and translational diffusion in and out of the laser spot. The fast fluorescent transitions result in a Poisson distribution of the number of photons which is then averaged over slow fluctuations of the local transfer efficiency and the total number of photons. The contribution of various processes to the distribution and the variance of the energy-transfer efficiency are analyzed.

Computer Simulation↗
PubMed2004

Estimating the degree of saturation in mutant screens.

Large-scale screens for loss-of-function mutants have played a significant role in recent advances in developmental biology and other fields. In such mutant screens, it is desirable to estimate the degree of "saturation" of the screen (i.e., what fraction of the possible target genes has been identified). We applied Bayesian and maximum-likelihood methods for estimating the number of loci remaining undetected in large-scale screens and produced credibility intervals to assess the uncertainty of these estimates. Since different loci may mutate to alleles with detectable phenotypes at different rates, we also incorporated variation in the degree of mutability among genes, using either gamma-distributed mutation rates or multiple discrete mutation rate classes. We examined eight published data sets from large-scale mutant screens and found that credibility intervals are much broader than implied by previous assumptions about the degree of saturation of screens. The likelihood methods presented here are a significantly better fit to data from published experiments than estimates based on the Poisson distribution, which implicitly assumes a single mutation rate for all loci. The results are reasonably robust to different models of variation in the mutability of genes. We tested our methods against mutant allele data from a region of the Drosophila melanogaster genome for which there is an independent genomics-based estimate of the number of undetected loci and found that the number of such loci falls within the predicted credibility interval for our models. The methods we have developed may also be useful for estimating the degree of saturation in other types of genetic screens in addition to classical screens for simple loss-of-function mutants, including genetic modifier screens and screens for protein-protein interactions using the yeast two-hybrid method.

Animals↗
PubMed2005

Correlation function and generalized master equation of arbitrary age.

We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation. These three methods yield exact expressions, thus coinciding with the recent result by Godrèche and Luck [J. Stat. Phys. 104, 489 (2001)]. Actually, non-Poisson statistics yields infinite memory at the probability level, thereby breaking any form of Markovian approximation, including the one adopted herein, to find an approximated analytical formula. For this reason, we check the accuracy of this approximated formula by comparing it with the numerical treatment of the second of the three exact expressions. We find that, although not exact, a simple analytical expression for the correlation function of arbitrary age is very accurate. We establish a connection between the correlation function and a generalized master equation of the same age. Thus this formalism, related to models used in glassy materials, allows us to illustrate an approach to the statistical treatment of blinking quantum dots, bypassing the limitations of the conventional Liouville treatment.

Journal Article↗
PubMed1988

Sister-chromatid exchange (SCE) rate in normal and abnormal sexual development in males and females.

Thirty-three patients with abnormal sexual development (9 male hypogonads, 20 females with primary amenorrhea and 4 cases of ambiguous genitalia), 10 normal males and 8 normal females (below the age of 30 years) were evaluated for SCE/cell and for SCE distribution according to chromosome groups (A to G). Smokers and alcoholics and subjects under medication were excluded from the study. The average rates of SCE/cell in male hypogonads, primary amenorrhea and ambiguous genitalia were 4.23 +/- 1.51, 4.02 +/- 0.90 and 4.33 +/- 1.34, respectively, whereas in normal males and females the average rates were 4.27 +/- 0.69 and 4.49 +/- 0.87, respectively. The SCE data followed a Poisson distribution. Chi-square testing showed a statistically significant difference only in B-group chromosomes when male hypogonads were compared with normal males (p less than 0.02) and females with primary amenorrhea were compared with normal females (p less than 0.02), suggesting the importance of the study of SCE frequency distribution at chromosome group level to bring out the differences otherwise concealed in average rates.

Adult↗
PubMed1987

An approximation for the distribution of the scan statistic.

The scan statistic evaluates whether an apparent cluster of disease in time is due to chance. The statistic employs a 'moving window' of length w and finds the maximum number of cases revealed through the window as it scans or slides over the entire time period T. Computation of the probability of observing a certain size cluster, under the hypothesis of a uniform distribution, is infeasible when N, the total number of events, is large, and w is of moderate or small size relative to T. We give an approximation that is an asymptotic upper bound, easy to compute, and, for the purposes of hypothesis testing, more accurate than other approximations presented in the literature. The approximation applies both when N is fixed, and when N has a Poisson distribution. We illustrate the procedure on a data set of trisomic spontaneous abortions observed in a two year period in New York City.

Abortion, Spontaneous↗
PubMed2003

Contribution of the polymer standards' polydispersity to the observed band broadening in size-exclusion chromatography.

The contribution of the polydispersity of polymer standards to the observed band broadening in size-exclusion chromatography was evaluated. Initially, theoretical predictions based on an equation by Knox et al. were found to overestimate this contribution, greatly due to the fact that the polydispersity values specified by the manufacturers are upper limits and therefore too high to be applied in this context. An improved estimate of the polydispersity values was obtained from the size-exclusion chromatography results and these new values were used to reassess the polydispersity contribution to band broadening. For two of three columns tested the best molar-mass-distribution parameters, i.e. those the least affected by extra-column and intra-column band broadening effects, can be obtained for polymers with a molar mass in the effective range of the given column and at rather low mobile-phase flow rates. At those conditions, for low-molar-mass polymers, the estimated polydispersity index values approach the theoretical ones derived from a Poisson distribution.

Chromatography, Gel↗
PubMed1983

Sister chromatid exchange distributions in rabbit lymphocytes treated with streptonigrin.

Streptonigrin (NSC-45383), a direct-acting clastogen which induces SCEs in vivo and chromosome aberrations both in vivo and in vitro, was evaluated for SCE induction in both G0 and stimulated rabbit lymphocytes. Determinations were made for 16 cultures from seven female rabbits. These included controls as well as cells exposed to 90 micrograms/kg in vivo, cells pulse-treated with 50 ng/ml in vitro, and a culture continuously exposed to 5 ng/ml in vitro. For all cultures the SCE/cell frequency was determined from 20 complete (44 chromosome) metaphases and, in selected cultures, SCEs on individual chromosomes (880 per culture from 20 cells) were enumerated to determine SCE/chromosome frequency and the chromosomal distribution of SCEs. Analysis of variance and least significant difference tests of the square root x transformed SCE/cell data show that cells exposed to streptonigrin while dividing have significantly higher (P less than 0.01) frequencies (over double the control 5.3 SCE/cell value) whereas treated G0 cells were not significantly different from the controls. Dispersion analysis of both SCE/cell and SCE/chromosome data confirms the adequacy of the Poisson distribution for spontaneous or baseline but not streptonigrin-induced SCEs.

Animals↗
PubMed1977

Thermodynamic limits on the size and size distribution of nucleic acids synthesized in vitro: the role of pyrophosphate hydrolysis.

The free-energy change of phosphodiester bond formation from nucleoside triphosphates is more favorable than with nucleoside diphosphates as substrates. Base-stacking interactions can make significant contributions to both delta G degrees ' values. Pyrophosphate hydrolysis when it accompanies the former reaction dominates all thermodynamic considerations. Three experimental situations are discussed in which high-molecular-weight polynucleotides are synthesized without a strong driving force for covalent bond formation. For one of these, a kinetic scheme is presented which encompasses an early narrow Poisson distribution of chain lengths with ultimate passage to a disperse equilibrium population of chain sizes. Hydrolytic removal of pyrophosphate expands the time scale for this undesirable process by a factor of 10(9), while it enormously elevates the thermodynamic ceiling for the average degrees of polymerization in the other two examples. The electron micrographically revealed broad size population from an early study of partial replication of a T7 DNA template is found to adhere (fortuitously) to a disperse most probable representation. Some possible origins are examined for the branched structures in this product, as well as in a later investigation of replication of this nucleic acid. The achievement of both very high molecular weights and sharply peaked size distributions in polynucleotides synthesized in vitro will require coupling to inorganic pyrophosphatase action as in vivo.

Calorimetry↗
PubMed2003

Generalized master equation via aging continuous-time random walks.

We discuss the problem of the equivalence between continuous-time random walk (CTRW) and generalized master equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site for extended times. The sojourn times have a distribution density psi(t) that is assumed to be an inverse power law with the power index micro. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case where psi(t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is nonstationary, thereby implying aging, while the Onsager principle is valid only in the case of fully aged systems. The case of a Poisson distribution of sojourn times is the only one with no aging associated to it, and consequently with no need to establish special initial conditions to fulfill the Onsager principle. We consider the case of a dichotomous fluctuation, and we prove that the Onsager principle is fulfilled for any form of regression to equilibrium provided that the stationary condition holds true. We set the stationary condition on both the CTRW and the GME, thereby creating a condition of total equivalence, regardless of the nature of the waiting-time distribution. As a consequence of this procedure we create a GME that is a bona fide master equation, in spite of being non-Markov. We note that the memory kernel of the GME affords information on the interaction between system of interest and its bath. The Poisson case yields a bath with infinitely fast fluctuations. We argue that departing from the Poisson form has the effect of creating a condition of infinite memory and that these results might be useful to shed light on the problem of how to unravel non-Markov quantum master equations.

Journal Article↗
PubMed1999

Immunogold localization of AMPA and NMDA receptors in somatic sensory cortex of albino rat.

We performed an electron microscopic study of S-1 cortex by using postembedding immunogold histochemistry to examine the subcellular distribution of alpha-amino-3-hydroxy-5-methylisoxazole-4-propionate (AMPA) receptors (assessed with an antibody recognizing the glutamate receptor 2 and 3 [GluR2 and GluR3] subunits) and to compare this distribution with that of N-methyl-D-aspartate (NMDA) receptors (assessed with an antibody for the NR1 subunit). Both receptors were concentrated at active zones of asymmetric synapses, often directly apposed to presynaptic dense bodies. GluR2/3 showed a bias for long active zones, whereas short active zones expressed GluR2/3 at substantially lower levels; in contrast, labeling for NR1 was independent of synaptic size. Particle counts suggested that synaptic labeling was Poisson distributed and implied that the majority of synapses express both receptors. Quantitative analysis indicates that approximately one-half of synapses express high levels of GluR2/3 and that the remainder express GluR2/3 at a much lower level. Approximately three-fourths of synapses express NR1 at a uniform level; the remainder, which may lack NR1 completely, include synapses with especially large active zones. The present results suggest that the smallest active zones may play a special role in synaptic plasticity.

Animals↗
PubMed2000

Growth of an Initial Mass Function Cluster in a Turbulent Dense Core.

A simple model of condensation growth and collapse in a turbulent dense core yields a distribution of stellar masses that matches the main features of the stellar initial mass function (IMF). In this model, stars in the "flat" and "power-law" parts of the IMF come from condensations with negligible and substantial growth, respectively. The mass accretion rate of a condensation is proportional to its mass, and the probability of stopping accretion is equal in every time interval, so the growth is exponential and its duration follows a Poisson distribution. For mass growth e-folding time taugrow and mean duration taustop, the stellar mass m has a probability density per logarithmic mass interval of approximately m-x, where x identical withtaugrow&solm0;taustop. This power-law relation matches the IMF when taugrow approximately taustop, as is expected if each of these times is set by the same properties of the surrounding core gas. We specify exponential growth arising from Bondi accretion onto a stationary Bonnor-Ebert sphere, in a core heated and stirred by associated stars. This growth is exponential, unlike the Bondi accretion onto a star, but "slow," with taugrow greater than the free-fall time of the condensation by a factor of approximately 4. We specify random stopping as due to sudden turbulent compression, which causes the condensation to collapse and stop accreting. For these mechanisms, a core with a density of 104 cm-3 grows a cluster of approximately 100 IMF-following stars with a mass range of 1-25 M middle dot in circle in 1.4 Myr, in accord with the masses and ages of embedded clusters.

Journal Article↗
PubMed1989

A Markov formulation of the repair-misrepair model of cell survival.

Tobias' repair-misrepair (RMR) model of cell survival is formulated as a Markov process, a sequence of discrete repair steps occurring at random times, and the probability of a sequence of viable repairs is calculated. The Markov formulation describes the time evolution of the probability distribution for the number of lesions in a cell. The probability of cell survival is calculated from the distribution of the initial number of lesions and the probabilities of the repair events. The production of lesions is formulated in accordance with the principles of microdosimetry, and the distribution of the initial number of lesions is obtained as an approximation for high and low linear energy transfer cases. The Markov formulation of the RMR model uses the same biological hypotheses as the original version with two statistical approximations deleted. These approximations are the neglect of the effect of statistical fluctuations in calculating the average rate of repair of lesions and the assumption that the final number of unrepaired and lethally misrepaired lesions has a Poisson distribution. The quantitative effect of these approximations is calculated, and a basis is provided for an alternative approach to calculating survival probabilities.

Cell Survival↗
PubMed1995

The distribution of transposable elements on X chromosomes from a natural population of Drosophila simulans.

The distribution of 13 transposable element families along 15 X chromosomes from an African natural population of Drosophila simulans was determined by in situ hybridization to polytene chromosomes. The transposable elements cloned from Drosophila melanogaster all hybridized with Drosophila simulans chromosomes. The number of copies per family was 3.5 times lower in the latter species and correlated with the copy number per family in Drosophila melanogaster. With the exception of 297, the copy number per chromosome followed a Poisson distribution. Element frequencies per chromosome band were generally low. However, several sites of the distal region and the base of the X chromosome had high frequencies of occupation. Elements had higher abundance at the base of the chromosome compared to distal regions. Overall, the distribution of transposable elements in Drosophila simulans is similar to that found in Drosophila melanogaster. These data provide evidence for the operation of a force (or forces) opposing transpositional increase in copy number, and that this force is weaker at the bases of chromosomes, consistent with the idea that recombination between elements at non-homologous sites contains TE copy number. The reduction in copy number of all TE families in Drosophila simulans compared to Drosophila melanogaster can be explained by stronger selection against transposable element multiplication and/or lower rates of transposition in Drosophila simulans.

Africa↗
PubMed1997

Distribution of myocardial macrophages in the normal human heart.

Macrophages are important in inflammatory processes in heart disease and in transplantation rejection. A resurgence of interest in the macrophage has emanated from recent evidence implicating it as an effector cell in atherosclerosis and transplantation rejection. The detailed distribution of the macrophage within the normal human heart is unknown. We quantified macrophage numbers in the different chambers of the heart. Large tissue blocks (1.5-2.0 cm3) were removed from specific sites in 5 'normal' control hearts (2 males, 3 females, age range 19-46 y). Paraffin-embedded sections were stained with a CD68 pan macrophage marker. Positive cells were enumerated within 20 random fields. Results were analysed using a generalised linear modelling method using the Poisson distribution. Macrophages were identified within septa, and often close to blood vessels, in the myocardium, and in the majority of areas in all hearts. Macrophage numbers varied significantly between areas (range 0-6 cells/high power field; P < 0.001), and between the 5 hearts analysed (P < 0.001). In general, there were significantly more macrophages in the ventricles (RV P < 0.01, LV P < 0.05), but these differences were affected by heart differences. This study provides a baseline for the range of macrophage numbers within normal hearts, thus enabling comparisons with macrophage numbers within diseased and transplanted hearts.

Adult↗
PubMed1990

On the analysis of high order moments of fluorescence fluctuations.

A simple, straightforward analysis to characterize the distribution of aggregate sizes in a reversible aggregation system at equilibrium is presented. The method, an extension of fluorescence correlation spectroscopy (FCS), is based on measurements of higher order moments of spontaneous fluctuations of fluorescence intensity emitted from a defined open region of the sample. These fluctuations indicate fluctuations of the numbers of the fluorescent molecules in the observation region. Shot noise resulting from the random character of fluorescence emission and from the photoelectric detection system is modeled as a Poisson distribution and is subtracted from the measured photon count fluctuation moments to yield the desired fluorescence fluctuation moments. This analysis can also be used to estimate the fraction of immobile fluorophores in FCS measurements.

Mathematics↗