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PubMed1994

Translating stochastic density-dependent individual behavior with sensory constraints to an Eulerian model of animal swarming.

Density-dependent social behaviors such as swarming and schooling determine spatial distribution and patterns of resource use in many species. Lagrangian (individual-based) models have been used to investigate social groups arising from hypothetical algorithms for behavioral interactions, but the Lagrangian approach is limited by computational and analytical constraints to relatively small numbers of individuals and relatively short times. The dynamics of "group properties", such as population density, are often more ecologically useful descriptions of aggregated spatial distributions than individual movements and positions. Eulerian (partial differential equation) models directly predict these group properties; however, such models have been inadequately tied to specific individual behaviors. In this paper, I present an Eulerian model of density-dependent swarming which is derived directly from a Lagrangian model in which individuals with limited sensing distances seek a target density of neighbors. The essential step in the derivation is the interpretation of the density distribution as governing the occurrence of animals as Poisson points; thus the number of individuals observed in any spatial interval is a Poisson-distributed random variable. This interpretation appears to be appropriate whenever a high degree of randomness in individual positions is present. The Eulerian model takes the form of a nonlinear partial integro-differential equation (PIDE); this equation accurately predicts statistically stationary swarm characteristics, such as expected expected density distribution. Stability analysis of the PIDE correctly predicts transients in the stochastic form of the aggregation model. The model is presented in one-dimensional form; however, it illustrates an approach that can be equally well applied in higher dimensions, and for more sophisticated behavioral algorithms.

Algorithms↗
PubMed1996

Practical guidelines for process validation and process control of white cell-reduced blood components: report of the Biomedical Excellence for Safer Transfusion (BEST) Working Party of the International Society of Blood Transfusion (ISBT).

BACKGROUND: The increased use of white (WBC)-reduced blood components has prompted many institutions to develop quality assurance programs directed to such component preparation processes. For consistent preparation of WBC-reduced blood components that meet clinical needs as well as national standards, a program of process validation and control should be instituted. This involves controlling key factors that affect WBC reduction as well as periodic monitoring of the residual cellular content of components. Practical guidelines for the implementation of such a program are provided. STUDY DESIGN AND METHODS: A program involving three phases of monitoring was developed by individuals belonging to an international working party of the International Society of Blood Transfusion. RESULTS: The first phase, process validation, evaluates a minimum of 20 consecutive units (a minimum of 60 units when nonparametric measurements are used) to document the successful local implementation of a new or substantially modified process. Ongoing process control employing Levey-Jennings type control charts is used to demonstrate that the process remains stable over time. Process capability assessment and conformance with standards are evaluated once residual WBCs are counted in a sufficient number of units. This enables a facility to claim with a specified degree of confidence that a stated proportion of WBC-reduced units will meet national standards. Two approaches to determine the number of units that should be selected for counting are presented. The first approach considers units as either acceptable or not acceptable and assumes that the distribution of failed (or nonconforming) units approximates the Poisson distribution. The second approach takes into consideration the observed WBC content of the tested units, with the assumption that the residual WBC content in WBC-reduced components follows a lognormal distribution. A method to assess the lognormal distribution of residual WBCs is presented. Specific tables based on each of these approaches are provided to guide the reader in the design of a program that will verify conformance with any national standard at specific confidence levels. The approach can be generalized to other process control applications. CONCLUSION: Guidelines are presented for process validation, process control, and assessment of conformance in the production of WBC-reduced blood components. Policy makers retain the responsibility to establish, on the basis of the expected use of WBC-reduced components, requirements for the frequency of testing and for the proportion of prepared units that are expected with a stated degree of confidence to meet the standards. Facilities preparing WBC-reduced components can monitor key factors that influence the preparation of WBC-reduced blood, can periodically assess their conformance with the standards, and can intervene to correct adverse changes in the process. This approach can be used to ensure the consistent quality of WBC-reduced blood components.

Blood Component Removal↗
PubMed2001

How many deleterious mutations are there in the human genome?

An estimate of the number of deleterious mutations in the human genome is made using data on the frequency of rare recessive disease in cousin marriages and in the general population. Sexual reproduction ensures that deleterious mutations are distributed at random in zygotes with an approximate Poisson distribution. The mean of this distribution is the sum of the mean number of deleterious mutations in zygotes which contribute to the next generation (Y) and the mean number of new mutations which arise in each human generation (X). The estimates are that X is between 1 and 2.6 and Y is between 12 and 32. A mathematical model based on redundancy is then used to predict how zygote survival will vary with the number of deleterious mutations. The form of this relationship is the same as that seen in experiments on cell survival following radiation-induced mutational damage and this provides independent support for this theoretical approach. The zygotes that survive to contribute to the next generation have a skewed distribution with a mean of Y. It is argued that the number of deleterious mutations in the genome is an important variable in health and disease.

Genes, Recessive↗
PubMed1991

Pairwise comparisons of mitochondrial DNA sequences in stable and exponentially growing populations.

We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.

Animals↗
PubMed1986

Quantal release of acetylcholine evoked by focal depolarization at the Torpedo nerve-electroplaque junction.

To analyse evoked acetylcholine (ACh) release in the electric organ of Torpedo marmorata, a loose patch-clamp technique was used that allowed with a single extracellular electrode both focal depolarization of nerve endings and recording of the post-synaptic currents produced by the released transmitter. Two different types of post-synaptic response could be evoked by depolarizing pulses of increasing intensity: a graded response appearing with a delay of 0.6 ms (pulses of 0.2 ms duration), and an all-or-none response characterized by a mean delay of 1.4 ms. Both responses had a similar maximal amplitude and a similar rise time of 0.6 ms. The graded response was evoked in all places where spontaneous miniature electroplaque currents (m.e.e.s) could be recorded. It was not modified by 1 microM-tetrodotoxin (TTX), but was Ca2+ dependent and was abolished by Cd2+ (0.2 mM) or Mg2+ (10 mM). The all-or-none response could be evoked in only 30% of places where m.e.c.s. were recorded, it was highly TTX sensitive, Ca2+ dependent, and abolished by Cd2+ (0.2 mM) or Mg2+ (10 mM). K+ channel blocking agents, such as 4-aminopyridine (4-AP) or tetraethylammonium (TEA), which are known to prolong the duration of action potentials, prolonged the delay of the all-or-none response, but not that of the graded response. At low strength stimulation, the graded response was clearly evoked in a quantal way, with the quantum corresponding to the amplitude of spontaneous m.e.c.s. The amplitude distribution of the evoked responses closely followed a Poisson distribution. The maximum synchronous release of transmitter was found to be approximately 1.3 quanta/micron2 of presynaptic membrane and a mean quantal size of about 7000 ACh molecules was estimated from the charge transfer of m.e.c.s. The nerve terminal time constant was calculated from strength-duration curves obtained with depolarizing pulses just able to evoke either the all-or-none response or the first few quanta of the graded response. Respective mean values of 0.22 and 0.40 ms were found. Increasing the duration of the depolarizing pulse had two consequences: it differently affected the delay of the all-or-none response and that of the graded response; it increased the mean quantal content of the graded response. Both effects could not simply be accounted for by the influence of the nerve terminal time constant.(ABSTRACT TRUNCATED AT 400 WORDS)

Acetylcholine↗
PubMed1998

A microdosimetric-kinetic theory of the dependence of the RBE for cell death on LET.

Experiments with cultured mammalian cells exposed to ionizing radiation of varying LET are examined in the context of a microdosimetric-kinetic (MK) model of radiation induced mammalian. cell killing similar to the site model of the theory of dual radiation action. The experimentally measured RBE, in the limit of zero dose, increases linearly with LET for LET less than a value that lies in the range of about 40-90 keV per micron. It is shown that the tendency of the RBE to increase linearly with LET can be explained as a result of the random variation of specific energy among microscopic sized domains (sites), into which the nucleus may be partitioned, and the effect of this variation on the formation of lethal lesions by pairwise combination of repairable primary lesions in DNA. the microscopic subunits corresponding to a site have diameter in the range of 0.56-0.75 microns. The linearity of RBE with increasing LET implies that value of the quadratic parameter of the linear-quadratic survival relation (beta) is constant, at least for LET low enough to be in the linear range, and this in turn implies the production of primary DNA lesion, likely double strand breaks, does not increase with LET. the experiments, interpreted with MK model, also imply that the repairability and potential for lethality of the primary DNA lesion does not change with variation of LET within the linear range. The failure of RBE to maintain its linear increase for higher values of LET, and the resulting RBE maximum at about 100 keV per micron, are likely primarily due to the departure of the distribution of lethal lesions among cells from the Poisson distribution. Some implications concerning the use of radiation to treat cancer are noted.

Animals↗
PubMed2001

Assessing the risk of primary amoebic meningoencephalitis from swimming in the presence of environmental Naegleria fowleri.

Free-living Naegleria fowleri amoebae cause primary amoebic meningoencephalitis (PAM). Because of the apparent conflict between their ubiquity and the rarity of cases observed, we sought to develop a model characterizing the risk of PAM after swimming as a function of the concentration of N. fowleri. The probability of death from PAM as a function of the number of amoebae inhaled is modeled according to results obtained from animals infected with amoeba strains. The calculation of the probability of inhaling one or more amoebae while swimming is based on a double hypothesis: that the distribution of amoebae in the water follows a Poisson distribution and that the mean quantity of water inhaled while swimming is 10 ml. The risk of PAM for a given concentration of amoebae is then obtained by summing the following products: the probability of inhaling n amoebae x the probability of PAM associated with inhaling these n amoebae. We chose the lognormal model to assess the risk of PAM because it yielded the best analysis of the studentized residuals. Nonetheless, the levels of risk thereby obtained cannot be applied to humans without correction, because they are substantially greater than those indicated by available epidemiologic data. The curve was thus adjusted by a factor calculated with the least-squares method. This provides the PAM risk in humans as a function of the N. fowleri concentration in the river. For example, the risk is 8.5 x 10(-8) at a concentration of 10 N. fowleri amoebae per liter.

Amebiasis↗
PubMedDate not supplied

Counting statistics.

The low radiation dose rates used in nuclear medicine necessitate image formation and measurements that are severely count limited. This limitation may mask our ability to perceive contrast in an image or may affect our confidence in quantitative functional measurements. The randomness of the signal can be described by using the Poisson probability distribution with its associated mean and variance. The validity of a measurement and uncertainties in a result can be determined by examining the count statistics. If multiple measurements are used to derive a result, confidence levels can be determined by examination of the propagation of errors. The statistical properties of the detected signal can also be evaluated to determine if the equipment is functioning properly. For example, the chi2 test can be used to determine if there is too much or too little variability in count samples. Finally, image formation with limited numbers of photons results in noisy images that may be difficult to interpret. An understanding of the trade-offs between contrast, noise, and object size is required to set proper image acquisition parameters and thereby ensure that the information required to make a diagnosis is contained in the final image.

Algorithms↗
PubMed1987

A probability distribution for out-migration.

"Under certain simplifying assumptions, an inflated generalized Poisson distribution has been proposed to study the trends for out-migration. This distribution has been fitted to data estimating the parameters by (i) method of moments and (ii) maximum likelihood method....Asymptotic expressions for variance and covariance of the maximum likelihood estimates are obtained." The method is tested using data from the Rural Development and Population Growth survey undertaken in Varanasi, India, in 1978.

Asia↗
PubMed1984

Distribution of SCEs in lymphocytes in persons with normal, slightly increased, and heavily increased SCEs.

The distribution of SCEs in lymphocytes was examined for 165 healthy persons (58 non-smokers and 107 smokers with cigarette consumption ranging from 1 to greater than 20 per day), and for 1 patient treated with melphalan, a cytostatic drug. The data from the healthy persons did not follow a Poisson distribution. A mixed Poisson that allowed different lambda values for the 30 cells scored from each person and postulated a gamma distribution for the lambda s within the 30 cells fitted all the data examined including those from the melphalan-treated patient. In the latter case the 7 samples taken at various times after the treatment could all be represented satisfactorily with a common parameter, c, in the gamma distribution for the lambda s, even though the mean SCEs/cell varied from 9.8 to 36.8. Because the c parameter determines the spread of lambda values within the 30 cells, this suggested that the effect of the cytostatic drug was to increase all the lambda s by a constant amount. The sum of the SCEs taken over all 30 cells in a sample is a convenient summary statistic, and the transformation y = square root s + square root s + 1 behaves as a normal variate with a constant variance within a group.

Adolescent↗
PubMed1988

The detection and importance of outliers in the in vivo micronucleus assay.

Micronucleus tests are generally analysed statistically for differences between the means of treated and control groups. 'Outliers' may either be rejected or grouped together with data from less responsive animals. In either case, a valuable indicator of a small, more sensitive (responder) population sub-group may then be missed. To alleviate this problem, we have developed an additional strategy, based on historic data, for the detection of any single animal with a significant increase in micronucleated polychromatic erythrocytes in an otherwise insignificant treatment group. Forty-one sets of negative control data (of five male and five female CD-1 mice each) have been analysed. Within each set there were no significant male to female differences and data were consistent with a Poisson distribution. Pooled data from all 41 sets showed slightly hyper-Poisson variation and were adequately described by the negative binomial distribution. The negative binomial probability generating function was used to show that six or more micronuclei per 1000 polychromatic cells from one treated animal would be significant for our laboratory, methodology and strain of mouse, provided that concurrent negative control data conformed with historic values. Changes in methodology desirable for this type of analysis include increasing the number of mice in each test group and possible compensation by a reduction in the number of test groups.

Animals↗
PubMed1986

Quantitative autoradiographic analysis of estradiol retention by cells in the preoptic area, hypothalamus and amygdala.

These experiments were done to compare quantitatively, on a cell-by-cell basis, estradiol retention by cells in the medial preoptic area, arcuate nucleus, ventrolateral subdivision of the ventromedial nucleus, and the caudal half of the medial nucleus of the amygdala. The steroid autoradiograms were prepared from 2 mu sections of brains from ovariectomized, adrenalectomized adult female rats that had been infused intravenously with [3H] estradiol (E2) in a regimen which kept circulating hormone concentration at or above proestrus levels for 3-4 h. Even in these brain regions, containing the most dense collections of E2-concentrating cells, a maximum of only 27-61% of the cells concentrated E2. Therefore, in these regions only a particular subset of the cells retain hormone; other cells in the region do not retain hormone. Frequency distribution histograms of the number of grains per cell versus the number of cells in each region showed a wide range in the amount of E2 retained per cell, and no modes among E2-retaining cells. The data followed a distribution markedly different from that predicted by a simple Poisson distribution, confirming that E2-retention does not result from a random, passive process such as diffusion. The overall quantitative characteristics of the frequency distribution histograms were similar across the four brain areas. Therefore, we propose that the different E2-sensitive functions of these brain areas must depend on differences in the neural connectivity or differences in hormone regulated peptide content of the areas.

Amygdala↗
PubMed1998

Analysis of chromosome aberrations in human peripheral lymphocytes induced by 5.4 keV x-rays.

Irradiation of human lymphocytes by x-rays has been seen, in past studies, to produce increasing frequencies of chromosome aberrations at lower x-ray energies. However, in one earlier irradiation experiment with chromium x-rays, the relative biological effectiveness (RBE) did not appear to be larger than that of hard x-rays, especially at higher doses. A possible reason for this unexpected result may have been the irradiation and culture conditions. We have, therefore, in the present study used a technique that has been developed in our laboratory to ensure uniformity of irradiation within lymphocytes and to avoid artefacts due to the cell cycle kinetics. Monolayers of 3-h-stimulated lymphocytes were exposed to 5.4 keV x-rays. A linear-quadratic dose-response was found for dicentrics. The comparison to an earlier finding with 220 kV x-rays shows the expected result of the RBE of the 5.4 keV x-rays to be above that of 220 kV x-rays. The intercellular distribution of dicentrics did not differ significantly from a Poisson distribution.

Cells, Cultured↗
PubMed2006

Control of meiotic recombination in Arabidopsis: role of the MutL and MutS homologues.

Immunocytochemistry reveals that the Arabidopsis mismatch repair proteins AtMSH4, AtMLH3 and AtMLH1 are expressed during prophase I of meiosis. Expression of AtMSH4 precedes AtMLH3 and AtMLH1 which co-localize as foci during pachytene. Co-localization between AtMSH4 and AtMLH3 occurs, but appears transient. AtMLH3 foci are not detected in an Atmsh4 mutant. However, localization of AtMSH4 is unaffected in Atmlh3, suggesting that recombination may proceed to dHj (double Holliday junction) formation. Mean chiasma frequency in Atmsh4 is reduced to 1.55 compared with 9.86 in wild-type. In contrast with wild-type, the distribution of residual crossovers in Atmsh4 closely fits a Poisson distribution. This is consistent with a two-pathway model for meiotic crossing-over whereby most crossovers occur via an AtMSH4-dependent pathway that is subject to interference, with the remaining crossovers arising via an interference-independent pathway. Loss of AtMLH3 results in an approx. 60% reduction in crossovers. Results suggest that dHj resolution can occur, but in contrast with wild-type where most or all dHjs are directed to form crossovers, the outcome is biased in favour of a non-crossover outcome. The results are compatible with a model whereby the MutL complex maintains or imposes a dHj conformation that ensures crossover formation.

Arabidopsis↗
PubMed1984

Dose-effect relationship of chromosome aberrations induced by 23 MeV alpha particles in human lymphocytes.

The dose-effect relationship and intercellular distribution of chromosome aberrations were studied in human peripheral blood lymphocytes irradiated in vitro with 23 MeV alpha particles. The frequency of dicentrics, mu, was best expressed by a linear-quadratic model, mu = 7.55 X 10(-1) D + 2.1 X 10(-2) D2, although the dose-quadratic component was not significantly different from zero giving a fit to a linear model mu = 7.93 X 10(-1) D also (D in Gy). The intercellular distributions of dicentrics were over-dispersed compared with Poisson distribution, and the dispersion index as expressed by the relative variance increased with the increase of mean dicentric yield. Stochastic considerations based on the relative variance indicated the presence of inter-track interaction in the formation of dicentrics by alpha particles. Modification of the dose-response relationship by selective loss of cells with more damage is discussed.

Adult↗
PubMed1963

Formation of mitochondria in Neurospora crassa. A quantitative radioautographic study.

Cells of a choline-requiring mutant of Neurospora crassa, labeled with radioactive choline, were transferred to unlabeled medium. At various times during their subsequent logarithmic growth, a highly purified mitochondrial fraction was prepared by sucrose density gradient centrifugation, and the distribution of label among individual mitochondria was determined by quantitative autoradiography. Preliminary experiments indicated that, under the conditions of this "washout" experiment, choline served as a stable mitochondrial label. Radioautographic analysis showed that, in fully labeled mycelia and for three mass doubling cycles in the unlabeled medium, radioactivity was randomly distributed among all mitochondria; i.e., the distribution of autographic grains among individual mitochondria followed a Poisson distribution. In experiments in which pulse labeling for 10 minutes was used, the label was randomly distributed among all mitochondria. The data suggest that the mitochondrial mass is increased by a continuous process of addition of new lecithin units to the already existing mitochondrial framework.

Autoradiography↗
PubMed2006

Exact moments in a continuous time random walk with complete memory of its history.

We present a continuous time generalization of a random walk with complete memory of its history [Phys. Rev. E 70, 045101(R) (2004)] and derive exact expressions for the first four moments of the distribution of displacement when the number of steps is Poisson distributed. We analyze the asymptotic behavior of the normalized third and fourth cumulants and identify new transitions in a parameter regime where the random walk exhibits superdiffusion. These transitions, which are also present in the discrete time case, arise from the memory of the process and are not reproduced by Fokker-Planck approximations to the evolution equation of this random walk.

Journal Article↗
PubMed2004

Evidence that thyroid hormone induces olfactory cellular proliferation in salmon during a sensitive period for imprinting.

Salmon have long been known to imprint and home to natal stream odors, yet the mechanisms driving olfactory imprinting remain obscure. The timing of imprinting is associated with elevations in plasma thyroid hormone levels, with possible effects on growth and proliferation of the peripheral olfactory system. Here, we begin to test this idea by determining whether experimentally elevated plasma levels of 3,5,3'-triiodothyronine (T(3)) influence cell proliferation as detected by the 5-bromo-2'-deoxyuridine (BrdU) cell birth-dating technique in the olfactory epithelium of juvenile coho salmon (Oncorhynchus kisutch). We also explore how natural fluctuations in thyroxine (T(4)) relate to proliferation in the epithelium during the parr-smolt transformation. In both studies, we found that BrdU labeled both single and clusters of mitotic cells. The total number of BrdU-labeled cells in the olfactory epithelium was significantly greater in fish with artificially elevated T(3) compared with placebo controls. This difference in proliferation was restricted to the basal region of the olfactory epithelium, where multipotent progenitor cells differentiate into olfactory receptor neurons. The distributions of mitotic cluster sizes differed significantly from a Poisson distribution for both T(3) and placebo treatments, suggesting that proliferation tends to be non-random. Over the course of the parr-smolt transformation, changes in the density of BrdU cells showed a positive relationship with natural fluctuations in plasma T(4). This relationship suggests that even small changes in thyroid activity can stimulate the proliferation of neural progenitor cells in the salmon epithelium. Taken together, our results establish a link between the thyroid hormone axis and measurable anatomical changes in the peripheral olfactory system.

Analysis of Variance↗