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PubMed2005

Highly nonrandom features of synaptic connectivity in local cortical circuits.

How different is local cortical circuitry from a random network? To answer this question, we probed synaptic connections with several hundred simultaneous quadruple whole-cell recordings from layer 5 pyramidal neurons in the rat visual cortex. Analysis of this dataset revealed several nonrandom features in synaptic connectivity. We confirmed previous reports that bidirectional connections are more common than expected in a random network. We found that several highly clustered three-neuron connectivity patterns are overrepresented, suggesting that connections tend to cluster together. We also analyzed synaptic connection strength as defined by the peak excitatory postsynaptic potential amplitude. We found that the distribution of synaptic connection strength differs significantly from the Poisson distribution and can be fitted by a lognormal distribution. Such a distribution has a heavier tail and implies that synaptic weight is concentrated among few synaptic connections. In addition, the strengths of synaptic connections sharing pre- or postsynaptic neurons are correlated, implying that strong connections are even more clustered than the weak ones. Therefore, the local cortical network structure can be viewed as a skeleton of stronger connections in a sea of weaker ones. Such a skeleton is likely to play an important role in network dynamics and should be investigated further.

Animals↗
PubMed1986

Distribution of 125I-insulin in cardiocytes at steady state binding conditions at 37 degrees C.

The distribution of 125I-insulin in cardiocytes was analyzed by light microscope autoradiography. Semithin sections were used to distinguish between surface-bound and internalized tracer. At 37 degrees C, when steady state binding conditions were reached, 40 to 60% of the cell-bound tracer was located in the plasma membrane region and the remainder was in the cell interior. Autoradiograms of whole cells were used to study the distribution of tracer molecules on the cell surface. Because Poisson distributions of silver grains were observed on 90% of the cells, it was concluded that the distribution of the insulin-receptor complexes was close to random. In contrast to the findings of Schlessinger et al., no aggregation of insulin-receptor complexes into patches was observed.

Animals↗
PubMed1963

Mitoses: distribution in mouse ear epidermis.

Epidermal cell mitoses occur in a random spatial (Poisson) distribution in the plane of the epidermis of the mouse. It is therefore unlikely that the focal accumulation of a local extracellular factor is responsible for the initiation of mitoses.

Animals↗
PubMed1989

Graphical and statistical approaches to data analysis for in situ hybridization.

Quantification of gene expression in a morphological context is an invaluable tool for neurobiological investigation. The ability to measure the quantity of specific mRNA molecules at the level of the single neuron permits one to monitor the modulation of complex cell synthetic activity of intact neuron populations. The cells of interest can be contiguous or dispersed in functionally significant patterns throughout a broad anatomical region of the brain. The application of quantitative in situ hybridization is technically difficult and labor intensive. Nevertheless, it has great utility for investigating gene expression from a structural perspective. (1) In situ hybridization permits one to ask questions concerning the anatomical pattern of neuronal gene expression. (2) It permits analyses concerning the initiation of expression, cell location, cell type, and alterations of level of expression within a spatial and temporal context. (3) In cases where blotting methods suggest a message exists at low copy, in situ hybridization permits queries at the single-cell level. For example, in situ hybridization can determine if very few cells are expressing the gene product or if many neurons dispersed throughout a brain region exhibit low mRNA copy number/cell. Quantitative analyses also allow detailed investigation of cell response to physiologically meaningful stimulation. Our application of statistical and numerical methods is a demonstration of the utility of probabilistic models; the mixture distribution accounted for data from both labeled and unlabeled sources. In agreement with many previous investigations, grain density over an unlabeled uniform source (oxytocinergic cells) was suitably described by the Poisson distribution. The population of labeled vasopressinergic cells, however, was best described by the negative binomial distribution. Previous investigations from different fields of biology show that the negative binomial can be used to describe many biological phenomena, and this distribution was considered in at least two previous investigations to evaluate autoradiographic data which did not fit the Poisson function. From a theoretical perspective, the probabilistic relationship between beta-particle decay (a Poisson function) and the distribution of message levels among individual neurons in a cell group (gamma distribution) prompts consideration of the negative binomial. For both data sets the observed variances were larger than the mean, and the labeled portion of the data sets exhibited positive skewness.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed2001

Statistical characteristics of climbing fiber spikes necessary for efficient cerebellar learning.

Mean firing rates (MFRs), with analogue values, have thus far been used as information carriers of neurons in most brain theories of learning. However, the neurons transmit the signal by spikes, which are discrete events. The climbing fibers (CFs), which are known to be essential for cerebellar motor learning, fire at the ultra-low firing rates (around 1 Hz), and it is not yet understood theoretically how high-frequency information can be conveyed and how learning of smooth and fast movements can be achieved. Here we address whether cerebellar learning can be achieved by CF spikes instead of conventional MFR in an eye movement task, such as the ocular following response (OFR), and an arm movement task. There are two major afferents into cerebellar Purkinje cells: parallel fiber (PF) and CF, and the synaptic weights between PFs and Purkinje cells have been shown to be modulated by the stimulation of both types of fiber. The modulation of the synaptic weights is regulated by the cerebellar synaptic plasticity. In this study we simulated cerebellar learning using CF signals as spikes instead of conventional MFR. To generate the spikes we used the following four spike generation models: (1) a Poisson model in which the spike interval probability follows a Poisson distribution, (2) a gamma model in which the spike interval probability follows the gamma distribution, (3) a max model in which a spike is generated when a synaptic input reaches maximum, and (4) a threshold model in which a spike is generated when the input crosses a certain small threshold. We found that, in an OFR task with a constant visual velocity, learning was successful with stochastic models, such as Poisson and gamma models, but not in the deterministic models, such as max and threshold models. In an OFR with a stepwise velocity change and an arm movement task, learning could be achieved only in the Poisson model. In addition, for efficient cerebellar learning, the distribution of CF spike-occurrence time after stimulus onset must capture at least the first, second and third moments of the temporal distribution of error signals.

Action Potentials↗
PubMed2005

Statistical motor number estimation assuming a binomial distribution.

The statistical method of motor unit number estimation (MUNE) uses the natural stochastic variation in a muscle's compound response to electrical stimulation to obtain an estimate of the number of recruitable motor units. The current method assumes that this variation follows a Poisson distribution. We present an alternative that instead assumes a binomial distribution. Results of computer simulations and of a pilot study on 19 healthy subjects showed that the binomial MUNE values are considerably higher than those of the Poisson method, and in better agreement with the results of other MUNE techniques. In addition, simulation results predict that the performance in patients with severe motor unit loss will be better for the binomial than Poisson method. The adapted method remains closer to physiology, because it can accommodate the increase in activation probability that results from rising stimulus intensity. It does not need recording windows as used with the Poisson method, and is therefore less user-dependent and more objective and quicker in its operation. For these reasons, we believe that the proposed modifications may lead to significant improvements in the statistical MUNE technique.

Adult↗
PubMed1999

An estimator of the mutant frequency in assays using transgenic animals.

The Poisson distribution is a fundamental probability model for count data, and is a natural model for the observed plaque counts in mutation assays using animals with lambda or PhiX174 transgenes. The Poisson likelihood for observed counts is a function of the mutant fraction, and it is straightforward to derive the associated maximum likelihood estimate of the mutant fraction and its variance. The estimate is easy to calculate, and if not the same, very similar to ad hoc estimates in current use. The model indicates the proper way to combine data from a number of plates, possibly prepared with different sample dilutions. The estimator of the mutant fraction is biased as a consequence of dividing by a random variable, the plaque count used to calculate the total recovered plaque-forming units. Fortunately, the bias becomes negligible as this count becomes large. On the other hand, increasing this count can increase the variance by decreasing the amount of sample assayed for mutant phages. Concurrent heed to the bias and the variance provides some guidance as to the optimum allocation of a sample into portions assayed for mutant phages and total recovered phages. The distribution of the estimate of the mutant fraction is related to the binomial distribution. This relationship implies a binomial distribution for the mutant count conditional on an overall count (either the sum of mutant and counted total plaques or the sum of counted mutant and non-mutant plaques). A special but important case occurs when each plate can be evaluated for mutant plaques and non-mutant plaques. Then, the observed proportion of mutants estimates the mutant fraction. More generally, the relationship to a binomial distribution provides a procedure for calculating a confidence interval.

Animals↗
PubMed1997

Density-Dependent Patch Exploitation and Acquisition of Environmental Information

We study density-dependent resource harvest patterns due to Bayesian foraging for different distributions of resources. We first consider a forager with information about the stochastic properties of its environment. In this case we show that when the number of food items per patch follows a distribution from the exponential family, the density dependence is given by the ratio sigma2/μ of the distribution of number of food items per patch. Bayesian foraging can therefore lead to positive (negative binomial distribution) or negative (binomial distribution) density dependent resource harvest and even to density independent (Poisson distribution) resource harvest, depending on the distribution of resources in the environment. In a second stage we incorporate learning about the distribution of resources in the whole environment. The mean of the distribution of number of food items per patch of a given environment is learnt faster than the variance of the distribution. Learning occurs faster in poorer than richer environments. Copyright 1997 Academic Press

Journal Article↗
PubMed1981

Chromosome aberrations induced by protons up to 31 MeV in cultured human cells.

Chromosome aberrations were induced in cultured human cells by proton beams of 31, 12, and 8 MeV. The frequencies of isochromatid breaks and dicentrics have been analysed as a function of proton energy and dose. Both effects are largely dependent on proton energy; isochromatid breaks increased linearly with the dose, whereas dicentrics show a definite parabolic behaviour. The experimental data were fitted to the analytic form Y = KDn and Y = alpha D + beta D2 and the best fitted values of the parameters are reported and discussed. The values of RBE for the isochromatid breaks are in the ratio 1.7:1.3:1 for 8, 12, and 31 MeV respectively. In the case of the dicentrics the RBE values are dose-dependent function of the type CD-n. The three distributions of dicentrics among the cells do not fit a Poisson distribution.

Cell Line↗
PubMed2001

CD8+ T cells in human uterine endometrial lymphoid aggregates: evidence for accumulation of cells by trafficking.

Lymphoid aggregates (LA) develop during the proliferative phase of the menstrual cycle in the human uterine endometrium (EM). They contain mostly CD8+ T cells and B cells. As these LA are absent immediately following menses, they may arise by division of cells resident in the EM, or by division of a limited number of precursor cells that traffic into the EM during the early proliferative phase of the menstrual cycle. Alternatively, they may arise by the continuous trafficking of cells into the EM throughout the proliferative phase of the menstrual cycle. In this study we investigated the distribution and frequency of CD8+ T cells in the aggregates using expression of Vbeta2 or Vbeta8 as markers of clonality and Ki-67 as a marker of dividing cells. Confocal microscopic analysis of endometrial tissues showed the random distribution of CD8+ T cells within aggregates within the same sample and in aggregates from different samples. Furthermore, comparisons of the distribution of Vbeta2 and Vb8 with expected values predicted from Poisson distribution values were not significantly different, suggesting that CD8+ T cells do not arise by division from single precursors. A low level of T-cell division within LAs was confirmed by positive staining for Ki-67. Dividing T cells were randomly dispersed throughout the LA and the frequency of dividing cells did not vary greatly between aggregates within the same tissue. Nearest-neighbour analysis of dividing cells showed no statistically significant deviations from a random distribution. Taken together, these results suggest that LA develop during the menstrual cycle largely by the trafficking of cells to nucleation sites within the EM, rather than by division of a limited number of precursor cells.

Apoptosis↗
PubMed1996

Quantum chaos in nano-sized billiards in layered two-dimensional semiconductor structures.

We consider two-dimensional, electron-rich cavities that can be created at a (AlGa)As-GaAs interface. In the modelling of such cavities we include features that are typical for small semiconductor structures or devices, i.e., soft walls representing electrostatic confinement and disorder due to ionized impurities. The introduction of soft walls is found to have a profound effect on the dynamic behaviour. There are situations in which there is a crossover from a Wigner distribution for the nearest level spacing to an effectively Poisson-like one as the confining walls are softened. The crossover occurs in a region which is accessible experimentally. A mechanism for the crossover is discussed in terms of groups of energy levels being separated from each other as walls become soft. The effects of disorder are found to be negligible for high-mobility samples, i.e., the motion of the particles is ballistic. These findings are of a general nature. Chaotic Robnik dots, circular dots with a special "dent," are also investigated. In this case there is no crossover from Wigner to Poisson distributions. An explanation for this difference is proposed. Finally, the effects of leads are investigated in an elementary way by simply attaching two stubs to a circular dot. For wide stubs, which in our simple model would correspond to open leads, we obtain Wigner statistics indicating a transition to irregular behaviour. A lead-induced transition of this kind appears consistent with recent measurements of the line-shape of the weak localization peak, observed in the low-temperature magnetoresistance of square semiconductor billiards. Finally, implications for conductance fluctuations are briefly commented on. (c) 1996 American Institute of Physics.

Journal Article↗
PubMed1985

The anion selectivity of GABA-mediated post-synaptic potentials in mouse hippocampal cells.

Intracellular recordings were made from CA1 and dentate cells of the mouse hippocampal slice. When potassium acetate was used to fill the electrodes, spontaneous synaptic activity was rarely seen in CA1 or dentate cells. In contrast, when electrodes filled with potassium chloride were used, spontaneous depolarizing post-synaptic potentials (p.s.p.s) were prominent. That these p.s.p.s were mediated by gamma-aminobutyric acid (GABA) was supported by the following: they were blocked by electrophoretic application of bicuculline methiodide; their appearance was associated with the reversal of the evoked GABA-mediated recurrent inhibitory post-synaptic potential (i.p.s.p.) and their appearance was associated with the positive displacement of the reversal potential for the response to GABA applied by electrophoresis close to the cell soma. The interval distribution for the p.s.p.s could not be fitted by a Poisson distribution. The anionic selectivity of the conductance evoked by GABA was investigated by using the potassium salts of a range of anions to fill the electrodes. Depolarizing spontaneous p.s.p.s were seen in all cells impaled with electrodes containing potassium chloride, iodide, bromide, nitrate, or chlorate. In these cells, the reversal potential for the response to electrophoretically applied GABA was displaced in the depolarizing direction and the evoked recurrent i.p.s.p. was reversed. When anions with hydrated shells larger than chlorate (bicarbonate, sulphate, chromate, acetate or citrate) were used, spontaneous depolarizing p.s.p.s were not seen, and the reversal potential for the response to somatic GABA application and for the evoked recurrent i.p.s.p. lay between -70 and -75 mV.

Action Potentials↗
PubMed1978

The distribution of bumps in the tail of the locust photoreceptor afterpotential.

An extended tail or prolonged depolarizing afterpotential (PDA) follows the receptor potential of a locust retinula cell when the stimulating light is in the intensity range that saturates the receptor potential. The amplitude and duration of this afterpotential depend on the intensity and duration of the stimulus. As the afterpotential decays, apparently exponentially, it becomes resolved into bumps, which we call light-induced dark bumps (LID bumps). The intervals between light-induced dark bumps are distributed in a way that is indistinguishable from a random (Poisson) distribution. As previously demonstrated, LID bumps are indistinguishable from bumps directly induced by low intensity light in light-adapted cells, which in turn grade into the slightly larger bumps produced, each by a single photon, in dark-adapted cells. The light-induced dark bumps continue for up to an hour in darkness, slowly becoming like dark-adapted bumps in amplitude and shape. To account for the random occurrence and discrete features of bumps after so long a latency, we propose that intense light generates a significant amount of an intermediate molecule or packet which decays slowly to start the same process that normally generates bumps with a short delay.

Animals↗
PubMed2001

Sampling for the sugarcane borer (Lepidoptera: Crambidae) on sugarcane in Louisiana.

A 3-yr study was conducted in 0.6- to 2.0-ha sugarcane fields throughout south Louisiana under varying sugarcane borer, Diatraea saccharalis (F.), density levels to determine the spatial dispersion of infestations and to develop a sequential sampling plan. Infestations of D. saccharalis were randomly dispersed. Infestation levels (percentage of stalks infested) ranged from 0.6 to 33.3%. Frequency distributions of the number of infested stalks indicated that the Poisson distribution best fit the data Tests of other distributions (negative binomial [aggregated], binomial [uniform], geometric, and hypergeometric) resulted in poorer fits. The sequential sampling plan devised, with lower and upper D. saccharalis infestation limits of 2 and 5% and 5 and 10%, required maximum average sample numbers of 7.1 and 5.5 (20-stalk samples), respectively, to make terminating management decisions. It is our assessment that implementation of these plans would decrease sampling effort by 50-60% when compared with sampling programs currently in use for D. saccharalis management decisions in Louisiana.

Animals↗
PubMed1996

Complete interference and nonrandom distribution of meiotic crossover in a mollusc, Mulinia lateralis (Say).

In gene mapping, the genetic distance between two genes is measured by the frequency of meiotic crossovers occurring between them. It is generally assumed that there is more than one crossover per chromosome, and the distribution of crossovers along chromosomes is random and follows a Poisson distribution (no interference), or that interference is inversely correlated with distance. Although those assumptions may be correct for some organisms, we report here a novel exception in the marine mollusc Mulinia lateralis Say. Using segregation analysis of gynogenetic diploids, we found surprisingly high gene-centromere recombinant frequencies for most of the 13 allozyme loci studied. For at least six loci, there was always one and only one crossover occurring between the gene and its centromere, suggesting complete interference where the occurrence of one crossover completely suppressed the occurrence of another. The complete interference was confirmed by the cytogenetic observation that there was only one chiasma for all bivalents. Further, sites of the single crossover seem not to be randomly distributed along chromosomes, but preferentially located in a recombination hot-region proximal to the centromere. The restricted distribution of a single crossover per chromosome provides one explanation for the unique phenomenon of heterozygote deficiency in M. lateralis and other molluscs.

Animals↗
PubMed1981

[Frequency of chromosome aberrations induced in human peripheral lymphocytes by in vitro 60Co gamma quanta at doses of 1 to 5 Gr. in an analysis of the 1st-division cells at different fixation times].

The quantitative analysis of chromosomal aberrations in the first division cells of 50-, 54-, 58-, 52- and 66-hour peripheral blood lymphocytes cultures of healthy donors was performed after irradiation in vitro with 60Co gamma-quantums at doses 1--5 Gy. Cells of the first division were identified by a differential staining of sister chromatid method using 5-bromdeoxyuridine. No significant differences in frequencies of aberrant cells and aberrations of chromosomal type were found between cultures fixed at different times. The distribution of dicentrics in cells did not differ from the Poisson distribution regardless of fixation times and doses. On the basis of these findings it is concluded that chromosomes of human peripheral blood lymphocytes passing the cell cycle at different rates have approximately equal radiosensitivity.

Chromosome Aberrations↗
PubMed1981

[Radiotherapeutically induced chromosome aberrations: studies in "biological dosimetry"].

The yield of chromosome aberrations (dicentric chromosomes, ring chromosomes) induced in lymphocytes of four radiotherapy patients was determined. In each case this yield was drastically increased when compared with the spontaneous incidence, the dicentric frequencies increasing by the following factors: 604, 525, 600, and 725. With the aid of the dicentric yield obtained, the following equivalent whole body doses were estimated ("biological dosimetry"): 309, 286, 308, and 341 rd. Comparing the observed with the theoretical number of cells with 0, 1, 2, 3 ... dicentrics ("distribution analysis"), we found a highly significant departure from the Poisson distribution, as was to be expected after partial body irradiation. The distribution analysis seems principally suited to discriminate between partial and whole body irradiation.

Adult↗
PubMed2006

Non-normal path analysis in the presence of measurement error and missing data: a Bayesian analysis of nursing homes' structure and outcomes.

Path analytic models are useful tools in quantitative nursing research. They allow researchers to hypothesize causal inferential paths and test the significance of these paths both directly and indirectly through a mediating variable. A standard statistical method in the path analysis literature is to treat the variables as having a normal distribution and to estimate paths using several least squares regression equations. The parameters corresponding to the direct paths have point and interval estimates based on normal distribution theory. Indirect paths are a product of the direct path from the independent variable to the mediating variable and the direct path of the mediating variable to the dependent variable. However, in the case of non-normal distributions, the point and interval estimates of the indirect path become much more difficult to estimate. We address the issue of calculating indirect point and interval estimates in the case of non-normally distributed data. Our substantive application is a nursing home research problem in which the variables in the path analysis of interest involve variables with normal, Bernoulli, or Poisson distributions. Additionally, one of the Poisson variables is observed with error. This paper addresses estimating point and interval estimation of indirect paths for variables with non-normal distributions in the presence of missing data and measurement error. We handle these difficulties from a fully Bayesian point of view. We present our substantive path analysis motivated from a nursing home structure, process, and outcomes model. Our results focus on the impact job turnover in the nursing homes has on nursing home outcomes.

Data Interpretation, Statistical↗