The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells

Simulated neural impulse trains were generated by a digital realization of the integrate-and-fire model. The variability in these impulse trains had as its origin a random noise of specified distribution. Three different distributions were used: the normal (Gaussian) distribution (no skew, normokurtic), a first-order gamma distribution (positive skew, leptokurtic), and a uniform distribution (no skew, platykurtic). Despite these differences in the distribution of the variability, the distributions of the intervals between impulses were nearly indistinguishable. These inter-impulse distributions were better fit with a hyperbolic gamma distribution than a hyperbolic normal distribution, although one might expect a better approximation for normally distributed inverse intervals. Consideration of why the inter-impulse distribution is independent of the distribution of the causative noise suggests two putative interval distributions that do not depend on the assumed noise distribution: the log normal distribution, which is predicated on the assumption that long intervals occur with the joint probability of small input values, and the random walk equation, which is the diffusion equation applied to a random walk model of the impulse generating process. Either of these equations provides a more satisfactory fit to the simulated impulse trains than the hyperbolic normal or hyperbolic gamma distributions. These equations also provide better fits to impulse trains derived from the maintained discharges of ganglion cells in the retinae of cats or goldfish. It is noted that both equations are free from the constraint that the coefficient of variation (CV) have a maximum of unity. The concluding discussion argues against the random walk equation because it embodies a constraint that is not valid, and because it implies specific parameters that may be spurious.     

Depolarization Laplace Transform Analysis of Exchangeable Hyperpolarized Xe for Detecting Ordering Phases and Cholesterol Content of Biomembrane Models

We present a highly sensitive nuclear-magnetic resonance technique to study membrane dynamics that combines the temporary encapsulation of spin-hyperpolarized xenon (¹²⁹Xe) atoms in cryptophane-A-monoacid (CrA_ma) and their indirect detection through chemical exchange saturation transfer. Radiofrequency-labeled Xe@CrA_ma complexes exhibit characteristic differences in chemical exchange saturation transfer-driven depolarization when interacting with binary membrane models composed of different molecular ratios of DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine) and POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine). The method is also applied to mixtures of cholesterol and POPC. The existence of domains that fluctuate in cluster size in DPPC/POPC models at a high (75–98%) DPPC content induces up to a fivefold increase in spin depolarization time τ at 297 K. In POPC/cholesterol model membranes, the parameter τ depends linearly on the cholesterol content at 310 K and allows us to determine the cholesterol content with an accuracy of at least 5%.     

Depolarization Laplace Transform Analysis of Exchangeable Hyperpolarized 129Xe for Detecting Ordering Phases and Cholesterol Content of Biomembrane Models

We present a highly sensitive nuclear-magnetic resonance technique to study membrane dynamics that combines the temporary encapsulation of spin-hyperpolarized xenon (¹²⁹Xe) atoms in cryptophane-A-monoacid (CrA_ma) and their indirect detection through chemical exchange saturation transfer. Radiofrequency-labeled Xe@CrA_ma complexes exhibit characteristic differences in chemical exchange saturation transfer-driven depolarization when interacting with binary membrane models composed of different molecular ratios of DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine) and POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine). The method is also applied to mixtures of cholesterol and POPC. The existence of domains that fluctuate in cluster size in DPPC/POPC models at a high (75–98%) DPPC content induces up to a fivefold increase in spin depolarization time τ at 297 K. In POPC/cholesterol model membranes, the parameter τ depends linearly on the cholesterol content at 310 K and allows us to determine the cholesterol content with an accuracy of at least 5%.     

The Distribution of Mutation Effects on Viability in Drosophila Melanogaster

Parameters of continuous distributions of effects and rates of spontaneous mutation for relative viability in Drosophila are estimated by maximum likelihood from data of two published experiments on accumulation of mutations on protected second chromosomes. A model of equal mutant effects gives a poor fit to the data of the two experiments; higher likelihoods are obtained with leptokurtic distributions or for models in which there is more than one class of mutation effect. Minimum estimates of mutation rates (events per generation) at polygenes affecting viability on chromosome 2 are 0.14 and 0.068, but estimates are strongly confounded with other parameters in the model. Separate information on rates of molecular divergence between Drosophila species and from rates of movement of transposable elements is used to infer the overall genomic mutation rate in Drosophila, and the viability data are analyzed with mutation rate as a known parameter. If, for example, a mutation rate for chromosome 2 of 0.4 is assumed, maximum likelihood estimates of mean mutant effect on relative viability are 0.4% and 1%, but the majority of mutations have very much smaller effects than these values as distributions are highly leptokurtic. The methodology is applied to estimate viability effects of single P element insertional mutations. The mean effect per insertion is found to be higher, and their distribution is found to be less leptokurtic than for spontaneous mutations. The equilibrium genetic variance of viability predicted by a mutation-selection balance model with parameters estimated from the mutation accumulation experiments is similar to laboratory estimates of genetic variance of viability from natural populations of Drosophila.     

Contrasting Diversity Values: Statistical Inferences Based on Overlapping Confidence Intervals

Ecologists often contrast diversity (species richness and abundances) using tests for comparing means or indices. However, many popular software applications do not support performing standard inferential statistics for estimates of species richness and/or density. In this study we simulated the behavior of asymmetric log-normal confidence intervals and determined an interval level that mimics statistical tests with P(α) = 0.05 when confidence intervals from two distributions do not overlap. Our results show that 84% confidence intervals robustly mimic 0.05 statistical tests for asymmetric confidence intervals, as has been demonstrated for symmetric ones in the past. Finally, we provide detailed user-guides for calculating 84% confidence intervals in two of the most robust and highly-used freeware related to diversity measurements for wildlife (i.e., EstimateS, Distance).     

On the distribution of developmental errors: comparing the normal, gamma, and log-normal distribution

The amount of between‐individual variation in the unobservable developmental instability (DI) has been the subject of intense recent debates. The unexpectedly high estimates of between‐individual variation in DI based on distributional characteristics of observable asymmetry values (of on average bilaterally symmetric traits) rely on statistical models that assume an underlying normal distribution of developmental errors. This prompted doubts on the assumption of the Gaussian nature of developmental errors. However, when applying other candidate distributions [log‐normal and gamma (γ)], recent analyses of empirical datasets have indicated that estimates remain generally high. Yet, all estimates were based on bilaterally symmetric traits, which did not allow for a formal comparison of the alternative distributions. In the present study, we extend a recent statistical model to allow statistical comparison of the different distributions based on traits that developed repeatedly under the same conditions, such as flower traits and regrown feathers. We analyse simulated and empirical data and show that: (1) it is statistically difficult to differentiate among the three alternatives when variances are small relative to the mean, as is often the case with DI; (2) the normal distribution fits the log‐normal or γ relatively well under those circumstances; (3) the deviance information criterion (DIC) is able to pick up differences in model fit among the three alternative distributions, yet more strongly so when levels of DI were high; (4) empirical datasets show a better fit of the normal over the log‐normal and γ‐distributions as judged by the DIC; and (5) estimates of between‐individual variation in DI in the three empirical datasets were relatively high (> 50%) under each distributional assumption. In conclusion, and based on our three datasets, the normal approximation appears to be a reasonable choice for statistical models of DI and the remarkably high estimates of variation in DI cannot be attributed to non‐normal developmental noise. Nevertheless, our method should be applied to a broad range of traits and organisms to evaluate the generality of this result. We argue that there is an urgent need for studies that reveal the underlying mechanisms of developmental noise and stability, as well as the role of developmental selection, in order to be able to determine the biological importance of the highly skewed distributions of developmental instability often observed. © 2007 The Linnean Society of London, Biological Journal of the Linnean Society, 2007, 92 , 197–210.     

Genetic Regulation of Development in Sorghum bicolor: II. Effect of the ma(3) Allele Mimicked by GA(3)

The photoperiodic behavior and other developmental and morphological differences of 11 maturity genotypes (as identified by JR Quinby 1967, Adv Agron 19: 267-305) of the milo group of Sorghum bicolor (L.) Moench were studied under 8, 10, 12, and 14 hour photoperiods. Sorghum is a quantitative short day plant. The genotypes studied differ in genes which modify photoperiodic behavior and thus maturity; the alleles are designated as Ma₁, ma₁, Ma₂, ma₂, Ma₃, ma₃, and ma₃^R (single symbols indicate homozygosity at the indicated gene loci). Based on floral initiation (differentiation) under 10, 12, and 14 hour photoperiods the 11 genotypes were assigned to three clases: (I) flower initiation delayed by 12 hour photoperiods (all genotypes with Ma₁Ma₂ but not ma₃^R), (II) flower initiation delayed by 14 hour photoperiods (all genotypes with Ma₁ma₂, ma₁Ma₂, or ma₁ma₂ but not ma₃^R), (III) flower initiation not drastically delayed by 14 hour photoperiods (all genotypes with ma₃^R). All of the class III genotypes were taller, had longer leaf sheaths, narrower and longer leaf blades, and less leaf area, than the other genotypes. In addition, the class III genotypes initiated rapid culm and thus internode elongation sooner after floral initiation than any of the class I or II genotypes. Dry weight did not differ between the class III genotypes and the others. The rate of leaf emergence in the class III genotypes and all others was indistinguishable until after floral initiation in the former. The allelic combination unique to class I, Ma₁Ma₂, makes plants very photoperiod sensitive without causing observable changes in morphology or other development events. The allelic combination unique to class III, ma₃^R, makes plants relatively photoperiod insensitive and results in several differences in morphology and development.     

Novel liquid chromatographic assay for the low-level determination of apomorphine in plasma

A novel HPLC assay which is rapid, reproducible and sensitive has been developed for the analysis of apomorphine in plasma. The assay incorporates boldine as an internal standard, and uses solid-phase extraction on C₁₈ mini-columns for sample clean-up and concentration, so enabling quantitation of apomorphine at 500 pg/ml using fluorescence detection (λ_ex 270 nm, λ_em). The HPLC assay comprised a 25 cm-long Techopakk C₁₈ column and a mobile phase of (0.25 M sodium dihydrogen phosphate plus 0.25% heptane sulphonic acid, to pH 3.3 with orthophosphoric acid) containing 30% (v/v) methanol and 0.003% (w/v) EDTA, run at a flow-rate of 1.5 ml/min. Calibration plots prepared in plasma were linear over the range 1–30 ng/ml, (limit of quantitation (LOQ)=490 PG/ML) with R.S.D. of 0.05% and R.E. of 5.0% at the level of 1 ng/ml. Preliminary pharmacokinetic data from two patients given apomorphine by 12 h subcutaneous infusion (patient A dose=35 mg and patient B dose=141 mg) showed apomorphine elimination from plasma to fit a two-compartment model, with initial half-lives of 8.2 and 46.6 min, elimination half-lives of 76.4 and 166.5 min and area under the plasma concentration-time curve (AUC) values of 236 and 405 ng h/ml, respectively.     

Distribution of Polymorphus minutus among its intermediate hosts

Hirsch R. P. 1979. Distribution of Polymorphus minutus among its intermediate hosts. International journal for Parasitology10: 243–248. In 1971, Crofton investigated patterns of distribution of Polymorphus minutus in the intermediate host, Gammarus pulex. Among his conclusions were: (1) P. minutus populations occur in patterns similar to negative binomial distributions, and (2) parasite-induced host mortality results in patterns similar to truncated (high end) negative binomial distributions. Those conclusions, however, were not tested by statistical analyses. To test Crofton's observations, Chi-square goodness of fit tests were applied to data used by Crofton and an additional two stations sampled by Hynes & Nicholas in 1963. Analyses were expanded to include five theoretical distributions, four patterns of host mortality and various rates of host mortality. Truncated forms of negative binomial, positive binomial and Poisson distributions were also investigated where nontruncated distributions failed to fit observed distributions. It was found that negative binomial distributions most frequently describe patterns of P. minutus distribution with the exception of one population described by Poisson and another by positive binomial distributions. Crofton's assumption that truncated distributions result from parasite-induced host mortality seems unlikely in light of those analyses.     

Understanding the structure of cognitive noise

Human cognition is fundamentally noisy. While routinely regarded as a nuisance in experimental investigation, the few studies investigating properties of cognitive noise have found surprising structure. A first line of research has shown that inter-response-time distributions are heavy-tailed. That is, response times between subsequent trials usually change only a small amount, but with occasional large changes. A second, separate, line of research has found that participants’ estimates and response times both exhibit long-range autocorrelations (i.e., 1/f noise). Thus, each judgment and response time not only depends on its immediate predecessor but also on many previous responses. These two lines of research use different tasks and have distinct theoretical explanations: models that account for heavy-tailed response times do not predict 1/f autocorrelations and vice versa. Here, we find that 1/f noise and heavy-tailed response distributions co-occur in both types of tasks. We also show that a statistical sampling algorithm, developed to deal with patchy environments, generates both heavy-tailed distributions and 1/f noise, suggesting that cognitive noise may be a functional adaptation to dealing with a complex world.     

The distribution of the effects of genes affecting quantitative traits in livestock

Meta-analysis of information from quantitative trait loci (QTL) mapping experiments was used to derive distributions of the effects of genes affecting quantitative traits. The two limitations of such information, that QTL effects as reported include experimental error, and that mapping experiments can only detect QTL above a certain size, were accounted for. Data from pig and dairy mapping experiments were used. Gamma distributions of QTL effects were fitted with maximum likelihood. The derived distributions were moderately leptokurtic, consistent with many genes of small effect and few of large effect. Seventeen percent and 35% of the leading QTL explained 90% of the genetic variance for the dairy and pig distributions respectively. The number of segregating genes affecting a quantitative trait in dairy populations was predicted assuming genes affecting a quantitative trait were neutral with respect to fitness. Between 50 and 100 genes were predicted, depending on the effective population size assumed. As data for the analysis included no QTL of small effect, the ability to estimate the number of QTL of small effect must inevitably be weak. It may be that there are more QTL of small effect than predicted by our gamma distributions. Nevertheless, the distributions have important implications for QTL mapping experiments and Marker Assisted Selection (MAS). Powerful mapping experiments, able to detect QTL of 0.1σ_p, will be required to detect enough QTL to explain 90% the genetic variance for a quantitative trait.     

Photoperiod and plant growth regulator combinations influence growth and physiological responses in Pelargonium sidoides DC.

The aim of the present study was to evaluate the influence of photoperiod and meta-methoxytopolin riboside (MemTR)-auxin combinations on in vitro growth and physiological responses of Pelargonium sidoides DC. Shoot proliferation was highest under the conventional 16-h photoperiod. Based on the superiority of MemTR among other cytokinins from our previous study, it was selected for evaluating the cytokinin-auxin combination effect under long-day conditions. MemTR-auxin combinations had a significant effect on shoot proliferation compared to the control. The highest shoot proliferation rate (4.5 shoots/explant) was obtained on Murashige and Skoog medium supplemented with a combination of MemTR (1.0 μM) and α-naphthaleneacetic acid (NAA; 0.5 μM). Furthermore, combinations of MemTR and auxins had a synergistic effect on the concentration of photosynthetic pigments. On the other hand, photoperiod had no significant effect on the concentration of photosynthetic pigments. Formation of leaf glandular trichomes was influenced by photoperiod. Both 12- and 16-h photoperiods led to higher glandular trichome densities on the abaxial leaf surfaces of P. sidoides compared to plants grown under the 24-h photoperiod. MemTR-auxin combinations had a significant effect on the concentration of total phenolic compounds and flavonoids.     

Fuzzy Logic Based Edge Detection in Smooth and Noisy Clinical Images

Edge detection has beneficial applications in the fields such as machine vision, pattern recognition and biomedical imaging etc. Edge detection highlights high frequency components in the image. Edge detection is a challenging task. It becomes more arduous when it comes to noisy images. This study focuses on fuzzy logic based edge detection in smooth and noisy clinical images. The proposed method (in noisy images) employs a 3×3 mask guided by fuzzy rule set. Moreover, in case of smooth clinical images, an extra mask of contrast adjustment is integrated with edge detection mask to intensify the smooth images. The developed method was tested on noise-free, smooth and noisy images. The results were compared with other established edge detection techniques like Sobel, Prewitt, Laplacian of Gaussian (LOG), Roberts and Canny. When the developed edge detection technique was applied to a smooth clinical image of size 270×290 pixels having 24 dB ‘salt and pepper’ noise, it detected very few (22) false edge pixels, compared to Sobel (1931), Prewitt (2741), LOG (3102), Roberts (1451) and Canny (1045) false edge pixels. Therefore it is evident that the developed method offers improved solution to the edge detection problem in smooth and noisy clinical images.     

Predicting Chemical Environments of Bacteria from Receptor Signaling

Sensory systems have evolved to respond to input stimuli of certain statistical properties, and to reliably transmit this information through biochemical pathways. Hence, for an experimentally well-characterized sensory system, one ought to be able to extract valuable information about the statistics of the stimuli. Based on dose-response curves from in vivo fluorescence resonance energy transfer (FRET) experiments of the bacterial chemotaxis sensory system, we predict the chemical gradients chemotactic Escherichia coli cells typically encounter in their natural environment. To predict average gradients cells experience, we revaluate the phenomenological Weber''s law and its generalizations to the Weber-Fechner law and fold-change detection. To obtain full distributions of gradients we use information theory and simulations, considering limitations of information transmission from both cell-external and internal noise. We identify broad distributions of exponential gradients, which lead to log-normal stimuli and maximal drift velocity. Our results thus provide a first step towards deciphering the chemical nature of complex, experimentally inaccessible cellular microenvironments, such as the human intestine.     

Mechanisms of pollen deposition by insect pollinators

Summary Studies of pollen dispersal in insect-pollinated plants have often documented highly leptokurtic patterns of pollen deposition that can increase the likelihood of long-distance mating. To examine potential causes of highly leptokurtic deposition, we introduce four functions that arise when (1) the duration of pollinator visits to pollen sources is limited, (2) the rate of pollen deposition varies randomly among pollinators and/or among visits, (3) the rate of pollen deposition changes monotonically over time or (4) pollen is carried in layers or compartments on the pollinator's body that differ in deposition rate. Maximum likelihood techniques were used to fit deposition functions to data obtained from honey bees (Apis mellifera L.) visiting mustard plants (Brassica campestris L.) that contained a marker gene. Each of the alternative leptokurtic functions fit the experimental data better than a simple exponential function and the best-fit function predicted a mean pollen dispersal distance more than three times greater than the exponential. We argue that studies of pollen deposition need to test a broader range of deposition models to assess outcrossing distance in plant populations accurately.     

Three-dimensional FRET reconstruction microscopy for analysis of dynamic molecular interactions in live cells

Analysis of cellular pathways requires concentration measurements of dynamically interacting molecules within the three-dimensional (3D) space of single living cells. Förster resonance energy transfer (FRET) microscopy from widefield, from confocal, and potentially from superresolution microscopes can access this information; however, these measurements are distorted by the inherent 3D blurring of optical imaging, spectral overlap of fluorophores, and detection noise. We propose a mathematical model of these processes and demonstrate, through simulation, how these distortions limit the dynamic range and sensitivity of conventional FRET microscopy. Using this model, we devise and validate a new approach (called 3D-FRET stoichiometry reconstruction, 3DFSR) for reconstructing 3D distributions of bound and free fluorescent molecules. Previous attempts to reconstruct 3D-FRET data relied on sequential spectral unmixing and deconvolution, a process that corrupts the detection statistics. We demonstrate that 3DFSR is superior to these approaches since it simultaneously models spectral mixing, optical blurring, and detection noise. To achieve the full potential of this technique, we developed an instrument capable of acquiring 3D-FRET data rapidly and sensitively from single living cells. Compared with conventional FRET microscopy, our 3D-FRET reconstruction technique and new instrumentation provides orders of magnitude gains in both sensitivity and accuracy wherein sustained high-resolution four-dimensional (x,y,z,t) imaging of molecular interactions inside living cells was achieved. These results verify previous observations that Cdc42 signaling is localized to the advancing margins of forming phagosomes in macrophages.     

High-Bandwidth Protein Analysis Using Solid-State Nanopores

High-bandwidth measurements of the ion current through hafnium oxide and silicon nitride nanopores allow the analysis of sub-30 kD protein molecules with unprecedented time resolution and detection efficiency. Measured capture rates suggest that at moderate transmembrane bias values, a substantial fraction of protein translocation events are detected. Our dwell-time resolution of 2.5 μs enables translocation time distributions to be fit to a first-passage time distribution derived from a 1D diffusion-drift model. The fits yield drift velocities that scale linearly with voltage, consistent with an electrophoretic process. Further, protein diffusion constants (D) are lower than the bulk diffusion constants (D₀) by a factor of ∼50, and are voltage-independent in the regime tested. We reason that deviations of D from D₀ are a result of confinement-driven pore/protein interactions, previously observed in porous systems. A straightforward Kramers model for this inhibited diffusion points to 9- to 12-kJ/mol interactions of the proteins with the nanopore. Reduction of μ and D are found to be material-dependent. Comparison of current-blockage levels of each protein yields volumetric information for the two proteins that is in good agreement with dynamic light scattering measurements. Finally, detection of a protein-protein complex is achieved.     

Statistical optimisation of medium components for chitinase production byPaenibacillus sabina strain JD2

Paenibacillus sabina strain JD2, a chitinolytic marine bacterium, was isolated from sea dumps collected at Sultanpur near Bhavnagar, India and its nutritional requirement for chitinase production was defined using statistical optimisation method. Effect of 8 different medium components on chitinase production byPaenibacillus sabina strain JD2 was screened by Plackett-Burman design. The screened medium components were further used in central composite design where chitinase production, pH and biomass responses were used in different models to evaluate fit ones. After performing power transformation, quadratic model was found to be fit for chitinase response and 2F1 model was found to be fit for biomass response. Whilst for pH response, quadratic model was found to be fit without any requirement of power transformation. In multiresponse analysis, medium formulation consisting of (g/l): chitin 18, yeast extract 0.50, and CaCl₂ 0.08, was found to predict 82.93 U/ml of chitinase with overall highest desirability of 0.842 as compared to other formulations. The selection of model was done on basis of high adjusted R² value and loweredp-value for each model in individual analysis of each response. Through desirability analysis, it was found that biomass and pH played an important role in increasing the chitinase production byPaenibacillus sabina strain JD2. Through statistical optimisation method, 2.74-fold increase in chitinase production was achieved as compared to unoptimised medium.