Biology of communities estimation of species richness of a community by its species structure,as illustrated by the macrophytes of Vityaz Bay in the Sea of Japan

Five methods of computing species richness in community are discussed using the example of a well-studied macrophytic taxocoen: (1) fitting an ogive for lognormal distribution; (2) model fitting of a rank curve for this distribution; (3) iterative computation of statistical moments using Hald’s method; (4) computation of these moments by explicit functions; and (5) model fitting of a “species-area” curve. According to the repeatability of results and simplicity of computing, the best method is the computation of statistical moments by explicit functions. The degree of our knowledge about a particular community could be considered as the ratio of the number of actually distinguished species to the greatest expected number.     

Ligand binding distributions in nucleic acids

We illustrate a new method for the determination of the complete binding polynomial for nucleic acids based on experimental titration data with respect to ligand concentration. From the binding polynomial, one can then calculate the distribution function for the number of ligands bound at any ligand concentration. The method is based on the use of a finite set of moments of the binding distribution function, which are obtained from the titration curve. Using the maximum-entropy method, the moments are then used to construct good approximations to the binding distribution function. Given the distribution functions at different ligand concentrations, one can calculate all of the coefficients in the binding polynomial no matter how many binding sites a molecule has. Knowledge of the complete binding polynomial in turn yields the thermodynamics of binding. This method gives all of the information that can be obtained from binding isotherms without the assumption of any specific molecular model for the nature of the binding. Examples are given for the binding of Mn(2+) and Mg(2+) to t-RNA and for the binding of Mg(2+) and I(6) to poly-C using literature data.     

Generalized Exponential Distribution in Flood Frequency Analysis for Polish Rivers

Many distributions have been used in flood frequency analysis (FFA) for fitting the flood extremes data. However, as shown in the paper, the scatter of Polish data plotted on the moment ratio diagram shows that there is still room for a new model. In the paper, we study the usefulness of the generalized exponential (GE) distribution in flood frequency analysis for Polish Rivers. We investigate the fit of GE distribution to the Polish data of the maximum flows in comparison with the inverse Gaussian (IG) distribution, which in our previous studies showed the best fitting among several models commonly used in FFA. Since the use of a discrimination procedure without the knowledge of its performance for the considered probability density functions may lead to erroneous conclusions, we compare the probability of correct selection for the GE and IG distributions along with the analysis of the asymptotic model error in respect to the upper quantile values. As an application, both GE and IG distributions are alternatively assumed for describing the annual peak flows for several gauging stations of Polish Rivers. To find the best fitting model, four discrimination procedures are used. In turn, they are based on the maximized logarithm of the likelihood function (K procedure), on the density function of the scale transformation maximal invariant (QK procedure), on the Kolmogorov-Smirnov statistics (KS procedure) and the fourth procedure based on the differences between the ML estimate of 1% quantile and its value assessed by the method of moments and linear moments, in sequence (R procedure). Due to the uncertainty of choosing the best model, the method of aggregation is applied to estimate of the maximum flow quantiles.     

Evaluation and Minimization of Uncertainty in ITC Binding Measurements: Heat Error,Concentration Error,Saturation, and Stoichiometry

BackgroundIsothermal titration calorimetry (ITC) is uniquely useful for characterizing binding thermodynamics, because it straightforwardly provides both the binding enthalpy and free energy. However, the precision of the results depends on the experimental setup and how thermodynamic results are obtained from the raw data.MethodsExperiments and Monte Carlo analysis are used to study how uncertainties in injection heat and concentration propagate to binding enthalpies in various scenarios. We identify regimes in which it is preferable to fix the stoichiometry parameter, N, and evaluate the reliability of uncertainties provided by the least squares method.ResultsThe noise in the injection heat is mainly proportional in character, with ~ 1% and ~ 3% uncertainty at 27C and 65C, respectively; concentration errors are ~ 1%. Simulations of experiments based on these uncertainties delineate how experimental design and curve fitting methods influence the uncertainty in the final results.ConclusionsIn most cases, experimental uncertainty is minimized by using more injections and by fixing N at its known value. With appropriate technique, the uncertainty in measured binding enthalpies can be kept below ~ 2% under many conditions, including low C values.General SignificanceWe quantify uncertainties in ITC data due to heat and concentration error, and identify practices to minimize these uncertainties. The resulting guidelines are important when ITC data are used quantitatively, such as to test computer simulations of binding. Reproducibility and further study are supported by free distribution of the new software developed here.     

Protein denaturant binding polynomials

We show how moments of the denaturant binding distribution function can be extracted from experimental data on the denaturation of a protein as a function of the concentration of denaturant and how in turn these moments can be used to construct the denaturant binding distribution function. This approach is similar to our recent work on using the maximum-entropy method to construct ligand-binding distributions from moments obtained from titration curves for nucleic acids and proteins. As an example we take literature data on the denaturation of ferro- and ferricytochrome c by guanidine hydrochloride and from it construct the denaturant binding polynomial and binding distribution function for the unfolded protein.     

Fluorescence pattern photobleaching recovery for samples with multi-component diffusion

The translational mobility of proteins and lipids in phospholipid bilayers is often not well described as ideal self diffusion. One of the best methods for characterizing such non-ideal diffusion is to use fluorescence pattern photobleaching recovery. In this method, the spatial gradient of the monitoring and bleaching intensity is created by using epi-fluorescence and an expanded Gaussian-shaped laser beam which passes though a Ronchi ruling placed at the back image plane of a microscope. A difficulty arises when the fluorescence recovery from the exchange of slowly diffusing molecules between illuminated and non-illuminated stripes temporally overlaps with the recovery from the exchange of more rapidly diffusing molecules through the gradient produced by the broad Gaussian shape of the illumination. In the work presented here, a general theory is developed that describes the shape of the resulting fluorescence recovery curve for these typical experimental conditions. Approximate expressions amenable to non-linear curve fitting are also given. The new theoretical formalism has been demonstrated on data for the translational mobility of a fluorescent lipid probe in phospholipid bilayers deposited on planar-fused silica substrates.     

Flow cytometry as a new method for the measurement of electrophoretic mobility of erythrocytes using membrane charge staining by fluoresceinated polycations.

The binding of FITC-labeled poly-L-ornithine and poly-L-lysine to fresh or neuraminidase treated human, rat or rabbit erythrocytes was investigated by simultaneous cell volume and cell membrane fluorescence measurements in a flow cytometer. The cell volume was converted into cell surface and the distribution curve of the fluorescence/micrometer2 cell surface was calculated from all histogram classes by a computer program. The mean fluorescence/micrometer2 cell surface as a measure of the density of the negative charges on the cell surface was directly proportional to the elctrophoretic mobility of the erythrocytes, showing that polycation binding can effectively be used for the measurement of the electrophoretic mobility of erythrocytes. The computer fitting of the experimental two parameter histograms by two dimensional Gaussian normal distributions was found to be a very efficient way of data reduction, and a good separation of overlapping cell clusters was possible even in the case of low total numbers of cells in the histogram.     

Accurate quantification of diffusion and binding kinetics of non-integral membrane proteins by FRAP

Non-integral membrane proteins frequently act as transduction hubs in vital signaling pathways initiated at the plasma membrane (PM). Their biological activity depends on dynamic interactions with the PM, which are governed by their lateral and cytoplasmic diffusion and membrane binding/unbinding kinetics. Accurate quantification of the multiple kinetic parameters characterizing their membrane interaction dynamics has been challenging. Despite a fair number of approximate fitting functions for analyzing fluorescence recovery after photobleaching (FRAP) data, no approach was able to cope with the full diffusion-exchange problem. Here, we present an exact solution and matlab fitting programs for FRAP with a stationary Gaussian laser beam, allowing simultaneous determination of the membrane (un)binding rates and the diffusion coefficients. To reduce the number of fitting parameters, the cytoplasmic diffusion coefficient is determined separately. Notably, our equations include the dependence of the exchange kinetics on the distribution of the measured protein between the PM and the cytoplasm, enabling the derivation of both k(on) and k(off) without prior assumptions. After validating the fitting function by computer simulations, we confirm the applicability of our approach to live-cell data by monitoring the dynamics of GFP-N-Ras mutants under conditions with different contributions of lateral diffusion and exchange to the FRAP kinetics.     

Estimation of Clustering Parameters Using Gaussian Process Regression

We propose a method for estimating the clustering parameters in a Neyman-Scott Poisson process using Gaussian process regression. It is assumed that the underlying process has been observed within a number of quadrats, and from this sparse information the distribution is modelled as a Gaussian process. The clustering parameters are then estimated numerically by fitting to the covariance structure of the model. It is shown that the proposed method is resilient to any sampling regime. The method is applied to simulated two-dimensional clustered populations and the results are compared to a related method from the literature.     

Quantitative analysis of electrophoresis data: novel curve fitting methodology and its application to the determination of a protein-DNA binding constant.

A computer program, GelExplorer, which uses a new methodology for obtaining quantitative information about electrophoresis has been developed. It provides a straightforward, easy-to-use graphical interface, and includes a number of features which offer significant advantages over existing methods for quantitative gel analysis. The method uses curve fitting with a nonlinear least-squares optimization to deconvolute overlapping bands. Unlike most curve fitting approaches, the data is treated in two dimensions, fitting all the data across the entire width of the lane. This allows for accurate determination of the intensities of individual, overlapping bands, and in particular allows imperfectly shaped bands to be accurately modeled. Experiments described in this paper demonstrate empirically that the Lorentzian lineshape reproduces the contours of an individual gel band and provides a better model than the Gaussian function for curve fitting of electrophoresis bands. Results from several fitting applications are presented and a discussion of the sources and magnitudes of uncertainties in the results is included. Finally, the method is applied to the quantitative analysis of a hydroxyl radical footprint titration experiment to obtain the free energy of binding of the lambda repressor protein to the OR1 operator DNA sequence.     

Model Testing in Radioligand/Receptor Interaction by Monte Carlo Simulation

Abstract

Monte Carlo simulations have been applied for evaluating the reliability of parameter estimates as well as for testing models in radioligand saturation binding experiments. Scatchard analysis was compared to the nonlinear least-square curve fitting method for one-site saturation binding curves. It was found that linear regression analysis from the transformed data in the Scatchard plot yielded generally less accurate parameter estimates than nonlinear regression analysis of untransformed data. The advantage of the nonlinear least-squares curve fitting method was especially pronounced in cases where the scatter and number of data points, as well as the radioligand concentration range, were chosen similar to less optimal experimental conditions. Under such circumstances, several K_D and B_max values derived by Scatchard analysis led to physically impossible negative values whereas the same data analyzed by nonlinear regression yielded reasonable parameter estimates. Furthermore, it was found that for both means of analysis, K_D and B_max correlated positively. In another set of Monte Carlo experiments, saturation binding curves involving two receptor sites were generated and subsequently analyzed according to both a one-site and a two-site model. The confidence with which one is able to distinguish the two-site model from nonlinear least-squares curve fitting was then estimated for optimal, as well as for, less ideal experimental condigions.     

时间分辨荧光光谱测量结果的一种数据处理改进方法

在综合矩方法和拉普拉斯变换方法原理的基础上,本文报道一种时间相关单光子计数测出的荧光衰变动力学曲线的数据处理的改进方法.此方法使我们能在花费时间较少的条件下得出和用最小二乘法拟合相比拟的准确分析结果.这一方法的优点已被用于分析香豆素102+DCM和香豆素102+PBBO激光染料乙醇溶液的双指数荧光衰变过程的结果所证实,此外,本文也讨论了仪器时间漂移校正及拉普拉斯变换的数据截取问题.     

Separation of 5'-ribonucleoside monophosphates by ion-pair reverse-phase high-performance liquid chromatography

We have developed computer programs for characterization of ligand-binding systems in terms of continuous affinity distributions of arbitrary shape based on a numerical finite difference method. This method provides an excellent initial estimate of the affinity distribution, which can be further refined by means of nonlinear least-squares curve fitting. The method has been extensively tested for several cases including receptor heterogeneity, cooperativity, and for several examples of experimental design (e.g., ligand concentrations), and various levels of random and systematic experimental errors. The results provide a guide to experimental design, and indicate limits to the resolution obtained by ligand-binding studies, irrespective of the method of analysis.     

Fluctuation analysis in small chemically reacting systems

A theory of noise fluctuations is developed which is applicable to systems of any size in which unimolecular or bimolecular reactions are occurring. The main difference between small and large reacting systems is that in the former the probability of finding a particle in a particular state does not obey a Gaussian distribution, but satisfies a distribution which reflects the mechanism of the chemical reaction. This difference is reflected in the main result of the theory: an autocorrelation function that is expressible as a sum of exponentials, the amplitudes of which are explicit functions of the moments of the distribution. Thus, by using small systems, the autocorrelation function,in principle, allows the elucidation of reaction mechanisms. Numerical simulations indicate that for reacting systems having ten or fewer particles, the deviation of the autocorrelation function from a single exponential should be easily detectable, and that estimates of the first four moments of the distribution should be possible. Accurate inference of the distribution, however, will require further mathematical and experimental advances.     

Radiation pressure on a biconcave human Red Blood Cell and the resulting deformation in a pair of parallel optical traps

We calculated the three‐dimensional optical stress distribution and the resulting deformation on a biconcave human red blood cell (RBC) in a pair of parallel optical trap. We assumed a Gaussian intensity distribution with a spherical wavefront for each trapping beam and calculated the optical stress from the momentum transfer associated with the reflection and refraction of the incident photons at each interface. The RBC was modelled as a biconcave thin elastic membrane with uniform elasticity and a uniform thickness of 0.25 μm. The resulting cell deformation was determined from the optical stress distribution by finite element software, Comsol Structure Mechanics Module, with Young's modulus (E) as a fitting parameter in order to fit the theoretical results for cell elongation to our experimental data. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Failure of adaptive self-organized criticality during epileptic seizure attacks

Critical dynamics are assumed to be an attractive mode for normal brain functioning as information processing and computational capabilities are found to be optimal in the critical state. Recent experimental observations of neuronal activity patterns following power-law distributions, a hallmark of systems at a critical state, have led to the hypothesis that human brain dynamics could be poised at a phase transition between ordered and disordered activity. A so far unresolved question concerns the medical significance of critical brain activity and how it relates to pathological conditions. Using data from invasive electroencephalogram recordings from humans we show that during epileptic seizure attacks neuronal activity patterns deviate from the normally observed power-law distribution characterizing critical dynamics. The comparison of these observations to results from a computational model exhibiting self-organized criticality (SOC) based on adaptive networks allows further insights into the underlying dynamics. Together these results suggest that brain dynamics deviates from criticality during seizures caused by the failure of adaptive SOC.     

Mixed model analysis of censored longitudinal data with flexible random-effects density

Mixed models are commonly used to represent longitudinal or repeated measures data. An additional complication arises when the response is censored, for example, due to limits of quantification of the assay used. While Gaussian random effects are routinely assumed, little work has characterized the consequences of misspecifying the random-effects distribution nor has a more flexible distribution been studied for censored longitudinal data. We show that, in general, maximum likelihood estimators will not be consistent when the random-effects density is misspecified, and the effect of misspecification is likely to be greatest when the true random-effects density deviates substantially from normality and the number of noncensored observations on each subject is small. We develop a mixed model framework for censored longitudinal data in which the random effects are represented by the flexible seminonparametric density and show how to obtain estimates in SAS procedure NLMIXED. Simulations show that this approach can lead to reduction in bias and increase in efficiency relative to assuming Gaussian random effects. The methods are demonstrated on data from a study of hepatitis C virus.     

Interpreting the equatorial diffraction pattern of collagenous tissues in the light of molecular motion.

The equatorial diffraction pattern associated with collagenous tissues, particularly type I collagen, is diffuse and clearly unlike that from crystals. Hukins and Woodhead-Galloway proposed a statistical model that they termed a "liquid crystal" for collagen fibers in tendons. Fratzl et al. applied this model to both unmineralized and mineralized turkey leg tendon, a model that ignores the organization imposed by the well-known cross-linking. The justification for adopting this model is that the curve fits the data. It is shown that the data can be equally well matched by fitting a least-squares curve consisting of a second-order polynomial plus a Gaussian. The peak of the Gaussian is taken as the equatorial spacing of the collagen. A physical explanation for this model is given, as is a reason for the changes in the spacing with changes in water content of the tissue. The diffusion is attributed to thermally driven agitation of the molecules, in accordance with the Debye-Waller theory including the Gaussian distribution. The remainder of the diffusion is attributed to other scattering sources like the mineral crystallites.     

State vector models of the cell cycle II: The first three moments of the transit time distribution.

A discrete time state vector model (the Hahn model) has been used to simulate many experiments in cell kinetics. In the first paper in this series the authors described a new method to define the parameters of the Hahn model suitable for use in automatic fitting of fraction of labelled mitoses (FLM) experiments. In this paper it is shown how to compute the first three moments of the transit time distribution which arises from a Hahn model. These moments are compared analytically and numerically to the corresponding moments of the distribution the authors used to define the Hahn model. Finally, the problems involved in estimating the moments of the transit time distribution observed in fitting FLM data using a Hahn model are discussed.     

Robust Gaussian Graphical Modeling Via l1 Penalization

Summary Gaussian graphical models have been widely used as an effective method for studying the conditional independency structure among genes and for constructing genetic networks. However, gene expression data typically have heavier tails or more outlying observations than the standard Gaussian distribution. Such outliers in gene expression data can lead to wrong inference on the dependency structure among the genes. We propose a l₁ penalized estimation procedure for the sparse Gaussian graphical models that is robustified against possible outliers. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its own likelihood. An efficient computational algorithm based on the coordinate gradient descent method is developed to obtain the minimizer of the negative penalized robustified‐likelihood, where nonzero elements of the concentration matrix represents the graphical links among the genes. After the graphical structure is obtained, we re‐estimate the positive definite concentration matrix using an iterative proportional fitting algorithm. Through simulations, we demonstrate that the proposed robust method performs much better than the graphical Lasso for the Gaussian graphical models in terms of both graph structure selection and estimation when outliers are present. We apply the robust estimation procedure to an analysis of yeast gene expression data and show that the resulting graph has better biological interpretation than that obtained from the graphical Lasso.