Improved method for measuring the apparent CO2 photocompensation point resolves the impact of multiple internal conductances to CO2 to net gas exchange

There is a growing interest in accurate and comparable measurements of the CO₂ photocompensation point (Γ*), a vital parameter to model leaf photosynthesis. The Γ* is measured as the common intersection of several CO₂ response curves, but this method may incorrectly estimate Γ* by using linear fits to extrapolate curvilinear responses and single conductances to convert intercellular photocompensation points (C_i*) to chloroplastic Γ*. To determine the magnitude and minimize the impact of these artefacts on Γ* determinations, we used a combination of meta‐analysis, modelling and original measurements to develop a framework to accurately determine C_i*. Our modelling indicated that the impact of using linear fits could be minimized based on the measurement CO₂ range. We also propose a novel method of analysing common intersection measurements using slope–intercept regression. Our modelling indicated that slope–intercept regression is a robust analytical tool that can help determine if a measurement is biased because of multiple internal conductances to CO₂. Application of slope–intercept regression to Nicotiana tabacum and Glycine max revealed that multiple conductances likely have little impact to C_i* measurements in these species. These findings present a robust and easy to apply protocol to help resolve key questions concerning CO₂ conductance through leaves.     

Prediction of Side Chain Orientations in Proteins by Statistical Machine Learning Methods

Abstract

We develop ways to predict the side chain orientations of residues within a protein structure by using several different statistical machine learning methods. Here side chain orientation of a given residue i is measured by an angle Ω_i between the vector pointing from the center of the protein structure to the C^α _i atom and the vector pointing from the C^α _i atom to the center of its side chain atoms. To predict the Ω_i angles, we construct statistical models by using several different methods such as general linear regression, a regression tree and bagging, a neural network, and a support vector machine. The root mean square errors for the different models range only from 36.67 to 37.60 degrees and the correlation coefficients are all between 30% and 34%. The performances of different models in the test set are, thus, quite similar, and show the relative predictive power of these models to be significant in comparison with random side chain orientations.     

Frequency responses of cat rapidly adapting mechanoreceptive fibers

The frequency responses of 11 rapidly adapting (RA) fibers in cat were studied by representing the average firing rate as a function of sinusoidal stimulus amplitude and stimulus frequency. Specifically, rate-intensity functions at different stimulation frequencies were fitted by four-parameter (a₀, a₁, a₂, a₃), piece-wise linear functions using nonlinear regression (n = 59; R² > 0.877). Rate-intensity functions at intermediate frequencies were found by linear interpolation. The result of this analysis is rate–amplitude–frequency functions plotted as two-dimensional surfaces. The surfaces consist of five regions separated and sufficiently defined by four space curves. At 14 different frequencies, the statistical distribution of each rate-intensity-function parameter could be approximated by a particular lognormal distribution (n = 56; R² > 0.796). The Kolmogorov–Smirnov test fails to reject this hypothesis for each combination of frequency and parameter (56 tests; p > 0.39). Therefore, at a given frequency, the variation of the parameters can be represented by lognormal distributions with specific means and standard deviations. Responses of six RA fibers, which are different from the data-set used for modeling, were compared with the stochastic model at different frequencies. The parameters of those fibers were tested against the null hypotheses that they were sampled from the particular parameter distributions dictated by the model. The Kolmogorov–Smirnov test fails to reject all the hypotheses at the α = 0.05 level (44 tests). At the α = 0.10 level, only a few test parameters were found to be departing from the model (a₀ and a₁ at 5?Hz; a₂ at 20?Hz; a₂ and a₃ at 50?Hz). The remaining test parameters could be accurately described by the model. Having confirmed the validity of the model, the logarithmic means and the logarithmic standard deviations of the lognormally distributed rate-intensity-function parameters were estimated in the frequency range of 4–200?Hz. The rate–amplitude–frequency surfaces sampled from the established stochastic model completely characterize the rate responses of RA fibers to sinusoidal stimuli and are superior to tuning curves which require selecting criterion responses. The current rate-response model is promising for future computational work, especially on population modeling.     

A Comparison of Different Estimation Methods for Fungicide EC50 and EC95 Values

EC₅₀ and EC₉₅ (the effective concentrations to cause inhibitions by 50 and 95%, respectively) are commonly used to express fungicide potency. Different methods are currently employed to calculate EC₅₀ and EC₉₅ values. In this study, EC₅₀ and EC₉₅ values for fungicide epoxiconazole against 34 isolates of Sclerotinia sclerotiorum were calculated with seven different methods. Results showed that for both EC₅₀ and EC₉₅ calculations, there was no significant difference among three statistical programs IBM spss ^®, GraphPad Prism^® and dps ^® (P ≥ 0.066). Methods linear log (linear regression of mycelial growth inhibition vs. logarithmic concentration) and interpolation log (linear interpolation from inhibition and logarithmic concentration data) were not significantly different (P ≥ 0.058) from IBM spss in EC₅₀ calculations. These results indicate that among the seven methods, the three statistical programs IBM spss , GraphPad Prism, dps and linear log method are appropriate for EC₅₀ calculations. But for EC₉₅ calculations, only the three statistical programs are recommended, and GraphPad Prism is likely to give a little higher values than spss and dps .     

The determination of sensitivity parameters for auxin-induced H+-efflux from Avena coleoptile segments

Abstract A method is described for the measurement of auxin-induced H⁺-efflux from small populations of Avena coleoptile segments. The method allows the simultaneous investigation of the kinetics of rapid auxin responses over a wide concentration range. IAA promoted linear rates of H⁺-efflux and the change in amplitude of response occurred mainly over a low, narrow concentration range (10–50 μmol m^-3). The sigmoidal curve of best-fit to each set of dose-response data was determined using non-linear regression techniques, allowing the objective determination of characteristic tissue sensitivity parameters (R_MIN, R_MAX, K_D and p). The sensitivity parameters for the auxin-type herbicide fluroxypyr are also presented as well as IAA parameters determined in the presence of abscisic acid and the ‘antiauxin’ PCIB. The interpretation of the parameter values and the potential use of sensitivity parameter analysis for the evaluation of theories concerning plant hormone action and interaction is discussed.     

The effect of structural parameters and positive charge distance on the interaction free energy of antimicrobial peptides with membrane surface

Many attempts have been made to find hints explaining the relationship between physicochemical and structural properties of antimicrobial peptides (AMPs) which are relevant to their antimicrobial activities. We here found that there is a difference in the percentages of hydrophobic, hydrophilic, and charged residues between AMPs killing both bacteria and fungi (Group A) and AMPs that only kill bacteria (Group B). The percentage of charged residues in Group A AMPs is highly elevated, while in Group B the percentage of hydrophobic residues is increased. This result suggests a sequence-based mechanism of selectivity for AMPs. Moreover, we examined how the distance between basic residues affects the interaction free energy of AMPs with the membrane surface, since most of the known AMPs act by membrane perturbation. We measured the average distance between basic residues throughout the 3D structure of AMPs by defining D_pr parameter and calculated the interaction free energy for 10 AMPs that interacted with the DPPC membrane using molecular dynamics simulation. We found that the changes of the interaction free energy correlates with the change of D_pr by a linear regression coefficient of r^2?=?.47 and a cubic regression coefficient of r^2?=?.70.     

Toxicity and persistence of Spinosad® (Conserve 0.024% and Tracer 24%) to Zizyphus fruit fly,Carpomyia incompleta Becker (Diptera: Tephritidae), under laboratory conditions

Two forms of the insecticide (Spinosad^®) are recommended by the Egyptian Ministry of Agriculture and Reclaimed Areas for the control of the fruit flies. One form is for partial spray on fruit trees and one form is for soil treatment. (a) Conserve 0.024% application: statistical analysis indicated that the toxicity regression line had a linear order with a coefficient of determination R² = 0.779. The LC₅₀ was determined by both mathematically and from the illustrated line as 95.17 ppm. Persistent regression line was of the first-order line with regression coefficient of ?16, simple correlation of 0.977 and coefficient of determination of 0.9552. The T₅₀ was found to be 2.2 days. (b) Tracer 24% application: toxicity regression line has a linear order; the simple correlation was found to be 0.819; and the coefficient of determination (R²) was found to be 0.6712. The LC50 was determined by both mathematically and from the illustrated line as 15.5 ppm. Spinosad has a different mode of action from other pesticides and is most effective when applied in planned programmes with other insecticides of different mode of action. Moreover, users must avoid the use of same active ingredient or mode of action on consecutive generations of insect. However, repeated applications to control a single generation are acceptable. Thus, we strongly recommend applying Spinosad as a soil application to control the last generation of the summer season.     

Inference on Collapsibility in Generalized Linear Models

GREENLAND and MICKEY (1988) derived a closed-form collapsibility test and confidence interval for IxJxK contingency tables with qualitative factors, and presented a small simulation study of its performance. We show how their method can be extended to regression models linear in the natural parameter of a one-parameter exponential family, in which the parameter of interest is the difference of “crude” and “adjusted” regression coefficients. A simplification of the method yields a generalization of the test for omitted covariates given by HAUSMAN (1978) for ordinary linear regression. We present an application to a study of coffee use and myocardial infarction, and a simulation study which indicates that the simplified test performs adequately in typical epidemiologic settings.     

Accurate kinetic parameter estimation during progress curve analysis of systems with endogenous substrate production

We have identified an error in the published integral form of the modified Michaelis–Menten equation that accounts for endogenous substrate production. The correct solution is presented and the error in both the substrate concentration, S, and the kinetic parameters V_m, K_m, and R resulting from the incorrect solution was characterized. The incorrect integral form resulted in substrate concentration errors as high as 50% resulting in 7–50% error in kinetic parameter estimates. To better reflect experimental scenarios, noise containing substrate depletion data were analyzed by both the incorrect and correct integral equations. While both equations resulted in identical fits to substrate depletion data, the final estimates of V_m, K_m, and R were different and K_m and R estimates from the incorrect integral equation deviated substantially from the actual values. Another observation was that at R = 0, the incorrect integral equation reduced to the correct form of the Michaelis–Menten equation. We believe this combination of excellent fits to experimental data, albeit with incorrect kinetic parameter estimates, and the reduction to the Michaelis–Menten equation at R = 0 is primarily responsible for the incorrectness to go unnoticed. However, the resulting error in kinetic parameter estimates will lead to incorrect biological interpretation and we urge the use of the correct integral form presented in this study. Biotechnol. Bioeng. 2011;108: 2499–2503. © 2011 Wiley Periodicals, Inc.     

Buckley–James boosting model based on extreme learning machine and random survival forests

Buckley–James (BJ) model is a typical semiparametric accelerated failure time model, which is closely related to the ordinary least squares method and easy to be constructed. However, traditional BJ model built on linearity assumption only captures simple linear relationships, while it has difficulty in processing nonlinear problems. To overcome this difficulty, in this paper, we develop a novel regression model for right-censored survival data within the learning framework of BJ model, basing on random survival forests (RSF), extreme learning machine (ELM), and L₂ boosting algorithm. The proposed method, referred to as ELM-based BJ boosting model, employs RSF for covariates imputation first, then develops a new ensemble of ELMs—ELM-based boosting algorithm for regression by ensemble scheme of L₂ boosting, and finally, uses the output function of the proposed ELM-based boosting model to replace the linear combination of covariates in BJ model. Due to fitting the logarithm of survival time with covariates by the nonparametric ELM-based boosting method instead of the least square method, the ELM-based BJ boosting model can capture both linear covariate effects and nonlinear covariate effects. In both simulation studies and real data applications, in terms of concordance index and integrated Brier sore, the proposed ELM-based BJ boosting model can outperform traditional BJ model, two kinds of BJ boosting models proposed by Wang et al., RSF, and Cox proportional hazards model.     

Correlation of Tm and sequence of DNA duplexes with delta H computed by an improved empirical potential method

T_m values for 20 DNA duplexes with different repeating base sequences provided the data base for developing a rational and relatively simple methodology for computing apparent enthalpies for the helix → coil transitions of DNA helices, ΔH _calc. The computational variables and their range of acceptable values were selected on the basis of physically plausible arguments. Over 350,000 different combinations of the variables were tested for degree of fit. It was therby possible to find a combination giving a high degree of linear fit between T_m and ΔH _calc (correlation coefficient, 0.99), with T_m values deviating (on average) from the regression line by only ±2.17°C. Most of this uncertainty is attributed to experimental limitations, although computational approximations also contribute. With ΔH _calc for the melting of each of the unique complementary dinucleotide fragments computed by the method developed, it is possible to estimate T_m and (relative) ΔH _calc reliable for the melting of any particular DNA [with base pairs G(I)·C and A·T] given only its base sequence. The ΔH_calc values for the complementary dinucleotide fragments, together with statistical considerations, make it apparent that T_m of DNAs with repeating base sequence show only an approximate linear dependence on G·C content because A·T and G·G pairs do not contribute to helix stability independently of the base-pair sequence in which they occur. In fact, the nearestneighbor stacking interactions are so significant that certain complementary dinucleotide fragment sequences with 0,50, and 100% G·C content have the same stability.     

A Mixed Model for Binary Data: The Modified X2-test

In this paper, a statistical model for clinical trials is presented for the special situation that a varying and unstructered number of binary responses is obtained from each subject. The assumptions of the model are the following: 1.) For each subject there is a (constant) individual Bernoulli parameter determining the distribution of the binary responses of this subject. 2.) The Bernoulli parameters associated with the subjects are realizations of independent random variables with distributions P_g in treatment group g(g = 1, 2, …, G). 3.) Given the value of the Bernoulli parameter, the observations are stochastically independent within each subject. Under these assumptions, a test statistic is derived to test the hypothesis H₀:E(P₁) = E(P₂) = … = E(P_G). It is proven and demonstrated by simulations, that the test statistic asymptotically (i.e. for a large number of subjects) follows the X²-distribution.     

Experimental Design for Bayesian Estimations in the Linear Regression Model Taking Costs into Account

It is assumed that a known, correct, linear regression model (model I) is given. Let the problem be based on a Bayesian estimation of the regression parameter so that any available a priori information regarding this parameter can be used. This Bayesian estimation is, squared loss, an optimal strategy for the overall problem, which is divided into an estimation and a design problem. For practical reasons, the effort involved in performing the experiment will be taken into account as costs. In other words, the experimental design must result in the greatest possible accuracy for a given total cost (restriction of the sample size n). The linear cost function k(x) = 1 + c (x - a)/(b - a) is used to construct costoptimal experimental designs for simple linear regression by means of V = H = [a, b] in a way similar to that used for classical optimality criteria. The complicated structures of these designs and the difficulty in determining them by a direct approach have made it appear advisable to describe an iterative procedure for the construction of cost-optimal designs.     

Misconceptions about the comparison of intrinsic rates of natural increase

The intrinsic rate of natural increase (r_m) is a common measurement in entomology to describe and evaluate the growth and adaptation of a population of arthropods to certain environmental conditions. Following the method of Birch, the r_m is the solution of an exponential equation, which depends on the whole life cycle of each female and her survival time. A simplification of this equation was provided by Wyatt and White, which allows the study to be shortened as it does not depend on any survival times and only a part of the life cycle of the females. Therefore, this method has become quite popular among entomologists. As the r_m is a population parameter, it lacks any variance and thus a valid statistical comparison of r_ms for different populations is not straightforward. Hence, many approaches include statistical misconceptions. We discuss those approaches, apply them to real data and demonstrate some drawbacks of them. Furthermore, we present an easy to implement and consistent method for the comparison of r_ms.     

A Primer on Interpreting Regression Models

Abstract: We perceive a need for more complete interpretation of regression models published in the wildlife literature to minimize the appearance of poor models and to maximize the extraction of information from good models. Accordingly, we offer this primer on interpretation of parameters in single- and multi-variable regression models. Using examples from the wildlife literature, we illustrate how to interpret linear zero-intercept, simple linear, semi-log, log-log, and polynomial models based on intercepts, coefficients, and shapes of relationships. We show how intercepts and coefficients have biological and management interpretations. We examine multiple linear regression models and show how to use the signs (+, -) of coefficients to assess the merit and meaning of a derived model. We discuss 3 methods of viewing the output of 3-dimensional models (y, x₁, x₂) in 2-dimensional space (sheet of paper) and illustrate graphical model interpretation with a 4-dimensional logistic regression model. Statistical significance or Akaike best-ness does not prevent the appearance of implausible regression models. We recommend that members of the peer review process be sensitive to full interpretation of regression models to forestall bad models and maximize information retrieval from good models     

On the analysis of straight line data in pharmacology and biochemistry

The determination of drug potency, efficacy and receptor affinity constants, common calculations in pharmacology and biochemistry, require estimates of the slope and intercept of a linear regression line obtained from measured points (x_i, y_i). Three questions not explicitly covered in the basic statistical literature and, consequently, answered differently by scientists, arise often. (1) When there exist several y's corresponding to each value of the controlled parameter x, should all of these be used as points or only their average value at that x in constructing the line? (2) What are precise confidence limits of an abscissa corresponding to a specified ordinale? (3) What are confidence limits for the intercepts of a regression line whose slope is constrained to +1 or -1? In this paper we show that all the data should be used (question 1) and provide derivations for the formulas used to get the confidence limits mentioned in questions (2) and (3).     

Oxygen transfer coefficients by dynamic model moment analysis

A new method to estimate the oxygen transfer coefficient (K_La) from the experimental dynamic response data is presented. Employing a linear model which allows for gas phase, diffusion film, and oxygen electrode dynamics, the first moment of the response curve is simply related to the sum of the model parameters. Two separate experiments are used to characterize the measurement dynamics and to measure the unknown K_La parameter. The simple calculation procedure involves only measuring the area above the response curves.     

Toxicity and efficacy of selected pesticides and new acaricides to stored product mites (Acari: Acaridida)

Stored product mites can often infest stored products, but currently there is little information regarding the efficacy of pesticides that can be used for control. In this study we evaluated several common pesticides formulated from single active ingredients (a.i.) or commercially available mixtures (chlorpyrifos, deltamethrin, beta-cyfluthrin, and a combination of deltamethrin and S-bioallethrin), plus an acaricide composed of permethrin, pyriproxyfen and benzyl benzolate, for efficacy against Acarus siro, Tyrophagus putrescentiae, and Aleuroglyphus ovatus. The pesticides were incorporated into the mite diets in a dose range of 10–1000 μg a.i. g⁻¹ diet. Concentrations for suppression of 50 and 90% population growth and eradication (rC₀) of mites were fit to linear regression models. None of the tested pesticides gave complete eradication of A. siro, which was the most tolerant of the three mite species tested. The most effective pesticide Allergoff 175 CS was a combination product (a nano-capsule suspension of permethrin, pyriproxyfen and benzyl benzolate) labeled for dust mites, with rC₀ range of 463–2453 μg a.i. (permethrin) g⁻¹ diet depending on the species. Least effective were chlorpyrifos and deltamethrin.     

Efficient Estimation of Protein Binding Constants

Assays of cyclic AMP typically employ a Scatchard-like data analysis to estimate the total binding protein R_T and the dissociation constant K_d. The linear regression procedure employed is statistically ad hoc because the response variable (bound counts) occurs on both sides of the Scatchard equation. The alternative analysis presented here is derived from the cyclic AMP binding reaction. The resulting data analysis, employing non-linear least squares, results in estimators that on the basis of Monte Carlo studies have less bias and greater precision than the Scatchard method.     

Evaluation of missing data imputation methods for human osteometric measurements

It is not uncommon for biological anthropologists to analyze incomplete bioarcheological or forensic skeleton specimens. As many quantitative multivariate analyses cannot handle incomplete data, missing data imputation or estimation is a common preprocessing practice for such data. Using William W. Howells' Craniometric Data Set and the Goldman Osteometric Data Set, we evaluated the performance of multiple popular statistical methods for imputing missing metric measurements. Results indicated that multiple imputation methods outperformed single imputation methods, such as Bayesian principal component analysis (BPCA). Multiple imputation with Bayesian linear regression implemented in the R package norm2, the Expectation–Maximization (EM) with Bootstrapping algorithm implemented in Amelia, and the Predictive Mean Matching (PMM) method and several of the derivative linear regression models implemented in mice, perform well regarding accuracy, robustness, and speed. Based on the findings of this study, we suggest a practical procedure for choosing appropriate imputation methods.