Thomas M. Gerig

Effects of mixtures of four phenolic acids on leaf area expansion of cucumber seedlings grown in Portsmouth B1 soil materials.

Cucumber seedlings growing in a 1∶2 mixture of soil (Portsmouth B1) and sand adjusted to pH 5.2 were treated every other day five times with 0, 0.0625, 0.125, 0.25, or 0.5 μmol/g soil of ferulic, caffeic,p-coumaric,p-hydroxybenzoic, protocatechuic, sinapic, syringic, or vanillic acids. Treatments began when seedlings were 8 days old. The effects on mean absolute rates of leaf expansion were used to estimate the relative potencies of these phenolic acids to ferulic acid. Based on the results of this experiment, ferulic,p-coumaric,p-hydroxybenzoic, and vanillic acids were chosen for further study. Materials and procedures were identical in the second study, but treatments consisted of mixtures of the four phenolic acids at concentration combinations designed to achieve 40 % or 60 % inhibition of absolute rates of leaf expansion. Using joint action analysis, a model describing the action of the phenolic acid mixtures was developed. A model involving only two factor terms was sufficient to describe the observed responses of cucumber leaf area to the phenolic acid mixtures. The action ofp-hydroxybenzoic acid on absolute rates of leaf expansion was inhibited by the presence of the other three phenolic acids. No other antagonisms or synergisms existed among the four compounds.

Effects of mixtures of phenolic acids on phosphorus uptake by cucumber seedlings

To determine how individual phenolic acids in a mixture might affect phosphorus (P) uptake, 15-day-old cucumber seedlings grown in solution culture were treated with ferulic, vanillic,p-coumaric, or equimolar mixtures of these phenolic acids. Phenolic acid and P uptake were determined by solution depletion. The joint action of the mixtures of these phenolic acids on P uptake was primarily additive. Thus, as the number of phenolic acids increased in the mixture, the concentrations of the individual phenolic acids in the mixture required to bring about a given response declined. Seedling uptake of individual phenolic acids from solution mixtures of phenolic acids was reduced when compared to the uptake of phenolic acids from single phenolic acid solutions. The magnitude of the reduction varied with phenolic acid and concentration. The dose required for 50% inhibition of P uptake was approximately two to three times higher for vanillic acid (6.73 mM) than for ferulic (2.27 mM) andp-coumaric acids (3.00 mM) when dose was based on the initial treatment concentrations. The dose required for 50% inhibition of P uptake was not significantly different for the three phenolic acids (42 ± 5 μmol/g root fresh weight) when dose was based on phenolic acid uptake. Potential reasons for these differences are discussed.

Simultaneous effects of ferulic andp-coumaric acids on cucumber leaf expansion in split-root experiments

Experiments were conducted to determine how plant responses to mixtures of allelochemicals may change as the proportion of roots in contact with allelochemicals is modified. Thirteen-day-old cucumber seedlings were treated with ferulic and/orp-coumaric acid in a split-root nutrient culture system. Leaf areas were determined just prior to treatment and at harvest, 24 hr after treatment. Ferulic acid was more inhibitory to cucumber leaf expansion thanp-coumaric acid. The effects of ferulic andp-coumaric acids on leaf expansion were additive. For individual acids, mixtures of ferulic andp-coumaric acids in the same container and combinations of ferulic andp-coumaric acids in separate containers, the inhibition of leaf expansion was directly related to the product of the concentration of the acid(s) and the proportion of roots treated with the acid(s). Pretreatment with 0.2 or 0.4 mM ferulic acid and subsequent treatment with 0.5 mM ferulic acid failed to show evidence of acclimation by cucumber seedlings.

Effects of mixtures of phenolic acids on leaf area expansion of cucumber seedlings grown in different pH portsmouth A1 soil materials.

Cucumber seedlings growing in A1horizon Portsmouth soil material adjusted to pH 5.2, 6.0, or 6.9 were treated with 0, 0.25 or 0.5, μmol/ g soil ferulic acid,p-coumaric acid, vanillic acid, or an equal mixture (0.5 μmol/g total) of two acids every other day. A total of five treatments was given starting with day 7 from seeding. Absolute rates of leaf expansion were determined for seedlings. The experiment was terminated when seedlings were 17 days old. All three phenolic acids inhibited leaf expansion. The dose required for 50% inhibition of absolute rates of leaf expansion increased as pH of the soil systems increased. The order of toxicity based on 50% dose and relative potency were as follows: ferulic acid > vanillic acid =p-coumaric acid. Effects of mixtures of phenolic acids on absolute rates of leaf expansion, when compared to the effects of individual phenolic acids, were found to be antagonistic for the ferulic-vanillic acid mixture and the ferulic-p-coumaric acid mixture in the pH 5.2 soil systems. Several phenolic acid treatments were required before antagonistic effects of mixtures were evident. In all other instances, when treatment effects were significant, the effects of individual phenolic acids were additive.

Statistical analysis of the joint inhibitory action of similar compounds.

A statistical model is presented that characterizes the joint action of similar compounds when the response variable is continuous. The model allows for antagonistic and synergistic as well as similar joint (additive) action of compounds. It also allows for differential potencies in the compounds. A method of statistical analysis using nonlinear regression analysis is presented along with sample SAS code for carrying it out. An efficient experimental design is given in the form of a set of mixture combinations. Two generalizations of the model are discussed. An example is presented relating the joint action of ferulic and vanillic acids to the growth of cucumber seedlings.

MLE in Two Normal Samples with Equal but Unknown Population Coefficients of Variation

Abstract Maximum likelihood estimates are derived for the parameters of two normal populations with coefficients of variation equal but unknown. Formulas are provided for calculating the asymptotic variances and covariances of the estimates. The relative efficiency of the proposed mean estimator with respect to the sample mean is shown to be greater than one. The effect of departures from the assumptions of normality and of equal coefficients of variation on this relative efficiency are studied. An example is provided with data from wildlife populations to illustrate the proposed methods.

Time series realizations obtained according to an experimental design

Abstract This article presents a data analysis approach consisting of a synthesis of experimental design methods and spectral methods of time series analysis which is appropriate in exploratory situations where the recording process generates a long sequence of correlated observations.

Modification of an inhibition curve to account for effects of a second compound

Three methods are proposed for modifying a logistic inhibition curve for a primary compound to account for the role of a second compound. The assumptions underlying each of the three resulting models-similar joint action, multiplicative, and modification-are discussed. The models are compared and model selection procedures are given. An example is presented in which the inhibiting effect ofp-coumaric acid on the growth of morning-glory plants is modified by the addition of glucose.

Computing methods for linear models subject to linear parametric constraints

An efficient and accurate computational form for β which minimizes using the Moore-Penrose g-inverse is given, No rank conditions are imposed on R or X, The results are applied (i) to estimate the parameters in linear model which are subject to linear equality constraints and (ii) to obtain the generalized inverse of X″X which yields a solution of the normal equations subject to non-estimable constraints on the parameters.

Computations for constrained linear models

Abstract The article presents an algorithm for linear regression computations subject to linear parametric equality constraints, linear parametric inequality constraints, or a mixture of the two. No rank conditions are imposed on the regression specification or the constraint specification. The algorithm requires a full Moore-Penrose g-inverse which entails extra computational effort relative to other orthonormalization type algorithms. In exchange, auxiliary statistical information is generated: feasibility of a set of constraints may be checked, estimability of a linear parametric function may be checked, and bias and variance may be decomposed by source.