A dye-binding induced conformational transition of poly-(methacrylic acid) by Auramine O in aqueous solutions. I. Experimental results

Binding of auramine O to poly-(methacrylic acid) (PMA) has been established over a large range of C⁰_p/C⁰_d values using spectroscopic methods (UV absorption and visible fluorescence emission spectra), equilibrium and sedimentation dialysis, potentiometric and viscosimetric titrations. All the results show qualitative agreement with those obtained previously with the system crystal violet-PMA although the binding seems to be less strong for auramine O than for crystal violet. From dialysis experiments binding isotherms were obtained at three different degrees of neutralization α'; at α' = 0.10 the results could be fitted to a Langmuir isotherm but at α' equal to 0.40 and 0.65 deviations with respect to such an isotherm occur. The results of potentiometric and viscosimetric titrations confirm that the conformational transition which the dye-free PMA exhibits upon ionization is affected by the dye binding. The region in which the conformational transion occurs is broadened and is less sharply defined in the presence of auramine O.     

Estimation of prediction error variances via Monte Carlo sampling methods using different formulations of the prediction error variance

Calculation of the exact prediction error variance covariance matrix is often computationally too demanding, which limits its application in REML algorithms, the calculation of accuracies of estimated breeding values and the control of variance of response to selection. Alternatively Monte Carlo sampling can be used to calculate approximations of the prediction error variance, which converge to the true values if enough samples are used. However, in practical situations the number of samples, which are computationally feasible, is limited. The objective of this study was to compare the convergence rate of different formulations of the prediction error variance calculated using Monte Carlo sampling. Four of these formulations were published, four were corresponding alternative versions, and two were derived as part of this study. The different formulations had different convergence rates and these were shown to depend on the number of samples and on the level of prediction error variance. Four formulations were competitive and these made use of information on either the variance of the estimated breeding value and on the variance of the true breeding value minus the estimated breeding value or on the covariance between the true and estimated breeding values.