Helle Sørensen

A review of independent action compared to concentration addition as reference models for mixtures of compounds with different molecular target sites

From a theoretical point of view, it has often been argued that the model of independent action (IA) is the most correct reference model to use for predicting the joint effect of mixtures of chemicals with different molecular target sites. The theory of IA, however, relies on a number of assumptions that are rarely fulfilled in practice. It has even been argued that, theoretically, the concentration addition (CA) model could be just as correct. In the present study, we tested the accuracy of both IA and CA in describing binary dose-response surfaces of chemicals with different molecular targets using statistical software. We compared the two models to determine which best describes data for 158 data sets. The data sets represented 98 different mixtures of, primarily, pesticides and pharmaceuticals tested on one or several of seven test systems containing one of the following: Vibrio fischeri, activated sludge microorganisms, Daphnia magna, Pseudokirchneriella subcapitata, Lemna minor, Tripleurospermum inodorum, or Stellaria media. The analyses showed that approximately 20% of the mixtures were adequately predicted only by IA, 10% were adequately predicted only by CA, and both models could predict the outcome of another 20% of the experiment. Half of the experiments could not be correctly described with either of the two models. When quantifying the maximal difference between modeled synergy or antagonism and the reference model predictions at a 50% effect concentration, neither of the models proved significantly better than the other. Thus, neither model can be selected over the other on the basis of accuracy alone.

Hormesis in mixtures — Can it be predicted?

Binary mixture studies are well established for mixtures of pollutants, pesticides, or allelochemicals and sound statistical methods are available to evaluate the results in relation to reference models. The majority of mixture studies are conducted to investigate the effect of one compound on the inhibitory action of another. However, since stimulatory responses to low concentrations of chemicals are gaining increased attention and improved statistical models are available to describe this phenomenon of hormesis, scientists are challenged by the question of what will happen in the low concentration range when all or some of the chemicals in a mixture induce hormesis? Can the mixture effects still be predicted and can the size and concentration range of hormesis be predicted? The present study focused on binary mixtures with one or both compounds inducing hormesis and evaluated six data sets of root length of Lactuca sativa L. and areal growth of Lemna minor L., where substantial and reproducible hormetic responses to allelochemicals and herbicides have been found. Results showed that the concentration giving maximal growth stimulatory effects (M) and the concentration where the hormetic effect had vanished (LDS) could be predicted by the most-used reference model of concentration addition (CA), if the growth inhibitory concentrations (EC50) followed CA. In cases of deviations from CA at EC50, the maximum concentration M and the LDS concentration followed the same deviation patterns, which were described by curved isobole models. Thus, low concentration mixture effects as well as the concentration range of hormesis can be predicted applying available statistical models, if both mixture partners induce hormesis. Using monotonic concentration-response models instead of biphasic concentration-response models for the prediction of joint effects, thus ignoring hormesis, slightly overestimated the deviation from CA at EC20 and EC50, but did not alter the general conclusion of the mixture study in terms of deviation from the reference model. Mixture effects on the maximum stimulatory response were tested against the hypothesis of a linear change with mixture ratio by constructing 95% prediction intervals based on the single concentration-response curves. Four out of the six data sets evaluated followed the model of linear interpolation reasonably well, which suggested that the size of the hormetic growth stimulation can be roughly predicted in mixtures from knowledge of the concentration-response relationships of the individual chemicals.

Reproducibility of binary‐mixture toxicity studies

Binary-mixture studies often are conducted with the aim of elucidating the effect of one specific chemical on the biological action of another. The results can be interpreted in relation to reference models by the use of response-surface analyses and isobolograms. The amount of data needed for these analyses is, however, extensive, and the experiments therefore rarely are repeated. In the present study, we investigate the reproducibility of isobole shapes of binary-mixture toxicity experiments in terms of deviation from the reference model of concentration addition (CA), dose-level dependence, and isobole asymmetry. We use data from four herbicide mixtures tested in three to five independent experiments on the aquatic test plant Lemna minor and the terrestrial plant Tripleurospermum inodorum. The results showed that the variation both within and among experiments was approximately half the size for the aquatic test system compared to the terrestrial system. As a consequence, a consistent deviation from CA could be obtained in three of four herbicide mixtures for L. minor, whereas this was only the case for one or two of the herbicide mixtures tested on T. inodorum. For one mixture on T. inodorum, both CA synergism and antagonism were detected. Dose-dependent effects could not be repeated consistently, just as the asymmetry found in some isoboles could not. The study emphasizes the importance of repeating mixture toxicity experiments, especially for test systems with large variability, and using caution when drawing biological conclusions from the test results.

An isobole-based statistical model and test for synergism/antagonism in binary mixture toxicity experiments

Synergism and antagonism are often defined in relation to the model of Concentration Addition (CA). Hence, it is vital for the conclusion of mixture toxicity studies to be able to test whether an observed deviation from CA reflects a true deviation or whether it is simply due to random variation. In this paper we consider a non-linear regression model for the classical ray designs for binary mixture experiments. The model combines dose–response curves for each mixture in the experiment with an isobole model, describing possible deviations from CA. The method allows us to test whether the chosen isobole model is reasonable for the data and to test the hypothesis of CA. Furthermore, it provides us with a measure of the degree of synergism/antagonism. The method is flexible since both the dose–response relationships and the isobole model can be chosen arbitrarily. We demonstrate the use of the method on datasets where combinations of pesticides are tested on a floating plant, Lemna minor, and an algae, Pseudokirchneriella subcapitata. Furthermore, we conduct a simulation study in order to explore the power with which a specific deviation from CA can be distinguished in different test-systems.

Can the joint effect of ternary mixtures be predicted from binary mixture toxicity results

The joint effect of the majority of chemical mixtures can be predicted using the reference model of Concentration Addition (CA). It becomes a challenge, however, when the mixtures include chemicals that synergise or antagonise the effect of each other. In this study we examine if the deviation from CA of seven ternary mixtures of interacting chemicals can be predicted from knowledge of the binary mixture responses involved. We hypothesise that the strongest interactions will take place in the binary mixtures and that the size of the ternary mixture response can be predicted from knowledge of the binary interactions. The hypotheses were tested using a stepwise modelling approach of incorporating the information held in binary mixtures into a ternary mixture model, and comparing the model predictions with observed ternary mixture toxicity data derived from studies of interacting chemical mixtures on the floating plant Lemna minor and the bacteria Vibrio fischeri. The results showed that for both the antagonistic and the synergistic ternary mixtures the ternary model predictions were superior to the conventional CA reference model and provided robust estimations of the size of the experimentally derived ternary mixture toxicity effects.

A multilevel nonlinear mixed-effects approach to model growth in pigs.

Growth functions have been used to predict market weight of pigs and maximize return over feed costs. This study was undertaken to compare 4 growth functions and methods of analyzing data, particularly one that considers nonlinear repeated measures. Data were collected from an experiment with 40 pigs maintained from birth to maturity and their BW measured weekly or every 2 wk up to 1,007 d. Gompertz, logistic, Bridges, and Lopez functions were fitted to the data and compared using information criteria. For each function, a multilevel nonlinear mixed effects model was employed because it allowed for estimation of all growth profiles simultaneously, and different sources of variation (i.e., sex, pig, and litter effects) were incorporated directly into the parameters. Furthermore, variance in-homogeneity and within-pig correlation were introduced to the functions. Inclusion of a variance of power function and a continuous autoregressive process of first order rendered a substantially improved fit to data for all 4 growth functions. The Lopez function provided the best fit to the data set and was used for characterizing mean growth curves for the 3 sexes (barrows, boars, and gilts). It was estimated that the maximum growth rate occurs at 117, 134, and 96 kg of BW for barrows, boars, and gilts, respectively. Hence, the gilts reached their maximum growth rate at an earlier stage in life compared with boars. Mature size of pigs varied systematically with sex and was estimated to be 466, 537, and 382 kg of BW for the barrows, boars, and gilts, respectively. These estimates are significantly affected by the duration of the experimental period, and it is recommended that future studies looking at estimating the mature size in animals are conducted long enough so that the BW visually stabilizes. Furthermore, studies should consider adding continuous autoregressive process when analyzing nonlinear mixed models with repeated measures.

Agreement between accelerometric symmetry scores and clinical lameness scores during experimentally induced transient distension of the metacarpophalangeal joint in horses.

REASONS FOR PERFORMING STUDY Equine lameness examination is based on subjective visual scoring of lameness. Instrumented objective methods for lameness examinations may be complicated to perform and the equipment is often stationary. Accelerometry has a potential clinical use; however, the reduction and interpretation of equine accelerometric data are not yet routine and the value of accelerometry in equine lameness examination is unclear. OBJECTIVES To use accelerometric data to calculate 2 different accelerometric symmetry scores and to evaluate the agreement of these with traditional lameness scores done by experienced equine practitioners. METHODS Six sound horses were equipped with a 3 axis 10G piezoresistant accelerometer at the lowest point of the back. Horses were trotted and video recorded at 0, 3, 15, 30, 45 and 60 min after injection of saline into one metacarpophalangeal joint. Video recordings were scored in a blind manner according to the AAEP scale by 2 experienced practitioners. Interobserver agreements and 2 symmetry scores S and A, developed on the basis of Fourier transformation of the obtained accelerometric data, were calculated and regression analysis between AAEP scores and symmetry scores was performed. RESULTS Interobserver agreements were 70%. There was a statistically significant relationship between AAEP lameness scores and both symmetry scores. CONCLUSIONS Both symmetry scores showed a significant relationship with the AAEP scores and can be a valuable tool in the detection and quantification of lameness. While the S score was able to detect changes in degree of lameness, the A score was capable of detecting the lame diagonal. However, more research is needed for the development of a combined accelerometric score to take advantage of the strengths of each of the symmetry scores.

An introduction with medical applications to functional data analysis

Functional data are data that can be represented by suitable functions, such as curves (potentially multi-dimensional) or surfaces. This paper gives an introduction to some basic but important techniques for the analysis of such data, and we apply the techniques to two datasets from biomedicine. One dataset is about white matter structures in the brain in multiple sclerosis patients; the other dataset is about three-dimensional vascular geometries collected for the study of cerebral aneurysms. The techniques described are smoothing, alignment, principal component analysis, and regression.

Comparison of the puborectal muscle on MRI in women with POP and levator ani defects with those with normal support and no defect

Introduction and hypothesisThe objective of this study was to compare puborectal muscle integrity and bulk in women with both major levator ani (LA) defects on MRI and pelvic organ prolapse (POP) to women with normal LA muscle and normal support.MethodsThis is a case-control study comparing 24 cases with known major LA defects and POP to 24 controls with normal LA and normal support. Axial T-2 weighted MRI scans of the pelvis were evaluated for integrity of the puborectal muscle and degree of muscle bulk.ResultsThere were no significant group differences in age, body mass index, vaginal deliveries, or hysterectomy status. In all 48 subjects, the puborectal muscle was visible and had no disruption noted. There was no difference in muscle bulk between groups (control/case, thin 42% vs. 25%, average 42% vs. 38%, thick-17% vs. 38%; P = 0.47).ConclusionsDefects and loss of muscle bulk in the puborectal muscle are not seen on MRI in women with major LA defects and POP.

Coexistence facilitates interspecific biofilm formation in complex microbial communities.

Social interactions in which bacteria respond to one another by modifying their phenotype are central determinants of microbial communities. It is known that interspecific interactions influence the biofilm phenotype of bacteria; a phenotype that is central to the fitness of bacteria. However, the underlying role of fundamental ecological factors, specifically coexistence and phylogenetic history, in biofilm formation remains unclear. This study examines how social interactions affect biofilm formation in multi-species co-cultures from five diverse environments. We found prevalence of increased biofilm formation among co-cultured bacteria that have coexisted in their original environment. Conversely, when randomly co-culturing bacteria across these five consortia, we found less biofilm induction and a prevalence of biofilm reduction. Reduction in biofilm formation was even more predominant when co-culturing bacteria from environments where long-term coexistence was unlikely to have occurred. Phylogenetic diversity was not found to be a strong underlying factor but a relation between biofilm induction and phylogenetic history was found. The data indicates that biofilm reduction is typically correlated with an increase in planktonic cell numbers, thus implying a behavioral response rather than mere growth competition. Our findings suggest that an increase in biofilm formation is a common adaptive response to long-term coexistence.