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Theory of synergistic effects: Hill-type response surfaces as 'null-interaction' models for mixtures.

ABSTRACT: The classification of effects caused by mixtures of agents as synergistic, antagonistic or additive depends critically on the reference model of 'null interaction'. Two main approaches are currently in use, the Additive Dose (ADM) or concentration addition (CA) and the Multiplicative Survival (MSM) or independent action (IA) models. We compare several response surface models to a newly developed Hill response surface, obtained by solving a logistic partial differential equation (PDE). Assuming that a mixture of chemicals with individual Hill-type dose-response curves can be described by an n-dimensional logistic function, Hill's differential equation for pure agents is replaced by a PDE for mixtures whose solution provides Hill surfaces as 'null-interaction' models and relies neither on Bliss independence or Loewe additivity nor uses Chou's unified general theory.An n-dimensional logistic PDE decribing the Hill-type response of n-component mixtures is solved. Appropriate boundary conditions ensure the correct asymptotic behaviour. Mathematica 11 (Wolfram, Mathematica Version 11.0, 2016) is used for the mathematics and graphics presented in this article.The Hill response surface ansatz can be applied to mixtures of compounds with arbitrary Hill parameters. Restrictions which are required when deriving analytical expressions for response surfaces from other principles, are unnecessary. Many approaches based on Loewe additivity turn out be special cases of the Hill approach whose increased flexibility permits a better description of 'null-effect' responses. Missing sham-compliance of Bliss IA, known as Colby's model in agrochemistry, leads to incompatibility with the Hill surface ansatz. Examples of binary and ternary mixtures illustrate the differences between the approaches. For Hill-slopes close to one and doses below the half-maximum effect doses MSM (Colby, Bliss, Finney, Abbott) predicts synergistic effects where the Hill model indicates 'null-interaction'. These differences increase considerably with increasing steepness of the individual dose-response curves.The Hill response surface ansatz contains the Loewe additivity concept as a special case and is incompatible with Bliss independent action. Hence, when synergistic effects are claimed, those dose combinations deserve special attention where the differences between independent action approaches and Hill estimations are large.

SUBMITTER: Schindler M

PROVIDER: S-EPMC5541435 | biostudies-other | 2017 Aug

REPOSITORIES: biostudies-other

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Project description:BackgroundHigh-throughput amplicon sequencing of marker genes, such as the 16S rRNA gene in Bacteria and Archaea, provides a wealth of information about the composition of microbial communities. To quantify differences between samples and draw conclusions about factors affecting community assembly, dissimilarity indices are typically used. However, results are subject to several biases, and data interpretation can be challenging. The Jaccard and Bray-Curtis indices, which are often used to quantify taxonomic dissimilarity, are not necessarily the most logical choices. Instead, we argue that Hill-based indices, which make it possible to systematically investigate the impact of relative abundance on dissimilarity, should be used for robust analysis of data. In combination with a null model, mechanisms of microbial community assembly can be analyzed. Here, we also introduce a new software, qdiv, which enables rapid calculations of Hill-based dissimilarity indices in combination with null models.ResultsUsing amplicon sequencing data from two experimental systems, aerobic granular sludge (AGS) reactors and microbial fuel cells (MFC), we show that the choice of dissimilarity index can have considerable impact on results and conclusions. High dissimilarity between replicates because of random sampling effects make incidence-based indices less suited for identifying differences between groups of samples. Determining a consensus table based on count tables generated with different bioinformatic pipelines reduced the number of low-abundant, potentially spurious amplicon sequence variants (ASVs) in the data sets, which led to lower dissimilarity between replicates. Analysis with a combination of Hill-based indices and a null model allowed us to show that different ecological mechanisms acted on different fractions of the microbial communities in the experimental systems.ConclusionsHill-based indices provide a rational framework for analysis of dissimilarity between microbial community samples. In combination with a null model, the effects of deterministic and stochastic community assembly factors on taxa of different relative abundances can be systematically investigated. Calculations of Hill-based dissimilarity indices in combination with a null model can be done in qdiv, which is freely available as a Python package ( https://github.com/omvatten/qdiv ). In qdiv, a consensus table can also be determined from several count tables generated with different bioinformatic pipelines. Video Abstract.

Project description:BackgroundDespite the great concern triggered by the environmental crisis worldwide, the loss of temporal key functions and processes involved in biodiversity maintenance has received little attention. Species are restricted in their life cycles by environmental variables because of their physiological and behavioral properties; thus, the timing and duration of species' presence and their activities vary greatly between species within a community. Despite the ecological relevance of such variation, there is currently no measure that summarizes the key temporal aspects of biological diversity and allows comparisons of community phenological patterns. Here, we propose a measure that synthesizes variability of phenological patterns using the Hill numbers-based attribute diversity framework.MethodsWe constructed a new phenological diversity measure based on the aforementioned framework through pairwise overlapping distances, which was supplemented with wavelet analysis. The Hill numbers approach was chosen as an adequate way to define a set of diversity values of different order q, a parameter that determines the sensitivity of the diversity measure to abundance. Wavelet transform analysis was used to model continuous variables from incomplete data sets for different phenophases. The new measure, which we call Phenological Hill numbers (PD), considers the decouplings of phenophases through an overlapping area value between pairs of species within the community. PD was first tested through simulations with varying overlap in phenophase magnitude and intensity and varying number of species, and then by using one real data set.ResultsPD maintains the diversity patterns of order q as in any other diversity measure encompassed by the Hill numbers framework. Minimum PD values in the simulated data sets reflect a lack of differentiation in the phenological curves of the community over time; by contrast, the maximum PD values reflected the most diverse simulations in which phenological curves were equally distributed over time. PD values were consistent with the homogeneous distribution of the intensity and concurrence of phenophases over time, both in the simulated and the real data set.DiscussionPD provides an efficient, readily interpretable and comparable measure that summarizes the variety of phenological patterns observed in ecological communities. PD retains the diversity patterns of order q characteristic of all diversity measures encompassed by the distance-based Hill numbers framework. In addition, wavelet transform analysis proved useful for constructing a continuous phenological curve. This methodological approach to quantify phenological diversity produces simple and intuitive values for the examination of phenological diversity and can be widely applied to any taxon or community's phenological traits.

Project description:BACKGROUND: The identification of protein-protein interaction sites is a computationally challenging task and important for understanding the biology of protein complexes. There is a rich literature in this field. A broad class of approaches assign to each candidate residue a real-valued score that measures how likely it is that the residue belongs to the interface. The prediction is obtained by thresholding this score.Some probabilistic models classify the residues on the basis of the posterior probabilities. In this paper, we introduce pairwise conditional random fields (pCRFs) in which edges are not restricted to the backbone as in the case of linear-chain CRFs utilized by Li et al. (2007). In fact, any 3D-neighborhood relation can be modeled. On grounds of a generalized Viterbi inference algorithm and a piecewise training process for pCRFs, we demonstrate how to utilize pCRFs to enhance a given residue-wise score-based protein-protein interface predictor on the surface of the protein under study. The features of the pCRF are solely based on the interface predictions scores of the predictor the performance of which shall be improved. RESULTS: We performed three sets of experiments with synthetic scores assigned to the surface residues of proteins taken from the data set PlaneDimers compiled by Zellner et al. (2011), from the list published by Keskin et al. (2004) and from the very recent data set due to Cukuroglu et al. (2014). That way we demonstrated that our pCRF-based enhancer is effective given the interface residue score distribution and the non-interface residue score are unimodal.Moreover, the pCRF-based enhancer is also successfully applicable, if the distributions are only unimodal over a certain sub-domain. The improvement is then restricted to that domain. Thus we were able to improve the prediction of the PresCont server devised by Zellner et al. (2011) on PlaneDimers. CONCLUSIONS: Our results strongly suggest that pCRFs form a methodological framework to improve residue-wise score-based protein-protein interface predictors given the scores are appropriately distributed. A prototypical implementation of our method is accessible at http://ppicrf.informatik.uni-goettingen.de/index.html.

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Theory of synergistic effects: Hill-type response surfaces as 'null-interaction' models for mixtures.

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