Non-additive Interactions Research Articles

Surface residues and nonadditive interactions stabilize a consensus homeodomain protein

Despite the widely reported success of consensus design in producing highly stabilized proteins, little is known about the physical mechanisms underlying this stabilization. Here, we explore the potential sources of stabilization by performing a systematic analysis of the 29 substitutions that we previously found to collectively stabilize a consensus homeodomain compared with an extant homeodomain. By separately introducing groups of consensus substitutions that alter or preserve charge state, occur at varying degrees of residue burial, and occur at positions of varying degrees of conservation, we determine the extent to which these three features contribute to the consensus stability enhancement. Surprisingly, we find that the largest total contribution to stability comes from consensus substitutions on the protein surface and that the largest per substitution contributions come from substitutions that maintain charge state. This finding suggests that, although consensus proteins are often enriched in charged residues, consensus stabilization does not result primarily from interactions involving charged residues. Although consensus substitutions at strongly conserved positions also contribute disproportionately to stabilization, significant stabilization is also contributed from substitutions at weakly conserved positions. Furthermore, we find that identical consensus substitutions show larger stabilizing effects when introduced into the consensus background than when introduced into an extant homeodomain, indicating that synergistic, stabilizing interactions among the consensus residues contribute to consensus stability enhancement of the homeodomain. By measuring DNA binding affinity for the same set of variants, we find that, although consensus design of the homeodomain increases both affinity and folding stability, it does so using a largely nonoverlapping set of substitutions.

Aberrant RNA splicing due to genetic incompatibilities in sunflower hybrids.

Genome-scale studies have revealed divergent mRNA splicing patterns between closely related species or populations. However, it is unclear whether splicing differentiation is a simple byproduct of population divergence, or whether it also acts as a mechanism for reproductive isolation. We examined mRNA splicing in wild domesticated sunflower hybrids and observed 45 novel splice forms that were not found in the wild or domesticated parents, in addition to 16 high-expression parental splice forms that were absent in one or more hybrids. We identify loci associated with variation in the levels of these splice forms, finding that many aberrant transcripts were regulated by multiple alleles with nonadditive interactions. We identified particular spliceosome components that were associated with 21 aberrant isoforms, more than half of which were located in or near regulatory QTL. These incompatibilities often resulted in alteration in the protein-coding regions of the novel transcripts in the form of frameshifts and truncations. By associating the splice variation in these genes with size and growth rate measurements, we found that the cumulative expression of all aberrant transcripts was correlated with a significant reduction in growth rate. Our results lead us to propose a model where divergent splicing regulatory loci could act as incompatibility loci that contribute to the evolution of reproductive isolation.

Quantitative kinetic theory of flocking with three-particle closure.

We consider aligning self-propelled particles in two dimensions. Their motion is given by Langevin equations and includes nonadditive N-particle interactions. The qualitative behavior is as for the famous Vicsek model. We develop a kinetic theory of flocking beyond mean field. In particular, we self-consistently take into account the full pair correlation function. We find excellent quantitative agreement of the pair correlations with direct agent-based simulations within the disordered regime. Furthermore we use a closure relation to incorporate spatial correlations of three particles. In that way we achieve good quantitative agreement of the onset of flocking with direct simulations. Compared to mean-field theory, the flocking transition is shifted significantly toward lower noise because directional correlations favor disorder. We compare our theory with a recently developed Landau-kinetic theory.

Density functional for the lattice gas from fundamental measure theory.

We construct a density functional for the lattice gas or Ising model on square and cubic lattices based on lattice fundamental measure theory. To treat the nearest-neighbor attractions between the lattice gas particles, the model is mapped to a multicomponent model of hard particles with additional lattice polymers where effective attractions between particles arise from the depletion effect. The lattice polymers are further treated via the introduction of polymer clusters (labelled by the numbers of polymer they contain) such that the model becomes a multicomponent model of particles and polymer clusters with nonadditive hard interactions. The density functional for this nonadditive hard model is constructed with lattice fundamental measure theory. The resulting bulk phase diagram recovers the Bethe-Peierls approximation and planar interface tensions show a considerable improvement compared to the standard mean-field functional and are close to simulation results in three dimensions. We demonstrate the existence of planar interface solutions at chemical potentials away from coexistence when the equimolar interface position is constrained to arbitrary real values.

Long-range additive and nonadditive potentials in a hybrid system: Ground-state atom, excited-state atom, and ion

We report a theoretical study on the long-range additive and nonadditive potentials for a three-body hybrid atom-atom-ion system composed of one ground $S$ state Li atom, one excited $P$ state Li atom and one ground $S$ state Li$^+$ ion, Li($2\,^{2}S$)-Li($2\,^{2}P$)-Li$^+(1\,^{1}S$). The interaction coefficients are evaluated with highly accurate wave functions calculated variationally in Hylleraas coordinates. For this hybrid system the three-body nonadditive collective interactions (appearing in second-order) induced by the energy degeneracy and enhanced by the induction effect of the Li$^+$ ion through the internal electric field can be strong and even stronger than the two-body additive interactions at the same order. We find that for particular geometries the two-body additive interactions of the system sum to zero leaving only three-body nonadditive collective interactions making the present system potentially a platform to explore quantum three-body collective effects. We also extract first-principles leading coefficients of the long-range electrostatic, induction, and dispersion energies of Li$^+_2$ electronic states correlating to Li($2\,^{2}P$)-Li$^+(1\,^{1}S$), which until now were not available in the literature. The results should be especially valuable for the exploration of schemes to create trimers with ultracold atoms and ions in optical lattices.

Unexpected words or unexpected languages? Two ERP effects of code-switching in naturalistic discourse

Bilingual speakers often switch between languages in conversation without any advance notice. Psycholinguistic research has found that these language shifts (or code-switches) can be costly for comprehenders in certain situations. The present study explores the nature of these costs by comparing code-switches to other types of unexpected linguistic material. To do this, we used a novel EEG paradigm, the Storytime task, in which we record readings of natural texts, and then experimentally manipulate their properties by splicing in words. In this study, we manipulated the language of our target words (English, Spanish) and their fit with the preceding context (strong-fit, weak-fit). If code-switching incurs a unique cost beyond that incurred by an unexpected word, then we should see an additive pattern in our ERP indices. If an effect is driven by lexical expectation alone, then there should be a non-additive interaction such that all unexpected forms incur a similar cost. We found three effects: a general prediction effect (a non-additive N400), a post-lexical recognition of the switch in languages (an LPC for code-switched words), and a prolonged integration difficulty associated with weak-fitting words regardless of language (a sustained negativity). We interpret these findings as suggesting that the processing difficulties experienced by bilinguals can largely be understood within more general frameworks for understanding language comprehension. Our findings are consistent with the broader literature demonstrating that bilinguals do not have two wholly separate language systems but rather a single language system capable of using two coding systems.

The X factor: A robust and powerful approach to X-chromosome-inclusive whole-genome association studies.

The X‐chromosome is often excluded from genome‐wide association studies because of analytical challenges. Some of the problems, such as the random, skewed, or no X‐inactivation model uncertainty, have been investigated. Other considerations have received little to no attention, such as the value in considering nonadditive and gene–sex interaction effects, and the inferential consequence of choosing different baseline alleles (i.e., the reference vs. the alternative allele). Here we propose a unified and flexible regression‐based association test for X‐chromosomal variants. We provide theoretical justifications for its robustness in the presence of various model uncertainties, as well as for its improved power when compared with the existing approaches under certain scenarios. For completeness, we also revisit the autosomes and show that the proposed framework leads to a more robust approach than the standard method. Finally, we provide supporting evidence by revisiting several published association studies. Supporting Information for this article are available online.

Classifying ecosystem stressor interactions: Theory highlights the data limitations of the additive null model and the difficulty in revealing ecological surprises.

Understanding how multiple co-occurring environmental stressors combine to affect biodiversity and ecosystem services is an on-going grand challenge for ecology. Currently, progress has been made through accumulating large numbers of smaller-scale empirical studies that are then investigated by meta-analyses to detect general patterns. There is particular interest in detecting, understanding and predicting 'ecological surprises' where stressors interact in a non-additive (e.g. antagonistic or synergistic) manner, but so far few general results have emerged. However, the ability of the statistical tools to recover non-additive interactions in the face of data uncertainty is unstudied, so crucially, we do not know how well the empirical results reflect the true stressor interactions. Here, we investigate the performance of the commonly implemented additive null model. A meta-analysis of a large (545 interactions) empirical dataset for the effects of pairs of stressors on freshwater communities reveals additive interactions dominate individual studies, whereas pooling the data leads to an antagonistic summary interaction class. However, analyses of simulated data from food chain models, where the underlying interactions are known, suggest both sets of results may be due to observation error within the data. Specifically, we show that the additive null model is highly sensitive to observation error, with non-additive interactions being reliably detected at only unrealistically low levels of data uncertainty. Similarly, plausible levels of observation error lead to meta-analyses reporting antagonistic summary interaction classifications even when synergies co-dominate. Therefore, while our empirical results broadly agree with those of previous freshwater meta-analyses, we conclude these patterns may be driven by statistical sampling rather than any ecological mechanisms. Further investigation of candidate null models used to define stressor-pair interactions is essential, and once any artefacts are accounted for, the so-called 'ecological surprises' may be more frequent than was previously assumed.

Nonadditive genetic effects induce novel phenotypic distributions in male mating traits of F1 hybrids.

Hybridization is a source of phenotypic novelty and variation because of increased additive genetic variation. Yet, the roles of nonadditive allelic interactions in shaping phenotypic mean and variance of hybrids have been underappreciated. Here, we examine the distributions of male-mating traits in F1 hybrids via a meta-analysis of 3208 effect sizes from 39 animal species pairs. Although additivity sets phenotypic distributions of F1s to be intermediate, F1s also showed recessivity and resemblance to maternal species. F1s expressed novel phenotypes (beyond the range of both parents) in 65% of species pairs, often associated with increased phenotypic variability. Overall, however, F1s expressed smaller variation than parents in 51% of traits. Although genetic divergence between parents did not impact phenotypic novelty, it increased phenotypic variability of F1s. By creating novel phenotypes with increased variability, nonadditivity of heterozygotic genome may play key roles in determining mating success of F1s, and their subsequent extinction or speciation.

The limits of normal approximation for adult height

Adult height inspired the first biometrical and quantitative genetic studies and is a test-case trait for understanding heritability. The studies of height led to formulation of the classical polygenic model, that has a profound influence on the way we view and analyse complex traits. An essential part of the classical model is an assumption of additivity of effects and normality of the distribution of the residuals. However, it may be expected that the normal approximation will become insufficient in bigger studies. Here, we demonstrate that when the height of hundreds of thousands of individuals is analysed, the model complexity needs to be increased to include non-additive interactions between sex, environment and genes. Alternatively, the use of log-normal approximation allowed us to still use the additive effects model. These findings are important for future genetic and methodologic studies that make use of adult height as an exemplar trait.

On kernel machine learning for propensity score estimation under complex confounding structures.

Post marketing data offer rich information and cost-effective resources for physicians and policy-makers to address some critical scientific questions in clinical practice. However, the complex confounding structures (e.g., nonlinear and nonadditive interactions) embedded in these observational data often pose major analytical challenges for proper analysis to draw valid conclusions. Furthermore, often made available as electronic health records (EHRs), these data are usually massive with hundreds of thousands observational records, which introduce additional computational challenges. In this paper, for comparative effectiveness analysis, we propose a statistically robust yet computationally efficient propensity score (PS) approach to adjust for the complex confounding structures. Specifically, we propose a kernel-based machine learning method for flexibly and robustly PS modeling to obtain valid PS estimation from observational data with complex confounding structures. The estimated propensity score is then used in the second stage analysis to obtain the consistent average treatment effect estimate. An empirical variance estimator based on the bootstrap is adopted. A split-and-merge algorithm is further developed to reduce the computational workload of the proposed method for big data, and to obtain a valid variance estimator of the average treatment effect estimate as a by-product. As shown by extensive numerical studies and an application to postoperative pain EHR data comparative effectiveness analysis, the proposed approach consistently outperforms other competing methods, demonstrating its practical utility.

A comparison of methods for interpreting random forest models of genetic association in the presence of non-additive interactions

BackgroundNon-additive interactions among genes are frequently associated with a number of phenotypes, including known complex diseases such as Alzheimer’s, diabetes, and cardiovascular disease. Detecting interactions requires careful selection of analytical methods, and some machine learning algorithms are unable or underpowered to detect or model feature interactions that exhibit non-additivity. The Random Forest method is often employed in these efforts due to its ability to detect and model non-additive interactions. In addition, Random Forest has the built-in ability to estimate feature importance scores, a characteristic that allows the model to be interpreted with the order and effect size of the feature association with the outcome. This characteristic is very important for epidemiological and clinical studies where results of predictive modeling could be used to define the future direction of the research efforts. An alternative way to interpret the model is with a permutation feature importance metric which employs a permutation approach to calculate a feature contribution coefficient in units of the decrease in the model’s performance and with the Shapely additive explanations which employ cooperative game theory approach. Currently, it is unclear which Random Forest feature importance metric provides a superior estimation of the true informative contribution of features in genetic association analysis.ResultsTo address this issue, and to improve interpretability of Random Forest predictions, we compared different methods for feature importance estimation in real and simulated datasets with non-additive interactions. As a result, we detected a discrepancy between the metrics for the real-world datasets and further established that the permutation feature importance metric provides more precise feature importance rank estimation for the simulated datasets with non-additive interactions.ConclusionsBy analyzing both real and simulated data, we established that the permutation feature importance metric provides more precise feature importance rank estimation in the presence of non-additive interactions.

Evaluation of the dioxin-like toxicity in soil samples from Thua Thien Hue province using the AhR-CALUX bioassay – An update of Agent Orange contamination in Vietnam

In this study, an AhR-responsive reporter-gene cell-based bioassay CALUX was used to assess the biological potency of dioxins and dioxin-like PCBs (dl-PCBs) in top soil samples collected from a former airbase (A-So) and remote regions from urban and agricultural areas in Thua Thien Hue, Vietnam. In top soil collected from A-So airbase, Bioanalytical EQuivalent (BEQ) concentrations of up to 2700 pg 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) per g dry weight (pg BEQ-TCDD g−1 dw) were assessed. Interestingly, while BEQ values for dl-PCBs were found to be up to 13 pg BEQ-TCDD g−1 dw, the dl-PCB activity was not detected in all the hotspot sample extracts. In contrasts, BEQ values for dioxin like compounds from remote regions were much lower and occasionally below the quantification limits of the method. The BEQ activities obtained in this study have a similar trend to the WHO-TEQ results for the samples collected in the A-So airbase. However, BEQ values were higher than those of TEQ, probably reflecting the presence of additional AhR ligands and/or possible non-additive interactions in the sample mixture. This study confirms that after more than 60 years, a strong residual pollution of PCDD/Fs remains on this former air base following the use and storage of Agent Orange during the Vietnam War, raising a health risk for populations exposed in this area because livestock animals graze there.

Analysis framework and experimental design for evaluating synergy-driving gene expression.

The mechanisms by which genetic risk variants interact with each other, as well as environmental factors, to contribute to complex genetic disorders remain unclear. We describe in detail our recently published approach to resolve distinct additive and synergistic transcriptomic effects after combinatorial manipulation of genetic variants and/or chemical perturbagens. Although first developed for CRISPR-based perturbation studies of isogenic human induced pluripotent stem cell-derived neurons, our methodology can be broadly applied to any RNA sequencing dataset, provided that raw read counts are available. Whereas other differential expression analyses reveal the effect of individual perturbations, here we specifically query interactions between two or more perturbagens, resolving the extent of non-additive (synergistic) interactions between perturbations. We discuss the careful experimental design required to resolve synergistic effects and considerations of statistical power and how to quantify observed synergy between experiments. Additionally, we speculate on potential future applications and explore the obvious limitations of this approach. Overall, by interrogating the effect of independent factors, alone and in combination, our analytic framework and experimental design facilitate the discovery of convergence and synergy downstream of gene and/or treatment perturbations hypothesized to contribute to complex diseases. We think that this protocol can be successfully applied by any scientist with bioinformatic skills and basic proficiency in the R programming language. Our computational pipeline ( https://github.com/nadschro/synergy-analysis ) is straightforward, does not require supercomputing support and can be conducted in a single day upon completion of RNA sequencing experiments.

Revisiting the emergence of order in active matter.

The emergence of orientational order plays a central role in active matter theory and is deeply based in the study of active systems with a velocity alignment mechanism, whose most prominent example is the so-called Vicsek model. Such active systems have been used to describe bird flocks, bacterial swarms, and active colloidal systems, among many other examples. Under the assumption that the large-scale properties of these models remain unchanged as long as the polar symmetry of the interactions is not affected, implementations have been performed using, out of convenience, either additive or non-additive interactions; the latter are found for instance in the original formulation of the Vicsek model. Here, we perform a careful analysis of active systems with velocity alignment, comparing additive and non-additive interactions, and show that the macroscopic properties of these active systems are fundamentally different. Our results call into question our current understanding of the onset of order in active systems.

Gene action and combining ability analysis for seed yield and its component traits in castor (Ricinus communis L.)

Evaluation of 20 hybrids were involving nine parents in LxT analysis, data recorded on eleven agronomical characters. Among parents, Geeta, NAUCI 8 and NAUCI 9 exhibited high gca effects for seed yield per plant and were observed as good general combiner for seed yield and most of its contributing characters and these may be utilized in further breeding programme. The cross combinations viz., Geeta x NAUCI 6, Geeta x NAUCI 8 and SKP 72 x NAUCI 9 recorded the highest sca effects for seed yield per plant. The variance due to females x males was higher for all the characters as revealed by combining ability analysis signifying the preponderance of non-additive gene interactions among the hybrid under such circumstances, recurrent selection for sca as well as heterosis breeding seems to be the most appropriate breeding method for development of good hybrids for fulfilment of current as well as future needs.

The complexity of co-limitation: nutrigenomics reveal non-additive interactions of calcium and phosphorus on gene expression in Daphnia pulex.

Many lakes across Canada and northern Europe have experienced declines in ambient phosphorus (P) and calcium (Ca) supply for over 20 years. While these declines might create or exacerbate nutrient limitation in aquatic food webs, our ability to detect and quantify different types of nutrient stress on zooplankton remains rudimentary. Here, we used growth bioassay experiments and whole transcriptome RNAseq, collectively nutrigenomics, to examine the nutritional phenotypes produced by low supplies of P and Ca separately and together in the freshwater zooplankter Daphnia pulex. We found that daphniids in all three nutrient-deficient categories grew slower and differed in their elemental composition. Our RNAseq results show distinct responses in singly limited treatments (Ca or P) and largely a mix of these responses in animals under low Ca and P conditions. Deeper investigation of effect magnitude and gene functional annotations reveals this patchwork of responses to cumulatively represent a co-limited nutritional phenotype. Linear discriminant analysis identified a significant separation between nutritional treatments based upon gene expression patterns with the expression patterns of just five genes needed to predict animal nutritional status with 99% accuracy. These data reveal how nutritional phenotypes are altered by individual and co-limitation of two highly important nutritional elements (Ca and P) and provide evidence that aquatic consumers can respond to limitation by more than one nutrient at a time by differentially altering their metabolism. This use of nutrigenomics demonstrates its potential to address many of the inherent complexities in studying interactions between multiple nutritional stressors in ecology and beyond.

Defining the Response of Caenorhabditis elegans to Multiple Simultaneous Stressors

Cells are constantly subjected to a variety of intrinsic and extrinsic stresses—oxidative, protein misfolding, osmotic—and respond by activating a range of molecular pathways to mitigate and repair damage—oxidative stress response, unfolded protein response, osmotic stress response. While individual stress response pathways have been described in detail, and some interventions improve resistance to multiple forms of stress (e.g. dietary restriction, insulin signaling inhibition), surprisingly little is known about how these responses differ when cells are challenged with multiple types of stress simultaneously. The molecular architecture underlying multi-stress response has broad implications for aging and age-associated disease. One characteristic of aging is a progressive increase in multiple categories of cellular stress accompanied by a decline in cellular stress response capability. Human diseases rarely involve a single form of stress—Alzheimer’s disease is characterized by neuroinflammation, oxidative stress, and misfolded proteins, while cancer exhibits oxidative stress, DNA damage, and localized hypoxia. Determining how cells respond differently to one form of stress in the presence of another is critical to building an accurate model of the aging cellular environment. We are using Caenorhabditis elegans to systematically evaluate the molecular network that cells employ when challenged by multiple simultaneous stressors and how different stress combinations impact organismal survival and health. Here we present our initial characterization of C. elegans response to multiple categories of cellular stress (oxidative, osmotic, ER, Golgi, heavy metal), which stressors elicit non-additive interactions when combined, and how these combinations impact survival, health, and established stress response pathways.

Formation of Excimers in Isoquinolinyl Pyrazolate Pt(II) Complexes: Role of Cooperativity Effects.

The interplay between noncovalent interactions involving metal complexes may lead to the formation of aggregates (i.e., ground state dimers, trimers, n-mers, etc.), and this is often linked to dramatic changes in their physical and chemical properties as compared to the original properties of the isolated units. Dimers and trimers can also be formed in the excited state potential energy surfaces, i.e., excimers. Excimers are short-lived but are also often characterized by different optical properties from those of the isolated units. Understanding the nature of noncovalent interactions and the presence or not of cooperativity effects in both aggregates and excimers is thus extremely important to rationalize these variations. In this study, we present computational investigations on isoquinolinyl pyrazolate Pt(II) complexes. Our results highlight that cooperativity effects between noncovalent interactions, which are modulated by sterically demanding substituents and metallophilic Pt···Pt interactions, are present only on certain investigated excimers. We use density functional theory (DFT) calculations to examine the cooperativity effects and the changes in the photophysical properties. Different descriptors of cooperativity effects between noncovalent interactions, including the synergetic, genuine nonadditive, and total interaction energies, were evaluated for a series of Pt(II) aggregates and excimers. In addition, energy decomposition analysis (EDA) calculations were performed to rationalize the origins of the cooperative effects. The cooperative effects in trimer excimers (in their lowest triplet excited state, i.e., T1) led to shortened Pt···Pt contacts as compared to the trimer aggregates. Furthermore, this synergy between noncovalent interactions is ultimately responsible for the formation of the excimers and the striking changes in the measured photophysical properties. More in detail, we report a change in the character of the lowest-lying triplet excited state when going from dimer excimers (i.e., of mixed triplet ligand-centered and triplet metal-to-ligand charge transfer (3LC/3MLCT) character) to trimer excimers (i.e., of triplet metal-metal-to-ligand charge transfer (3MMLCT) character). The EDA reveals that the total interaction energy on trimer excimers is subtly controlled by the electrostatic and dispersion terms.

Interactions Between Maternal, Paternal, Developmental, and Immediate Environmental Effects on Anti-predator Behavior of the Snail Physa acuta

Transgenerational plasticity, which occurs when the environment experienced by parents changes the phenotype of offspring, is widespread in animal and plant species. Both maternal and paternal environments can underlie transgenerational plasticity, but experimental studies unraveling how their effects interact together and with the personal (both developmental and immediate) environments are still rare. Yet unraveling these interactions is fundamental to understanding how offspring integrate past and present environmental cues to produce adaptive phenotype. Using the hermaphroditic and freshwater snail Physa acuta, we tested how predator cues experienced by offspring, mothers and fathers interact to shape offspring anti-predator behavior. We raised a first generation of snails in the laboratory with or without chemical predator cues and realized full-factorial crosses to disentangle maternal and paternal cues. We then raised the second generation of snails with or without predator cues and assessed, when adults, their escape behavior in two immediate environments (with or without predator cues) and activity in the immediate environment without predator cues. We found that personal, maternal, and paternal predator cues interacted to shape offspring escape behavior and activity. Firstly, for escape behavior, snails integrated the cues from developmental and parental environments only when exposed to predator cues in their immediate environment, suggesting that personal immediate experience must corroborate the risky parental environment to reveal transgenerational plasticity. For activity, this same hypothesis helps explain why no clear pattern of transgenerational plasticity was revealed, as activity was only measured without predator cues in the immediate environment. Secondly, a single maternal exposure to predator cues decreased offspring escape behavior while a single paternal exposure had no effect, surprisingly demonstrating sex-specific transgenerational plasticity for a simultaneous hermaphroditic species. Thirdly, when both mother and father were exposed, paternal cues were integrated by offspring according to their own developmental environment. The paternal exposure then mitigated the reduction in escape behavior due to the maternal exposure only when offspring developed in control condition. Overall, our study highlighted complex patterns of sex-specific transgenerational plasticity resulting from non-additive interactions between parental, developmental and immediate experiences.