Non-additive Interactions Research Articles

A practical introduction to Random Forest for genetic association studies in ecology and evolution.

Large genomic studies are becoming increasingly common with advances in sequencing technology, and our ability to understand how genomic variation influences phenotypic variation between individuals has never been greater. The exploration of such relationships first requires the identification of associations between molecular markers and phenotypes. Here, we explore the use of Random Forest (RF), a powerful machine-learning algorithm, in genomic studies to discern loci underlying both discrete and quantitative traits, particularly when studying wild or nonmodel organisms. RF is becoming increasingly used in ecological and population genetics because, unlike traditional methods, it can efficiently analyse thousands of loci simultaneously and account for nonadditive interactions. However, understanding both the power and limitations of Random Forest is important for its proper implementation and the interpretation of results. We therefore provide a practical introduction to the algorithm and its use for identifying associations between molecular markers and phenotypes, discussing such topics as data limitations, algorithm initiation and optimization, as well as interpretation. We also provide short R tutorials as examples, with the aim of providing a guide to the implementation of the algorithm. Topics discussed here are intended to serve as an entry point for molecular ecologists interested in employing Random Forest to identify trait associations in genomic data sets.

Mitochondrial Recombination Reveals Mito-Mito Epistasis in Yeast.

Genetic variation in mitochondrial DNA (mtDNA) provides adaptive potential although the underlying genetic architecture of fitness components within mtDNAs is not known. To dissect functional variation within mtDNAs, we first identified naturally occurring mtDNAs that conferred high or low fitness in Saccharomyces cerevisiae by comparing growth in strains containing identical nuclear genotypes but different mtDNAs. During respiratory growth under temperature and oxidative stress conditions, mitotype effects were largely independent of nuclear genotypes even in the presence of mito-nuclear interactions. Recombinant mtDNAs were generated to determine fitness components within high- and low-fitness mtDNAs. Based on phenotypic distributions of isogenic strains containing recombinant mtDNAs, we found that multiple loci contributed to mitotype fitness differences. These mitochondrial loci interacted in epistatic, nonadditive ways in certain environmental conditions. Mito-mito epistasis (i.e., nonadditive interactions between mitochondrial loci) influenced fitness in progeny from four different crosses, suggesting that mito-mito epistasis is a widespread phenomenon in yeast and other systems with recombining mtDNAs. Furthermore, we found that interruption of coadapted mito-mito interactions produced recombinant mtDNAs with lower fitness. Our results demonstrate that mito-mito epistasis results in functional variation through mitochondrial recombination in fungi, providing modes for adaptive evolution and the generation of mito-mito incompatibilities.

Is there synergistic interaction between fungicides inhibiting different enzymes in the ergosterol biosynthesis pathway in toxicity tests with the green alga Raphidocelis subcapitata?

Products used for plant protection or as biocides often contain more than one active substance together with numerous formulation additives. The environmental risk assessment for such commercial mixtures applies as default the concept of concentration addition. There is remaining regulatory concern, however, that underestimation of risks can occur if components in the mixture interact synergistically, i.e., elicit effects greater than those predicted by concentration addition. While cases of true synergism appear to be rare, the combination of substances targeting different steps in the same biosynthesis pathway was pointed out as one potential case of synergistic interaction although mechanistic explanations are lacking. The present study aimed to verify this hypothesis using the green alga Raphidocelis subcapitata as the regulatory standard test organism for which such synergism had been indicated earlier. Algal growth inhibition tests were conducted with mixtures of ergosterol biosynthesis inhibitors (tebuconazole, fenpropidin, and fenpropimorph). The fungicides were first tested individually to derive reliable data for a mixture toxicity prediction. The here determined toxicity estimates for two of the fungicides were considerably lower than the endpoints in the regulatory dossiers, which had been used for earlier mixture toxicity predictions. Experimentally observed toxicity estimates for the mixtures deviated <2.6-fold from the predicted values. Hence, the hypothesis of synergistic interaction between fungicides targeting different enzymes in the ergosterol biosynthesis was clearly not confirmed for the green alga R. subcapitata. Overall, the present study demonstrates the importance of reliable and correct input data for mixture toxicity predictions in order to avoid erroneous conclusions on non-additive (synergistic) interactions.

Pathway-induced allelic spectra of diseases in the presence of strong genetic effects.

Complex diseases are frequently modeled as following an additive model that excludes both intra- and inter-locus interaction, while at the same time reports on non-additive biological structures are ample, prominently featuring numerous metabolic and signaling pathways. Using extensive forward population simulations, we explored the impact of three basic pathway motifs on the relationship between epidemiological parameters, including disease prevalence, relative risk, sibling recurrence risk as well as causal variant number and allele frequency. We found that some but not all pathway motifs can shift the relationships between these parameters in comparison to the classical additive liability threshold model. The strongest deviations were observed with linear, cascade-like motifs that form an integral part of many reported pathways. We also modeled maturity-onset diabetes of the young (MODY) as a combination of different basic pathway motifs and observed a good concordance in epidemiological parameter values between our simulated data under this model and those reported in the literature. Given the widespread nature of pathways, including those in the etiology of human diseases, our results re-emphasize the need for non-additive interaction modeling of genetic variants to become an additional standard approach in analyzing human genetic data.

Effects and interactions of myostatin and callipyge mutations: I. Growth and carcass traits.

Objectives were to document effects of the Texel myostatin mutation (MSTN) on growth and carcass traits and also test whether or not interactions with the callipyge mutation (CLPG) could be detected. Twelve rams heterozygous at both loci on the two different chromosomes were mated to 215 terminal-sire type composite crossbred ewes genotyped as non-carriers for both loci. A total of 365 lambs were born, 362 of those were genotyped and 236 lambs contributed carcass data to estimate effects and interactions among the four genotype combinations produced. The four genotype combinations were defined as follows: ++/++ for wild-type at both loci; ++/C+ for wild-type at MSTN and heterozygous at CLPG; M+/++ for heterozygous at MSTN and wild-type at CLPG; and M+/C+ for heterozygous at both loci. The two independently segregating sire-derived alleles represent different breed-of-origin contrasts at each locus (Texel vs. composite origin for MSTN and Dorset vs. Texel origin for CLPG). Birth weight was recorded on all lambs, and subsequent body weights were adjusted to 56 (weaning), 70, and 140 d of age. Within sire-sex-genotype subgroups, naturally reared lambs were assigned to one of eight slaughter groups accounting for variation in birth date. Lambs were serially slaughtered at weekly intervals, 30 lambs per group, from roughly 26 to 33 wk of age. In addition to standard carcass traits, subjective leg scores were assigned and widths of carcasses were measured at the widest points of the shoulder and rump. Differences in birth weight were detected (P < 0.01) for the combination of the two loci and birth type, with single-born differences among genotypes exceeding differences among twin born progeny. Those interaction differences among genotypes were not as important at weaning (P = 0.36). Impact on growth rate differences among the genotypes during the post-weaning period were variable and dependent on sex of the lamb (P < 0.01). A synergistic interaction between MSTN and CLPG was observed for leg muscling scores (P < 0.05) but no other measures of carcass shape were affected. One copy of MSTN had a more modest impact on fat deposition and muscle conformation than did CLPG and did not interact (all values P > 0.20). Although some non-additive interactions that vary by trait and sex were detected, in general the data are consistent with the two mutations acting on muscle growth through independent pathways.

Multistressor effects on river biofilms under global change conditions

Freshwater ecosystems are confronted with multiple chemical, biological and physical stressors. Co-occurring stressors commonly result in additive responses, but non-additive interactions may also occur, hindering our predicting capacity. Despite growing interest in multiple stressor research, the response of freshwater communities to co-occurring chemical and climate change-related physical stressors remains largely unexplored. Here, we used a microcosm approach to evaluate the effect of the combined action of chemical and physical stressors on river biofilms. Results showed that additive responses dominated, whereas 14.5% of all responses were non-additive (75% antagonisms and 25% synergisms). Among these non-additive interactions, physical stressors dominated over chemicals and drove the overall responses. Overall, the occurrence of these non-additive interactions, together with the dominance of the climate-change related physical stressors, might lead to unexpected responses as a result of climate change.

Nonadditive interactions and phase transitions in strongly confined colloidal systems.

The behaviour of colloids can be controlled effectively by tuning the solvent-mediated interactions among them. An extensively studied example is the temperature-induced aggregation of suspended colloids close to the consolute point of their binary solvent. Here, using mean field theory and Monte Carlo simulations, we study the behaviour of colloids confined to a narrow slit containing a nearly-critical binary liquid mixture. We found that the effective interactions in this system are highly non-additive. In particular, the effective interactions among the colloids can be a few times stronger than the corresponding sum of the effective pair potentials. Inter alia, this non-additivity manifests itself in the phase behaviour of confined colloids, which depends sensitively on the slit width and temperature. In addition, we demonstrate the possibility of a first-order bridging transition between colloids confined to a slit and suspended in a phase-separated fluid well below the critical point of the solvent and at its critical composition in the bulk. This transition is accompanied by a remarkably large hysteresis loop, in which the force between the colloids varies by two orders of magnitude.

Two time scales for self and collective diffusion near the critical point in a simple patchy model for proteins with floating bonds.

Using dynamic Monte Carlo and Brownian dynamics, we investigate a floating bond model in which particles can bind through mobile bonds. The maximum number of bonds (here fixed to 4) can be tuned by appropriately choosing the repulsive, nonadditive interactions among bonds and particles. We compute the static and dynamic structure factor (intermediate scattering function) in the vicinity of the gas-liquid critical point. The static structure exhibits a weak tetrahedral network character. The intermediate scattering function shows a temporal decay deviating from a single exponential, which can be described by a double exponential decay where the two time scales differ approximately by one order of magnitude. This time scale separation is robust over a range of wave numbers. The analysis of clusters in real space indicates the formation of noncompact clusters and shows a considerable stretch in the instantaneous size distribution when approaching the critical point. The average time evolution of the largest subcluster of given initial clusters with 10 or more particles also shows a double exponential decay. The observation of two time scales in the intermediate scattering function at low packing fractions is consistent with similar findings in globular protein solutions with trivalent metal ions that act as bonds between proteins.

Catalytic and non-catalytic synergistic effects and their individual contributions to improved combustion performance of coal/biomass blends

This study focuses on the synergistic properties of three types of coal when co-fired with oat straw at different blending ratios. The results demonstrated non-additive interaction between oat straw and coal samples. The catalytic effect of oat straw ash and the non-catalytic effect of its organic constituents on these coal samples were isolated and analysed to measure their contribution to the confirmed synergistic effects during co-firing. The results showed a level of synergy suppression between catalytic and non-catalytic effects due to the overlapping function of the catalytic AAEMs and the radical propagation promoted by organic content of biomass. A novel index, i.e., synergy combination efficiency, was therefore proposed and used to quantify the level of synergistic promotion or synergistic inhibition occurring during the co-firing of these fuel blends. It was found that at a blending ratio of 30 wt% oat straw, the Guizhou coal achieved a synergy factor (S.F) of 1.50, with non-catalytic and catalytic synergy contributing 69.1% and 30.9% respectively. This coal blend showed the highest synergistic promotion with a combined efficiency of 194%, which demonstrated the potential of the use of co-firing synergy to improve combustion performance of poor quality coals.

Nonadditive Interactions Mediated by Water at Chemically Heterogeneous Surfaces: Nonionic Polar Groups and Hydrophobic Interactions.

We explore how two nonionic polar groups (primary amine and primary amide) influence hydrophobic interactions of neighboring nonpolar domains. We designed stable β-peptide sequences that generated globally amphiphilic (GA) helices, each with a nonpolar domain formed by six cyclohexyl side chains arranged along one side of the 14-helix. The other side of the helix was dominated by three polar side chains, from β3-homolysine (K) and/or β3-homoglutamine (Q) residues. Variations in this polar side chain array included exclusively β3-hLys (GA-KKK) and β3-hLys/β3-hGln mixtures (e.g., GA-QKK and GA-QQK). Chemical force measurements in aqueous solution versus methanol allowed quantification of the hydrophobic interactions of the β-peptide with the nonpolar tip of an atomic force microscope (AFM). At pH 10.5, where the K side chain is largely uncharged, we measured hydrophobic adhesive interactions mediated by GA-KKK to be 0.61 ± 0.04 nN, by GA-QKK to be 0.54 ± 0.01 nN, and by GA-QQK to be 0 ± 0.01 nN. This finding suggests that replacing an amine group (K side chain) with a primary amide group (Q side chain) weakens the hydrophobic interaction generated by the six cyclohexyl side chains. AFM studies with solid-supported mixed monolayers containing an alkyl component (60%) and a component bearing either a terminal amide or an amine group (40%) revealed analogous trends. These observations from two distinct experiment systems indicate that proximal nonionic polar groups have pronounced effects on hydrophobic interactions generated by a neighboring nonpolar domain, and that the magnitude of the effect depends strongly on polar group identity.

Generalized concentration addition accurately predicts estrogenic potentials of mixtures and environmental samples containing partial agonists

Cell-based bioanalytical tools are considered one alternative to overcome limitations of sensitivities of instrumental, analytical chemistry for monitoring estrogenic chemicals in the environment. Because these tools also reflect non-additive interactions of chemicals in mixtures, their outcomes often deviate from outcomes of chemical analytical approaches that assume additivity, e.g. the concentration addition (CA) model. Often this is because CA is unable to adequately represent effects of partial agonists, i.e. estrogens with lesser efficacies compared to 17β-estradiol. A generalized concentration addition (GCA) model has been proposed to address this shortcoming. In the present study, we investigated effects of mixtures of isomers of nonylphenol as partial model agonists in a cell-based estrogenicity assay. Whether the GCA model was able to more accurately predict the outcomes of these and previously published mixture experiments was evaluated, as well as the potency of a set of comprehensively characterized sewage effluent samples, compared to CA. If samples contained partial agonists, the GCA model consistently predicted potencies of mixtures and extracts of environmental samples more accurately than did the CA model. These findings enable more accurate estimations of potencies of estrogenicity explained by concentrations of agonists and partial agonists, thus significantly improving the ability to identify causative chemicals.

Widespread epistasis regulates glucose homeostasis and gene expression.

The relative contributions of additive versus non-additive interactions in the regulation of complex traits remains controversial. This may be in part because large-scale epistasis has traditionally been difficult to detect in complex, multi-cellular organisms. We hypothesized that it would be easier to detect interactions using mouse chromosome substitution strains that simultaneously incorporate allelic variation in many genes on a controlled genetic background. Analyzing metabolic traits and gene expression levels in the offspring of a series of crosses between mouse chromosome substitution strains demonstrated that inter-chromosomal epistasis was a dominant feature of these complex traits. Epistasis typically accounted for a larger proportion of the heritable effects than those due solely to additive effects. These epistatic interactions typically resulted in trait values returning to the levels of the parental CSS host strain. Due to the large epistatic effects, analyses that did not account for interactions consistently underestimated the true effect sizes due to allelic variation or failed to detect the loci controlling trait variation. These studies demonstrate that epistatic interactions are a common feature of complex traits and thus identifying these interactions is key to understanding their genetic regulation.

Characterizing interactions between fire and other disturbances and their impacts on tree mortality in western U.S. Forests

Abstract Increasing evidence that pervasive warming trends are altering disturbance regimes and their interactions with fire has generated substantial interest and debate over the implications of these changes. Previous work has primarily focused on conditions that promote non-additive interactions of linked and compounded disturbances, but the spectrum of potential interaction patterns has not been fully considered. Here we develop and define terminology, expand on the existing conceptual framework and review the patterns and mechanisms of disturbance interactions with a focus on interactions between fire and other forest disturbances and a specific emphasis on resulting tree mortality. The types of interactions reflect the positive, negative, or neutral responses to the incidence, intensity, and effects of the interaction. These types of interactions are not always mutually exclusive, but can be distinct. The collective effect of the interactions will determine the longer-term ecosystem response that can result in a resistant, resilient, or compounded interaction. Our review indicates that the interactions of drought, bark beetles, or pathogens with fire often result in neutral or maintained interactions that do not negatively or positively influence the incidence or intensity following fire. The effect of these disturbance interactions on tree mortality ranged from antagonistic (reduced mortality compared to individual disturbances) to synergistic (greater mortality compared to individual disturbances) within and among disturbance interaction types but often resulted in additive effects (mortality is consistent with the summation of the two disturbances). Synergistic effects on tree mortality have been observed when the severity of the initial disturbance is moderate to high and time between disturbances is relatively short. When the sequence of disturbance interaction is reversed (e.g., fire precedes other disturbances) the conditions can generally promote impeded interactions (lower incidence of interaction), reduced interactions (lower intensity of interaction), and antagonistic interactions (lower tree mortality). While recent research on fire-disturbance interactions has increased over the last decade and provided important insights, more research that identifies the specific thresholds of incidence, intensity, and effects of interaction by region and forest type are needed to better assist management solutions that promote desired outcomes in rapidly changing ecosystems.

Biochar As Plant Growth Promoter: Better Off Alone or Mixed with Organic Amendments?

Biochar is nowadays largely used as a soil amendment and is commercialized worldwide. However, in temperate agro-ecosystems the beneficial effect of biochar on crop productivity is limited, with several studies reporting negative crop responses. In this work, we studied the effect of 10 biochar and 9 not pyrogenic organic amendments (NPOA), using pure and in all possible combinations on lettuce growth (Lactuca sativa). Organic materials were characterized by 13C-CPMAS NMR spectroscopy and elemental analysis (pH, EC, C, N, C/N and H/C ratios). Pure biochars and NPOAs have variable effects, ranging from inhibition to strong stimulation on lettuce growth. For NPOAs, major inhibitory effects were found with N poor materials characterized by high C/N and H/C ratio. Among pure biochars, instead, those having a low H/C ratio seem to be the best for promoting plant growth. When biochars and organic amendments were mixed, non-additive interactions, either synergistic or antagonistic, were prevalent. However, the mixture effect on plant growth was mainly dependent on the chemical quality of NPOAs, while biochar chemistry played a secondary role. Synergisms were prevalent when N rich and lignin poor materials were mixed with biochar. On the contrary, antagonistic interactions occurred when leaf litter or woody materials were mixed with biochar. Further research is needed to identify the mechanisms behind the observed non-additive effects and to develop biochar-organic amendment combinations that maximize plant productivity in different agricultural systems.

The nature of three-body interactions in DFT: Exchange and polarization effects.

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar2-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Chemical components retention and modelling of antioxidant activity using neural networks in oven dried tomato slices with and without osmotic dehydration pre-treatment

This study investigated the comparative retention of chemical and bioactive components in oven dried tomato slices with and without 10% saline osmotic dehydration (OD) pre-treatment. Antioxidant activity of tomato slices was modelled from phytochemical parameters using artificial neural networks (ANNs) trained with multiplayer perceptron (MLP). Increase in water loss, solid gain, weight reduction and performance ratio obtained for tomato slices in 10% saline osmo-active solution indicated that moisture diffusion occurred faster than solid impregnation. Higher moisture diffusivity in slices with OD pre-treatment suggested faster water removal. A two-way ANOVA conducted revealed statistically significant effects of treatment methods, immersion time intervals and their synergistic interactions on moisture, ash, carbohydrate, energy, minerals (except sodium), antioxidant activity, flavonoid, lycopene, β-carotene contents. Statistical significance of both effects with non-significant and non-additive interactions were obtained for crude fat, crude protein, fatty acids, crude fibre and total phenols. Antioxidant activities modelled with ANNs had MLP architectures of 4-3-1 (R2 = 0.992) and 4-3-2-1 (R2 = 0.995) for oven dried tomato slices with and without OD pre-treatment respectively. High correlation coefficients R2 = 0.998 (without OD pre-treatment) and R2 = 0.999 (with OD pre-treatment) were obtained between experimentally determined antioxidant activity using 2,2-diphenyl-1-picrylhydrazyl and modelled antioxidant activity using ANNs.

Anisotropic hydrodynamic function of dense confined colloids.

Dense colloidal dispersions exhibit complex wave-vector-dependent diffusion, which is controlled by both direct particle interactions and indirect nonadditive hydrodynamic interactions mediated by the solvent. In bulk the hydrodynamic interactions are probed routinely, but in confined geometries their studies have been hitherto hindered by additional complications due to confining walls. Here we solve this issue by combining high-energy x-ray photon correlation spectroscopy and small-angle x-ray-scattering experiments on colloid-filled microfluidic channels to yield the confined fluid's hydrodynamic function in the short-time limit. Most importantly, we find the confined fluid to exhibit a strongly anisotropic hydrodynamic function, similar to its anisotropic structure factor. This observation is important in order to guide future theoretical research.

Grid-based stochastic search for hierarchical gene-gene interactions in population-based genetic studies of common human diseases

BackgroundLarge-scale genetic studies of common human diseases have focused almost exclusively on the independent main effects of single-nucleotide polymorphisms (SNPs) on disease susceptibility. These studies have had some success, but much of the genetic architecture of common disease remains unexplained. Attention is now turning to detecting SNPs that impact disease susceptibility in the context of other genetic factors and environmental exposures. These context-dependent genetic effects can manifest themselves as non-additive interactions, which are more challenging to model using parametric statistical approaches. The dimensionality that results from a multitude of genotype combinations, which results from considering many SNPs simultaneously, renders these approaches underpowered. We previously developed the multifactor dimensionality reduction (MDR) approach as a nonparametric and genetic model-free machine learning alternative. Approaches such as MDR can improve the power to detect gene-gene interactions but are limited in their ability to exhaustively consider SNP combinations in genome-wide association studies (GWAS), due to the combinatorial explosion of the search space. We introduce here a stochastic search algorithm called Crush for the application of MDR to modeling high-order gene-gene interactions in genome-wide data. The Crush-MDR approach uses expert knowledge to guide probabilistic searches within a framework that capitalizes on the use of biological knowledge to filter gene sets prior to analysis. Here we evaluated the ability of Crush-MDR to detect hierarchical sets of interacting SNPs using a biology-based simulation strategy that assumes non-additive interactions within genes and additivity in genetic effects between sets of genes within a biochemical pathway.ResultsWe show that Crush-MDR is able to identify genetic effects at the gene or pathway level significantly better than a baseline random search with the same number of model evaluations. We then applied the same methodology to a GWAS for Alzheimer’s disease and showed base level validation that Crush-MDR was able to identify a set of interacting genes with biological ties to Alzheimer’s disease.ConclusionsWe discuss the role of stochastic search and cloud computing for detecting complex genetic effects in genome-wide data.

Capturing Many-Body Interactions with Classical Dipole Induction Models.

The nonadditive many-body interactions are significant for structural and thermodynamic properties of condensed phase systems. In this work we examined the many-body interaction energy of a large number of common organic/biochemical molecular clusters, which consist of 18 chemical species and cover nine common organic elements, using the Møller–Plesset perturbation theory to the second order (MP2) [Møller et al. Phys. Rev.1934, 46, 618.]. We evaluated the capability of Thole-based dipole induction models to capture the many-body interaction energy. Three models were compared: the original model and parameters used by the AMOEBA force field, a variation of this original model where the damping parameters have been reoptimized to MP2 data, and a third model where the damping function form applied to the permanent electric field is modified. Overall, we find the simple classical atomic dipole models are able to capture the 3- and 4-body interaction energy across a wide variety of organic molecules in various intermolecular configurations. With modified Thole models, it is possible to further improve the agreement with MP2 results. These models were also tested on systems containing metal/halogen ions to examine the accuracy and transferability. This work suggests that the form of damping function applied to the permanent electrostatic field strongly affects the distance dependence of polarization energy at short intermolecular separations.

Large-scale interaction effects reveal missing heritability in schizophrenia, bipolar disorder and posttraumatic stress disorder

Genetic susceptibility factors behind psychiatric disorders typically contribute small effects individually. A possible explanation for the missing heritability is that the effects of common variants are not only polygenic but also non-additive, appearing only when interactions within large groups are taken into account. Here, we tested this hypothesis for schizophrenia (SZ) and bipolar disorder (BP) disease risks, and identified genetic factors shared with posttraumatic stress disorder (PTSD). When considered independently, few single-nucleotide polymorphisms (SNPs) reached genome-wide significance. In contrast, when SNPs were selected in groups (containing up to thousands each) and the collective effects of all interactions were estimated, the association strength for SZ/BP rose dramatically with a combined sample size of 7187 cases and 8309 controls. We identified a large number of genes and pathways whose association was significant only when interaction effects were included. The gene with highest association was CSMD1, which encodes a negative regulator of complement activation. Pathways for glycosaminoglycan (GAG) synthesis exhibited strong association in multiple contexts. Taken together, highly associated pathways suggested a pathogenesis mechanism where maternal immune activation causes disruption of neurogenesis (compounded by impaired cell cycle, DNA repair and neuronal migration) and deficits in cortical interneurons, leading to symptoms triggered by synaptic pruning. Increased risks arise from GAG deficiencies causing complement activation and excessive microglial action. Analysis of PTSD data sets suggested an etiology common to SZ/BP: interneuron deficiency can also lead to impaired control of fear responses triggered by trauma. We additionally found PTSD risk factors affecting synaptic plasticity and fatty acid signaling, consistent with the fear extinction model. Our results suggest that much of the missing heritability of psychiatric disorders resides in non-additive interaction effects.