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Our ability to understand the genotype-to-phenotype relationship is hindered by the lack of detailed understanding of phenotypes at a single-cell level. To systematically assess cell-to-cell phenotypic variability, we combined automated yeast genetics, high-content screening and neural network-based image analysis of single cells, focussing on genes that influence the architecture of four subcellular compartments of the endocytic pathway as a model system. Our unbiased assessment of the morphology of these compartments—endocytic patch, actin patch, late endosome and vacuole—identified 17 distinct mutant phenotypes associated with ~1,600 genes (~30% of all yeast genes). Approximately half of these mutants exhibited multiple phenotypes, highlighting the extent of morphological pleiotropy. Quantitative analysis also revealed that incomplete penetrance was prevalent, with the majority of mutants exhibiting substantial variability in phenotype at the single-cell level. Our single-cell analysis enabled exploration of factors that contribute to incomplete penetrance and cellular heterogeneity, including replicative age, organelle inheritance and response to stress.

Genes have been historically classified as either essential or non-essential based on their requirement for viability. However, some genes are essential in some genetic backgrounds but non-essential in others, thus challenging the binary classification of gene essentiality. Such dispensable essential genes represent a valuable model for understanding the incomplete penetrance of loss-of-function mutations that is often observed in natural populations. Here, we compiled data from multiple studies on essential gene dispensability inSaccharomyces cerevisiaeto comprehensively characterize these genes. In analyses spanning different evolutionary time-scales, ranging fromS. cerevisiaestrains to human cell lines, dispensable essential genes exhibited distinct phylogenetic properties compared to other essential and non-essential genes. Integration of interactions with suppressor genes that can bypass the gene essentiality revealed the high functional modularity of the bypass suppression network. Furthermore, dispensable essential and bypass suppressor gene pairs reflected simultaneous changes in the mutational landscape ofS. cerevisiaestrains. Importantly, species in which dispensable essential genes were non-essential tended to carry bypass suppressor mutations in their genomes. Overall, our study offers a comprehensive view of dispensable essential genes and illustrates how their interactions with bypass suppressor genes reflect evolutionary outcomes.

Genetic suppression occurs when the deleterious effects of a primary “query” mutation, such as a disease-causing mutation, are rescued by a suppressor mutation elsewhere in the genome. To capture existing knowledge on suppression relationships between human genes, we examined 2,400 published papers for potential interactions identified through either genetic modification of cultured human cells or through association studies in patients. The resulting network encompassed 476 unique suppression interactions that frequently linked genes that function in the same biological process. Suppressors were strongly enriched for genes with a role in stress response or signaling, suggesting that deleterious mutations can often be buffered by modulating signaling cascades or immune responses. Suppressor mutations tended to be deleterious when they occurred in absence of the query mutation, in apparent contrast with their protective role in the presence of the query. We formulated and quantified mechanisms of genetic suppression that could explain 71% of interactions and provided mechanistic insight into disease pathology. Finally, we used these observations to accurately predict suppressor genes in the human genome. The emerging frequency of suppression interactions and range of underlying mechanisms suggest that compensatory mutations may exist for the majority of genetic diseases.

The toroidal nucleus is a novel chromosomal instability (CIN) biomarker which complements the micronucleus. Understanding the specific biological stresses leading to the formation of each CIN-associated phenotype requires the evaluation of large panels of biological images collected from different genetic backgrounds and environmental conditions. However, the quantification of toroidal nuclei is currently a manual process which is unviable on a large scale. Here, we present PIQUE (Processing of Images for the QUantification of toroidal nuclEi), a tool that automates the identification of toroidal nuclei, minimizing false positives while highly agreeing with the manual quantifications. Additionally, PIQUE identifies micronuclei for a convenient comparison of both CIN biomarkers. PIQUE is an open-source ImageJ plugin with a user-friendly interface that enables a wide scientific community to easily study the novel toroidal nucleus for the analysis of CIN levels in cellular models.AvailabilityThe plugin, the user manual, and the images used for the evaluation of PIQUE are available upon request from the authors.Contactcarles.pons@irbbarcelona.organdcaroline.mauvezin@ub.edu

The EMBL-EBI Complex Portal is a knowledgebase of macromolecular complexes providing persistent stable identifiers. Entries are linked to literature evidence and provide details of complex membership, function, structure and complex-specific Gene Ontology annotations. Data are freely available and downloadable in HUPO-PSI community standards and missing entries can be requested for curation. In collaboration with Saccharomyces Genome Database and UniProt, the yeast complexome, a compendium of all known heteromeric assemblies from the model organism Saccharomyces cerevisiae, was curated. This expansion of knowledge and scope has led to a 50% increase in curated complexes compared to the previously published dataset, CYC2008. The yeast complexome is used as a reference resource for the analysis of complexes from large-scale experiments. Our analysis showed that genes coding for proteins in complexes tend to have more genetic interactions, are co-expressed with more genes, are more multifunctional, localize more often in the nucleus, and are more often involved in nucleic acid-related metabolic processes and processes where large machineries are the predominant functional drivers. A comparison to genetic interactions showed that about 40% of expanded co-complex pairs also have genetic interactions, suggesting strong functional links between complex members.

Chromosomal instability (CIN) is a hallmark of cancer, which is characterized by the gain or loss of chromosomes as well as the rearrangement of the genetic material during cell division. Detection of mitotic errors such as misaligned chromosomes or chromosomal bridges (also known as lagging chromosomes) is challenging as it requires the analysis and manual discrimination of chromosomal aberrations in mitotic cells by molecular techniques. In interphase cells, more frequent in the cell population than mitotic cells, two distinct nuclear phenotypes are associated with CIN: the micronucleus and the toroidal nucleus. Several methods are available for the detection of micronuclei, but none for toroidal nuclei. Here, we provide a method to quantify the presence of both nuclear biomarkers for the evaluation of CIN status in non-mitotic cells particularly suited for genotoxicity screens.

SummaryHundreds of different protein complexes that perform important functions across all cellular processes, collectively comprising the “complexome” of an organism, have been identified1. However, less is known about the fraction of the interactome that exists outside the complexome, in the “outer-complexome”. To investigate features of “inner”- versus outer-complexome organisation in yeast, we generated a high-quality atlas of binary protein-protein interactions (PPIs), combining three previous maps2–4 and a new reference all-by-all binary interactome map. A greater proportion of interactions in our map are in the outer-complexome, in comparison to those found by affinity purification followed by mass spectrometry5–7 or in literature curated datasets8–11. In addition, recent advances in deep learning predictions of PPI structures12 mirror the existing experimentally resolved structures in being largely focused on the inner complexome and missing most interactions in the outer-complexome. Our new PPI network suggests that the outer-complexome contains considerably more PPIs than the inner-complexome, and integration with functional similarity networks13–15 reveals that interactions in the inner-complexome are highly detectable and correspond to pairs of proteins with high functional similarity, while proteins connected by more transient, harder-to-detect interactions in the outer-complexome, exhibit higher functional heterogeneity.

Environmental impacts on gene networks A phenotype can be affected by genes interacting with other genes, the environment, or both other genes and the environment (a differential interaction). To better understand how these interactions function in yeast, Costanzo et al. mapped gene-gene interactions using single- and double-mutant deletions and temperature-sensitive alleles under 14 environmental conditions. Many deleted or temperature-sensitive nonessential genes affected yeast fitness both positively and negatively under at least one of the environmental conditions tested. In these cases, up to 24% of yeast genes were affected. A minority of these differential interactions point to previously unknown genetic connections across functional networks, informing on how genetic architecture responds to environmental variation. Science , this issue p. eabf8424

The consequence of a mutation can be influenced by the context in which it operates. For example, loss of gene function may be tolerated in one genetic background, and lethal in another. The extent to which mutant phenotypes are malleable, the architecture of modifiers and the identities of causal genes remain largely unknown. Here, we measure the fitness effects of ~ 1,100 temperature‐sensitive alleles of yeast essential genes in the context of variation from ten different natural genetic backgrounds and map the modifiers for 19 combinations. Altogether, fitness defects for 149 of the 580 tested genes (26%) could be suppressed by genetic variation in at least one yeast strain. Suppression was generally driven by gain‐of‐function of a single, strong modifier gene, and involved both genes encoding complex or pathway partners suppressing specific temperature‐sensitive alleles, as well as general modifiers altering the effect of many alleles. The emerging frequency of suppression and range of possible mechanisms suggest that a substantial fraction of monogenic diseases could be managed by modulating other gene products., A survey of ~ 1,100 temperature‐sensitive alleles of yeast essential genes in ten diverse strains shows that natural genetic variants frequently suppress deleterious mutations. Genetic mapping and allele replacement identify causal suppressor genes.

The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately represented by a phylogenetic tree, and rooted phylogenetic networks that describe such complex processes have been introduced as a generalization of rooted phylogenetic trees. In fact, estimating rooted phylogenetic networks from genomic sequence data and analyzing their structural properties is one of the most important tasks in contemporary phylogenetics. Over the last two decades, several subclasses of rooted phylogenetic networks (characterized by certain structural constraints) have been introduced in the literature, either to model specific biological phenomena or to enable tractable mathematical and computational analyses. In the present manuscript, we provide a thorough review of these network classes, as well as provide a biological interpretation of the structural constraints underlying these networks where possible. In addition, we discuss how imposing structural constraints on the network topology can be used to address the scalability and identifiability challenges faced in the estimation of phylogenetic networks from empirical data., Comment: 54 pages, 13 figures

Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this paper, we generalize a complete polynomial invariant on trees to a class of phylogenetic networks called separable networks, which will include orchard networks. Networks are becoming increasingly important for their ability to represent reticulation events, such as hybridization, in evolutionary history. We provide a function from the space of internally multi-labelled phylogenetic networks, a more generic graph structure than phylogenetic networks where the reticulations are also labelled, to a polynomial ring. We prove that the separability condition allows us to characterize, via the polynomial, the phylogenetic networks with the same number of leaves and same number of reticulations by considering their internally labelled versions. While the invariant for trees is a polynomial in Z [ x 1 , … , x n , y ] where n is the number of leaves, the invariant for internally multi-labelled phylogenetic networks is an element of Z [ x 1 , … , x n , λ 1 , … , λ r , y ], where r is the number of reticulations in the network. When the networks are considered without leaf labels the number of variables reduces to r + 2.

The consequence of a mutation can be influenced by the context in which it operates. For example, loss of gene function may be tolerated in one genetic background, but lead to lethality in another. The extent to which mutant phenotypes are malleable, the complexity of the architecture of modifiers, and the identities of causal genes and pathways remain largely unknown. Here, we measure the fitness effects of ~1,500 temperature sensitive alleles of yeast essential genes in the context of variation from ten different natural genetic backgrounds, and map the modifiers for 19 combinations. Altogether, fitness defects for 183 of the 530 tested genes (35%) could be suppressed by standing genetic variation in at least one wild strain. Suppression was generally driven by gain-of-function of a single, strong modifier gene. The validated causes included both variants in protein interaction partners or pathway members suppressing specific genes, as well as general modifiers altering the effect of many temperature sensitive alleles. The emerging frequency of suppression and range of possible suppression mechanisms suggest that a substantial fraction of monogenic diseases could be repressed by modulating other gene products.

The EMBL-EBI Complex Portal is a knowledgebase of macromolecular complexes providing persistent stable identifiers. Entries are linked to literature evidence and provide details of complex membership, function, structure and complex-specific Gene Ontology annotations. Data is freely available and downloadable in HUPO-PSI community standards and missing entries can be requested for curation. In collaboration with Saccharomyces Genome Database and UniProt, the yeast complexome, a compendium of all known heteromeric assemblies from the model organism Saccharomyces cerevisiae, was curated. This expansion of knowledge and scope has led to a 50% increase in curated complexes compared to the previously published dataset, CYC2008. The yeast complexome is used as a reference resource for the analysis of complexes from large-scale experiments. Our analysis showed that genes coding for proteins in complexes tend to have more genetic interactions, are co-expressed with more genes, are multifunctional, localize more often in the nucleus, and are more often involved in nucleic acid-related metabolic processes and processes where large machineries are the predominant functional drivers. A comparison to genetic interactions showed that about 40% of expanded co-complex pairs also have genetic interactions, suggesting strong functional links between complex members.

Objetivo El test del aliento con 13C-urea (TAU) es la prueba no invasiva más utilizada para diagnosticar Helicobacter pylori (H. pylori). La posible interferencia de la toma de antiácidos en su resultado es aún controvertida. El estudio se dirige a confirmar la no interferencia del almagato en la determinación de H. pylori mediante el TAU. Pacientes y métodos Estudio observacional, multicéntrico, en pacientes adultos en tratamiento con almagato y a los que se indicó un TAU (TAUKIT®). Cuando el resultado del TAU fue negativo, se suprimió la toma de almagato durante 30 días y se repitió un segundo TAU. En los pacientes cuyo resultado fue positivo, no se realizaron más determinaciones. La variable principal a estudio fue el porcentaje de pacientes que teniendo resultado negativo en la primera prueba de aliento, tras suprimir la toma de almagato y repetirla, ésta se positivizó (falsos negativos del TAU, posiblemente atribuibles a almagato). Resultados De los 167 pacientes evaluables, 59% fueron mujeres, la media de edad fue de 49 años y 97% de los casos presentaban sintomatología digestiva. El resultado del primer TAU fue negativo en un 71% de casos. De éstos, en la segunda prueba de TAU tras suprimir almagato, este resultado se confirmó en el 97,5%. El porcentaje de falsos negativos sobre el total de casos evaluados fue del 1,8%. Conclusiones La toma de almagato tiene una interferencia mínima o nula en el resultado del TAU para el diagnóstico de la infección por H. pylori; por tanto, se puede utilizar en las semanas previas a la realización del TAU, Objective The 13C-urea breath test (UBT) is the most widely used non-invasive diagnostic test for Helicobacter pylori. Debate continues to surround the possible interference of antacid intake on its result. This study aims to confirm the non-interference of almagate in the determination of H. pylori by UBT. Patients and methods Observational, multicentre study in adult patients treated with almagate in whom a UBT (TAUKIT®) was indicated. When the UBT result was negative, use of almagate was stopped for 30 days and the UBT was repeated. When the result was positive, no further determinations were made. The primary endpoint was the percentage of patients who, having had a negative result in the first breath test, were positive in the second after having stopped taking almagate (UBT false negatives, possibly attributable to almagate). Results Of the 167 evaluable patients, 59% were female, average age was 49 and 97% had gastrointestinal symptoms. The result of the first UBT was negative in 71% of cases. Of these, in the second UBT test after stopping the almagate, the negative result was confirmed in 97.5%. Out of the total number of cases evaluated, the rate of false negatives was 1.8%. Conclusions Taking almagate has minimal or no interference in the result of UBT for the diagnosis of H. pylori infection. It can therefore be used in the weeks prior to a UBT, El presente trabajo ha sido financiado por Almirall, S.A., Barcelona y también ha sido posible gracias a la aportación gratuita de los test de urea por parte de Isomed Pharma (kit TAUKIT 100 mg de 13C).

Essential genes tend to be highly conserved across eukaryotes, but, in some cases, their critical roles can be bypassed through genetic rewiring. From a systematic analysis of 728 different essential yeast genes, we discovered that 124 (17%) were dispensable essential genes. Through whole‐genome sequencing and detailed genetic analysis, we investigated the genetic interactions and genome alterations underlying bypass suppression. Dispensable essential genes often had paralogs, were enriched for genes encoding membrane‐associated proteins, and were depleted for members of protein complexes. Functionally related genes frequently drove the bypass suppression interactions. These gene properties were predictive of essential gene dispensability and of specific suppressors among hundreds of genes on aneuploid chromosomes. Our findings identify yeast's core essential gene set and reveal that the properties of dispensable essential genes are conserved from yeast to human cells, correlating with human genes that display cell line‐specific essentiality in the Cancer Dependency Map (DepMap) project., A systematic analysis of 728 different essential yeast genes identifies 124 (17%) dispensable essential genes. Whole‐genome sequencing is used to identify the genome alterations underlying the bypass suppression.

Objective The 13C-urea breath test (UBT) is the most widely used non-invasive diagnostic test for Helicobacter pylori. Debate continues to surround the possible interference of antacid intake on its result. This study aims to confirm the non-interference of almagate in the determination of H. pylori by UBT. Patients and methods Observational, multicentre study in adult patients treated with almagate in whom a UBT (TAUKIT®) was indicated. When the UBT result was negative, use of almagate was stopped for 30 days and the UBT was repeated. When the result was positive, no further determinations were made. The primary endpoint was the percentage of patients who, having had a negative result in the first breath test, were positive in the second after having stopped taking almagate (UBT false negatives, possibly attributable to almagate). Results Of the 167 evaluable patients, 59% were female, average age was 49 and 97% had gastrointestinal symptoms. The result of the first UBT was negative in 71% of cases. Of these, in the second UBT test after stopping the almagate, the negative result was confirmed in 97.5%. Out of the total number of cases evaluated, the rate of false negatives was 1.8%. Conclusions Taking almagate has minimal or no interference in the result of UBT for the diagnosis of H. pylori infection. It can therefore be used in the weeks prior to a UBT.

Phylogenetic networks provide a mathematical model to represent the evolution of a set of species where, apart from speciation, reticulate evolutionary events have to be taken into account. Among these events, lateral gene transfers need special consideration due to the asymmetry in the roles of the species involved in such an event. To take into account this asymmetry, LGT networks were introduced. Contrarily to the case of phylogenetic trees, the combinatorial structure of phylogenetic networks is much less known and difficult to describe. One of the approaches in the literature is to classify them according to their level and find generators of the given level that can be used to recursively generate all networks. In this paper, we adapt the concept of generators to the case of LGT networks. We show how these generators, classified by their level, give rise to simple LGT networks of the specified level, and how any LGT network can be obtained from these simple networks, that act as building blocks of the generic structure. The stochastic models of evolution of phylogenetic networks are also much less studied than those for phylogenetic trees. In this setting, we introduce a novel two-parameter model that generates LGT networks. Finally, we present some computer simulations using this model in order to investigate the complexity of the generated networks, depending on the parameters of the model.

et al., Global insights into cellular organization and genome function require comprehensive understanding of the interactome networks that mediate genotype–phenotype relationships1,2. Here we present a human ‘all-by-all’ reference interactome map of human binary protein interactions, or ‘HuRI’. With approximately 53,000 protein–protein interactions, HuRI has approximately four times as many such interactions as there are high-quality curated interactions from small-scale studies. The integration of HuRI with genome3, transcriptome4 and proteome5 data enables cellular function to be studied within most physiological or pathological cellular contexts. We demonstrate the utility of HuRI in identifying the specific subcellular roles of protein–protein interactions. Inferred tissue-specific networks reveal general principles for the formation of cellular context-specific functions and elucidate potential molecular mechanisms that might underlie tissue-specific phenotypes of Mendelian diseases. HuRI is a systematic proteome-wide reference that links genomic variation to phenotypic outcomes., This work was primarily supported by the National Institutes of Health (NIH) National Human Genome Research Institute (NHGRI) grant U41HG001715 (M.V., F.P.R., D.E.H., M.A.C., G.D.B. and J.T.) with additional support from NIH grants P50HG004233 (M.V. and F.P.R.), U01HL098166 (M.V.), U01HG007690 (M.V.), R01GM109199 (M.A.C.), Canadian Institute for Health Research (CIHR) Foundation Grants (F.P.R. and J. Rak), the Canada Excellence Research Chairs Program (F.P.R.) and an American Heart Association grant 15CVGPS23430000 (M.V.). D.-K.K. was supported by a Banting Postdoctoral Fellowship through the Natural Sciences and Engineering Research Council (NSERC) of Canada and by the Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Education (2017R1A6A3A03004385). C. Pons was supported by a Ramon Cajal fellowship (RYC-2017-22959). G.M.S. was supported by NIH Training Grant T32CA009361. M.V. is a Chercheurv Qualifié Honoraire from the Fonds de la Recherche Scientifique (FRS-FNRS, Wallonia-Brussels Federation, Belgium).

Endocytosis is a conserved process that mediates the internalization of nutrients and plasma membrane components, including receptors, for sorting to endosomes and the vacuole (lysosome). We combined systematic yeast genetics, high-content screening, and neural network-based image analysis of single cells to screen for genes that influence the morphology of four main endocytic compartments: coat proteins, actin patches, late endosome, and vacuole. This unbiased approach identified 17 mutant phenotypes and ∼1600 genes whose perturbation affected at least one of the four compartments. Numerous mutants were associated with multiple phenotypes, indicating that morphological pleiotropy is often seen within the endocytic pathway. Morphological profiles based on the 17 aberrant phenotypes were highly correlated for functionally related genes, enabling prediction of gene function. Incomplete penetrance was prevalent, and single-cell analysis enabled exploration of the mechanisms underlying cellular heterogeneity, which include replicative age, organelle inheritance, and stress response.

Global insights into cellular organization and function require comprehensive understanding of interactome networks. Similar to how a reference genome sequence revolutionized human genetics, a reference map of the human interactome network is critical to fully understand genotype-phenotype relationships. Here we present the first human “all-by-all” binary reference interactome map, or “HuRI”. With ~53,000 high-quality protein-protein interactions (PPIs), HuRI is approximately four times larger than the information curated from small-scale studies available in the literature. Integrating HuRI with genome, transcriptome and proteome data enables the study of cellular function within essentially any physiological or pathological cellular context. We demonstrate the use of HuRI in identifying specific subcellular roles of PPIs and protein function modulation via splicing during brain development. Inferred tissue-specific networks reveal general principles for the formation of cellular context-specific functions and elucidate potential molecular mechanisms underlying tissue-specific phenotypes of Mendelian diseases. HuRI thus represents an unprecedented, systematic reference linking genomic variation to phenotypic outcomes.

The Integrated Microbial Genome/Virus (IMG/VR) system v.2.0 (https://img.jgi.doe.gov/vr/) is the largest publicly available data management and analysis platform dedicated to viral genomics. Since the last report published in the 2016, NAR Database Issue, the data has tripled in size and currently contains genomes of 8389 cultivated reference viruses, 12 498 previously published curated prophages derived from cultivated microbial isolates, and 735112 viral genomic fragments computationally predicted from assembled shotgun metagenomes. Nearly 60% of the viral genomes and genome fragments are clustered into 110384 viral Operational Taxonomic Units (vOTUs) with two or more members. To improve data quality and predictions of host specificity, IMG/VR v.2.0 now separates prokaryotic and eukaryotic viruses, utilizes known prophage sequences to improve taxonomic assignments, and provides viral genome quality scores based on the estimated genome completeness. New features also include enhanced BLAST search capabilities for external queries. Finally, geographic map visualization to locate user-selected viral genomes or genome fragments has been implemented and download options have been extended. All of these features make IMG/VR v.2.0 a key resource for the study of viruses., US Department of Energy Joint Genome Institute, a DOE Office of Science User Facility [DE-AC02-05CH11231] and used resources of the National Energy Research Scientific Computing Center, supported by the Office of Science of the US Department of Energy. J.C.P. and M.L. were partially supported by the Spanish Ministry of Economy and Competitiveness and European Regional Development Fund [DPI2015-67082-P] (MINECO/FEDER). Funding for open access charge: The corresponding author will pay for publication charges.

Although we now routinely sequence human genomes, we can confidently identify only a fraction of the sequence variants that have a functional impact. Here, we developed a deep mutational scanning framework that produces exhaustive maps for human missense variants by combining random codon mutagenesis and multiplexed functional variation assays with computational imputation and refinement. We applied this framework to four proteins corresponding to six human genes: UBE2I (encoding SUMO E2 conjugase), SUMO1 (small ubiquitin‐like modifier), TPK1 (thiamin pyrophosphokinase), and CALM1/2/3 (three genes encoding the protein calmodulin). The resulting maps recapitulate known protein features and confidently identify pathogenic variation. Assays potentially amenable to deep mutational scanning are already available for 57% of human disease genes, suggesting that DMS could ultimately map functional variation for all human disease genes.

Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer. One way to obtain such a network is by starting with a (rooted) phylogenetic tree $T$, called a base tree, and adding arcs between arcs of $T$. The class of phylogenetic networks that can be obtained in this way is called tree-based networks and includes the prominent classes of tree-child and reticulation-visible networks. Initially defined for binary phylogenetic networks, tree-based networks naturally extend to arbitrary phylogenetic networks. In this paper, we generalise recent tree-based characterisations and associated proximity measures for binary phylogenetic networks to arbitrary phylogenetic networks. These characterisations are in terms of matchings in bipartite graphs, path partitions, and antichains. Some of the generalisations are straightforward to establish using the original approach, while others require a very different approach. Furthermore, for an arbitrary tree-based network $N$, we characterise the support trees of $N$, that is, the tree-based embeddings of $N$. We use this characterisation to give an explicit formula for the number of support trees of $N$ when $N$ is binary. This formula is written in terms of the components of a bipartite graph., 20 pages, 6 figures

Although we now routinely sequence human genomes, we can confidently identify only a fraction of the sequence variants that have a functional impact. Here we developed a deep mutational scanning framework that produces exhaustive maps for human missense variants by combining random codon-mutagenesis and multiplexed functional variation assays with computational imputation and refinement. We applied this framework to four proteins corresponding to six human genes: UBE2I (encoding SUMO E2 conjugase), SUMO1 (small ubiquitin-like modifier), TPK1 (thiamin pyrophosphokinase), and CALM1/2/3 (three genes encoding the protein calmodulin). The resulting maps recapitulate known protein features, and confidently identify pathogenic variation. Assays potentially amenable to deep mutational scanning are already available for 57% of human disease genes, suggesting that DMS could ultimately map functional variation for all human disease genes.

INTRODUCTION Genetic interactions occur when mutations in different genes combine to result in a phenotype that is different from expectation based on those of the individual mutations. Negative genetic interactions occur when a combination of mutations leads to a fitness defect that is more exacerbated than expected. For example, synthetic lethality occurs when two mutations, neither of which is lethal on its own, generate an inviable double mutant. Alternatively, positive genetic interactions occur when genetic perturbations combine to generate a double mutant with a greater fitness than expected. Global digenic interaction studies have been useful for understanding the functional wiring diagram of the cell and may also provide insight into the genotype-to-phenotype relationship, which is important for tracking the missing heritability of human health and disease. Here we describe a network of higher-order trigenic interactions and explore its implications. RATIONALE Variation in phenotypic outcomes in different individuals is caused by genetic determinants that act as modifiers. Modifier loci are prevalent in human populations, but knowledge regarding how variants interact to modulate phenotype in different individuals is lacking. Similarly, in yeast, traits including conditional essentiality—in which certain genes are essential in one genetic background but nonessential in another—often result from an interplay of multiple modifier loci. Because complex modifiers may underlie the genetic basis of physiological states found in natural populations, it is critical to understand the landscape of higher-order genetic interactions. RESULTS To survey trigenic interactions, we designed query strains that sampled key features of the global digenic interaction network: (i) digenic interaction strength, (ii) average number of digenic interactions, and (iii) digenic interaction profile similarity. In total, we tested ~400,000 double and ~200,000 triple mutants for fitness defects and identified ~9500 digenic and ~3200 trigenic negative interactions. Although trigenic interactions tend to be weaker than digenic interactions, they were both enriched for functional relationships. About one-third of trigenic interactions identified “novel” connections that were not observed in our digenic control network, whereas the remaining approximately two-thirds of trigenic interactions “modified” a digenic interaction, suggesting that the global digenic interaction network is important for understanding the trigenic interaction network. Despite their functional enrichment, trigenic interactions also bridged distant bioprocesses. We estimate that the global trigenic interaction network is ~100 times as large as the global digenic network, highlighting the potential for complex genetic interactions to affect the biology of inheritance. CONCLUSION The extensive network of trigenic interactions and their ability to generate functionally diverse phenotypes suggest that higher-order genetic interactions may play a key role in the genotype-to-phenotype relationship, genome size, and speciation.