Master regulators of biological systems in higher dimensions.

A longstanding goal of biology is to identify the key genes and species that critically impact evolution, ecology, and health. Network analysis has revealed keystone species that regulate ecosystems and master regulators that regulate cellular genetic networks. Yet these studies have focused on pairwise biological interactions, which can be affected by the context of genetic background and other species present, generating higher-order interactions. The important regulators of higher-order interactions are unstudied. To address this, we applied a high-dimensional geometry approach that quantifies epistasis in a fitness landscape to ask how individual genes and species influence the interactions in the rest of the biological network. We then generated and also reanalyzed 5-dimensional datasets (two genetic, two microbiome). We identified key genes (e.g., the rbs locus and pykF) and species (e.g., Lactobacilli) that control the interactions of many other genes and species. These higher-order master regulators can induce or suppress evolutionary and ecological diversification by controlling the topography of the fitness landscape. Thus, we provide a method and mathematical justification for exploration of biological networks in higher dimensions.

Microbiome interactions shape host fitness.

Gut bacteria can affect key aspects of host fitness, such as development, fecundity, and lifespan, while the host, in turn, shapes the gut microbiome. However, it is unclear to what extent individual species versus community interactions within the microbiome are linked to host fitness. Here, we combinatorially dissect the natural microbiome of Drosophila melanogaster and reveal that interactions between bacteria shape host fitness through life history tradeoffs. Empirically, we made germ-free flies colonized with each possible combination of the five core species of fly gut bacteria. We measured the resulting bacterial community abundances and fly fitness traits, including development, reproduction, and lifespan. The fly gut promoted bacterial diversity, which, in turn, accelerated development, reproduction, and aging: Flies that reproduced more died sooner. From these measurements, we calculated the impact of bacterial interactions on fly fitness by adapting the mathematics of genetic epistasis to the microbiome. Development and fecundity converged with higher diversity, suggesting minimal dependence on interactions. However, host lifespan and microbiome abundances were highly dependent on interactions between bacterial species. Higher-order interactions (involving three, four, and five species) occurred in 13-44% of possible cases depending on the trait, with the same interactions affecting multiple traits, a reflection of the life history tradeoff. Overall, we found these interactions were frequently context-dependent and often had the same magnitude as individual species themselves, indicating that the interactions can be as important as the individual species in gut microbiomes.

Cluster partitions and fitness landscapes of the Drosophila fly microbiome.

The concept of genetic epistasis defines an interaction between two genetic loci as the degree of non-additivity in their phenotypes. A fitness landscape describes the phenotypes over many genetic loci, and the shape of this landscape can be used to predict evolutionary trajectories. Epistasis in a fitness landscape makes prediction of evolutionary trajectories more complex because the interactions between loci can produce local fitness peaks or troughs, which changes the likelihood of different paths. While various mathematical frameworks have been proposed to investigate properties of fitness landscapes, Beerenwinkel et al. (Stat Sin 17(4):1317-1342, 2007a) suggested studying regular subdivisions of convex polytopes. In this sense, each locus provides one dimension, so that the genotypes form a cube with the number of dimensions equal to the number of genetic loci considered. The fitness landscape is a height function on the coordinates of the cube. Here, we propose cluster partitions and cluster filtrations of fitness landscapes as a new mathematical tool, which provides a concise combinatorial way of processing metric information from epistatic interactions. Furthermore, we extend the calculation of genetic interactions to consider interactions between microbial taxa in the gut microbiome of Drosophila fruit flies. We demonstrate similarities with and differences to the previous approach. As one outcome we locate interesting epistatic information on the fitness landscape where the previous approach is less conclusive.

The geometry of partial fitness orders and an efficient method for detecting genetic interactions.

We present an efficient computational approach for detecting genetic interactions from fitness comparison data together with a geometric interpretation using polyhedral cones associated to partial orderings. Genetic interactions are defined by linear forms with integer coefficients in the fitness variables assigned to genotypes. These forms generalize several popular approaches to study interactions, including Fourier-Walsh coefficients, interaction coordinates, and circuits. We assume that fitness measurements come with high uncertainty or are even unavailable, as is the case for many empirical studies, and derive interactions only from comparisons of genotypes with respect to their fitness, i.e. from partial fitness orders. We present a characterization of the class of partial fitness orders that imply interactions, using a graph-theoretic approach. Our characterization then yields an efficient algorithm for testing the condition when certain genetic interactions, such as sign epistasis, are implied. This provides an exponential improvement of the best previously known method. We also present a geometric interpretation of our characterization, which provides the basis for statistical analysis of partial fitness orders and genetic interactions.

Novel Insights into the Aortic Mechanical Properties of Mice Modeling Hereditary Aortic Diseases.

OBJECTIVE: Hereditary aortic diseases (hADs) increase the risk of aortic dissections and ruptures. Recently, we have established an objective approach to measure the rupture force of the murine aorta, thereby explaining the outcomes of clinical studies and assessing the added value of approved drugs in vascular Ehlers-Danlos syndrome (vEDS). Here, we applied our approach to six additional mouse hAD models. MATERIAL AND METHODS: We used two mouse models (Fbn1C1041G and Fbn1mgR ) of Marfan syndrome (MFS) as well as one smooth-muscle-cell-specific knockout (SMKO) of Efemp2 and three CRISPR/Cas9-engineered knock-in models (Ltbp1, Mfap4, and Timp1). One of the two MFS models was subjected to 4-week-long losartan treatment. Per mouse, three rings of the thoracic aorta were prepared, mounted on a tissue puller, and uniaxially stretched until rupture. RESULTS: The aortic rupture force of the SMKO and both MFS models was significantly lower compared with wild-type mice but in both MFS models higher than in mice modeling vEDS. In contrast, the Ltbp1, Mfap4, and Timp1 knock-in models presented no impaired aortic integrity. As expected, losartan treatment reduced aneurysm formation but surprisingly had no impact on the aortic rupture force of our MFS mice. CONCLUSION: Our read-out system can characterize the aortic biomechanical integrity of mice modeling not only vEDS but also related hADs, allowing the aortic-rupture-force-focused comparison of mouse models. Furthermore, aneurysm progression alone may not be a sufficient read-out for aortic rupture, as antihypertensive drugs reducing aortic dilatation might not strengthen the weakened aortic wall. Our results may enable identification of improved medical therapies of hADs.