Genome-driven evolutionary game theory helps understand the rise of metabolic interdependencies in microbial communities

Metabolite exchanges in microbial communities give rise to ecological interactions that govern ecosystem diversity and stability. It is unclear, however, how the rise of these interactions varies across metabolites and organisms. Here we address this question by integrating genome-scale models of metabolism with evolutionary game theory. Specifically, we use microbial fitness values estimated by metabolic models to infer evolutionarily stable interactions in multi-species microbial “games”. We first validate our approach using a well-characterized yeast cheater-cooperator system. We next perform over 80,000 in silico experiments to infer how metabolic interdependencies mediated by amino acid leakage in Escherichia coli vary across 189 amino acid pairs. While most pairs display shared patterns of inter-species interactions, multiple deviations are caused by pleiotropy and epistasis in metabolism. Furthermore, simulated invasion experiments reveal possible paths to obligate cross-feeding. Our study provides genomically driven insight into the rise of ecological interactions, with implications for microbiome research and synthetic ecology.We gratefully acknowledge funding from the Defense Advanced Research Projects Agency (Purchase Request No. HR0011515303, Contract No. HR0011-15-C-0091), the U.S. Department of Energy (Grants DE-SC0004962 and DE-SC0012627), the NIH (Grants 5R01DE024468 and R01GM121950), the national Science Foundation (Grants 1457695 and NSFOCE-BSF 1635070), MURI Grant W911NF-12-1-0390, the Human Frontiers Science Program (grant RGP0020/2016), and the Boston University Interdisciplinary Biomedical Research Office ARC grant on Systems Biology Approaches to Microbiome Research. We also thank Dr Kirill Korolev and members of the Segre Lab for their invaluable feedback on this work. (HR0011515303 - Defense Advanced Research Projects Agency; HR0011-15-C-0091 - Defense Advanced Research Projects Agency; DE-SC0004962 - U.S. Department of Energy; DE-SC0012627 - U.S. Department of Energy; 5R01DE024468 - NIH; R01GM121950 - NIH; 1457695 - national Science Foundation; NSFOCE-BSF 1635070 - national Science Foundation; W911NF-12-1-0390 - MURI; RGP0020/2016 - Human Frontiers Science Program; Boston University Interdisciplinary Biomedical Research Office ARC)Published versio

Costless metabolic secretions as drivers of interspecies interactions in microbial ecosystems

Metabolic exchange mediates interactions among microbes, helping explain diversity in microbial communities. As these interactions often involve a fitness cost, it is unclear how stable cooperation can emerge. Here we use genome-scale metabolic models to investigate whether the release of “costless” metabolites (i.e. those that cause no fitness cost to the producer), can be a prominent driver of intermicrobial interactions. By performing over 2 million pairwise growth simulations of 24 species in a combinatorial assortment of environments, we identify a large space of metabolites that can be secreted without cost, thus generating ample cross-feeding opportunities. In addition to providing an atlas of putative interactions, we show that anoxic conditions can promote mutualisms by providing more opportunities for exchange of costless metabolites, resulting in an overrepresentation of stable ecological network motifs. These results may help identify interaction patterns in natural communities and inform the design of synthetic microbial consortia.We thank Dr. Niels Klitgord for pioneering ideas that inspired launch of this work. We are also grateful to David Bernstein, Joshua E. Goldford, Meghan Thommes, Demetrius DiMucci, and all members of the Segre Lab for helpful discussions. A.R.P. is supported by a National Academies of Sciences, Engineering, and Medicine Ford Foundation Predoctoral Fellowship and a Howard Hughes Medical Institute Gilliam Fellowship. This work was supported by funding from the Defense Advanced Research Projects Agency (purchase request no. HR0011515303, contract no. HR0011-15-C-0091), the U.S. Department of Energy (grants DE-SC0004962 and DE-SC0012627), the NIH (grants 5R01DE024468, R01GM121950, and Sub_P30DK036836_P&F), the National Science Foundation (grants 1457695 and NSFOCE-BSF 1635070), MURI Grant W911NF-12-1-0390, the Human Frontiers Science Program (grant RGP0020/2016), and the Boston University Inter-disciplinary Biomedical Research Office. (National Academies of Sciences, Engineering, and Medicine Ford Foundation Predoctoral Fellowship; Howard Hughes Medical Institute Gilliam Fellowship; HR0011515303 - Defense Advanced Research Projects Agency; HR0011-15-C-0091 - Defense Advanced Research Projects Agency; DE-SC0004962 - U.S. Department of Energy; DE-SC0012627 - U.S. Department of Energy; 5R01DE024468 - NIH; R01GM121950 - NIH; Sub_P30DK036836_PF - NIH; 1457695 - National Science Foundation; NSFOCE-BSF 1635070 - National Science Foundation; W911NF-12-1-0390 - MURI Grant; RGP0020/2016 - Human Frontiers Science Program; Boston University Inter-disciplinary Biomedical Research Office)Published versio

Species interactions differ in their genetic robustness

Conflict and cooperation between bacterial species drive the composition and function of microbial communities. Stability of these emergent properties will be influenced by the degree to which species' interactions are robust to genetic perturbations. We use genome-scale metabolic modeling to computationally analyze the impact of genetic changes when Escherichia coli and Salmonella enterica compete, or cooperate. We systematically knocked out in silico each reaction in the metabolic network of E. coli to construct all 2583 mutant stoichiometric models. Then, using a recently developed multi-scale computational framework, we simulated the growth of each mutant E. coli in the presence of S. enterica. The type of interaction between species was set by modulating the initial metabolites present in the environment. We found that the community was most robust to genetic perturbations when the organisms were cooperating. Species ratios were more stable in the cooperative community, and community biomass had equal variance in the two contexts. Additionally, the number of mutations that have a substantial effect is lower when the species cooperate than when they are competing. In contrast, when mutations were added to the S. enterica network the system was more robust when the bacteria were competing. These results highlight the utility of connecting metabolic mechanisms and studies of ecological stability. Cooperation and conflict alter the connection between genetic changes and properties that emerge at higher levels of biological organization.The authors thank reviewers for comments that substantially improved this manuscript. BG and DS were partially supported by grants from the US Department of Energy (DE-SC0004962) and NIH (R01GM089978 and R01GM103502). (DE-SC0004962 - US Department of Energy; R01GM089978 - NIH; R01GM103502 - NIH)Published versio

Visualization of metabolic interaction networks in microbial communities using VisANT 5.0

The complexity of metabolic networks in microbial communities poses an unresolved visualization and interpretation challenge. We address this challenge in the newly expanded version of a software tool for the analysis of biological networks, VisANT 5.0. We focus in particular on facilitating the visual exploration of metabolic interaction between microbes in a community, e.g. as predicted by COMETS (Computation of Microbial Ecosystems in Time and Space), a dynamic stoichiometric modeling framework. Using VisANT's unique metagraph implementation, we show how one can use VisANT 5.0 to explore different time-dependent ecosystem-level metabolic networks. In particular, we analyze the metabolic interaction network between two bacteria previously shown to display an obligate cross-feeding interdependency. In addition, we illustrate how a putative minimal gut microbiome community could be represented in our framework, making it possible to highlight interactions across multiple coexisting species. We envisage that the "symbiotic layout" of VisANT can be employed as a general tool for the analysis of metabolism in complex microbial communities as well as heterogeneous human tissues.This work was supported by the National Institutes of Health, R01GM103502-05 to CD, ZH and DS. Partial support was also provided by grants from the Office of Science (BER), U.S. Department of Energy (DE-SC0004962), the Joslin Diabetes Center (Pilot & Feasibility grant P30 DK036836), the Army Research Office under MURI award W911NF-12-1-0390, National Institutes of Health (1RC2GM092602-01, R01GM089978 and 5R01DE024468), NSF (1457695), and Defense Advanced Research Projects Agency Biological Technologies Office (BTO), Program: Biological Robustness In Complex Settings (BRICS), Purchase Request No. HR0011515303, Program Code: TRS-0 Issued by DARPA/CMO under Contract No. HR0011-15-C-0091. Funding for open access charge: National Institutes of Health. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. (R01GM103502-05 - National Institutes of Health; 1RC2GM092602-01 - National Institutes of Health; R01GM089978 - National Institutes of Health; 5R01DE024468 - National Institutes of Health; DE-SC0004962 - Office of Science (BER), U.S. Department of Energy; P30 DK036836 - Joslin Diabetes Center; W911NF-12-1-0390 - Army Research Office under MURI; 1457695 - NSF; HR0011515303 - Defense Advanced Research Projects Agency Biological Technologies Office (BTO), Program: Biological Robustness In Complex Settings (BRICS); HR0011-15-C-0091 - DARPA/CMO; National Institutes of Health)Published versio

Mixing by polymers: experimental test of decay regime of mixing

By using high molecular weight fluorescent passive tracers with different diffusion coefficients and by changing the fluid velocity we study dependence of a characteristic mixing length on the Peclet number, $Pe$, which controls the mixing efficiency. The mixing length is found to be related to $Pe$ by a power law, $L_{mix}\propto Pe^{0.26\pm 0.01}$, and increases faster than expected for an unbounded chaotic flow. Role of the boundaries in the mixing length abnormal growth is clarified. The experimental findings are in a good quantitative agreement with the recent theoretical predictions.Comment: 4 pages,5 figures. accepted for publication in PR

The Finite Field Kakeya Problem

A Besicovitch set in AG(n,q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n greater than 4.Comment: 13 page

Monte-Carlo simulation of events with Drell-Yan lepton pairs from antiproton-proton collisions

The complete knowledge of the nucleon spin structure at leading twist requires also addressing the transverse spin distribution of quarks, or transversity, which is yet unexplored because of its chiral-odd nature. Transversity can be best extracted from single-spin asymmetries in fully polarized Drell-Yan processes with antiprotons, where valence contributions are involved anyway. Alternatively, in single-polarized Drell-Yan the transversity happens convoluted with another chiral-odd function, which is likely to be responsible for the well known (and yet unexplained) violation of the Lam-Tung sum rule in the corresponding unpolarized cross section. We present Monte-Carlo simulations for the unpolarized and single-polarized Drell-Yan $\bar{p} p^{(\uparrow)} \to \mu^+ \mu^- X$ at different center-of-mass energies in both configurations where the antiproton beam hits a fixed proton target or it collides on another proton beam. The goal is to estimate the minimum number of events needed to extract the above chiral-odd distributions from future measurements at the HESR ring at GSI. It is important to study the feasibility of such experiments at HESR in order to demonstrate that interesting spin physics can be explored already using unpolarized antiprotons.Comment: Deeply revised text with improved discussion of kinematics and results; added one table; 12 figures. Accepted for publication in Phys. Rev.

Intrauterine growth curves in a high-income population

OBJECTIVE: growth curves can be used to assess intrauterine growth, to predict diseases in newborns, and to characterize different populations. The objective of this study was to obtain intrauterine growth curves of newborns from the maternity ward of the Hospital Albert Einstein (MAE) and compare them with intrauterine growth curves of a population from California, USA. METHODS: We plotted the growth curves according to weight at birth and gestational age, which was obtained according to information from the mother, after the 32nd week of gestation, between February 1995 and February 1999. We calculated the birth weights for the 10th, 50th, and 90th percentiles of weight at birth for each gestational age and compared them with those of the growth curves from California. RESULTS: The growth curves for the 10th and the 50th percentiles did not differ from the California growth curves. For the 90th percentile, however, the MAE growth curves were lower than those of California. The MAE population presented fewer small-for-gestational age (SGA) and big-for-gestational age (BGA) newborns when assessed according to the California curves. The categories of SGA, normal, and BGA for both male and female newborns indicated a statistically significant relation with the weight gain of mothers. CONCLUSIONS: The two populations assessed in this study were different according to intrauterine growth curves. Further studies should be carried out in order to identify specific factors that may be acting on the MAE population.OBJETIVO: as curvas de percentil constituem uma das formas de avaliação do crescimento intra-uterino e podem predizer doenças do recém-nascido como também caracterizar uma população. Este trabalho teve por objetivo construir as curvas de crescimento intra-uterino dos recém-nascidos da Maternidade do Hospital Albert Einstein (MAE), hospital que atende a uma população de alto nível socioeconômico, e comparar com as curvas de crescimento intra-uterino de uma população norte-americana da Califórnia. MÉTODOS: foram construídas curvas de crescimento intra-uterino a partir do peso do recém-nascido de parto único, tomado logo após o nascimento, e da idade gestacional segundo informações maternas, a partir da 32ª. semana de idade gestacional, abrangendo os nascimentos ocorridos na MAE no período de fevereiro de 1995 a fevereiro de 1999. Foram calculados os percentis 10, 50 e 90 do peso ao nascer para cada idade gestacional e comparados com os das curvas da Califórnia. RESULTADOS: as curvas dos percentis 10 e 50 na população da MAE não diferiram das curvas da Califórnia. Para o percentil 90, a curva da MAE ficou abaixo das curvas da Califórnia. Houve número menor de pequenos e grandes para a idade gestacional (PIG e GIG) quando classificados pelas curvas da Califórnia. A classificação em PIG, AIG, GIG mostrou-se relacionada significantemente com o ganho de peso materno nos dois sexos. CONCLUSÕES: as duas populações analisadas segundo as curvas de crescimento intra-uterino são diferentes entre si; deverão ser identificados fatores específicos que atuem na população da MAE.UNIFESP-EPMSociedade Beneficente Israelita Brasileira Hospital Albert Einstein Instituto de Ensino e PesquisaUSPPrefeitura Municipal de São Paulo Serviços em SaúdeUNIFESP, EPMSciEL

On Invariant Notions of Segre Varieties in Binary Projective Spaces

Invariant notions of a class of Segre varieties \Segrem(2) of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains \Segrem(2) and is invariant under its projective stabiliser group \Stab{m}{2}. By embedding PG(2^m - 1, 2) into \PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant under \Stab{m}{2} as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according as $m$ is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a \Stab{m}{2}-invariant geometric spread of lines of PG(2^m - 1, 2). This spread is also related with a \Stab{m}{2}-invariant non-singular Hermitian variety. The case $m=3$ is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under \Stab{3}{2}, while the points of PG(7, 2) form five orbits.Comment: 18 pages, 1 figure; v2 - version accepted in Designs, Codes and Cryptograph

q-breathers in Discrete Nonlinear Schroedinger lattices

$q$-breathers are exact time-periodic solutions of extended nonlinear systems continued from the normal modes of the corresponding linearized system. They are localized in the space of normal modes. The existence of these solutions in a weakly anharmonic atomic chain explained essential features of the Fermi-Pasta-Ulam (FPU) paradox. We study $q$-breathers in one- two- and three-dimensional discrete nonlinear Sch\"{o}dinger (DNLS) lattices -- theoretical playgrounds for light propagation in nonlinear optical waveguide networks, and the dynamics of cold atoms in optical lattices. We prove the existence of these solutions for weak nonlinearity. We find that the localization of $q$-breathers is controlled by a single parameter which depends on the norm density, nonlinearity strength and seed wave vector. At a critical value of that parameter $q$-breathers delocalize via resonances, signaling a breakdown of the normal mode picture and a transition into strong mode-mode interaction regime. In particular this breakdown takes place at one of the edges of the normal mode spectrum, and in a singular way also in the center of that spectrum. A stability analysis of $q$-breathers supplements these findings. For three-dimensional lattices, we find $q$-breather vortices, which violate time reversal symmetry and generate a vortex ring flow of energy in normal mode space.Comment: 19 pages, 9 figure