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Appendix A Contributed Manuscripts A1 STRAIN-RESOLVED COMMUNITY GENOMIC ANALYSIS OF GUT MICROBIAL COLONIZATION IN A PREMATURE INFANT1 Michael J. Morowitz,2,3 Vincent J. Denef,4 Elizabeth K. Costello,5 Brian C. Thomas,4 Valeriy Poroyko,2 David A. Relman,5,6,7 and Jillian F. Banfield 4,8,9 1 Reprinted with permission from Proceedings of the National Academy of Sciences, Morowitz et al. (2010). Strain-resolved community genomic analysis of gut microbial colonization in a premature infant. doi: 10.1073/pnas.1010992108. A correction has been published http://www.pnas.org/content/108/11/4512.3.short. 2 Department of Surgery, University of Chicago Pritzker School of Medicine, Chicago, IL 60637. 3 Present address: Department of Surgery, University of Pittsburgh Medical Center, Pittsburgh, PA 15213. 4 Department of Earth and Planetary Science, University of California, Berkeley, CA 94720. 5 Department of Microbiology and Immunology, Stanford University School of Medicine, Stanford, CA 94305. 6 Department of Medicine, Stanford University School of Medicine, Stanford, CA 94305. 7 Veteran's Affairs Palo Alto Heath Care System, Palo Alto, CA 94304. 8 Department of Environmental Science, Policy, and Management, University of California, Berke- ley, CA 94720. 9 To whom correspondence should be addressed. E-mail: email@example.com. Author contributions: M.J.M., V.J.D., and J.F.B. designed research; M.J.M., V.J.D., E.K.C., B.C.T., V.P., and J.F.B. performed research; V.J.D., B.C.T., and J.F.B. contributed new reagents/analytic tools; M.J.M., V.J.D., E.K.C., D.A.R., and J.F.B. analyzed data; and M.J.M., V.J.D., E.K.C., D.A.R., and J.F.B. wrote the paper. The authors declare no conflict of interest. This Direct Submission article had a prearranged editor. Edited by Jeffrey I. Gordon, Washington University School of Medicine, St. Louis, MO, and approved November 30, 2010 (received for review August 7, 2010). Freely available online through the PNAS open access option. Data deposition: The sequences reported in this paper have been deposited in the Sequence Read Archive (accession no. SRA026959) and GenBank database. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/ pnas.1010992108/-/DCSupplemental. 97
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98 THE SOCIAL BIOLOGY OF MICROBIAL COMMUNITIES The intestinal microbiome is a critical determinant of human health. Alterations in its composition have been correlated with chronic disorders, such as obesity and inflammatory bowel disease in adults, and may be associ- ated with neonatal necrotizing enterocolitis in premature infants. Increasing evidence suggests that strain-level genomic variation may underpin distinct ecological trajectories within mixed populations, yet there have been few strain-resolved analyses of genotypephenotype connections in the context of the human ecosystem. Here, we document strainlevel genomic divergence during the first 3 wk of life within the fecal microbiota of an infant born at 28-wk gestation. We observed three compositional phases during coloniza- tion, and reconstructed and intensively curated population genomic datasets from the third phase. The relative abundance of two Citrobacter strains sharing ~99% nucleotide identity changed significantly over time within a community dominated by a nearly clonal Serratia population and harboring a lower abundance Enterococcus population and multiple plasmids and bac- teriophage. Modeling of Citrobacter strain abundance suggests differences in growth rates and host colonization patterns. We identified genotypic varia- tion potentially responsible for divergent strain ecologies, including hotspots of sequence variation in regulatory genes and intergenic regions, and in genes involved in transport, flagellar biosynthesis, substrate metabolism, and host colonization, as well as differences in the complements of these genes. Our results demonstrate that a community genomic approach can elucidate gut microbial colonization at the resolution required to discern medically relevant strain and species population dynamics, and hence improve our ability to diagnose and treat microbial community-mediated disorders. Intestinal microbes influence human health through harvesting of energy from dietary substrates, production of essential nutrients, and protection against colonization by pathogens (Dethlefsen et al., 2007; Hooper et al., 2002). Al- though the adult gut microbiota is highly variable between individuals, it displays limited diversity at the phylum level: only two bacterial phyla (Bacteroidetes and Firmicutes) contribute 90% of all microbes (Eckburg et al., 2005). In infants, early assembly of the gut microbiota has been linked to development of innate immune responses and terminal differentiation of intestinal structures (Hooper et al., 2001). The dynamic process of colonization has been well studied at high taxonomic levels (Palmer et al., 2007) and seems predictable based on competi- tive interactions between and within the dominant phyla (Trosvik et al., 2010). Yet at lower taxonomic levels, and at early stages of development, our knowledge of this process is incomplete. Strain-level analyses of clinical isolates using multilocus sequence typing (MLST) and comparative genomics have been used to differentiate closely re- lated organisms (Hanage et al., 2009; Palmer et al., 2010). However, important contextual information may be lost when interpreting genomic variation between
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APPENDIX A 99 strains isolated from different communities. Microbial population dynamics can be strongly influenced by synergism and competition with coexisting microor- ganisms and through phage predation (Sandaa et al., 2009). The mobile element pool, which is generally excluded when analyzing isolates, can rapidly give rise to the genomic variation that underpins strain differentiation (Oliver et al., 2009). Cultivation-independent genomic analyses of time-series samples provide a way to link shifts in population abundance to genetic characteristics that under- lie physiological traits, such as virulence. Here, we analyzed human intestinal colonization during the neonatal period. We conducted a 16S rRNA gene-based survey of fecal samples collected daily during the first 3 wk of life of a premature infant and reconstructed and manually curated population genomic datasets for the dominant gut microorganisms in the third of three colonization phases. We chose to focus on the premature infant microbiome because, in addition to its medical relevance, the limited number of dominant bacterial species in the com- munity allows for deep sequence coverage of multiple subpopulations. Results and Discussion Study Subject We studied fecal samples from a female infant delivered by caesarean sec- tion at 28-wk gestation due to premature rupture of membranes. She was treated empirically with broad-spectrum antibiotics (ampicillin/gentamicin) for the first 7 d of life but did not receive antibiotics during the remainder of the study period. She received enteral feedings with maternal breast milk between the fourth and ninth days of life. Feedings were withheld between days 9 and 13 because of abdominal distension. On day 13, feedings were slowly resumed with artificial infant formula (Similac Special Care 20 cal/fl oz; Abbott Nutrition). She also received parenteral nutrition until caloric intake from enteral nutrition was ad- equate (day 28). She had no major illnesses during her hospitalization and was discharged to home at 64 d of life. Fecal samples were collected daily as available between days 5 and 21. Day-to-Day Dynamics of Community Composition Sequencing of amplified bacterial 16S rRNA genes (SI Materials and Meth- ods and Table S1 A and B) from 15 fecal samples collected on different days during the first 3 wk revealed three distinct community configurations demarcated by rapid transitions. This finding is consistent with previously reported coloniza- tion patterns in term infants: relative stability over days to months punctuated by rapid compositional change (Koenig et al., 2010; Palmer et al., 2007). Marked shifts in abundant lineages around days 9 and 15 seemed to follow dietary adjust- ments. On days 5 through 9, communities were largely composed of Leuconostoc,
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100 FIGURE A1-1 Multiple stable compositional states in the developing gut microbiota of the premature infant. ( A) Relative abundance of the 20 most dominant bacterial taxa in 15 fecal samples collected between Figure days 5 and 21. Sequences were classified to the highest taxonomic level A1-1.eps to which they could be confidently assigned. Dots indicate metagenomic landscape, survey dates. Relevant clinical features are shown along the x axis. bitmap (B) Principal coordinates analysis of unweighted UniFrac distances between fecal microbiotas shown in A and those from recently published surveys of adults (Costello et al., 2009; Eckburg et al., 2005; Palmer et al., 2007), term infants (Palmer et al., 2007), and preterm infants (Msh- vildadze et al., 2010; Wang et al., 2009), and from a survey of gut microbes from premature infants in a companion study (Fig. S8). Each circle corresponds to a collection of 16S rRNA gene sequences colored according to study. Samples from this work (black circles) are labeled by day. The percentage of variation explained by the plotted principal coordinates is indicated on the axes. Large-scale alterations in the infant's gut microbiota composition occurred around days 9 and 15.
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APPENDIX A 101 Weissella, and Lactococcus (Fig. A1-1A). The genera Pseudomonas and Staphy- lococcus, which were relatively scarce on days 8 and 9, became abundant by day 10. On days 10 through 13, species richness and evenness were relatively low (Table S1) and Pseudomonadaceae predominated (Fig. A1-1A). After resuming feedings on day 13, taxa characteristic of the next phase appeared (Fig. A1-1A). On days 16 through 21, species richness and evenness recovered (Table S1) and the family Enterobacteriaceae and its constituent genera Citrobacter and Serratia came into the majority. Sample clustering based on community-wide similarity in membership and structure (Fig. A1-1B and Fig. S1 CF) further delineated three microbiome configurations. Bacterial community membership and structure were significantly more similar within, than between these colonization phases (P <0.001; PERMANOVA with Monte Carlo). A crossstudy comparison sug- gests that the infant studied here harbored similar bacteria to those found in other premature infants surveyed using equivalent methods, especially during the first and third colonization phases (Fig. A1-1B) (de la Cochetiere et al., 2004; Gewolb et al., 1999; Palmer et al., 2007; Mackie et al., 1999; Magne et al., 2006; Millar et al., 1996; Mshvildadze et al., 2010; Schwiertz et al., 2003; Wang et al., 2009). Metagenomic Data Processing Genome-wide sequencing of DNA from fecal samples collected on days 10, 16, 18, and 21 yielded 245 Mbp of metagenomic sequence data. These data were coassembled using Newbler, keeping track of each read's sample of origin for quantification. Quantification of community composition based on read abun- dance can be confounded by DNA extraction and sequencing biases (Morgan et al., 2010). However, we could analyze relative abundance shifts across the third colonization phase because the same biases were expected in all samples (Fig. A1-2). We identified three major sequence "bins" for Serratia, Citrobacter, and Enterococcus, which dominated the third phase of colonization (Figs. A1-1A and A1-2). Projecting the smaller contig data (5001,500 bp) onto an emergent self- organizing map generated based on tetranucleotide frequencies of contigs >1,500 bp and reference genomes allowed us to assign additional fragments to Entero- coccus and provide partial coverage for one or more Pseudomonas populations from the day 10 sample (SI Materials and Methods and Fig. S2). Most fragments from other minor populations were assigned to higher taxonomic levels (mostly Enterobacteriaceae) (Table S3 in Dataset S1). We also identified multiple plas- mid and phage populations, some of which were completely sequenced (Table S4 in Dataset S1). Manual curation resulted in a Serratia genome (strain UC1SER) with nine gaps, seven of which involve rRNA operons. Based on the sequence coverage of Serratia (17×) compared with other bacterial contigs (Table S2), UC1SER dominated the community genomic datasets from the formula fed (third) phase. We detected remarkably low levels of nucleotide polymorphisms in the UC1SER
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102 THE SOCIAL BIOLOGY OF MICROBIAL COMMUNITIES FIGURE A1-2 Population dynamics based on metagenomic profiling. Distribution of the Figure reads over the curated sequence bins acrossA1-2.eps each library (as percentage of all reads in the bitmap libraries from day 10, 16, 18, and 21, respectively). sequences (close to the expected sequencing substitution error rate), and only very few regions in which gene content varied. Serratia, a genus comprising motile, facultative anaerobes from the family Enterobacteriaceae, is found in many environments. The UC1SER genome as- sembled de novo from metagenomic data was compared with the publicly avail- able genomes of Serratia proteamaculans (21) and Serratia marcescens (Sanger Institute, United Kingdom). S. marcescens is an important opportunistic pathogen and a known cause of nosocomial disease in neonatal intensive care units (22). S. proteamaculans is an endophytic bacterium rarely identified in human specimens. All curated UC1SER genome fragments (up to 2.36 Mb in length) share a synten- ous backbone with the previously reported genomes, although numerous genomic
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APPENDIX A 103 differences were noted relative to the previously sequenced species (Table S5 in Dataset S1). For syntenous orthologs, UC1SER predicted proteins share 97.3% average amino acid identity (AAI) over 4,089 genes and 88.6% AAI over 3,672 genes with S. marcescens and S. proteamaculans, respectively. Given the overall synteny with S. marcescens and S. proteamaculans across reconstructed genome fragments, we ordered the nine UC1SER genome fragments according to the reference genomes (Table S5 in Dataset S1). Assembly of a Near-Clonal Serratia Genome and Comparative Genomics Within syntenous regions in UC1SER, there are small clusters of genes that occur elsewhere in S. marcescens and S. proteamaculans. These clusters encode proteins involved in protocatechuate utilization, fimbrial biosynthesis and ex- port, nitrate reduction, general secretion, siderophore (enterobactin) synthesis and transport, tetrathionate reduction and regulation, osmoprotectant transport, and general metabolism, including amino acid biosynthesis. These rearranged or "indel" regions show elevated sequence divergence relative to syntenous or- thologs (AAI of 77 and 58% relative to S. marcescens and S. proteamaculans, respectively). Thus, these regions may contribute to metabolic variation that dif- ferentiates these species. Regions of the UC1SER genome that are absent in one or both of the other Serratia species encode factors involved in transport (most notably iron uptake) and regulation, outer membrane and exopolysaccharide biosynthesis, adhesion, antibiotic biosynthesis, virulence, quorum sensing, biosynthesis of the redox co- factor pyrroloquinoline quinone, arsenate resistance, and propanoate metabolism (Table S5 in Dataset S1). Only UC1SER contains pga operon genes involved in polysaccharide synthesis for biofilm adhesion and a regulon for allantoin utiliza- tion, which may be associated with virulence (Chou et al., 2004). It is also the only genome with yjf-sga operon genes (phosphotransferase system components sgaH, U, E), which enable some strains of gut bacteria to use vitamin C as an energy source (Campos et al., 2008). UC1SERalso has a large nonribosomal pep- tide biosynthesis protein not found in the other genomes. In contrast to the other reconstructed genomes in this study, UC1SER contains few mobile element- derived sequences. Analyses of Two Ecologically Distinct Citrobacter Subpopulations Based on 16S rRNA gene sequences on assembled contigs, Citrobacter in the third colonization phase is closely related to Citrobacter freundii. Despite average coverage of 13× on larger Citrobacter fragments, automated assembly resulted in a highly fragmented genome. Citrobacter contigs displayed many dial- lelic sites among their reads that were almost always linked (i.e., no evidence for homologous recombination), indicating the presence of two coassembled strain
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104 THE SOCIAL BIOLOGY OF MICROBIAL COMMUNITIES populations. Examination of most contig ends revealed path bifurcation (Fig. A1-3A) because of local strain sequence divergence, differences in gene content, and intergenic region length (see below). Manual curation resolved these bifurcations and reduced the number of Citrobacter contigs from 1,400 to 10 (the largest curated contig is 2.55 Mb) (Fig. A1-3B). The final contigs are generally syntenous with the Citrobacter 30_2 strain draft genome (Broad Institute, Cambridge, MA) and the complete Citrobacter koseri ATCC BAA-895 genome (Washington University, St. Louis, MO). Consequently, the fragments were oriented and ordered by reference to the C. koseri genome to generate a final genome representation for the dominant strain, UC1CIT-i (Table S6 in Dataset S2). Of the ten genome gaps, eight are the rRNA-encoding regions that could not be resolved, one is within a prophage, and one is in the intergenic region between genes on contig ends that are adjacent in both isolate genomes. Citrobacter species are facultative anaerobes from the family Enterobacte- riaceae and are commonly found as commensals within the mammalian intestinal tract. Like Serratia, they have been frequently documented as pathogens in pre- mature newborns (Doran, 1999) (e.g., in cases of neonatal meningitis). Citrobac- ter 30_2 was isolated from a patient with Crohn disease, whereas C. koseri was isolated from an infant with meningitis. UC1CIT strains lack a "supercontig" of 402 genes reported as part of Citrobacter 30_2; based on our assembly and the functional annotation, we suspect this supercontig derives from a megaplasmid. As expected based upon the known physiology of human-associated Citro- bacter strains (Doran, 1999), the UC1CIT strains have numerous genes for uptake and utilization of a wide variety of substrates. Similar to C. koseri and Citrobacter 30_2, the UC1CIT strains are predicted to express curli and fimbriae that mediate biofilm formation and binding to host epithelial cells (Barnhart and Chapman, 2006) (Table S6 in Dataset S2). Interestingly, the UC1CIT strains and C. koseri have dual flagellar systems but Citrobacter sp. 30_2 lacks a lateral flagellar ap- paratus (Table S7 in Dataset S2). Lateral flagella confer swarming motility in viscous fluids (e.g., mucus) and have been associated with virulence, adhesion, and biofilm formation (Gavķn et al., 2002; Merino et al., 2006). UC1CIT sequence variation occurs genome-wide, but one sequence type dominates at most loci (Table S6 in Dataset S2). Given evidence for clonal rather than recombined strains, we defined the minor strain type (UC1CIT-ii) by separating reads primarily using polymorphism patterns in Strainer (Eppley et al., 2007) (Fig. A1-3C), which allowed for direct comparison of the two aligned strains. UC1CIT-ii sequence blocks (up to a few kilobases in length) share 98.5% average nucleotide identity with UC1CIT-i. In regions of shared gene content, 90% of the UC1CIT-ii genome was reconstructed. When the UC1CIT-ii strain blocks were linked and intervening gaps filled by UC1CIT-i sequence, the strains shared 99.1 ± 0.3% average nucleotide identity across their genomes (Table S8 in Dataset S2). The true level of similarity for orthologous sequences likely lies between these values.
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APPENDIX A 105 FIGURE A1-3 Analyses of two ecologically Figure divergent A1-3.eps Citrobacter UC1CIT subpopulations. (A) Schematic representation of part of the fragmented UC1CIT assembly. At the ends of bitmap many Citrobacter contigs (e.g., contig number 699), reads that partially coassembled led to two sequence paths because they became too divergent (e.g., reads placed in contigs 697 vs. 640) or contained completely novel sequence (reads placed in 642 vs. 696). (B) Condensing of these paths by manual curation reduced the number of contigs, increased average (white bar, left axis) and maximum contig length (black bars, right axis), and reduced cumulative length of contigs (auto, automatic assembly, cur (i+ii), curated UC1CIT-i and -ii strain contigs; cur (i), curated UC1CIT-i contigs). (C) After curation, reads from the strains were grouped based on single nucleotide polymorphism patterns using Strainer. (D) Shifts in pro- portion (of the respective library total number of reads) of UC1CIT-i and UC1CIT-ii reads over time. Error bar indicates SD between UC1CIT contigs. (E) A chemostat model of the colon, only allowing for differences in growth rate, was used to predict generation time dif- ferences needed to explain the observed dynamics in D. (F) Simulation based on a model that incorporated intestinal wall attachment fitted to the observed strain abundances when strain UC1CIT-ii had a higher affinity to the intestinal wall and the UC1CIT-i luminal maximum growth rate max,u was higher than the growth rate of UC1CIT-ii.
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106 THE SOCIAL BIOLOGY OF MICROBIAL COMMUNITIES Based on the relative frequency of strain-associated reads in the combined dataset for days 10, 16, 18, and 21, UC1CIT-i comprised 77% of the Citrobacter population (SI Materials and Methods and Table S8 in Dataset S2). However, the relative abundance of the strains changed dramatically during the third coloniza- tion phase (Fig. A1-3D and Table S8 in Dataset S2). Possible explanations for the strain abundance shifts include: (i) a bloom of a strain-specific phage that decimated the UC1CIT-ii population around day 18; (ii) a reduced growth rate of UC1CIT-ii when it was outcompeted for resources by UC1CIT-i, Serratia or Enterococcus populations; and (iii) a higher potential of UC1CIT-ii for intes- tinal wall colonization, leading to an observed decrease in the luminal (fecal) population. A phage bloom is unlikely because we did not observe an increase in the abundance of Citrobacter phage sequences across the time series. To evaluate the other hypotheses, we constructed two models of bacterial growth in the colon (SI Materials and Methods and Fig. S3). First, using a simplified colon chemo- stat model, we calculated the differences in growth rates needed to fit the strain population abundance shifts from days 16 to 18 and days 18 to 21 (Fig. A1-3E). Assuming approximately equal numbers of cells per milliliter luminal content, the model predicts nearly constant generation times for UC1CIT-i. The UC1CIT- ii generation time estimates equaled those for UC1CIT-i between days 18 and 21, but increased above the colon transit time (CTT) between days 16 and 18, resulting in washout between days 16 and 18. Based on CTT in children (12 84 h) (Wagener et al., 2004) and estimates for Escherichia coli generation times in animal models (2 h) (Rang et al., 1999), results from this model guided us to select parameters for a second model (SI Materials and Methods). The second model incorporated intestinal wall-associated growth and enabled fitting of the empirical data by assuming three orders of magnitude higher intestinal-wall affin- ity for UC1CIT-ii compared with UC1CIT-i (Fig. A1-3F and Fig. S3). In addition, to avoid rapid washout of UC1CIT-i, its maximum growth rate had to be doubled relative to UC1CIT-ii and the maximum growth rate of wall-adherent cells had to be lowered by an order of magnitude relative to luminal cells. Because these models were built upon a small amount of data, they are inherently limited in their ability to explain the Citrobacter strain behavior. However, they do strongly suggest that the strain shifts are not the result of random fluctuations. Regardless of whether the growth rates and intestinal niches differ, these Citrobacter strains are distinct in their ability to persist in, and interact with, the human host. The availability of genomic data for both strains provides the opportunity to identify possible metabolic characteristics upon which their physiological and ecological divergence is founded. A prominent form of variation that differentiated the two UC1CIT strains involved insertions and deletions in intergenic regions (Fig. A1-4 and Table S9 in Dataset S2). In most of the 31 observed cases, intergenic regions differed in length between the strains by >10% and in most cases differed by 30%. Most
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APPENDIX A 107 FIGURE A1-4(A) Citrobacter UC1CIT genomic overview. A larger version of this Figure figure is included as Fig. S9. (a) Outside A1-4.eps circle represents the ten contigs of the UC1CIT-i genome. Coloring indicates read temporal bitmap distribution clusters of the contigs condensed during curation. Genes unique to UC1CIT-i are generally located in areas colored in blue (Fig. S2 cluster 2, Table S11 in Dataset S2). (b) Orthologs to UC1CIT-i in UC1CIT-ii. (c and d) Orthologs to UC1CIT-i in Citrobacter sp. 30_2 and C. koseri. (e) UC1CIT-ii paths with gene content not shared by UC1CIT-i, colored based on read temporal distribution clusters (Table S12 in Dataset S2). (f) Highly divergent genes between the UC1CIT strains, colored by functional class. (Tables S6 and S10 in Dataset S2). (g) Intergenic regions marked by indels that differentiate the UC1CIT strains (Table S9 in Dataset S2). (B) Sum- mary of genomic differences between the UC1CIT strains.
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570 THE SOCIAL BIOLOGY OF MICROBIAL COMMUNITIES c3 ( - ms )2 [ms (1 + c3 ) - mt ( + p3 )] c4 = 2 ams condition iii) requires that ms(1 + yrc ) > mt (e + yrr ). After some algebra we 3 3 can see that this condition is false when the rest point is well-defined. It is now possible to determine the criteria describing the system mono- or bistability in function of the model parameters. By assuming the existence of both fixed points and by comparing the conditions of stability obtained from the linearisation analysis we derive the following relationships: mt · Monostability with only sensitives <1, ms m · Monostability with only tolerants , t > 1 + (1 - µ s ) ms · Bistability with both mutually exclusive sensitivities and tolerants mono- mt cultures 1 < < 1 + (1 - µs) . ms These criteria highlight two major concepts. First, it is necessary to have a negative feedback (i.e. y > 0) from sensitives to tolerants for bistability to arise. If no negative feedback is present the system can set only in one of the two mono- stable states. Second, the modulation effect of the antibiotic e. It is clear that an increase in antibiotic-killing needs to be counteracted by an increase in selective pressure in order to maintain sensitives stability. Two-dimensional Model The two dimensional model of eqs. (1) and (2) in the main text is obtained by: 1) substituting eq. (7) of the main text into eq. (6), 2) simplifying the satu- ration terms by dividing numerator and denominator by ms and 3) introducing f = m t / m s. We repeat the linear stability analysis and we determine three equiva- lent fixed points (Fig. A22-S1): r1 = (1/e, 0), which represents the sensitive monoculture, r2 = (0, 1), which represents the tolerants monoculture and r3 = f - 1 + (1 - f ) which represents a state where both groups coexist. r1 , f and r2 are always exist while state r3 exists if and only if 1 < f < 1 + . The Jacobian matrix J(r) now reads: f t f s 2 - - 2 ( s + f t ) ( s + f t ) J( ) = . f t f s -t - - s - 1 ( s + f t )2 ( s + f t )2
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APPENDIX A 571 FIGURE A22-S1 Vectorial field of forces and the phase-plane analysis for bistable condi- tions, for the following parameter values: ratio between tolerant and sensitive maximum Figure growth rate f = 1.1, antibiotic killing A22-S1.eps rate e = 1.1 and social interaction rate y = 0.7. We bitmap draw the three rest points r1 (blue circle), r2 (red circle) and r3 (empty circle), where r = ( rs, rt) is the vector having for components the sensitive s and tolerant t densities, and the system nullclines defined by drs /dt = 0 (red line), drt /dt = 0 (blue line) whose intersection individuate the saddle unstable rest point r3. r1 has eigenvalues l1 = -e and l2= ef - y/e - 1. Thus, since e is positive-defined, r1is stable if and only if ef < 1 + y/e. Equivalently, eigenvalues in r2 are -1 and 1/f - e. r2 is stable if and only if ef > 1. Since the characteristic polynomial of J is p = r2 + c1r + c2 the conditions for r3 stability are c1 = - l1 - l2 > 0 and c2 = l1l2 > 0. These conditions are equivalent to verifying that the real parts of l1 and l2 are strictly negative. The expression for c1 and c2 are the following: 2 (1 - f )(1 - f ) c1 = f - (1 - f ) c2 = [ (1 - f ) + ] . The first condition implies that y/e > (1 ef) (1- f)/f. The condition is true only in the particular case when f > 1, which by itself does not prove the instability of r3. However, in order to have c2 > 0, the argument inside the square bracket has to be negative (i.e. y/e < ef -1), which is the opposite of the one ensuring r3 existence. As a consequence, if r3 exists, it will be unstable analogously to the four-dimensional model of the previous section. The system stability features can be visualized by drawing the system d s d t nullclines (i.e. the curves represented by dt == 0 0 and =0 dt = 0) in the phase-plane defined by tolerant rt vs. sensitive rs densities (Fig. A22-S2). Tolerants domina- tion r2 is always obtained for parameter sets resulting in the tolerants nullcline
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572 THE SOCIAL BIOLOGY OF MICROBIAL COMMUNITIES FIGURE A22-S2Model nullclines analysis in the absence of noise. A: the tolerants Figure nullcline lies above the sensitives A22-S2.eps nullcline leading to tolerants dominance and sensitive extinction. The corresponding parameter set is f = 1.1, e = 1.1, y = 0.1. B: the sensitives bitmap nullcline lies above the tolerants nullcline leading to sensitives dominance and tolerants extinction. The corresponding parameter set is f = 1.0, e = 1.0, y = 5. C: the tolerants nullcline is steeper than the sensitives nullcline and their intersection is a saddle and un- stable point. The stable manifold of the saddle divides the interior of the quadrant into the sets of initial conditions leading to competitive dominance by one type of microbe and competitive exclusion of the other. The corresponding parameter set is f = 1.1, e = 1.0, y = 0.7. laying above the sensitives one (Fig. A22-S2A) and the reverse is true for sensi- tives dominance r1 (Fig. A22-S2B). Bistability is obtained when the nullclines intersect in the saddle unstable coexistence point r3 such that the stable manifold of the saddle divides the interior of the quadrant into the sets of initial conditions leading to competitive dominance by one type of microbes and competitive ex- clusion of the other. In absence of fluctuations, depending on the system initial conditions, a time-trajectory will be attracted in one of the two mutually exclusive stable states r1 or r2 where it will persist indefinitely (Fig. A22-S2C). The phase- plane is divided into two attracting basins, one around the tolerant mono-culture and the other around the sensitive mono-culture. Their size can be determined with a Monte Carlo search in the phase space (Fig. A22-S3). Noise-Induced Dynamics The integration of the Langevin dynamics in presence of bistability shows that the system time evolution in the presence of noise is non-trivial. The microbi- ota switches over-time between the antibiotic-tolerant and the antibiotic-sensitive dominations in a non-deterministic fashion that varies for different realizations of the noise. Additionally, in agreement with experimental observations on the level of isolation of individuals (Littman and Pamer, 2011; Ubeda et al., 2010), it ap- pears that the time of recovery to sensitive-domination depends on the magnitude of the noise variance (Fig. A22-S4B-D). We can think that the introduction of the noise leads to a diffusion process within the space of possible microbiota compositions such that the time of escape
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APPENDIX A 573 FIGURE A22-S3 Normalized-to-one areas of the basins of attraction, corresponding to sensitives (green curve) and tolerants (red curve), versus the antibiotic-killing e (A) or the social interaction y (B). Figure A22-S3.eps bitmap FIGURE A22-S4Time evolution of the sensitive (green) and tolerant (red) densities Figure obtained by solving the Langevin A22-S4.eps equations for f = 1.1, y = 0.7, e variable with time (see bitmap Panel A) and three different noise regimes. A: antibiotic treatment, B: D 0, C: D = 0.00033 and D: D = 0.001. The densities are obtained averaging over 100 noise realiza- tions and show the strong dependence of the return to sensitive domination after treatment on the noise level. Orange shaded region represents treatment conditions. The dynamics here shown qualitatively reproduces the behaviour observed in longitudinal microbiome data (see Fig. A22-5).
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574 THE SOCIAL BIOLOGY OF MICROBIAL COMMUNITIES FIGURE A22-S5A: most probable bacterial density r change with respect the noise parameter D when the boundary condition are fixed at negative values far enough from Figure A22-S5.eps the location of the stable states. The set of parameters used is f = 1.1, e = 1.1 and y = 0.4. This configuration is not physical sincebitmap we allow negative values of the densities. How- ever, we show that the theoretical prediction of the linear coefficients reported in the main text (see Results section) coincides with the numerical simulation here reported. B: plot of four different stationary distributions for f = 1.1, e = 1.1, y = 0.4 and D = 0.01, 0.015, 0.02, 0.025 obtained solving numerically the FPE with the following boundary conditions: Ps(-1, rt) = 0 and Ps( rs, -1) = 0. from each stable or meta-stable state becomes strictly finite. The strength of the diffusive motion is given by the size of the noise variance, D. Increasing D, the system spends a shorter time to wander far from the initial configuration which coincides with the increase of the probability of crossing the attracting basins separatrix in shorter time. Previous studies have characterized the mean residence time in each domination by computing the escape rate between the two stable states, in the limit of small D, in terms of stationary probability distribution (Borgis and Moreau, 1990; Gardiner, 1983). However, in our case this function is not known a priori since the system is non-conservative. Even though alternative numerical solutions (e.g. explicit integration of the Langevin equations or of the Fokker-Planck Equation) can be used to do so, these methods can be numerically very intensive and become prohibitive when the number of states increases (i.e. solving a partial differential equation in d >> 3 dimensions). As a consequence, in the main text we follow a new alternative theoretical framework based on transition state theory. Numerical estimates of the mean residence time In order to characterize the stochastic dynamical behaviour of the bacterial concentrations we can numerically estimate the moments of their joint probability distribution (P( r)) by sampling different possible trajectories connecting the two stable states multiple times.
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APPENDIX A 575 FIGURE A22-S6 Stationary path connecting the stable points 1 and 2. The red, green and black solid curves are the trajectories associated with different values of the initial velocity, 0.032 0.072 and 0.172 respectively Figure showingA22-S6.eps that the most probable path for small noise is concentrated along the unstable manifold bitmap as obtained for different sampled trajectories (data not shown). It is worth emphasizing that for conservative fields of forces, meaning F = -U, it easy to verify that r = ±F are both the uphill and downhill optimal path. The solution with the plus sign has null action S = 0 meaning that its probability is equal to unity for every value of the noise D. This means that the path is always deterministic: it describes a simple gradient descent that takes place even in absence of noise. On the contrary the r = -F is associated to the reverse path and has a finite action S > 0 meaning it is activated only in presence of noise since its probability is suppressed and has strictly null value when D = 0. The optimal path connecting two stable states is formed by an ascending trajectory toward the unstable point, given by r = -F, followed by a descending trajectory given by r = F . In presence of a non-conservative force, the scenario changes completely and the uphill and downhill trajectory are different since r = -F is no longer a solution of the optimal path equation any longer. Each time-trajectory is obtained by solving the Langevin equations with differ- ent realizations of the noise () using a Milstein integration scheme (Higham, 2001). In the main text, we compare the estimate of the residence time in each domination state (ti with i = 1, 2) obtained with this sampling technique with that determined using the novel theoretical framework. Supporting Figures for SVD
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576 FIGURE A22-S7 Plot of the correlation with principal component 2 (PC2) versus correlation with principal component 1 (PC1) for all the phylotypes detected in each subjects (A-C) from (Dethlefsen and Relman, 2011). Green (red) are the top 10 most correlated phylotypes with Figure PC1 (PC2) which significantly decrease (increase) in response A22-S7.eps to antibiotic treatment. landscape, bitmap
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FIGURE A22-S8 Log2 abundance versus samples for all the phylotypes detected in each subject (A-C) from Dethlefsen and Relman (2011) sorted from the most to least correlated with PC1. At the top we individuate Figure A22-S8.eps the most sensitive phylotypes to antibiotic (mostly decreasing in density) while at the bottom the most tolerant ones (mostly increasing landscape, bitmap in density). Differently from Fig. A22-5 in the main text, where only the top 20 sensitives and tolerants are shown, here we display all the detected phylotypes. 577
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578 THE SOCIAL BIOLOGY OF MICROBIAL COMMUNITIES FIGURE A22-S9 Ordination plot of the time samples based on their first two principal components. We can easily recognize the time points belonging to the three individuals Figure A22-S9.eps (inter-individual variability) and their evolution in response to treatment. Empty circles represent untreated samples, asterisks bitmap represent samples during treatment 1 and filled circles represent represent samples during treatment 2. References Alter O, Brown PO, Botstein D (2000) Singular value decomposition for genome-wide expression data processing and modeling. Proc Natl Acad Sci, 97(18):10101-10106. Borgis D, Moreau M (1990) On the escape rate from a metastable state in a non-potential system. Physica A 163:877-894. Dethlefsen L, Relman DA (2011) Incomplete recovery and individualized responses of the human distal gut microbiota to repeated antibiotic perturbation. Proc Natl Acad Sci U S A, 108 Suppl 1:4554-4561. Fay TH, Joubert SV (2010) Separatrices, Inter. Journ. Math. Educ. Scie. Tech. 41(3):412-419. Gardiner CW (1983) The escape time in nonpotential systems. J. Stat. Phys., 30(1):157-177. Gardiner CW (1997) Handbook of stochastic methods, Third Edition, eds Springer series in S ynergetics (Spinger Hedeilberg). Higham DJ (2001) An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev., 43:525-546. Hsu SB, Li YS, Waltam P (2000) Competition in the presence of a lethal external inhibitor. Math Biosc, 167:177-199. Langer JS (1967) Theory of condensation point. Ann Phys 41:108-157 Langer JS (1968) Theory of nucleation rates. Phys Rev Lett, 21(14):973-976.
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APPENDIX A 579 Littman DR, Pamer EG (2011) Role of the commensal microbiota in normal and pathogenic host immune responses. Cell Host & Microbe, 10(4):311-323. Mao-Jones J, Ritchie KB, Jones LE, Ellner SP (2009) How microbial community development com- position regulates coral disease development. Plos Bio.,8(3):e1000345. doi:10.1371/journal. pbio.1000345 Otto S, Day T (2007) A Biologist's guide to mathematical modeling Princeton, NJ: Princeton Uni- versity Press. Seifert U (2008) Stochastic thermodynamics: principles and perspectives.EPJ B, 64(3-4):423-431. Sidney Coleman (1988) Aspects of symmetry, eds Cambridge University Press. Ubeda C et al (2010) Vancomycin-resistant enterococcus domination of intestinal microbiota is enabled by antibiotic treatment in mice and precedes bloodstream invasion in humans. J Clin Invest, 120(12):4332-4341.
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