Genetic Drift Suppresses Bacterial Conjugation in Spatially Structured Populations

Transcription

1 944 Biophysial Journal Volume 106 February Geneti Drift Suppresses Baterial Conjugation in Spatially Strutured Populations Peter D. Freese, Kirill S. Korolev, { José I. Jiménez, jj and Irene A. Chen *** FAS Center for Systems Biology and Department of Physis, Harvard University, Cambridge, Massahusetts; Department of Physis, Massahusetts Institute of Tehnology, Cambridge, Massahusetts; { Department of Physis and Program in Bioinformatis, Boston University, Boston, Massahusetts; jj Faulty of Health and Medial Sienes, University of Surrey, United Kingdom; and **Department of Chemistry and Biohemistry, Program in Biomoleular Sienes and Engineering, University of California at Santa Barbara, Santa Barbara, California ABSTRACT Conjugation is the primary mehanism of horizontal gene transfer that spreads antibioti resistane among bateria. Although onjugation normally ours in surfae-assoiated growth (e.g., biofilms), it has been traditionally studied in wellmixed liquid ultures laking spatial struture, whih is known to affet many evolutionary and eologial proesses. Here we visualize spatial patterns of gene transfer mediated by F plasmid onjugation in a olony of Esherihia oli growing on solid agar, and we develop a quantitative understanding by spatial extension of traditional mass-ation models. We found that spatial struture suppresses onjugation in surfae-assoiated growth beause strong geneti drift leads to spatial isolation of donor and reipient ells, restriting onjugation to rare boundaries between donor and reipient strains. These results suggest that eologial strategies, suh as enforement of spatial struture and enhanement of geneti drift, ould omplement moleular strategies in slowing the spread of antibioti resistane genes. INTRODUCTION Antibiotis are one of the most important medial interventions of the last entury. Yet the extensive use of antibiotis has the effet of seleting for resistane among pathogeni bateria, whih already limits treatment of some major types of infetion (1). The inrease in resistane is primarily driven by the spread of resistane genes already present in natural ommunities. A major mehanism for horizontal gene transfer is baterial onjugation (), whih has spread resistane to b-latams and aminoglyosides to linially signifiant organisms (3). The important role of onjugation in the spread of antibioti resistane, and in mirobial evolution in general, motivates both fundamental study of onjugation and strategies to inhibit it. Conjugation requires physial ontat between a donor and reipient ell. The donor ell arries a onjugative plasmid, whih ontains genes neessary for onjugation and possibly other genes (e.g., enoding antibioti resistane). A ompetent donor ell expresses a pilus, whih binds to the reipient ell and mediates plasmid DNA transfer. For example, in the well-studied F fator system, an F þ donor ell transfers the plasmid to the reipient, initially an F ell, thus reating a new F þ transonjugant ell. Conjugation and maintenane of the plasmid slightly redues organismal fitness, and a large fitness ost is paid in the presene of ertain phages (e.g., the filamentous phages inluding M13, fd, and f1), whih attah speifially to the onjugative pilus. Indeed, addition of M13 or its attahment protein, g3p, redues the rate of onjugation from F þ ells and ould be an interesting strategy to suppress undesired horizontal gene transfer (4,5). Submitted August 7, 013, and aepted for publiation January 10, 014. *Correspondene: hen@hem.usb.edu Editor: Stanislav Shvartsman. Many linially and environmentally important habitats are spatially strutured beause bateria live in surfae-assoiated olonies and biofilms, where motility is limited (6,7). Although spatial struture is known to play an important role in evolutionary dynamis, its effet on onjugation dynamis has been largely unexplored. Indeed, modeling and experimental studies of onjugation have previously foused on simple well-mixed liquid systems like bath ultures and hemostats, whih an be desribed by massreation equations. These traditional approahes neglet important aspets of natural populations that result from spatial struture. More reently, experimental and theoretial efforts have been direted at studying onjugation in spatially strutured environments. Some studies show that onjugation an be quite prevalent in a biofilm (8,9), but others suggest that spread of onjugative plasmids in biofilms and on agar surfaes is quite limited (10,11). When plasmid-bearing ells provide a publi good (e.g., by detoxifying Hg þ from their surroundings), the relative frequeny of plasmid-bearing and plasmid-free ells also influenes the fitness advantage of the plasmid (1). Interpretation of results in spatially strutured environments has also been hampered by the diffiulty of distinguishing among donor, reipient, and transonjugant ells by mirosopy. In general, previous methods have not been able to resolve two of the three ell types in situ (13). Thus, these experimental results, whih are affeted by multiple fators (e.g., ell densities, plasmid harateristis, and the spatial sale of struturing), point toward a need for improved experimental systems as well as a quantitative theoretial framework to advane our fundamental understanding of onjugation. Models developed to desribe homogeneous environments do not properly apture dynamis on heterogeneous Ó 014 by the Biophysial Soiety /14/0/0944/11 $.00

2 Conjugation Suppressed in Spatial Populations 945 environments (14 16). Early models of onjugation in spatially strutured environments inluded unrealisti assumptions or did not allow measurement of transfer events per donor-reipient enounter, whih is neessary for omparison of onjugation rates aross different speies and situations (13,17,18). A more reent spatial model of onjugation (19) used ellular automata to simulate individual ells in a lattie and aptured features of experimental onjugation. Although this analysis onsidered the possibility of loal plasmid extintion, it was unable to ompletely determine geneti history during olony expansion experiments, beause donors and transonjugants ould not be disriminated in situ. This history is important beause in spatially strutured populations, only a small number of nearby ells ompete with eah other, leading to substantial demographi stohastiity (geneti drift) on short spatial sales (0). As a result, some genotypes beome extint loally, leading to a marosopi pattern of isogeni domains (setors) in a growing baterial olony. The number of setors tends to derease over time beause setors irreversibly disappear due to geneti drift when setor boundaries ross. We hypothesized that this spatial demixing of genotypes ould profoundly affet baterial onjugation beause plasmid transfer requires spatial proximity of the donor and reipient ells. In this study, we explored the dynamis of baterial onjugation in olonies grown on an agar surfae by ombining spatially resolved measurements and simulations. We visualized the spatial distribution of donor ells (F þ enoding tetrayline resistane, i.e., T r, with yan fluoresent protein expressed from a nononjugative plasmid) and reipient ells (initially F, tetrayline-sensitive T s, with yellow fluoresent protein expressed from a nononjugative plasmid). Beause the T r phenotype is arried on the F plasmid, transonjugants are T r yellow fluoresent ells. Populations of transonjugants ould be visually distinguished from F ells by a derease in fluoresene intensity aused by partial repression of the fluoresent protein, as well as by tetrayline resistane. Contrary to the general belief that biofilms failitate onjugation, we found that onjugation is substantially suppressed in surfae growth ompared to liquid ulture, onsistent with simulations of onjugation dynamis. Thus, spatial struture itself ould be an important fator in slowing down the spread of antibioti resistane. In addition, previous studies in liquid ulture showed that exogenous addition of M13 phage partiles or the soluble portion of the M13 minor oat protein g3p (g3p-n) results in nearly omplete inhibition of onjugation (4,5). We found a similar inhibitory effet of g3p-n in surfae-assoiated baterial olonies. The work presented here adds to prior experimental and theoretial studies of onjugation on spatially strutured environments by quantifying geneti drift, whih aounts for the limited penetration of the F plasmid into the spatially strutured environment, and by analyzing onjugation rates in the presene of an inhibitory agent. The results suggest that moleular antionjugation strategies ould generalize to natural spatially strutured populations. MATERIALS AND METHODS Baterial strains and ulture E. oli TOP10F 0 and TOP10 (mra D(mrr-hsdRMS-mrBC) F80laZDM15 DlaX74 rea1 arad 139 (ara leu) 7697 galu galk rpsl (StrR) enda1 nupg, obtained from Invitrogen, Carlsbad, CA) were used as donor (F þ ) or reipient (F ), respetively, of the F 0 plasmid (lai q, Tn10(tet R )). Plasmids ptr99a-eyfp (amp R ) and ptr99a-ecfp (amp R ) enoding, respetively, eyfp (Q95M, yellow) and ecfp (A06K, yan) were ourtesy of Howard Berg. The fluoresent markers were expressed from amp R seletable plasmids under an isopropyl-b-d-1-thiogalatopyranoside (IPTG)- induible promoter. Standard protools were used for ommon baterial and phage-related proedures (1). All strains were grown in Luria-Bertani (LB) medium on a regular basis. When needed, media were supplemented with ampiillin or arbeniillin (100 mg/ml), tetrayline (1 mg/ml), and IPTG (1 mm). Agar plates were made with 0 ml LB supplemented with arbeniillin and IPTG. Separate 3-mL overnight ultures of TOP10F 0 (transformed by ptr99a-ecfp) and TOP10 (transformed by ptr99a-eyfp) were inoulated in 3 ml of LB with ampiillin, ITPG, and tetrayline if appropriate. Overnight ultures were inoulated from a olony grown on medium with the appropriate antibioti(s) to selet for the desired plasmids, and grown at 37 C with shaking at 50 rpm overnight to saturation (OD 600 ~ 3 4 was determined by an Ultrospe ell density meter; GE Healthare, Pittsburgh, PA). F þ ells grown in medium supplemented with antibiotis were entrifuged for 5 min at 5000 rpm, the supernatant was disarded, and the pellet was resuspended in fresh LB medium laking antibiotis. Cultures were diluted for density measurement with appropriate medium to bring the OD 600 within the linear range of the ell density meter (i.e., <1 OD units). Strains were then mixed to the desired ratio as measured by optial density to reate the inoulant. A small volume of inoulant (1 0 ml) was pipetted onto the enter of an LB-agar plate ontaining arbeniillin and IPTG. The plates were then inubated for the desired length of time at 37 C in a bin ontaining wet paper towels to maintain high humidity. Detetion of transonjugants After the desired growth period, transonjugants were deteted by applying a tetrayline-soaked ring around the baterial olony. The enter of a.5- m-diameter filter paper disk (VWR, Bridgeport, NJ) was removed to reate a thin annulus with inner diameter 1.9 m. Tetrayline stok at 1 mg/ml was diluted to mg/ml with 50% ethanol. A quantity of 30 ml of the tetrayline mixture was applied uniformly onto an autolaved filter paper annulus, whih was then plaed around a growing baterial olony with sterilized foreps. Beause the number of setor boundaries is not very large, the number and size of transonjugant setors is expeted to vary from olony to olony even though there are millions of ells growing on a petri dish. We indeed observed muh higher variability in spatial ompared to liquid assays of onjugation and performed measurements on olonies in eah experiment to obtain reliable estimates of the averages. Appliation of g3p-n The g3p-n protein was prepared as desribed in Lin et al. (5). A quantity of 4.9 ml of g3p-n stok solution (41 mm) was mixed with 45 ml of phosphate-buffered saline per plate and a 50-mL aliquot was spread on Biophysial Journal 106(4)

3 946 Freese et al. eah plate with glass beads for 1 min until dry. Assuming uniform diffusion throughout the 0-mL agar plate, the expeted [g3p-n] is 10 nm, a onentration that gives 80% onjugation inhibition in liquid ulture (5). Mirosopy and image proessing Fluoresent images were obtained with a Lumar V.1 fluoresene stereosope (Zeiss, Oberkohen, Germany) and a Typhoon TRIO variable-mode imager (GE Healthare). Sanned plates were imaged from the bottom using yan laser exitation and detetion at 488 nm with 50-mm resolution. The initial radii of the olonies were measured within 1 h of inoulation by fitting of a irle using the stereosope s software; olonies that were not irular were disarded. The numbers of setors in eah olony were ounted manually. The software MATLAB R010 (The MathWorks, Natik, MA) was used to extrat the radii and setor boundaries of the olonies using the built-in edge-funtion. Modeling and simulations of onjugation in baterial olonies We formulated a minimal model of surfae-assoiated populations. Following the stepping-stone model of Kimura and Weiss (), spatially strutured populations are often modeled as an array of well-mixed populations (demes) that exhange migrants. Previous work demonstrated that geneti demixing in growing baterial olonies an be desribed by a one-dimensional stepping-stone model beause growth ours only lose to the nutrient-rih irumferene of the olony (3,4). Here, we formulated a model that, in addition to ompetition, geneti drift, and migration, inorporates horizontal gene transfer between ells. Beause previous work showed that the qualitative behavior of linearly and radially expanding populations is quite similar, and both types of expansions lead to setor formation (3), we, for simpliity, negleted the fat that the irumferene of the olony, and therefore the total population size, were hanging during the experiment. In our study, simulated populations were omposed of a linear set of L sim demes ontaining N ells of three possible types: F,F þ, and transonjugants with respetive proportions f, f þ, and f t. Eah deme was treated as a well-mixed population. To aount for daughter ells being displaed slightly from parent ells during olony growth, ells ould migrate to one of their two nearest-neighbor demes with probability m per generation. Reprodution and onjugation were modeled through a series of time steps at whih only two ells were updated, always preserving the total population size. In reprodution events, one individual died (or fell behind the expanding front in the ontext of our experiments), allowing another individual to reprodue and thus keep the population size onstant. A series of N time steps orresponded to one generation beause every individual was replaed one on average. Possible omposition-hanging events are given below with their orresponding probabilities P, whih depend on the fitness ost s of the F plasmid, onjugation rate r, and the loal proportions of the ell types F (f ), original yan F þ (f þ ), and transonjugant (f t ). These probabilities (see Eqs. 1 6 below) were formulated assuming that onjugation and ompetition our at a fixed probability per ell-ell interation within eah deme. Conjugation events derease the F population and inrease the transonjugant population, whereas ompetition dereases the F þ populations (donor strain and transonjugants) and inreases the F population beause the F plasmid imposes a fitness ost. For example, in Eq. 1 below, the probability that the F population inreases by one ell and the F þ population dereases by one ell is proportional to the probability of F and F þ interation given by the produt of their proportions (f * f þ ) and the sum of three terms desribing geneti drift (fator of 1), ompetition (s/), and onjugation ( r/). As expeted, this probability inreases as the fitness ost of the F plasmid inreases, and dereases as the onjugation rate inreases: Biophysial Journal 106(4) P f þ 1 N ; f þ 1 N ; f t ¼ f f þ 1 þ s r ; (1) P f 1 N ; f þ þ 1 N ; f t ¼ f f þ 1 s r ; () P f þ 1 N ; f þ ; f t 1 ¼ f f t 1 þ s N r ; (3) P f 1 N ; f þ ; f t þ 1 ¼ f f þ N r þ f f t 1 s þ r ; (4) P f ; f þ þ 1 N ; f t 1 ¼ f t f þ N ; (5) P f ; f þ 1 N ; f t þ 1 ¼ f t f þ N : (6) In the limit of infinite population size, when flutuations an be negleted, one an obtain a simple desription of the dynamis in terms of ordinary differential equations. The key idea is to ompute the average hange in the relative proportions of the different ell types using Eqs. 1 6 and then treat f, f þ, and f t as deterministi variables. For example, the hange of f per one time step (1/N of generation time) is given by 0 P E 1 6NB þp f þ 1 N ; f þ 1 N ; f t P f þ 1 N ; f þ ; f t 1 N P f 1 N ; f þ þ 1 N ; f t f 1 N ; f þ ; f t þ 1 N 13 C A7 5 ¼ 1 N f f þ 1 þ s r f f þ 1 s r þf f t 1 þ s r f f þ r þ f f t 1 s þ r! ¼ 1 N ðs rþf ðtþ f þ ðtþþf t ðtþ ; whih is the ombined effet of the four possible transitions that hange the number of F ells. After dividing by the time interval 1/N, and repeating the same alulation for f þ and f t, we obtain the following set of differential equations: d dt f ðtþ ¼ðs rþf ðtþ f þ ðtþþf t ðtþ ; (7) d dt f þ ðtþ ¼ sf ðtþf þ ðtþ; (8) d dt f t ðtþ ¼ðr sþf ðtþf t ðtþþrf ðtþf þ ðtþ: (9)

4 Conjugation Suppressed in Spatial Populations 947 The terms in Eq. 7 allow straightforward interpretation: F ells inrease due to seletion at rate s and derease due to onjugation at rate r, both of whih our proportional to the frequeny at whih F and F þ ells ome together. Equations 8 and 9 allow analogous interpretation in terms of appropriate events that hange the number of F þ and transonjugant ells. Multiple hoies of transition probabilities lead to the same behavior in the limit of infinite population size. However, the hoie does not affet the dynamis provided that s 1 and r 1, as is reasonable here, and that the dynamis are equivalent to the Moran model (5) of three neutral speies for s ¼ r ¼ 0. The reason is that the full dynamis of the ells an be desribed by stohasti differential equations with the deterministi terms given by Eqs. 7 9 while dependene of the stohasti terms on s and r an be negleted. After the N time steps of reprodution and onjugation events, migration was implemented suh that demes were hosen for migration in random order. When a deme was hosen, eah of the N individuals was sequentially seleted and migrated to the right deme with probability m/ and to the left deme with probability m/. If the individual was hosen to migrate, a random individual from the destination migrated bak to the origin so that the population size in eah deme was always onserved. To avoid edge artifats and to mimi the atual experiments, we imposed periodi boundary onditions so that a ell ould migrate from the last deme to the first deme and vie versa. Further details of the model are provided in Methods: Modeling Details in the Supporting Material. Parameterizing the model To use the model for quantitative preditions, we parameterized the model using experimental data. We employed the model to estimate the effetive onjugation rate in our experimental populations by finding the model parameters that lead to the same spatial distribution of F,F þ, and transonjugant ells as observed in the experiments. The proess of parameterizing the model is quite straightforward, provided the following three issues are taken into aount: 1. Spatial patterns are stohasti in both simulations and experiments, so the model should fit average properties of these patterns rather than patterns themselves.. Not all parameters in the simulation an be determined uniquely, beause the hoie of spatial and temporal sales in the simulations depends on the level of desired preision or oarse-graining that an be freely adjusted. 3. Our simulations have a onstant length, whereas the irumferene of the olonies inreases with time, so the proess of omparing the patterns has to take these differenes in the geometry into aount. We now briefly outline the parameter fitting proedure (also see Table 1); for the omplete desription, see Methods: Modeling Details in the Supporting Material. The spatial patterns that result from geneti drift and ompetition have been previously investigated in Korolev et al. (3,4,6), where the authors showed the population dynamis without onjugation that we study here an be desribed in terms of the following three quantities: 1. Effetive diffusion onstant, D s m ðdeme sizeþ=ðgeneration timeþ:. Effetive strength of geneti drift, D g ðdeme sizeþ=ðn generation timeþ: 3. Outward bending of more fit setors, v t s ðdeme sizeþ=ðgeneration timeþ: Korolev et al. (3,4,6) have omputed various statistis based on the spatial patterns of geneti demixing and ompetition that an be used to estimate these three parameters. Here we omit the derivations of their published results and only provide the mathematial expressions used in the analysis. Quantifying migration, geneti drift, and the fitness ost of the F plasmid Proedures for quantifying migration, geneti drift, and the fitness ost of the F plasmid are given in Methods: Modeling Details in the Supporting Material. Conneting experiments with simulations The experiments have definite physial measures of time and spae, but these are arbitrarily saled in simulations. For omputational effiieny, we used this freedom in hoosing spatial and temporal sales to selet ertain values of m and N (N ¼ 100, mn ¼ 5) and then determined the orresponding spatial and temporal sales by mathing experimental and simulation data. As we show in Data: Simulation Details in the Supporting Material, this hoie does not affet our estimate of the onjugation rate, whih we further verified by repeating model parameterization for different values of m and N (N ¼ 30, mn ¼ 1 and N ¼ 30, mn ¼ 10). To math experimental and simulation data, we defined four dimensionless quantities (invariants, Inv) derived from the six experimental parameters D g, D s, v t, h f t i (average fration of transonjugants), T exp (total time), and L exp (population front length): Inv 1 ¼ D s D g T ; (10) exp Inv ¼ D s D g L exp ; (11) Inv 3 ¼ v tt exp L exp ; (1) TABLE 1 Parameterization soures Parameter Experimental data Simulation data Migration (D s ) Wandering of setor boundaries Global heterozygosity (probability that two ells from the olony are the same type) Geneti drift (D g ) Number of surviving setors Loal heterozygosity (probability that two ells from a deme are the same type) Cost of the onjugative Bending of setor boundaries Bending of setor boundaries plasmid (s) Spatial and temporal sales Measured distane and time Deme number and size Desription of model parameters and their analogs in experimental and simulation data. Parameters were ombined to alulate dimensionless invariants, as desribed in the Materials and Methods, to math experimental and simulation data. Biophysial Journal 106(4)

5 948 Freese et al. Inv 4 ¼hf t i: (13) To establish a math, the values of these experimental invariants and their simulation ounterparts must be equal. In partiular, the first two invariants were used to find the number of simulation generations and demes (T sim and L sim, respetively). The third invariant was used to estimate the fitness ost of the plasmid, and the fourth invariant to estimate the onjugation rate. RESULTS Visualizing onjugation during olony expansion To visualize onjugation, we began experiments with F þ donor ells expressing ecfp (enhaned yan fluoresent protein) and F reipient ells expressing eyfp (enhaned yellow fluoresent protein). The two strains were grown to saturation overnight, mixed to the desired proportion (generally 1:1 F þ :F ) by optial density, inoulated onto agar plates in drops of 1 0 ml, and inubated at 37 C. The shemati of the experiment is shown in Fig. 1 A and expansion rates in Fig. S1 in the Supporting Material. The spatial distribution of F þ donor ells and initially F ells was visualized by fluoresene mirosopy. However, both transonjugant ells and F ells express eyfp, so we applied a ring of filter paper soaked in tetrayline to identify the T r transonjugants. Beause only F þ ells are able to grow in the presene of tetrayline (tet R being arried on the F plasmid), transonjugant setors appeared as yellow fluoresent setors that ontinued to grow after the appliation of tetrayline (Fig. 1 B). In the following, we refer to yan fluoresent F þ ells as F þ, yellow fluoresent F ells as F, and yellow fluoresent F þ ells as transonjugants. We observed that the appliation of tetrayline aused a derease in the fluoresene intensity of transonjugant ells, as illustrated by the differene between transonjugant and F ells (Fig. 1 B). This derease is attributed to the lai q being arried on the F plasmid that partially represses expression of the fluoresent protein, whih is under an IPTG-induible promoter. This intensity effet enables visualization of the boundaries of the transonjugant setor so the transonjugant an be traed bak to its origin, presumably lose to the onjugation event. A key feature of the spatial dynamis is the formation of monohromati setors omposed of ells desending from either yan or yellow fluoresent anestors (Fig. 1 B). Although a large number of individuals omprise the population, only a small number of individuals reprodue loally (i.e., at the nutrient-rih olony edge), leading to strong geneti drift. These demographi flutuations redue geneti diversity at the growing front and result in a single genotype reahing fixation loally and forming a small monohromati domain. Over time, some of these domains grow whereas others disappear due to the random walk-like motion of the setor boundaries. Transonjugant setors originate exlusively between a setor of F þ and F ells beause onjugation an only our when F þ and F ells are in physial ontat. FIGURE 1 Experimental setup. (A) F and F þ liquid ultures were grown to saturation overnight, mixed to the desired ratio (most often 1:1) as measured by optial density, and 1 0 ml was pipetted onto an agar plate. After 4 7 days of growth, a ring of tetrayline was applied around the olony, whih diffused through the agar and allowed only F þ and transonjugants to grow for two more days. Fluoresene mirosopy revealed transonjugants as yellow setors that ontinued to grow after tetrayline appliation. (B) A mixed olony was grown for four days before tetrayline appliation, followed by two days of additional growth. The inner irle is the drop of the initial inoulant (1 ml). One tetrayline is applied, only the F þ ells and dark-yellow transonjugants ontinue to grow. The tetrayline ring is outside the field of view. Sale bar is 1 mm. To see this figure in olor, go online. Limited spread of F plasmid in spatially strutured populations The fate of the F plasmid depends on whether it an spread in a population. The rate of spread is determined by the fitness advantage or disadvantage onferred by the F plasmid and by the rate of plasmid transfer from F þ to F ells during onjugation. In the presene of tetrayline, the F plasmid onfers a strong growth advantage and spreads in the population due to the inrease in the number of F þ ells, inluding transonjugants, relative to F ells. In the absene of tetrayline, the F plasmid imposes a metaboli ost on its host (7); therefore, to survive it must spread through onjugation faster than F ells outompete F þ ells. Previous experiments in the same system showed that the F plasmid spreads rapidly in Biophysial Journal 106(4)

6 Conjugation Suppressed in Spatial Populations 949 exponentially growing, well-mixed liquid ultures without tetrayline (5), in whih the transonjugant fration approahes 1 at a rate of 0.4 h 1. In striking ontrast, we saw that the fration of ells with the plasmid stayed approximately onstant or even slightly delined over time in a spatially strutured population (Fig. ; ompare with Fig. 1 from Lin et al. (5), reprinted as Fig. S). This qualitative hange in the fate of the F plasmid shows that onjugation studied in well-mixed liquid ultures is a poor analog for onjugation in surfae-assoiated olonies that more losely resemble natural populations. Aelerated loss of F plasmid in the presene of g3p To test whether moleular strategies for inhibiting onjugation were effetive in the spatially strutured population, we experimentally inhibited onjugation with a soluble form of the g3p protein of the M13 bateriophage (g3p-n). At a protein onentration that dereases onjugation by 80% in liquid medium, the proportion of transonjugant ells at the olony front dereased by ~69% (from 5. to 1.6%, measured by irumferene; Fig. 3). In addition, the average number of transonjugant setors dereased by ~53% (from.1 to 1.0, see Fig. S3), onfirming that g3p-n protein an indeed inhibit onjugation in surfae-assoiated populations as well as in well-mixed populations. Model of onjugation in spatially strutured populations We extended the one-dimensional stepping-stone model of olony expansion to inlude onjugation. In the spirit of the Moran model (5) of evolution at onstant population Relative proportion F + F Transonjugant Day FIGURE Dynamis of ell types in a onjugating spatially strutured population. In ontrast to the rapid asension of transonjugants in wellmixed ulture, transonjugants in spatial populations remain a small fration of the population, beause onjugation events are limited to the few boundaries between F þ and F setors. The radial position of day x was inferred as x/7 of total radial expansion during one-week growth without tetrayline. Data shown are mean 5 standard error (SE) of n ¼ 35 olonies (1 ml inoulum). To see this figure in olor, go online. Cirumferene proportion No g3p g3p size, in whih one individual reprodues and one individual dies during eah time step, eah generation onsisted of a series of updates at whih two ells were onsidered. As with previous modeling in this framework (3), these ells ould exhange positions during a migration event, or one ell ould die while the other divides during a reprodution event. In addition, here we introdued the possibility that one ell ould transfer a plasmid to another during a onjugation event. The probabilities of these events were parameterized by the migration rate m, fitness ost of the F plasmid s, and onjugation rate r. The strength of geneti drift was ontrolled by N, the population size of eah deme. The simulations were initialized by populating the demes with F þ and F ells drawn with equal probability. This proedure was similar to the well-mixed initial onditions in the experiments. Our simple model (Fig. 4, A and B) qualitatively aptured the experimentally observed formation of setors and the appearane of transonjugant setors (Fig. 4 C). As in the experiments, we found that transonjugant setors appeared between setors of F þ and F ells, and that the number of transonjugant ells was smaller in spatial populations ompared to well-mixed populations, suggesting that spatial struture ould at least partially explain the stark differene in the fate of the F plasmid between liquid ultures and surfae-assoiated olonies. Quantifiation of geneti drift and migration Geneti demixing, the most prominent feature of evolutionary dynamis in baterial olonies, is ontrolled by the strength of geneti drift and migration. We quantified migration by D s, the effetive diffusion onstant of setor boundaries, and geneti drift by D g, the inverse of the produt of the effetive population density and the F + F Transonjugant FIGURE 3 Cell types with and without onjugation inhibition by g3p-n. Cirumferene proportion of eah ell type after four days of growth for 1:1 F þ: F olonies (1 ml inoulum). The average proportion of transonjugants dereased threefold from % to % with addition of g3p. Data shown are mean 5 SE of n ¼ 44 olonies without g3p-n and n ¼ 8 olonies with g3p-n. To see this figure in olor, go online. Biophysial Journal 106(4)

7 950 Freese et al. A B C FIGURE 4 Simulation of onjugation during surfae-assoiated growth. (A) Overview of the simulation: growth of the olony s population front-outward over time is modeled by L sim demes with N individuals eah (indexed linearly with periodi boundary onditions). At the end of a generation, eah individual migrates to either adjaent deme with probability m/. (B) At eah generation, all individuals are sequentially seleted and undergo birth and death, whih inlude seletion (s) and onjugation (r) aording to the transition probabilities per generation (Eqs. 1 6) and the availability of interating partners within the same deme. The probabilities in panel B do not sum up to one beause some events do not hange the omposition of the population and therefore are not shown. (C) Simulated expansion shows good qualitative agreement with the experiments. This visualization with indexed deme position on the x axis and generation number on the y axis mimis experiments with F þ ells (shown as red here), F (green), and transonjugants (blue). Parameters orrespond to the N ¼ 100, mn ¼ 5 simulation set in Table S4 in the Supporting Material. To see this figure in olor, go online. generation time. Here we followed the approah that has been previously applied to nononjugating surfae-assoiated mirobial populations (4). For simpliity of the analysis, we performed experiments with two F strains with different fluoresent olors beause this avoids the ompliations of both the fitness ost of the F plasmid and onjugation. We onfirmed that experimental data indeed satisfied Eq. S3 in the Supporting Material and found D s /v jj ¼ 3 mm (Fig. 5 A). Note that the expansion veloity v jj ¼ 0.4 mm/day, and initial setor boundary position R i (varying from olony to olony and boundary to boundary), were both measured diretly (see Materials and Methods; and see Fig. S1). D s was also measured from simulations aording to Eq. S4 in the Supporting Material (see also Table S1 and Fig. S4, Fig. S5, and Fig. S6 in the Supporting Material). The strength of geneti drift was measured experimentally aording to Eq. S5 in the Supporting Material, whih predits that the number of setors grows as the square root of the initial olony radius. We varied R 0 by inoulating the olonies with different amounts of well-mixed liquid ulture and onfirmed the square-root dependene (Fig. 5 B and see Fig. S7). Then, D g /v jj ¼ was estimated by fitting Eq. S5 in the Supporting Material to the data using our previous estimate of D s. The fit to the simulation data also yields an estimate of D g, as desribed in the Materials and Methods (see Table S and Fig. S4, Fig. S5, and Fig. S6). Fitness ost of the F plasmid We observed slight boundary bending in the experimental data, suggesting a fitness ost to the F plasmid. This is onsistent with Eq. S7 in the Supporting Material (see also Fig. 5 C) and we thus estimated v t /v jj ¼ An analogous proedure was used in simulations (see Table S3). Quantifiation of onjugation In both experiments and simulations, we quantified onjugation by the fration of the olony irumferene oupied by the transonjugant ells (5. and 1.6% for 1-mL inoulum grown for four days without and with g3p-n, respetively; see Fig. 3). We emphasize that the number of transonjugant setors was not used to parameterize Biophysial Journal 106(4)

8 Conjugation Suppressed in Spatial Populations 951 A B C FIGURE 5 Quantifiation of setor patterns. (A) Diffusion of setor boundaries between differently labeled F ells of equal fitness was traked in olonies grown for 18 days. We plotted 1373 individual setor boundaries as a funtion of radial position R and initial boundary position R i in blue. The data were then split into 50 bins of equal length and averaged (red dots). The least-squares line onstrained through the origin, as predited by Eq. S3 in the Supporting Material, was fit to the first 0 bins, whih were not affeted by sampling noise. The slope of the fit was used to estimate D s /v jj. Pixel size is 50 mm. (B) Number of setors versus R 1/ 0. Initial radii for the 1,, 3, 6, 10, and 15 ml olonies were averaged separately and the mean number of setors 5 SE was alulated. For the three largest drop sizes (green), some very small setors would likely be annihilated if grown for more time, but further growth would likely have suffered from nutrient defiieny and dehydrating onditions, so the line of best fit was alulated from the 1-, -, and 3-mL drop sizes (blue) onstrained to the slope predited by Eq. S5 in the Supporting Material with the previously alulated value of D s /v jj. The y interepts from panel B and Fig. S7, a seond set of olonies, were averaged to 4, providing an estimate of D g /v jj.(c) The fitness differene between F þ and F ells in the absene of tetrayline was measured by plotting the setor boundary deviation as a funtion of the logarithm of the radial position. Boundaries were defined relative to F setors, and one boundary of eah setor was refleted so that all of them twist in the same diretion. Most of the 76 setor edges grow outward, orresponding to positive v t /v jj. The trajetories were split into 50 bins of equal length to obtain the average behavior (red). The least-squares line onstrained to pass through the origin as predited by Eq. S7 in the Supporting Material was fit to the first 15 bins (unaffeted by sampling noise) to yield v t /v jj. To see this figure in olor, go online. the model, but instead to hek the agreement between experiments and simulations. Math between experiments and modeling aurately quantifies onjugation Experimental data were used to parameterize the model as desribed in the Materials and Methods. The results of this mathing are summarized in Table and see also Table S4 and Table S5; visualizations are presented in Fig. S8. Note that we report onjugation rate per unit of time using the relation r exp ¼ r sim T sim /T exp beause rt is a dimensionless invariant. We heked whether the parameterized model was able to orretly predit additional biologial results, whih had not been inluded during parameterization (see Table, onsisteny heks), and obtained the following: 1. We found that the model parameterization suessfully aptured the inhibition of onjugation by g3p-n protein (Table ). Using experimental data from the surfaeassoiated populations, the modeling estimated that addition of 10 nm g3p-n redues the effetive onjugation rate by more than a fator of three, from h 1 to h 1. This redution is similar to previously reported results in liquid ulture (5), in whih 10 nm g3p-n redued the rate of transonjugant spread by a fator of.5.. Another suess of the model is the aurate predition of the number of transonjugant setors, both with and without g3p-n protein (Table, and see Fig. S6 and TABLE Quantifiation of onjugation in experiments and simulations Quantity Experimental measurement Simulation quantity Data utilized Time T ¼ 4 days T sim ¼ 495 generations Time of growth Length L ¼ 1.6 m L sim ¼ 1015 demes Average olony irumferene Migration D s /v jj ¼ 3 mm m ¼ 0.05/generation Random walk of boundaries Geneti drift D g /v jj ¼ N ¼ 100 Number of setors Plasmid ost v t /v jj ¼ s ¼ Deterministi bending of boundaries Conjugation rate without g3p r ¼ /h r ¼ , unitless Transonjugant irumferene proportion Conjugation rate with g3p r ¼ /h r ¼ , unitless Transonjugant irumferene proportion Consisteny hek: transonjugant setors Number of transonjugant setors without g3p Consisteny hek: transonjugant setors with g3p Number of transonjugant setors All quantities exept the onjugation rate were measured in experiments and their simulation ounterparts were fit to math the experimental setup. Then, the simulation onjugation rate was fit to the observed transonjugant irumferene proportion to determine the experimental onjugation rate. As a onsisteny hek, we observed that the number of setors in simulations agreed with experimental onditions without and with g3p-n protein even though these values were not used to math the onjugation rate. Biophysial Journal 106(4)

9 95 Freese et al. A B FIGURE 6 Simulation outome as a funtion of onjugation (r) and seletion (s). (A) Simulations of N ¼ 30, mn ¼ 1 were onduted over a range of 150 r values from 0 to 0.03 and 30 s values from 0 to The values that orrespond to four days of experimental growth without g3p are s ¼ and r ¼ (5.% transonjugants) as marked (blak dot). Coloring represents the total fration of individuals of eah type over the entire population at T sim ¼ 5 generations: (green regions) almost 100% F individuals, as expeted for high s; (white regions) equal mix of F þ, F, and transonjugants; and (yellow regions) 50% F þ and 50% F orresponding to low s and r in whih few population-hanging events our. (B) Shading of the relative population omposition for eah simulation in panel A. To see this figure in olor, go online. Fig. S7), whih was not used in parameterizing the model. Using our model, we explored how the fate of onjugative plasmid depends on the seletive oeffiient and onjugation rate in spatial populations (Fig. 6 and Fig. S9). As expeted, higher onjugation rates failitated plasmid spread whereas higher fitness osts inhibited it. Our model predits that the onjugative plasmid is lost when s > r beause the fration of plasmid-free F ells depends only on (s r); see Eq. 7. We expet this result to hold in more omplex ommunities as long as both ompetition and onjugation our loally (e.g., along the setor boundaries). Many natural onjugative plasmids might be living lose to an extintion threshold; otherwise, they would either spread rapidly or go extint. Although the threshold for plasmid spread (r ¼ s) is the same in both spatial and well-mixed populations, their evolution is quite different. When r z s,f þ ells in well-mixed populations are primarily transonjugants beause original F þ ells are outompeted. Therefore, geneti bakground of initially F þ ells is lost and the onjugative plasmid spreads primarily via horizontal transmission. In ontrast, spatial populations would have a muh smaller fration of transonjugants under similar onditions, whih is evident from the lak of transonjugant-dominated blue along the r ¼ s diagonal in Fig. 6. In spatial populations, ompetition and onjugation would our near the boundaries and the bulk of the original F þ ells will be shielded from ompetition with F ells. As a result, the geneti bakground of initially F þ ells is preserved and vertial transmission is a primary mehanism of plasmid persistene. Suh differenes are likely to play an important role in the evolution of both bateria and their onjugative plasmids. DISCUSSION We analyzed onjugation of an F plasmid arrying tetrayline resistane in baterial olonies growing on an agar surfae. The geneti history of the olony ould be visualized in the fluoresene pattern, whih distinguished among donor (F þ ), potential reipient (F ), and transonjugant ells. As expeted, onjugation events ourred only at boundary zones between F þ and F ells. However, in spatially strutured populations, the number of boundary zones was surprisingly small, even when the populations were initially well mixed, beause strong geneti drift at the olony edge led to stohasti separation of different strains in spae, i.e., geneti demixing. As a result, the F plasmid failed to spread in the population, in sharp ontrast to liquid ulture, where F and F þ ells easily ome in ontat and the F plasmid spreads through the population like an epidemi, approahing omplete onversion to the F þ genotype (5). We have extended previous models of onjugation to inlude spatial struture and geneti demixing during range expansions in baterial populations growing on a surfae. Stohasti simulations were neessary to apture the important element of geneti drift in the spatially strutured environment, beause drift determines the availability of zones in whih F þ and F ells an ontat one another. Our parameterization method using invariants meant that experimental invariants determined simulation invariants with no additional degrees of freedom. Our model makes the simplifying assumptions that onjugation and ompetition are first-order reations, and that both donor and transonjugant ells are immediately apable of future onjugation after a onjugation event, although a refratory period is known to follow onjugation events (8,9). We also negleted the irular geometry of the olonies and used disrete demes to model a ontinuous population. Nevertheless, our simulations based on a one-dimensional stepping-stone model aurately desribe experimental outomes and ould be used to estimate the effetive onjugation rates from the data. As noted by others, previous measurements of plasmid transfer rates in surfae-assoiated populations have been diffiult to interpret (15). The ommonly used endpoint method (30) provides a reliable estimate for Biophysial Journal 106(4)

10 Conjugation Suppressed in Spatial Populations 953 homogeneously-mixed populations, but it has also been applied to baterial populations with spatial struture (31 33), for whih assumptions of the method are violated. Although any pair of donor and reipient ells an onjugate in a well-mixed population, onjugation is restrited to spatial neighbors in a surfae-assoiated population, where the distribution of donors and reipients on very small spatial sales determines the rate of prodution of transonjugant ells (31,33,34). The approah taken here inorporates this ruial fat by treating the population as a set of demes onneted by nearest-neighbor migration and restriting plasmid transfer only to ells present in the same deme. The important role of stohasti flutuations, whih ause geneti demixing and a qualitative hange in onjugation behavior in the population, is also negleted by the endpoint method. Our method inludes these effets, and the resulting estimate of the effetive onjugation rate ould allow quantitative omparisons of transfer effiienies aross different plasmids and environments (13,35,36). Thus, visualization and analysis of expanding and onjugating mirobial populations on surfaes is analytially, experimentally, and omputationally tratable, enabling in-depth study of the dynamis of gene transfer. CONCLUSION Although the F plasmid is the most thoroughly studied onjugative system, many others exist and are medially important in the spread of antibioti resistane (37). Suh systems should be studied in realisti settings, suh as surfaes and biofilms, where stohasti effets heavily influene the geneti outome. Our findings suggest that strategies to enfore spatial struturing ould redue the spread of undesirable genes to new organisms even though the donor ells themselves may ontinue to reprodue and onstitute a large fration of the mirobial population. Suh eologial strategies are omplementary to attempts to blok onjugation at a moleular level. Indeed, we found that spatial struture from surfae growth ombined with an inhibitor of onjugation produes a multipliative derease in the onjugation rate. Suh antionjugation strategies may be worthy of further study as resistane to antibiotis beomes inreasingly widespread among pathogeni bateria. SUPPORTING MATERIAL Nine figures, seven tables and supplemental information are available at The authors thank David Nelson for advie and Erin O Shea for use of equipment. P.D.F. was supported by Harvard College Researh Program and Program for Researh in Siene and Engineering fellowships at Harvard College. K.S.K. was supported by an Massahusetts Institute of Tehnology Pappalardo Fellowship in Physis. J.I.J. was a Foundational Questions in Evolutionary Biology Fellow at Harvard University sponsored by the John Templeton Foundation. I.A.C. was a Bauer Fellow at Harvard University and is a Simons Investigator (grant No from the Simons Foundation). This work was also supported by National Institutes of Health grant No. GM to the National Centers of Systems Biology and grant No. RFP-1-05 from the Foundational Questions in Evolutionary Biology Fund. REFERENCES 1. Davies, J., and D. Davies Origins and evolution of antibioti resistane. Mirobiol. Mol. Biol. Rev. 74: Barlow, M What antimirobial resistane has taught us about horizontal gene transfer. In Horizontal Gene Transfer: Genomes in Flux. M. Gogarten, J. Gogarten, and L. Olendzenski, editors. Humana Press, Totowa, NJ, pp Waters, V. L Conjugative transfer in the dissemination of b- latam and aminoglyoside resistane. Front. Biosi. 4:D433 D Boeke, J. D., P. Model, and N. D. Zinder Effets of bateriophage f1 gene III protein on the host ell membrane. Mol. Gen. Genet. 186: Lin, A., J. Jimenez,., I. A. 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Prosser A model for baterial onjugal gene transfer on solid surfaes. FEMS Mirobiol. Eol. 44: Simonsen, L Dynamis of plasmid transfer on surfaes. J. Gen. Mirobiol. 136: Krone, S. M., R. Lu,., E. M. Top Modeling the spatial dynamis of plasmid transfer and persistene. Mirobiology. 153: Biophysial Journal 106(4)