Oscillatory dynamics in a bacterialcross-protection mutualismEugene Anatoly Yurtseva,1, Arolyn Conwilla,1, and Jeff Gorea,2

aPhysics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139

Edited by Alan Hastings, University of California, Davis, CA, and approved April 19, 2016 (received for review November 25, 2015)

Cooperation between microbes can enable microbial communitiesto survive in harsh environments. Enzymatic deactivation of antibi-otics, a common mechanism of antibiotic resistance in bacteria, is acooperative behavior that can allow resistant cells to protect sensitivecells from antibiotics. Understanding how bacterial populationssurvive antibiotic exposure is important both clinically and ecologi-cally, yet the implications of cooperative antibiotic deactivation onthe population and evolutionary dynamics remain poorly understood,particularly in the presence of more than one antibiotic. Here, weshow that two Escherichia coli strains can form an effective cross-protection mutualism, protecting each other in the presence of twoantibiotics (ampicillin and chloramphenicol) so that the coculture cansurvive in antibiotic concentrations that inhibit growth of either strainalone. Moreover, we find that daily dilutions of the coculture lead tolarge oscillations in the relative abundance of the two strains, withthe ratio of abundances varying by nearly four orders of magnitudeover the course of the 3-day period of the oscillation. At modestantibiotic concentrations, the mutualistic behavior enables long-termsurvival of the oscillating populations; however, at higher antibioticconcentrations, the oscillations destabilize the population, eventuallyleading to collapse. The two strains form a successful cross-protectionmutualism without a period of coevolution, suggesting that similarmutualisms may arise during antibiotic treatment and in naturalenvironments such as the soil.

mutualism | antibiotic resistance | cooperation | population dynamics |oscillations

Elucidating the roles of cooperative and competitive ecologicalinteractions is critical to understanding community forma-

tion, function, and stability. Cooperative interactions can occurwhen one individual or group provides nutrition, protection, ormobility to another (1, 2), and whether an interaction is cooperativeor competitive can depend on the environment (3). Reciprocalcooperative interactions, or mutualisms, arise when two partnerscooperate to increase each other’s fitness (1, 3–7). The ecolog-ical roles of mutualisms include stabilizing community structureand enabling survival in challenging environments (2, 5, 8, 9).Understanding microbial mutualisms will help clarify the im-

portant role they play in diverse natural communities. So far, themajority of studies of microbial mutualisms have focused oncross-feeding, the mutually beneficial exchange of metabolites(10–15). Studies involving cross-feeding amino acid auxotrophs(10–12) found that the division of labor within the mutualism canincrease the fitness of cross-feeding cocultures compared with aself-sufficient strain (10). The greatest gains seem to emergewhen amino acids are costly to produce (11). These mutualismscan even form immediately when complementary strains encountereach other and without a period of coevolution, although allowingtime for adaptation may increase their resilience (12).Another important microbial interaction involves the pro-

tection of one microbe by another, potentially enabling the for-mation of cross-protection mutualisms. Protective interactionsare especially interesting in the context of antibiotic resistance,where they can affect the success of antibiotic treatment andinfluence the evolution of antibiotic resistance (16–20). For ex-ample, the well-known inoculum effect refers to the observationthat inhibiting bacterial infections composed of more cells can

require disproportionally more antibiotic (21). Mechanisms thatallow bacteria to help each other survive antibiotic exposure includethe formation of protective structures like biofilms, coordination ofa group response (via quorum sensing), or production of enzymesthat modify and deactivate the target antibiotic (16, 17).The production of resistance enzymes is a common mecha-

nism of antibiotic resistance (22) and can be considered coop-erative because resistant cells can protect sensitive cells byreducing the concentration of active antibiotics in the environ-ment, allowing their sensitive neighbors to survive an otherwiselethal exposure (19, 23–28). Multiple examples of such protectiveinteractions have been observed in clinically relevant strainswhere pathogenic, but otherwise sensitive, strains were protectedagainst antibiotics by neighboring microbes (23, 29, 30). It isconceivable that the cooperative nature of antibiotic deactivationcould allow a bacterial community composed of multiple resistantbacterial strains to survive in a multidrug environment, even if somestrains were not individually resistant to each drug present. In thiswork, we investigate whether two bacterial populations can form across-protection mutualism in a two-drug environment and probethe dynamical properties of this mutualism.

ResultsTo explore the possibility of a microbial cross-protection mutu-alism, we developed a model system that consists of two strainsof Escherichia coli, each of which is resistant to a different an-tibiotic (Materials and Methods). Each strain produces an enzymethat deactivates one of the two antibiotics in the environment,thereby potentially allowing the other strain to survive in thepresence of the antibiotic to which it is sensitive. The first strainis ampicillin-resistant as a result of a plasmid carrying a geneencoding a β-lactamase enzyme, which deactivates ampicillin

Significance

Enzymatic deactivation of antibiotics is a cooperative behaviorthat can allow resistant cells to protect sensitive cells fromantibiotics. The prevalence of this mechanism of antibiotic re-sistance in clinical isolates and in soil bacteria makes it impor-tant both clinically and ecologically. Here, we demonstrateexperimentally that two populations of resistant bacteria canform a cross-protection mutualism in a two-drug environment,allowing the coculture to survive high antibiotic concentrationsat which neither of the two strains can survive alone. Moreover,we find that daily growth-dilution cycles result in large oscillationsin the relative abundances of the two strains, thus demonstratingthat mutualisms can display striking dynamical behavior.

Author contributions: E.A.Y., A.C., and J.G. designed research; E.A.Y. and A.C. performedresearch; E.A.Y. and A.C. developed models; E.A.Y. and A.C. analyzed data; and E.A.Y.,A.C., and J.G. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Freely available online through the PNAS open access option.1E.A.Y. and A.C. contributed equally to this work.2To whom correspondence should be addressed. Email: gore@mit.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1523317113/-/DCSupplemental.

6236–6241 | PNAS | May 31, 2016 | vol. 113 | no. 22 www.pnas.org/cgi/doi/10.1073/pnas.1523317113

Dow

nloa

ded

by g

uest

on

Aug

ust 3

1, 2

020

(Fig. 1A). This enzymatic deactivation occurs both in the peri-plasmic space of the cell and in the extracellular medium (28, 31)(SI Appendix, Fig. S1), thus leading to immediate benefits to thesensitive partner (19, 32). The second strain is chloramphenicol-resistant as a result of a plasmid carrying a gene encoding thechloramphenicol acetyltransferase type I enzyme, which deactivatesthe antibiotic chloramphenicol (33, 34) (Fig. 1A). Although thisenzymatic deactivation of chloramphenicol occurs inside the cell(28) (SI Appendix, Fig. S1), diffusion of chloramphenicol betweenthe media and the interior of resistant cells may cause the extra-cellular concentration of the antibiotic to decrease enough to allowthe growth of sensitive cells (28). These plasmids do not conjugate,and we did not observe horizontal gene transfer in our experiments(SI Appendix, Fig. S2). Given that each strain has the potential toprovide protection to the other strain, we hypothesized that the twostrains could help each other survive in an environment containingboth antibiotics (Fig. 1A).

The Two Strains Form a Cross-Protection Mutualism. To probe theextent to which the partnership between the two strains enablessurvival, we cocultured the strains in the presence of varyingconcentrations of the antibiotics ampicillin and chloramphenicol(Fig. 1B and Materials and Methods). We found that the cocul-tured strains were able to survive across a wide range of antibi-otic concentrations for the duration of a 10-day experiment whensubject to daily 100× dilutions into fresh media (Fig. 1C). Thisrange of antibiotic concentrations included concentrations atwhich neither of the two strains could survive alone (Fig. 1 D andE and SI Appendix, Figs. S3 and S4). In fact, survival of the co-culture extended to concentrations fourfold larger than the in-hibitory concentrations of the sensitive strains (black lines in Fig.1 C–E), and we did not observe a shift in the inhibitory con-centration of either strain over the course of the experiments.These two antibiotic resistant strains therefore form an effectiveobligatory mutualism.All cocultures that form a successful mutualism (Fig. 1C) must

survive multiple growth-dilution cycles, reaching a high populationdensity day after day (SI Appendix, Figs. S4 and S5). Although co-cultures grown at high antibiotic concentrations may survive onegrowth-dilution cycle, they collapse shortly thereafter, unable to

survive subsequent growth-dilution cycles (SI Appendix, Figs. S4 andS5). Thus, initial growth of a coculture does not necessarily mean thatthe mutualism is stable: To survive indefinitely over many growth-dilution cycles, the shifts that occur in the relative abundances of thetwo strains over the course of a day must be sustainable.

Growth-Dilution Cycles Give Rise to Strong Oscillatory Dynamics. Tobetter understand the underlying subpopulation dynamics of thismutualism, we tracked the subpopulation densities of the twostrains over many growth-dilution cycles. Because the antibioticresistance plasmids also encoded fluorescent proteins, we coulduse flow cytometry to measure the relative abundances (ratio ofthe subpopulation sizes) of the two strains (Materials and Meth-ods and SI Appendix, Fig. S6). Strikingly, the population dy-namics of the coculture in the region where there is an obligatorymutualism revealed oscillations in the abundances of the twopartner strains (Fig. 2), although the total population density atthe end of each cycle remained relatively steady. The oscillationsin the relative abundances typically had a period of 3 days andspanned four orders of magnitude (Fig. 3A). Because these os-cillations occurred with a period (3 days) longer than the periodof the daily dilution (1 day), they were not a trivial consequenceof the daily growth-dilution cycle.To see why this cross-protection mutualism might exhibit oscil-

lations, we consider the dynamics of the two bacterial populationsand the two antibiotics over the course of one growth-dilution cycle.Suppose that initially one of the strains is significantly moreabundant than the other. This first strain rapidly deactivates itstarget antibiotic, allowing the second strain, its mutualisticpartner, to start growing. The first strain can only start growingonce the second strain is abundant enough to deactivate thesecond antibiotic, which has so far inhibited growth of the firststrain. However, at this point, it is already too late for the firststrain to catch up with its partner, which is far more abundant.Hence, the mutualism exhibits oscillations because the strainthat is more abundant at the beginning of a growth cycle mightend up less abundant at the end of that cycle. Overall, this logicexplains how growth-dilution cycles can give rise to oscillatorydynamics. Of course, many of the oscillations that we observeexperimentally seem to have a period of 3 days (rather than

A

C

B

D

E

Fig. 1. Two strains of resistant bacteria can form amutualism in a multidrug environment by protectingeach other from antibiotics. (A) In an environmentcontaining the antibiotics ampicillin and chloramphen-icol, a mutualism forms between bacteria producing aβ-lactamase enzyme (which protects against ampicillin)and bacteria producing a chloramphenicol acetyl-transferase enzyme (which protects against chloram-phenicol). (B) In our serial dilution experiments, weperiodically diluted microbial cultures into fresh growthmedia, replenishing the supply of nutrients and antibi-otics. We determined the size of each subpopulation bycombining spectrophotometry measurements of thetotal culture density together with flow cytometrymeasurements of the relative abundances of each sub-population. (C) A coculture of the two strains can sur-vive above the concentrations at which the individualstrains survive alone, indicating that the two pop-ulations form an obligatory mutualism. The black linesindicate the region beyond which only the coculturecan survive. (D) An ampicillin-resistant monoculture cansurvive in high concentrations of ampicillin but cannotsurvive alone in chloramphenicol concentrations above2.2 μg/mL. (E) Similarly, a chloramphenicol-resistantmonoculture can survive in high concentrations ofchloramphenicol but cannot survive alone in ampicillinconcentrations above 2 μg/mL. The antibiotic concen-trations inD and E are the same as in C. The populationsshown in C–E were subject to five daily dilution cyclesat 100×.

Yurtsev et al. PNAS | May 31, 2016 | vol. 113 | no. 22 | 6237

ECOLO

GY

Dow

nloa

ded

by g

uest

on

Aug

ust 3

1, 2

020

2 days); this period arises because of asymmetries in how the twostrains grow in the presence of and deactivate the antibiotics.A simple mechanistic model incorporating the basic time dy-

namics of the two strains and the two antibiotics can indeed yieldan obligatory mutualism with period three oscillations (SI Ap-pendix, Fig. S7). Although the strains used in our experimentshave slightly different growth rates in the absence of antibiotics,our model suggests that this difference is not necessary for theoscillations to occur (SI Appendix, Fig. S7). Consistent with ourintuitive understanding of the population dynamics, this modelsuggests that the oscillations arise because of the daily dilutions(SI Appendix, Fig. S8), and a simulated bifurcation diagram dis-plays limit cycle dynamics of varying oscillation periods interspersedwith regions of chaos (SI Appendix, Fig. S9). In particular, ourmodel predicts that in a continuous culture experiment in which theantibiotics are continuously added (and cells continuously re-moved), there will be no oscillations in the population abundances(SI Appendix, Fig. S8), and instead the ratio between the two strainsshould approach a stable equilibrium.To test this prediction, we performed a (pseudo)continuous

experiment by diluting the cocultures every hour by a smallamount (1.2×) into fresh medium supplemented with ampicillinand chloramphenicol (10 μg/mL and 5.1 μg/mL, respectively),mimicking a chemostat operating at a fixed dilution rate; thedilution strength and cycle time in these experiments were cho-sen so that the effective daily dilution rate would be equivalent tothat in our daily dilution experiments. We found that with fre-quent dilution the coculture was able to form a stable mutualism,with the strains reaching a stable equilibrium ratio without os-cillations: Over the timescale of the experiment, coculturesstarting at different initial relative abundances converge toward astable equilibrium ratio (Fig. 3 and SI Appendix, Figs. S10 andS11). Moreover, a stable equilibrium was even observed forhigher dilution rates (SI Appendix, Fig. S12), and we could alsoremove the oscillations by reducing the dilution factor in dailydilution experiments (SI Appendix, Figs. S13 and S14). Gener-ally, when periodic forcing due to the growth-dilution cycles wasweak, oscillations did not emerge over the timescale for potentialoscillations (the time between subsequent growth-dilution cycles).These results argue that the growth-dilution cycles drive the oscil-lations we observe between the two strains in the mutualism.A major question concerning the observation of oscillations is

whether they are robust, transient, or neutrally stable. Robustoscillations typically converge to a limit cycle oscillation with acharacteristic period and amplitude, whereas transient oscilla-tions decay to an equilibrium. In contrast, in neutrally stableoscillations, both the amplitude and period may depend on theinitial conditions (e.g., the classic Lotka–Volterra model ofpredator–prey dynamics displays neutral oscillations; ref. 35).

To probe the nature of the oscillations observed in our ex-periments, we initiated cocultures at a wide range of startingfractions. Consistent with our oscillations being a true limit cycle,we found that a wide range of starting conditions all led to ap-parent period three oscillations with similar amplitudes (Fig.4A). Although this oscillation pattern resembles a period threelimit cycle, the combination of experimental noise and time re-quired to converge to the limit cycle make it difficult to un-ambiguously distinguish period three from longer periods (forinstance, a period six limit cycle could resemble a period threelimit cycle). These stable, limit cycle oscillations are present in arange of antibiotic concentrations, both inside and outside theregion where the mutualism is obligatory (Fig. 2 and SI Appendix,Figs. S15 and S16).

Oscillations Can Destabilize the Mutualism. Presumably sufficientlylarge densities of each partner are required for the mutualism tosurvive. To probe the subpopulation densities necessary for estab-lishing a mutualism at a given set of antibiotic concentrations, wemeasured trajectories of cocultures starting at a broad range of

Fig. 2. The subpopulation sizes of the two mutu-alists oscillate over a broad range of antibioticconcentrations, both inside and outside the regionwhere the mutualism is obligatory. Many of themutualisms settled into apparent period three os-cillations, which had a period (3 days) longer thanthe period between successive exposures to antibi-otics (1 day). These oscillations were substantial inmagnitude with the relative abundances of the twomutualists changing by as much as 104-fold. The redregion of each subplot represents the size of theampicillin-resistant subpopulation, and the blue re-gion represents the size of the chloramphenicol-resistant subpopulation. The green line delineatesthe range of antibiotic concentrations above whichneither strain can survive alone. In this experiment,the cocultures were diluted by 100× every 24 h intofresh media supplemented with antibiotics.

A B

Fig. 3. Oscillations in the relative abundances of the two mutualists aredriven by the periodic dilution of the coculture into fresh media containingantibiotics. (A) Under periodic exposure to antibiotics, the relative abun-dances of the two mutualists in the coculture oscillate by as much as 104-fold.(B) Under (pseudo)continuous exposure to antibiotics, the relative abundancesof the two mutualists converge to an equilibrium ratio, and we do not see anysign of the large amplitude oscillations present in A. To transition from theperiodic regime (A) to the (pseudo)continuous regime (B), we decreased thetime between consecutive dilutions from ΔT = 24 h to ΔT = 1 h and the di-lution strength from 100× to 1.2×. The death rate due to dilution, ln(dilutionstrength)/ΔT, is equivalent in both regimes. The detection limits on our flowcytometer were on the order of Namp/Nchlor = 10±3. In these experiments, theconcentrations of ampicillin and chloramphenicol in the fresh media were10 μg/mL and 5.1 μg/mL, respectively. See Fig. 2 and SI Appendix, Fig. S10 forthe population sizes corresponding to these trajectories.

6238 | www.pnas.org/cgi/doi/10.1073/pnas.1523317113 Yurtsev et al.

Dow

nloa

ded

by g

uest

on

Aug

ust 3

1, 2

020

initial conditions, including extreme relative subpopulation abun-dances and very low cell densities. When the initial population sizeof either mutualist was too small, the mutualism could not convergeto the limit cycle and ultimately collapsed (Fig. 4B).Based on our measurements of the population dynamics, we

propose a simple time-discrete framework to provide a qualita-tive explanation of the population dynamics of the mutualism inthe presence of periodic antibiotic exposure (Fig. 4C). In thisframework, depending on the initial population composition, themutualism either converges to a limit cycle or collapses. Theboundary that separates the set of trajectories that map to eachfate is called the separatrix. A deteriorating environment (eithervia increased antibiotic concentrations or via increased dilutionrates) could bring the limit cycle and the separatrix closer to-gether, increasing the likelihood that the oscillations would pushthe population composition of the mutualism too far to one side.To test the intuition provided by this framework, we mapped

the separatrix in a range of different chloramphenicol concen-trations (SI Appendix, Figs. S17 and S18). Because stochasticitycauses populations of similar compositions to have differentfates, thus blurring the separatrix, we took a probabilistic ap-proach in determining whether a coculture with a given relativeabundance of the two mutualists would collapse (Fig. 5 and SIAppendix, Figs. S19 and S20). We found that at relatively lowchloramphenicol concentrations, cocultures can successfully re-cover from the extreme changes in the relative abundance of thetwo mutualists brought on by the oscillations. Upon increasingthe concentration of chloramphenicol, trajectories passed closerto the separatrix and became more erratic, losing their charac-teristic period three oscillation (Fig. 5 and SI Appendix, Figs.S21–S23). At high chloramphenicol concentrations, the proba-bility of collapse increases rapidly when the relative abundanceof ampicillin-resistant cells falls below approximately 1:100 (Fig.5 and SI Appendix, Figs. S19 and S20). Thus, one extreme of theoscillation is more susceptible to collapse: When the populationof ampicillin-resistant strain in the mutualism becomes too small,it can no longer protect the chloramphenicol-resistant strain,leading to insufficient growth on the next day and ultimately tothe collapse of the coculture. It is interesting to note that, even atthe higher chloramphenicol concentrations, there exists an un-stable fixed point that in the absence of noise would allow forindefinite survival (SI Appendix, Fig. S24); in that sense, the

presence of oscillations decreases the range of antibiotic con-centrations in which the coculture can survive.

Invasion Can Disrupt the Oscillatory Dynamics. Up to now, we haveshown that the growth-dilution cycles can produce robust oscil-lations in our cross-protection mutualism, and explored theconsequences of these oscillations on the stability of the mutualism.However, because natural populations interact not only with theenvironment, but also with one another, we sought to understandwhether the observed oscillations can persist robustly in the face ofinvasion by other populations. An important source of potentialinvaders arises from within the mutualism itself (8). A mutation orhorizontal gene transfer event could create a mutant strain resistantto both antibiotics. Because this double-resistant strain does notrequire protection from the mutualistic strains to survive, it maybe able to invade the mutualism and destabilize the limit cycle.Indeed, after we added a small number of double-resistant

cells (Fig. 6 and Materials and Methods) to the mutualistic co-cultures on the sixth growth cycle, the double-resistant strainquickly displaced the ampicillin-resistant population, presumablybecause the cost of the chloramphenicol resistance plasmid isless than the growth inhibition induced by the chloramphenicolin the environment. The double-resistant strain and the chlor-amphenicol-resistant strain remain, with the double-resistantcells protecting the chloramphenicol-resistant cells from ampi-cillin, analogous to the situation described in ref. 19 where am-picillin-resistant cells protect sensitive cells. In this situationwhen there is no longer a cross-protection mutualism, there areno oscillations between the double-resistant and chlorampheni-col-resistant strains (Fig. 6).

DiscussionIn this work, we have shown that a pair of antibiotic-deactivatingE. coli strains can successfully form an obligatory mutualism in amultidrug environment. Because the capacity to form the mu-tualism only depends on the production of resistance enzymes,the mutualism does not require a period of coevolution as longas the enzymes are readily expressed. The cooperative nature ofantibiotic deactivation could allow a sensitive strain (SI Appendix,Fig. S25 and Materials and Methods) to use the two mutualists forprotection. Indeed, we find that sensitive cells naturally emerge inour experiments as a result of plasmid loss; however, these cells only

A B C

Fig. 4. In the presence of daily 100× dilutions, the two mutualists undergostable limit cycle oscillations. (A) We found that the relative abundance ofthe ampicillin-resistant subpopulation with respect to the chloramphenicol-resistant subpopulation settled into period three oscillations, even when testcultures started with different subpopulation abundances. The populationsize of these limit cycle trajectories remained close to the carrying capacity.(B) If the population size of each mutualist is sufficiently large, then the twomutualists settle into stable oscillations (colored trajectories); otherwise, themutualism collapses (gray trajectory). (C) A discrete-time framework of anobligatory mutualism featuring a “healthy state” characterized by a limitcycle (white region) and a “collapsed state” (gray region). A boundary (called aseparatrix) separates the sets of subpopulation compositions that converge toeach state. (A and B) Experiments were carried out in an environment insidethe region of obligatory mutualism (100× dilution strength, 24-h dilutioncycle, 10 μg/mL ampicillin, and 5.1 μg/mL chloramphenicol). The blue tra-jectories present in A and B are the same time series. Open circles indicatethe initial population composition for each trajectory.

Fig. 5. The large oscillations in the relative abundance of the two strains(Namp/Nchl) destabilize the mutualism in harsher environments, causing thepopulation to collapse. At low chloramphenicol concentrations (7.6 μg/mL),cocultures can successfully recover from the extreme changes in the relativeabundance caused by the oscillations. However, at higher chloramphenicolconcentrations (17.1 and 38.4 μg/mL), the probability of collapse (portrayedby the gradient in the background of each subplot) increases rapidly whenthe relative abundance of the ampicillin-resistant population falls below1:100, causing the oscillations to destabilize the mutualism. One extreme ofthe oscillation is more susceptible to collapse: When the population ofampicillin-resistant strain in themutualism becomes too small, it can no longerprotect the chloramphenicol-resistant strain from ampicillin, ultimately leadingto the collapse of the coculture. Red circles denote the last time point whenthe overall size of the population remained above the detection limit (see SIAppendix, Fig. S21 for the time series of the population sizes of the showntrajectories). In these experiments, the media contained 10 μg/mL ampicillinand the specified amount of chloramphenicol.

Yurtsev et al. PNAS | May 31, 2016 | vol. 113 | no. 22 | 6239

ECOLO

GY

Dow

nloa

ded

by g

uest

on

Aug

ust 3

1, 2

020

manage to attain a small portion of the total population size and donot disrupt the mutualism (SI Appendix, Figs. S26 and S27). A keycontribution to the robustness of the mutualism is that resistant cellspreferentially protect themselves against the antibiotic (19).The persistent survival over many dilution cycles that we ob-

served suggests that this obligatory mutualism can survive indefi-nitely over a broad range of antibiotic concentrations. However, wenote that while studying the stability of the mutualism over time, wefound that some cocultures only survive transiently in the presenceof the antibiotics, eventually collapsing despite reaching a highpopulation density during earlier dilution cycles (Fig. 2 and SIAppendix, Fig. S5). This finding is reminiscent of a previouslypublished report exploring the possibility of a bacterial mutual-ism between an ampicillin-resistant strain and a kanamycin-resistant strain, where the authors found that the coculture wasviable only for the first day of growth (36), presumably becausekanamycin deactivation was not sufficiently cooperative. Thisdistinction highlights the need to explore conditions in whichmutualisms are stable over the long term, which necessitatesunderstanding the underlying population dynamics.Ecologists have been long fascinated by the mechanisms that

can give rise to oscillations in population abundances (37–40).Especially intriguing are cases where population oscillationshave a different period than seasonal variations and, thus, cannotbe easily explained by changes in the environment (41–43). Forinstance, the predator–prey oscillations of the Canada lynx andthe snowshoe hare have a period of approximately 10 years andare thought to arise principally from the dynamics of predationrather than from seasonal variations in some abiotic factor (e.g.,temperature) (42). In contrast, historical data on the dynamics ofthe measles virus exhibit strong seasonal dependence becausemajor outbreaks typically occurred in the winter (43); however,the time between outbreaks (2 years) was not equal to the periodof the seasons (1 year) (43). In a study of larval, pupal, and adultbeetles, experimental control over periodically imposed adultmortality and recruitment rates resulted in cyclical populationdynamics (44), although again the period of population oscilla-tions was longer than the periodic forcing in the experiment.Interestingly, even in constant environments, the presence ofoscillations can depend on the parameter regime: The pop-ulation dynamics in a rotifer-algae (predator–prey) system couldbe modulated in the laboratory by changing the chemostat di-lution rate and nutrient inflow rate, shifting dynamics from co-existence at an equilibrium ratio to oscillations (45).Consumer–resource interactions (e.g., predator–prey or host–

parasite) often exhibit oscillatory dynamics in both static andperiodically varying environments, as evidenced by the largenumber of known examples in which this happens; however,

mutualisms are typically thought to stabilize population abun-dances over time. Previous observations of sustained oscillationsin mutualisms have been limited mostly to theoretical studies (6,7, 46–48). Here, we have shown that growth-dilution cycles in theenvironment can give rise to oscillations in the relative abundancesof the two mutualists, with an oscillation period longer than the timebetween consecutive growth-dilution cycles. This observation ofoscillations in a cross-protection mutualism leads one to speculatewhether periodic forcing can induce oscillations in other types ofmutualisms as well. Based on preliminary modeling (SI Appendix),we hypothesize that the ability of periodic forcing to induce oscil-lations may be more characteristic of cross-protection mutualismsthan of cross-feeding mutualisms. Consistent with this idea, a num-ber of studies of laboratory cross-feeding mutualisms observed thatthe relative abundance of the two mutualists converged to a fixedpoint (12, 15, 49). More broadly, metabolic codependence (althoughnot in the form of a cross-feeding mutualism) can give rise to os-cillations in the growth of peripheral and interior cells in a biofilm(50): The oscillations increase the community’s resilience to envi-ronmental stress by resolving the conflict of how the peripheral cellsboth protect and starve the interior cells. In all, these studies high-light the importance of understanding how the balance betweencooperative and competitive interactions influences ecological dy-namics in different environments.Given the abundance of antibiotic deactivating enzymes found

in both soil microbes (51–53) and in clinical pathogens (22, 54–56), we suspect that cross-protection mutualisms, or even morecomplex interaction networks (26), may frequently arise in nat-ural bacterial populations and that such mutualisms may oftenform between different species of bacteria. Our model alsosuggests that cell death due to antibiotic exposure is not neces-sary to form a mutualism (nor even oscillations, see SI Appendix),suggesting that mutualisms could form with different combina-tions of bacteriostatic or bactericidal antibiotics (28). In addition,the ability of the two strains to protect each other and survive ina multidrug environment may buy time for a multidrug resistantstrain to evolve. Because many plasmids carrying genes confer-ring resistance are readily spread via horizontal gene transfer(54, 57, 58), the type of cooperative interactions explored heremay be able to evolve rapidly. Although we did not observehorizontal gene transfer during our experiments (SI Appendix,Fig. S2), the results of our double-resistant invasion experimentsuggest that even if a double-resistant strain were to arise, thetradeoff between producing a resistance enzyme and overallfitness can prevent the double-resistant strain from fixing.Overall, this study adds to the growing evidence that protectiveinteractions arising from cooperative deactivation of antibioticscan play a significant role in shaping the structure of bacterial com-munities and regulating the spread of antibiotic resistance genes.

Materials and MethodsStrains. All strains are derived from Escherichia coli DH5α, which is sen-sitive to both ampicillin and chloramphenicol (SI Appendix, Fig. S25). Thechloramphenicol-resistant strain is an E. coli DH5α strain transformed withthe pBbS5c-RFP plasmid (59). The plasmid encodes a gene for chloram-phenicol acetyltransferase (type I) enzyme and a gene for monomeric redfluorescent protein. It has a pSC101 origin of replication. pbBS5c-RFP wasobtained from Jay Keasling (University of California, Berkeley, CA) viaAddgene (plasmid 35284) (59). The ampicillin-resistant strain is an E. coliDH5α strain transformed with a plasmid encoding a gene for the β-lactamaseenzyme (TEM-1) and a gene for enhanced yellow fluorescent protein (EYFP).The plasmid was assembled using the 2011 BioBrick distribution kit (60). Wecombined a constitutive promoter (J23116) with a sequence encoding a ri-bosome binding site, EYFP, and two stop codons (E0430). This construct wascloned into a vector containing the BioBrick pSB6A1 backbone. The double-resistant strain is an E. coli DH5α strain transformed with both plasmids.

Experiments. Initial single cultures of our strains were grown for 24 h inculture tubes (3 or 5 mL) in LB supplemented with antibiotic for selection(50 μg/mL ampicillin and 25 μg/mL chloramphenicol for the ampicillin-resistant strain and the chloramphenicol-resistant strain, respectively) at37 °C and shaken at 300 rpm (0.3 × g). The following day, 200 μL of

A B C

Fig. 6. A double-resistant strain can invade the mutualism and cause theoscillations to vanish, illustrating that the existence of oscillations dependson how resistance is allocated in the microbial population. (A) A double-resistant strain (carrying both resistance plasmids) does not require pro-tection from the mutualistic strains to survive. (B) In the absence ofthe invader, the ampicillin- and chloramphenicol-resistant subpopulationoscillate. (C) After introducing the double-resistant strain at the beginningof the seventh cycle (dashed gray line) to a replicate culture of B, the double-resistant invader established in the microbial population, outcompeting theampicillin-resistant subpopulation and removing the oscillations. (B and C)The concentrations of ampicillin and chloramphenicol were 10 μg/mL and7.5 μg/mL respectively.

6240 | www.pnas.org/cgi/doi/10.1073/pnas.1523317113 Yurtsev et al.

Dow

nloa

ded

by g

uest

on

Aug

ust 3

1, 2

020

cocultures of the two strains were grown at varying initial populationfractions in LB without antibiotics. Subsequently, serial dilution experimentswere done in well-mixed batch culture with a culture volume of 200 μL.Every cycle, the culture was diluted by a fixed amount into fresh LB mediumsupplemented with the antibiotics ampicillin and chloramphenicol. Exceptfor where noted otherwise, each cycle lasted 24 h and cultures were dilutedby 100×. Cultures were shaken at 500 rpm at a temperature of 37 °C. Growthmedium was prepared by using BD’s DifcoTM LB Broth (Miller) (catalog no.244620). Ampicillin stock was prepared by dissolving ampicillin sodium salt(Sigma-Aldrich catalog no. A9518) in LB at a concentration of 50 mg/mL. Thesolution was filter sterilized, stored frozen at −80 °C, and thawed beforeuse. Chloramphenicol stock was prepared by dissolving chloramphenicolpowder (Sigma-Aldrich catalog no. C0378) in 200 proof pure ethanol(KOPTEC) at a concentration of 25 mg/mL. This solution was filter sterilizedand stored at −20 °C . Prepared 96-well plates of media supplemented withantibiotics were stored at −80 °C and thawed 1 d before inoculation at 5 °C.

Measurement and Data Analysis. At the end of each growth cycle, we tookspectrophotometric (Thermo Scientific Varioskan Flash at 600 nm) and flowcytometry (Miltenyi BiotecMACSQuant VYB)measurements of the cultures todetermine subpopulation sizes. Relative abundances were confirmed byplating (SI Appendix, Fig. S6). Data analysis was performed using a combi-nation of Mathematica, matplotlib, and IPython. Flow cytometry data wereanalyzed using the python package FlowCytometryTools (61). Data areavailable upon request.

ACKNOWLEDGMENTS. This work was primarily supported by NIH Grant R01GM102311-01 and National Science Foundation CAREER Award PHY-1055154. The laboratory acknowledges support from the Pew Scholars inthe Biomedical Sciences Program Grant 2010-000224-007, NIH R00 Pathwaysto Independence Award GM085279-02, Sloan Foundation Fellowship BR2011-066, the Allen Distinguished Investigator Program, and NIH New InnovatorAward DP2. E.A.Y. was supported by the National Science Foundation GraduateResearch Fellowship under Grant 0645960.

1. Boucher DH, James S, Keeler KH (1982) The ecology of mutualism. Annu Rev Ecol Syst13:315–347.

2. Bruno JF, Stachowicz JJ, Bertness MD (2003) Inclusion of facilitation into ecologicaltheory. Trends Ecol Evol 18(3):119–125.

3. Bronstein JL (1994) Conditional outcomes in mutualistic interactions. Trends Ecol Evol9(6):214–217.

4. Bronstein JL (1994) Our current understanding of mutualism. Q Rev Biol 69(1):31–51.5. Stachowicz JJ (2001) Mutualism, facilitation, and the structure of ecological commu-

nities. Bioscience 51(3):235–246.6. Holland JN, DeAngelis DL (2010) A consumer-resource approach to the density-

dependent population dynamics of mutualism. Ecology 91(5):1286–1295.7. McGill B (2005) A mechanistic model of a mutualism and its ecological and evolu-

tionary dynamics. Ecol Modell 187(4):413–425.8. Bronstein JL (2001) The exploitation of mutualisms. Ecol Lett 4(3):277–287.9. Sachs JL, Simms EL (2006) Pathways to mutualism breakdown. Trends Ecol Evol 21(10):

585–592.10. Pande S, et al. (2014) Fitness and stability of obligate cross-feeding interactions that

emerge upon gene loss in bacteria. ISME J 8(5):953–962.11. Mee MT, Collins JJ, Church GM, Wang HH (2014) Syntrophic exchange in synthetic

microbial communities. Proc Natl Acad Sci USA 111(20):E2149–E2156.12. Shou W, Ram S, Vilar JMG (2007) Synthetic cooperation in engineered yeast pop-

ulations. Proc Natl Acad Sci USA 104(6):1877–1882.13. Hosoda K, et al. (2011) Cooperative adaptation to establishment of a synthetic bac-

terial mutualism. PLoS One 6(2):e17105.14. Wintermute EH, Silver PA (2010) Dynamics in the mixed microbial concourse. Genes

Dev 24(23):2603–2614.15. Hom EFY, Murray AW (2014) Plant-fungal ecology. Niche engineering demonstrates a

latent capacity for fungal-algal mutualism. Science 345(6192):94–98.16. Meredith HR, Srimani JK, Lee AJ, Lopatkin AJ, You L (2015) Collective antibiotic tol-

erance: Mechanisms, dynamics and intervention. Nat Chem Biol 11(3):182–188.17. Vega NM, Gore J (2014) Collective antibiotic resistance: Mechanisms and implications.

Curr Opin Microbiol 21:28–34.18. Lee HH, Molla MN, Cantor CR, Collins JJ (2010) Bacterial charity work leads to pop-

ulation-wide resistance. Nature 467(7311):82–85.19. Yurtsev EA, Chao HX, Datta MS, Artemova T, Gore J (2013) Bacterial cheating drives

the population dynamics of cooperative antibiotic resistance plasmids. Mol SystBiol 9:683.

20. Conlin PL, Chandler JR, Kerr B (2014) Games of life and death: Antibiotic resistanceand production through the lens of evolutionary game theory. Curr Opin Microbiol21:35–44.

21. Brook I (1989) Inoculum effect. Rev Infect Dis 11(3):361–368.22. Wright GD (2005) Bacterial resistance to antibiotics: Enzymatic degradation and

modification. Adv Drug Deliv Rev 57(10):1451–1470.23. Perlin MH, et al. (2009) Protection of salmonella by ampicillin-resistant Escherichia coli

in the presence of otherwise lethal drug concentrations. Proc R Soc Lond B Biol Sci276(1674):3759–3768.

24. Clark DR, et al. (2009) Evolution of altruists and cheaters in near-isogenic populationsof Escherichia coli. Front Biosci (Landmark Ed) 14:4815–4824.

25. Lenski RE, Hattingh SE (1986) Coexistence of two competitors on one resource andone inhibitor: A chemostat model based on bacteria and antibiotics. J Theor Biol122(1):83–93.

26. Kelsic ED, Zhao J, Vetsigian K, Kishony R (2015) Counteraction of antibioticproduction and degradation stabilizes microbial communities. Nature 521(7553):516–519.

27. Medaney F, Dimitriu T, Ellis RJ, Raymond B (2016) Live to cheat another day: Bacterialdormancy facilitates the social exploitation of β-lactamases. ISME J 10(3):778–787.

28. Nicoloff H, Andersson DI (2016) Indirect resistance to several classes of antibiotics incocultures with resistant bacteria expressing antibiotic-modifying or -degrading en-zymes. J Antimicrob Chemother 71(1):100–110.

29. Brook I (1984) The role of beta-lactamase-producing bacteria in the persistence ofstreptococcal tonsillar infection. Rev Infect Dis 6(5):601–607.

30. Hackman AS, Wilkins TD (1975) In vivo protection of Fusobacterium necrophorumfrom penicillin by Bacteroides fragilis. Antimicrob Agents Chemother 7(5):698–703.

31. Sykes RB, Matthew M (1976) The beta-lactamases of gram-negative bacteria andtheir role in resistance to beta-lactam antibiotics. J Antimicrob Chemother 2(2):115–157.

32. Tanouchi Y, Pai A, Buchler NE, You L (2012) Programming stress-induced altruisticdeath in engineered bacteria. Mol Syst Biol 8(1):626.

33. Shaw WV (1983) Chloramphenicol acetyltransferase: Enzymology and molecular bi-ology. CRC Crit Rev Biochem 14(1):1–46.

34. Deris JB, et al. (2013) The innate growth bistability and fitness landscapes of antibi-otic-resistant bacteria. Science 342(6162):1237435.

35. Nowak MA (2006) Evolutionary Dynamics (Belknap, Cambridge, MA).36. Hu B, Du J, Zou RY, Yuan YJ (2010) An environment-sensitive synthetic microbial

ecosystem. PLoS One 5(5):e10619.37. May RM (1974) Biological populations with nonoverlapping generations: Stable

points, stable cycles, and chaos. Science 186(4164):645–647.38. May RM (1976) Simple mathematical models with very complicated dynamics. Nature

261(5560):459–467.39. Kendall BE, et al. (1999) Why do populations cycle? a synthesis of statistical and

mechanistic modeling approaches. Ecology 80(6):1789–1805.40. Turchin P (2003) Complex population dynamics (Princeton Univ Press, Princeton), Vol 35.41. Turchin P, Taylor AD (1992) Complex dynamics in ecological time series. Ecology 73(1):

289–305.42. Molles MCJ (2009) Ecology: Concepts and Applications (McGraw-Hill Science/Engi-

neering/Math, Dubuque, IA), 5th Ed.43. Stone L, Olinky R, Huppert A (2007) Seasonal dynamics of recurrent epidemics. Nature

446(7135):533–536.44. Costantino RF, Desharnais RA, Cushing JM, Dennis B (1997) Chaotic dynamics in an

insect population. Science 275(5298):389–391.45. Fussmann GF, Ellner SP, Shertzer KW, Hairston NG, Jr (2000) Crossing the hopf bi-

furcation in a live predator-prey system. Science 290(5495):1358–1360.46. Yan XP, Li WT (2007) Bifurcation and global periodic solutions in a delayed facultative

mutualism system. Physica D 227(1):51–69.47. Li Y, Xu G (2001) Positive periodic solutions for an integrodifferential model of mu-

tualism. Appl Math Lett 14(5):525–530.48. Gilpin ME, Case TJ, Bender EA (1982) Counterintuitive oscillations in systems of

competition and mutualism. Am Nat 119(4):584–588.49. Yeoh HT, Bungay HR, Krieg NR (1968) A microbial interaction involving combined

mutualism and inhibition. Can J Microbiol 14(4):491–492.50. Liu J, et al. (2015) Metabolic co-dependence gives rise to collective oscillations within

biofilms. Nature 523(7562):550–554.51. Forsberg KJ, et al. (2012) The shared antibiotic resistome of soil bacteria and human

pathogens. Science 337(6098):1107–1111.52. D’Costa VM, Griffiths E, Wright GD (2007) Expanding the soil antibiotic resistome:

Exploring environmental diversity. Curr Opin Microbiol 10(5):481–489.53. D’Costa VM, McGrann KM, Hughes DW, Wright GD (2006) Sampling the antibiotic

resistome. Science 311(5759):374–377.54. Davies J (1994) Inactivation of antibiotics and the dissemination of resistance genes.

Science 264(5157):375–382.55. Brook I (2004) Beta-lactamase-producing bacteria in mixed infections. Clin Microbiol

Infect 10(9):777–784.56. Dugatkin LA, Perlin M, Lucas JS, Atlas R (2005) Group-beneficial traits, frequency-

dependent selection and genotypic diversity: An antibiotic resistance paradigm. ProcBiol Sci 272(1558):79–83.

57. Novick RP (1980) Plasmids. Sci Am 243(6):102–104, 106, 110 passim.58. Davies J, Davies D (2010) Origins and evolution of antibiotic resistance. Microbiol Mol

Biol Rev 74(3):417–433.59. Lee TS, et al. (2011) BglBrick vectors and datasheets: A synthetic biology platform for

gene expression. J Biol Eng 5(1):12.60. Shetty RP, Endy D, Knight TF, Jr (2008) Engineering BioBrick vectors from BioBrick

parts. J Biol Eng 2(1):5.61. Yurtsev E, Friedman J, Gore J (2015) FlowCytometryTools: Version 0.4.5, 10.5281/

zenodo.32991.

Yurtsev et al. PNAS | May 31, 2016 | vol. 113 | no. 22 | 6241

ECOLO

GY

Dow

nloa

ded

by g

uest

on

Aug

ust 3

1, 2

020