Antibiotics and Mathematics: some observations...two of which are truly novel—i.e., defined as...

Robert [email protected]

Department of MathematicsImperial College, London

Antibiotics and Mathematics:some observations

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mailto:[email protected]

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Action of /responses to antimicrobials

individuality/persistence:

membrane-disrupting

AmP CM15:

Antimicrobial peptides (AmPs) are a promising class of anti-microbials that have demonstrated activity against antibiotic-resistantbacteria, parasites, viruses and fungi16–19. The high-speed AFMwas used to measure the kinetics of the pre-death activity of apore-forming, membrane-disrupting AmP (CM15) on individuallive Escherichia coli cells in an aqueous solution20.

Electron microscopy and AFM experiments have demonstratedthe endpoint surface morphological changes of a population ofcells treated with AmPs21–23. Spectroscopic analyses of syntheticmembranes or vesicles have provided insight into the sizes andstructures of pores formed by AmPs24–26. However, to date, theearly-stage kinetics of the membrane-disrupting activity of anAmP on live cells have not been reported with a spatial resolutionof nanometres and temporal resolution of seconds.

In this work, bacteria were immobilized on cover slides coatedwith poly-L-lysine. The bacteria were imaged in aqueous solutionfor at least 10 min to ensure that the cells were not altered or dis-placed by the AFM tip and to ensure that the poly-L-lysine didnot change the cells in the timescales considered in our experiments.CM15 was added to the liquid droplet around the sample to a finalconcentration of 50 mg ml21, or five times the minimum inhibitoryconcentration (MIC)27. Images were acquired every 13 s.

Figure 2a shows AFM phase images of the surfaces of two bac-teria before and at several time points after the addition of CM15.The most obvious effect of the addition of CM15 is a change in

the surface state of the bacteria from smooth to corrugated. AFMphase data are shown because the changes are most apparentthere. The same changes in surface morphology are also visible inthe AFM amplitude data (Supplementary Fig. S2). The changesare more difficult to discern in the AFM height data due to thelarge background variation on the surface of the bacteria. Thechanges in the surfaces of the bacteria are consistent with publishedelectron microscopy data, which report ultra-structural damage tothe outside of peptide-treated bacterial cells21–23. Interestingly,there is a wide range in the time of onset of the change for individualbacteria. Bacterium 1 in Fig. 2a starts changing within 13 s of theaddition of CM15, and the change is completed in !60 s.Bacterium 2 does not start changing until !80 s, and the changeis not complete until !120 s.

Figure 2b shows a larger area of the same sample 12 min after theaddition of CM15 (bacteria 1 and 2 are in the centre of the image).Other bacteria (3 and 4) have still not changed. Figure 2c is a higher-resolution image of the smooth surface of bacterium 3, taken 16 minafter the addition of CM15. Eventually, this bacterium (Fig. 2d) andindeed all bacteria in the field of view become corrugated. We con-sidered several reasons for the cell-to-cell variation in onset time.The bacteria are all grown from a single clone, so we wouldexpect them to be genetically identical. They are located close toone another (within 10 mm), and are therefore exposed to thesame concentration of CM15 at the same time. It is likely that the

t = 0 s t = 13 s t = 26 s t = 39 s t = 52 s

t = 65 s

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Figure 2 | Escherichia coli cell disruption induced by CM15, imaged with high-speed AFM. a, Time series of CM15 antimicrobial action. CM15 injected att!26 s and images recorded every 13 s, with a resolution of 1,024" 256 pixels and a rate of 20 lines s21. The surface of the upper bacterium (1) startschanging within 13 s. The lower bacterium (2) resists changing for 78 s. b, Larger-area view recorded 12 min after addition of CM15. Most bacteria arecorrugated, but some are still smooth. c, High-resolution image of bacterium 3 showing that this bacterium is still smooth at t! 16 min. d, Image of the nowcorrugated bacterium 3 at t! 30 min. Eventually, all bacteria in the field of view are affected by CM15. Images were recorded in liquid in tapping mode witha tapping frequency of 110 kHz. Phase images are shown here for high contrast; amplitude data are shown in Supplementary Fig. S2. Images b–d wererecorded with a resolution of 1,024" 256 pixels at 2 lines s21.

NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.29 LETTERS

NATURE NANOTECHNOLOGY | VOL 5 | APRIL 2010 | www.nature.com/naturenanotechnology 281

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6 AmPs

The Greatest Threat to Global Health?

Introduction 15

(a) (b)

Figure 1: a) Photograph of a culture-plate showing the dissolution of staphylococcalcolonies in the neighbourhood of a Penicillium colony, reproduced from [40]. b) Ratesfor penicillin-resistant and meticillin-susceptible strains of Staphylococcus aureus in hos-pitals (closed symbols) and the community (open symbols), figure extracted from [22].

Mycobacterium tuberculosis has been reported to be resistant to as many as eight different

antibiotics, making some individuals with tuberculosis practically incurable [14]. Actually,

it is known that there is not a single antibiotic class for which bacteria have not evolved

drug-resistance mechanisms [62].

For decades, the antibiotic resistance problem was addressed with a world-wide effort in

finding new antimicrobial agents, but unfortunately the pharmaceutical industry has ba-

sically stopped developing novel antimicrobial substances, focusing their efforts on long-

term treatment of chronic conditions [56, 79]. For instance, the United States Food and

Drug Administration approval of new antibacterial agents decreased 56% from 1983 to

2002 [97].

The paucity of new antimicrobial agents has precipitated what the authors of [44] call “the

search for synergy”, referring to the efforts of the pharmaceutical and medical communities

to find antimicrobial agents that increase their efficacy when used in combination, a drug

interaction known as synergism. For example, the standard treatment protocol for tuber-

culosis in the 1980s was based on a three-drug combination cocktail: isoniazid, rifampin

and pyrazinamide [51]. This regimen was recommended by the American Thoracic Soci-

ety and the CDC when most patients were infected with a susceptible pathogen [1]. A few

(left) Alexander Fleming’s S. aureas lawn (c. 1928): Penicillium notatum has produced an antibacterial substance...

(right) penicillin-resistant and methicillin-resistant strains of S. aureus in hospitals (closed symbols) and the community (open symbols).

Q) How do we better understand/use the antibiotics we already have?

Pharma will just make more drugs, surely?

33 for inflammation/pain, 34 for metabolic/endocrine

disorders, and 32 for pulmonary disease. The biotech

companies were developing 24 drugs for inflammation/

immunomodulators, 14 drugs for metabolic/endocrine

disorders, and 13 for cancer.

The end result of the decline in antibiotic discovery

research is that FDA is approving few new antibiotics.

Since 1998, only 10 new antibiotics have been approved,

two of which are truly novel—i.e., defined as having a

new target of action, with no cross-resistance with other

antibiotics. In 2002, among 89 new medicines emerging

on the market, none was an antibiotic.

IOM’s 2003 report on microbial threats reinforces the

point, noting that although at first glance the situation

with respect to antibiotics currently in clinical

development looks encouraging, not one new class of

antibiotics is in late-stage development. “Rather these

‘new’ antibiotics belong to existing classes, including

macrolides and quinolones, that have been used to treat

humans for years,” IOM said.

Infectious disease experts are particularly concerned about

the dearth of new “narrow-spectrum” agents—that is,

drugs that fight a specific infectious organism. Many of the

antibiotics in development today are “broad-spectrum”—

meaning they are intended to work against a wide range

of organisms—which are more likely to contribute to the

development of resistance.

15

Antibacterial Year Novel

rifapentine 1998 No

quinupristin/dalfopristin 1999 No

moxifloxacin 1999 No

gatifloxacin 1999 No

linezolid 2000 Yes

cefditoren pivoxil 2001 No

ertapenem 2001 No

gemifloxacin 2003 No

daptomycin 2003 Yes

telithromycin 2004 No

Table 4: New Antibacterial AgentsApproved Since 1998

Source: Spellberg et al., Clinical Infectious Diseases, May 1, 2004 (modified)


Chart 2: Antibacterial AgentsApproved, 1983-2004

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0

1983-1987 1988-1992 1993-1997 1998-2002 2003-2004

Total # New Antibacterial Agents (5 year intervals)

Only about five newantibiotics are in the drugpipeline, out of more than506 agents in development.




























15


rifapentine 1998 No




linezolid 2000 Yes


ertapenem 2001 No


daptomycin 2003 Yes






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14

12

10

8

6

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0

1983-1987 1988-1992 1993-1997 1998-2002 2003-2004






























15


rifapentine 1998 No




linezolid 2000 Yes


ertapenem 2001 No


daptomycin 2003 Yes






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1983-1987 1988-1992 1993-1997 1998-2002 2003-2004



Graphics and statistics from 2004 IDSA white paper

As Antibiotic Discovery Stagnates ... A Public Health Crisis Brews

BAD BUGS, NO DRUGS

Infectious Diseases Society of America July 2004

Other resistant bacterial infections also are raising

significant public health concerns:

• In 1998, IOM reported an alarming rise in the

incidence of infections due to a bacterium called

enterococcus, which causes wound infections,

infections in blood, the urinary tract and heart, and

life-threatening infections acquired in hospitals.

Vancomycin has been a core treatment for

enterococci. The percentage of enterococci resistant to

vancomycin (VRE) has been increasing dramatically

since the late 1980s, according to CDC. In 2002, more

than 27 percent of tested enterococci samples from

intensive care units were resistant to vancomycin. (See

Chart 1 and Table 3.)

• The percentage of Pseudomonas aeruginosa bacteria

resistant to either ciprofloxacin or ofloxacin, two

common antibiotics of the fluoroquinolone class

(FQRP), has increased dramatically from the late 1980s

to the present. Recent CDC data show that in 2002,

nearly 33 percent of tested samples from intensive

care units were resistant to fluoroquinolones. P.

aeruginosa causes infections of the urinary tract, lungs,

and wounds and other infections commonly found in

intensive care units. (See Chart 1 and Table 3.) 11

60

50

40

30

20

10

0

1980 1985 1990 1995 2000

Year

% In

cid

ence MRSA

VREFQRP

Chart 1: Resistant Strains Spread Rapidly

Source: Centers for Disease Control and Prevention

This chart shows the increase in rates of resistance for three bacteria that are of concern to public health officials:methicillin-resistant Staphylococcus aureus (MRSA), vancomycin-resistant enterococci (VRE), and fluoroquinolone-resistantPseudomonas aeruginosa (FQRP). These data were collected from hospital intensive care units that participate in theNational Nosocomial Infections Surveillance System, a component of the CDC.

Drug/Pathogen Resistance (%)

Methicillin/S. aureus 57.1

Vancomycin/enterococci 27.5

Quinolone/P. aeruginosa 32.8

Methicillin/CNS 89.1

3rd-gen. Ceph./E. coli 6.3

3rd-gen. Ceph./K. pneumoniae 14.0

Imipenem/P. aeruginosa 22.3

3rd-gen. Ceph./P. aeruginosa 30.2

3rd-gen. Ceph./Enterobacter spp. 32.2

Penicillin/S. pneumoniae 11.3

Table 3: Percent of Drug Resistance in Hospital-Acquired Infections in 2002

Source: CDC National Nosocomial Infections SurveillanceSystem, August 2003 for all, except penicillin resistantStreptococcus pneumoniae, which is the Active BacterialCore Surveillance of the Emerging Infections Network.

This table provides a snapshot of selected drug-resistantpathogens associated with hospital infections in intensivecare unit patients during 2002. CNS=Coagulase-negativestaphylococci; 3rd Ceph=resistance to 3rd generationcephalosporins (either ceftriaxone, cefotaxime, orceftazidime); Quinolone=resistance to either ciprofloxacinor ofloxacin.

Resistance data from hospital ICUs

1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

sulfonamides

streptomycin

penicillin

tetracycine

vancomycin

erythromycin

methicillin

ampicillin

chloramphenicol

cephalosporins

linezolid

daptomycin

From antibiotic discovery to the first resistant isolate

‘A Race Against Resistance’, Deborah Hung, MD, PhDBroad Institute of MIT and Harvard and Department of Molecular Biology

Tracking the in vivo evolution of multidrugresistance in Staphylococcus aureus bywhole-genome sequencingMichael M. Mwangi*†, Shang Wei Wu‡§, Yanjiao Zhou‡§, Krzysztof Sieradzki‡, Herminia de Lencastre‡¶,Paul Richardson!, David Bruce!, Edward Rubin!, Eugene Myers**, Eric D. Siggia*†, and Alexander Tomasz‡††

*Physics Department, Cornell University, Ithaca, NY 14850; †Center for Studies in Physics and Biology and ‡Laboratory of Microbiology, The RockefellerUniversity, New York, NY 10021; §Department of Microbiology, Tianjin Medical University, Tianjin 300070, People’s Republic of China; ¶Laboratoryof Molecular Genetics, Instituto de Tecnologia Quımica e Biologica, Universidade Nova de Lisboa, Oeiras, Portugal; !United States Departmentof Energy Joint Genomic Institute, Walnut Creek, CA 94598; and **Howard Hughes Medical Institute, Janelia Farm Research Campus,Ashburn, VA 20146

Edited by John J. Mekalanos, Harvard Medical School, Boston, MA, and approved April 13, 2007 (received for review November 6, 2006)

The spread of multidrug-resistant Staphylococcus aureus (MRSA)strains in the clinical environment has begun to pose serious limitsto treatment options. Yet virtually nothing is known about howresistance traits are acquired in vivo. Here, we apply the power ofwhole-genome sequencing to identify steps in the evolution ofmultidrug resistance in isogenic S. aureus isolates recovered peri-odically from the bloodstream of a patient undergoing chemother-apy with vancomycin and other antibiotics. After extensive ther-apy, the bacterium developed resistance, and treatment failed.Sequencing the first vancomycin susceptible isolate and the lastvancomycin nonsusceptible isolate identified genome wide only 35point mutations in 31 loci. These mutations appeared in a sequen-tial order in isolates that were recovered at intermittent timesduring chemotherapy in parallel with increasing levels of resis-tance. The vancomycin nonsusceptible isolates also showed a100-fold decrease in susceptibility to daptomycin, although thisantibiotic was not used in the therapy. One of the mutated lociassociated with decreasing vancomycin susceptibility (the vraRoperon) was found to also carry mutations in six additionalvancomycin nonsusceptible S. aureus isolates belonging to differ-ent genetic backgrounds and recovered from different geographicsites. As costs drop, whole-genome sequencing will become auseful tool in elucidating complex pathways of in vivo evolution inbacterial pathogens.

S taphylococcus aureus has remained one of the most frequentcauses of a wide range of both hospital- and community-

acquired infections, from superficial skin and other soft tissueinfections to life threatening toxic shock, pneumonia, endocar-ditis, and septicemia. The spectacular adaptive capacity of thispathogen resulted in the emergence and worldwide spread oflineages that acquired resistance to the majority of availableantimicrobial agents. The choice of therapy against such multi-drug-resistant S. aureus (MRSA) strains has been narrowed to afew antibacterial agents, among them the glycopeptide antibioticvancomycin, which has become the mainstay of therapy world-wide. MRSA strains with reduced susceptibility to vancomycinhave been reported in clinical specimen since the late 1990s (1).In most of these so-called vancomycin intermediate-resistant S.aureus (VISA) isolates, decrease in drug susceptibility, as ex-pressed by the increase in the minimal inhibitory concentration(MIC) of vancomycin, is sufficient to cause complications intherapy and treatment failure (2–7). VISA-type resistance hasnow been identified in each of the globally spread pandemicclones of MRSA (8).

The genetic basis of VISA-type resistance to vancomycin isunknown. Unlike the most recently described and currently stillrare VRSA isolates which carry the Tn1546-linked resistancemechanism (9, 10), the VISA-type isolates do not seem to carryacquired genetic elements related to drug resistance: their

reduced susceptibility to vancomycin appears to be based on agradual adaptive process.

Examination of VISA-type isolates recovered from many partsof the world showed a number of different phenotypic alter-ations, including changes in cell morphology and changes in thecomposition, thickness, and/or turnover of cell walls (11, 12).Nevertheless, associating these altered properties with the mech-anism of resistance has remained problematic because of the lackof availability of an isogenic vancomycin susceptible ‘‘parental’’isolate that could be used as a valid comparison. For instance,comparing the sequences of the first clinical VISA isolate MU50to the genetically related vancomycin susceptible strain N315identified over 174 ORFs that carried nonsynonymous changes(13, 14). However, MRSA strain N315 was isolated 15 yearsearlier than strain Mu50 and from a different patient. Thus, it isnot clear how many of the 174 mutations are related to themechanism of drug resistance versus the different evolutionaryhistory of the strains.

Recently we obtained a series of MRSA isolates from theblood stream of a patient with congenital heart disease who wastreated extensively with vancomycin without success (15). Avail-able clinical data suggests that the primary site of infection wasendocarditis.‡‡ In addition to vancomycin, the patient alsoreceived a single dose of rifampin and a course of therapy withthe !-lactam antibiotic imipenem. After !12 weeks of therapyand replacement of a heart valve, the patient died because ofcomplications of the underlying disease.

The first isolate JH1 recovered before the beginning of chemo-therapy was fully susceptible to vancomycin (MIC " 1 "g/ml).Vancomycin therapy was begun between the culture isolation ofJH1 and JH2. The last isolate JH9 recovered at the end ofchemotherapy showed decreased susceptibility to vancomycin(MIC " 8 "g/ml). Comparison of the series of JH isolates by severalgenetic typing techniques indicated that they were isogenic (15, 16).The JH lineage was also related, although more remotely, to thefully sequenced MRSA strains N315 and MU50 (17).

Author contributions: A.T. designed research; M.M.M., S.W.W., and Y.Z. performed re-search; K.S., P.R., D.B., and E.R. contributed new reagents/analytic tools; M.M.M. H.d.L.,E.M., and E.D.S. analyzed data; and M.M.M., E.D.S., and A.T. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Abbreviations: MIC, minimal inhibitory concentration; MRSA, multidrug-resistant S.aureus; VISA, vancomycin intermediate-resistant S. aureus.††To whom correspondence should be addressed. E-mail: [email protected].‡‡Flayhart, D., Hanlon, A., Wakefield, T., Ross, T., Borio, L., Dick, J. (2001) in Abstracts of the

101st General Meeting of the American Society of Microbiology, May 20–24, 2001,Orlando, FL, Abstr. A-39.

This article contains supporting information online at www.pnas.org/cgi/content/full/0609839104/DC1.

© 2007 by The National Academy of Sciences of the USA

www.pnas.org"cgi"doi"10.1073"pnas.0609839104 PNAS # May 29, 2007 # vol. 104 # no. 22 # 9451–9456

MIC

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Resistance evolution is rapid: but how rapid?




















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An idea...?

Let p be the probability of acquiring the right resistance mutation in the right gene for a given drug. If p is small, p2 is even smaller, so why not combine two drugs?

rpoB gene, and RNAP purified from these mutants was SorS

in vitro. Thus, we conclude that these SorR mutants wereprobably uptake mutants.

RNAP-Sor crystallization and overall structureCrystals of Taq core RNAP were grown by a modification ofthe previously described conditions (Zhang et al, 1999; seeMaterials and methods). Crystals were then incubated over-night with 1mM Sor, followed by cryopreservation as de-scribed in Materials and methods.

The Sor-RNAP crystals were isomorphous to the nativecrystals and difference Fourier maps revealed strongelectron density located in the Rif pocket (Figure 3A).The previously determined X-ray structure of Sor (Jansenet al, 1989) was easily placed in the density. Small adjust-ments of Sor were made to better fit the density. In addition,some side chains of amino acids surrounding Sor displayedslightly different positions as well as lower B-factors relativeto the apoenzyme, indicating that Sor stabilized the positionof these residues. Adjustments of these residues into thedensity were made and the structure refined to 3.2 A(Table II).

Sor occupies the Rif pocketThe structure revealed that Sor exactly occupies the Rifbinding pocket (Figure 3B). Comparison of RNAP residuesinteracting with Rif or Sor (defined as RNAP residues within4 A of each antibiotic) revealed essentially a one-to-onecorrespondence (Figure 4A and B), such that all residuesthat interact with Rif also interact with Sor. Superimpositionof the two antibiotics within the RNAP binding pocketindicates that the overlapping binding determinants are pos-sible because of the remarkable correspondence in the overallshape of each antibiotic (Figure 3B).

Determinants for Rif and Sor activityDerivatives of Rif and their effects on antimicrobial activityhave been analyzed extensively (Brufani et al, 1964; Lanciniand Zanichelli, 1977; Arora, 1981, 1983, 1985; Arora andMain, 1984). Modifications of the ansa bridge, O1 or O2 of thenapthol ring, or the hydroxyls O9 or O10 greatly reduce itsinhibition activity in vitro. Modifications are only toleratedoff C3 of the napthol ring (Figure 1). This is supported by theRNAP-Rif structure, where most of the interactions occur

Figure 3 Sor-RNAP cocrystal structure and comparison with Rif. (A) Stereo view of Sor in its binding pocket of Taq core RNAP. Atoms arecolor-coded as follows: carbon atoms of the RNAP b subunit, cyan; carbon atoms of Sor, green; oxygen, red; nitrogen, blue; sulfur, yellow.Electron density, calculated using (|Fo

Sor!Fonat|) coefficients (Sor denotes the Sor-RNAP cocrystal, nat denotes the native core RNAP crystal), is

shown in magenta (contoured at 3s), and was computed using phases from the native RNAP model. Selected amino-acid residues discussed inthe text are labeled. (B) View of the antibiotic binding pocket of the RNAP b subunit (same view as A). The RNAP is shown as a surface view,with the b subunit colored blue, but with residues within 4 A of Sor colored yellow (to define the antibiotic binding pocket). Superimposed inthe binding pocket are the structures of Sor (green carbon atoms) and Rif (orange carbon atoms).

Table I Effects of RNAP b subunit substitutions on Rif and Sorresistance

Mutant (Ec/Taq)a RifR SorR Classb

Single amino-acid substitutionsWT ! !V(146/137)W ++ + IIS(512/392)P ++ ++ IQ(513/393)R !c ++ IIID(516/396)N ++ ++ IS(522/402)F ++ ++ IH(526/406)Y ++ ++ IH(526/406)P ++ ++ IH(526/406)Q + + IR(529/409)H ++ + IIR(529/409)L + + IR(529/409)C !c !S(531/411)F ++ + IIS(531/411)Y ++ ! IIA(532/412)V ++ + IIA(532/412)E + + IL(533/413)P ++ ! IIG(534/414)D + ! III(572/452)F ++ ! IIS(574/454)F + ++ III

Multiple substitutions or deletionsR(687/T566)H ! !V(137/128)/I(138/129)R ! !N(139/130)G/R(143/134)W ! !N(139/130)K/R(143/134)W ! !V(144/135)L/I(145/136)R + + ID540–544/420–424 ! !D540–545/420–425(L) ! + IIID540–543/420–423(P) ! + IIID538–540/D418–420 ! !D535–542/415–422 + + I

aMutations with differential effects on Rif versus Sor resistance aredenoted in bold. Levels of resistance are denoted as follows: !,sensitive; +, mild resistance; ++, strong resistance.bClass I (RifR/SorR); Class II (RifR/SorS); Class III (RifS/SorR).cSome mutants originally isolated as RifR did not score as RifR in thisassay because of the 24 h incubation time—longer incubation times(48 h) revealed weak Rif resistance.

The RNA polymerase/sorangicin complexEA Campbell et al

&2005 European Molecular Biology Organization The EMBO Journal VOL 24 | NO 4 | 2005 677

In this study, we determined the X-ray crystal structure ofTaq RNAP in complex with Sor in order to compare it to thepreviously determined RNAP-Rif structure. In addition, weperformed a detailed functional analysis of Sor and Rifinhibition of Ec and Taq RNAPs, as well as a systematicanalysis of crossresistance in Ec RNAP. The results show thatSor occupies the same RNAP b subunit pocket as Rif, with analmost complete overlap of RNAP binding determinants, andthat Sor inhibits transcription by the same mechanism as Rif.On the other hand, while Rif binding and inhibition are verysensitive to amino-acid substitutions that would be expectedto alter the shape of the antibiotic binding pocket, Sor is ableto bind and inhibit these RifR RNAPs effectively. We proposethat intrinsic conformational flexibility of Sor allows it toadapt to changes in the shape of the antibiotic bindingpocket. This may be an important general principle for thedesign of inhibitors against rapidly mutating targets (Das et al,2004).

Results

Sor inhibits transcription by Ec and Taq RNAPThe ability of Sor and Rif to inhibit transcription by Ec andTaq RNAP holoenzymes initiating at the T7 A1 promoter wasinvestigated. Both Rif and Sor effectively inhibited transcrip-tion by the Ec enzyme (Figure 2, lanes 1 and 9). In theabsence of antibiotics, RNAP produced the full-sized, 127 ntrun-off transcript (RO), a 105nt terminated transcript (T),which arose due to the presence of the tR2 terminatorbetween the promoter and the end of the template, as wellas two abortive transcripts. The abortive transcripts werelikely to be the trimer CpApU, initiated from the CpA primer,as well as a dimer, pppApU, initiated from the ATP present inthe reaction. The production of RO and T was essentiallycompletely inhibited when the concentration of either anti-biotic exceeded 1 mM (lanes 5–8 and 13–16). However, theamount of abortive products increased dramatically withincreasing amounts of each antibiotic. At the highest Sorconcentration of 1mM (lane 16), Sor decreased the amountsof abortive products, which is likely due to nonspecificinhibition of transcription.

The behavior of Taq RNAP in response to the drugs wasdifferent. As with Ec RNAP, increasing amounts of both Rif

and Sor inhibited synthesis of the long transcripts (RO and T)while causing a dramatic increase in abortive products. Asobserved previously, the Taq enzyme was resistant to theeffect of Rif—only at the highest concentrations of Rif (0.1–1mM) was there a significant effect (lanes 23 and 24). Evenat the highest concentration of Rif (1mM), the production oflong transcripts was only partially inhibited (lane 24). Incontrast, Taq RNAP was as sensitive to Sor as Ec RNAP; veryfew full-sized transcripts were produced when the Sor con-centration exceeded 1mM, and the expected abortive tran-scripts were dramatically overproduced (lanes 28–31). Fromthese experiments, we conclude that (i) Rif and Sor appear toinhibit transcription in a similar way, and (ii) Sor is anequally effective inhibitor for Ec and Taq RNAPs, while Rifis relatively ineffective against Taq RNAP, supporting thehypothesis that there are differences between the interactionof RNAP and each antibiotic.

Rif-resistant mutations and crossresistance to SorIn order to determine whether known RifR mutations(Ovchinnikov et al, 1983; Severinov et al, 1993) in theEc rpoB gene (coding for the RNAP b subunit) also lead toSor resistance, we performed systematic crossresistance com-parisons (Table I). Since these mutations were studied withthe Ec enzyme but analyzed in the context of the Taq RNAPstructure, throughout this manuscript we will refer to themutations in Ec rpoB numbering, followed by the Taq num-bering (Ec/Taq). Mutations causing Rif resistance occur infour distinct clusters in rpoB. The clusters are far from eachother in the b primary sequence, but come together to line theRif binding pocket in the three-dimensional structure(Campbell et al, 2001). One cluster of RifR mutants occursin conserved segment B of the b subunit (the N-terminalcluster); substitutions at position Val146/137 lead to strongRif resistance. Two additional clusters, Rif clusters I and II,harbor the majority of RifR mutants and occur betweenamino-acid positions 507–534/387–414 and 559–574/439–454, respectively. Finally, a single site in conserved segmentE, at amino-acid position EcArg687/TaqThr566, marks Rifcluster III.

Ec DH5a cells (RifS/SorS) were transformed with expres-sion plasmids overproducing 29 different b subunit mutantsthat conferred either Rif or stretpolydigin resistance

O

HO

O

O

OH

HO

O

O

O

O

OH

Sorangicin A

3

5

2223 24

25 26

2728

29

30

46

33

36

37

38 39

40

41

42

43

44

45

10116

7

NN

N

O

OH OH

OH

O

O

NH

OOHOH

O

O

O

Rifampicin

4340

39

3841

42

9

21

3 2

3

4

10

Figure 1 Chemical formulas for RNAP inhibitors Sor (top) and Rif (bottom). For clarity, only selected atoms discussed in the text arenumbered.

The RNA polymerase/sorangicin complexEA Campbell et al

&2005 European Molecular Biology Organization The EMBO Journal VOL 24 | NO 4 | 2005 675

An even better idea...?

If two drugs enhance each others inhibitory effect, it surely makes sense to deploy a synergistic drug combination: the ‘search for synergy’?

mutations alterbinding pocket

In addition, we used the fact that for any drug pair, includingstrongly synergistic or antagonistic ones, the strength of inter-actions varies for different drug ratios and dosages (26). There-fore, for all drug pairs, for each combination of concentrationsof two drugs, we measured the degree of synergy (S, defined inMaterials and Methods and in Fig. 4), which ranges from !1 forstrongly synergistic interactions to "1 for strongly antagonisticones, and compared it with the rate of adaptation (Fig. 4; see rawdata in Fig. S2). We find a positive correlation between synergyand the rate of adaptation (! # 0.683, P $ 0.001). Two aspectsof the data contribute to this correlation: the correlation amongthe means of the four drug pairs and the correlation within eachpair. To isolate the latter, we calculated the partial correlationbetween synergy and the rate of adaptation when controlling fordrug-pair membership, which yields ! # 0.533, P $ 0.001 (see SIText). Another factor that is likely to influence the rate ofadaptation is the initial inhibition of growth of the ancestralstrain in each environment. Again, we have verified that theobserved correlation between adaptation rate and synergy re-mains when accounting for the confounding factor of initialinhibition (see SI Text). Indeed, the partial correlation betweenrate of adaptation and degree of synergy when controlling forinitial inhibition supports the same conclusion as before (P $0.001), namely, that synergy promotes faster emergence of drugresistance.

DiscussionOur simple geometric model provides some insight into howsynergistic drug interactions may lead to faster adaptation (Fig.1). It should be noted that the same model also indicates theinfluence of another factor on the rate of adaptation: theavailability of mutations that confer simultaneous resistance toboth drugs (27, 28) (Fig. S1). It is certainly possible that the levelof pleiotropy in mutational effects contributes to the observeddifferences in the rates of adaptation between drug pairs in our

experiments. Indeed, drug pairs with similar mechanisms ofaction, such as ERY and DOX, could have increased pleiotropy.Conversely, pleiotropy could inhibit evolution if mutation con-

0.750.37

0.190.09

0

10050

2512

63 0

< 0.001

0.01

[DOX] (µg/ml)[ERY] (µg/ml)

Rat

e of

ata

ptat

ion,

!

0.001

0.01

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! (1/hr2)

0.750.37

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107

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!

Synergy Antagonism

0.750.37

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bitio

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bitio

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[ER

Y] (

µ g/m

l)

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5

[DOX] (µ g/ml)

[CIP

] (ng

/ml)A B

C D

Fig. 3. Different drug pairs vary profoundly in their impact on the rate of adaptation. (A and B) For two pairs of drugs (A, synergistic ERY-DOX; B, antagonisticCIP-DOX), the initial level of inhibition is shown for a matrix of concentrations of the two drugs. The level of inhibition is defined as 1 " r/r0, where r is the growthrate of the population in the presence of antibiotics and r0 is the drug-free growth rate. The solid line corresponds to the line of 50% inhibition and is also shownon a linear scale in the insets (see Fig. 1 for comparison). (C and D) The rate of adaptation for the drug combinations shown in A and B. The arrow in C pointsto a region of drug concentrations where the rate of adaptation for the synergistic ERY-DOX combination is accelerated relative to the single-drug treatments.This acceleration is surprising because the more expected outcome of combining drugs is for adaptation to slow down.

!1 !0.5 0 0.5 1

10!3

10!2

CIP!AMIAMI!DOXERY!DOXCIP!DOX

Correlation coefficient:" = 0.683

Antagonism Synergy

Degree of synergy, S

Rat

e of

ada

ptat

ion,

(1

/hr2

)

Fig. 4. The degree of synergy and the rate of adaptation are positively corre-lated: The more synergistically the drugs interact, the faster the bacteria evolveresistance. Shown are data from all four drug pairs in our study (legend). Each dotrepresents the rate of adaptation for a given drug pair and concentrations versusthe degree of synergy (S). The variability in rates of adaptation has two contri-butions: an error of approx 25% due to errors in measuring growth rates, and aninherent stochasticity of the mutation process (see Materials and Methods andFigs. S3 and S4). For a combination (x,y) of drug concentrations, S is measured asthe deviation from the neutral expectation defined by Bliss independence: S #(fx0/f00)(f0y/f00) " fxy/f00, where fxy denotes wild-type growth rates when theconcentration of one drug is x and that of the other is y. Following this definition,positive values of S corresponds to synergistic interactions and negative values toantagonistic ones. The solid line is the best fit to all 116 data points from all of thedrug pairs.

Hegreness et al. PNAS ! September 16, 2008 ! vol. 105 ! no. 37 ! 13979

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Accelerated evolution of resistancein multidrug environmentsMatthew Hegreness*†, Noam Shoresh*, Doris Damian‡, Daniel Hartl†§, and Roy Kishony*¶!

*Department of Systems Biology, Harvard Medical School, 200 Longwood Avenue, Boston, MA 02115; †Department of Organismic and Evolutionary Biologyand ¶School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138; and ‡Vertex Pharmaceuticals Inc., Cambridge, MA 02139

Edited by Francisco J. Ayala, University of California, Irvine, CA, and approved July 24, 2008 (received for review June 19, 2008)

The emergence of resistance during multidrug chemotherapy im-pedes the treatment of many human diseases, including malaria,TB, HIV, and cancer. Although certain combination therapies havelong been known to be more effective in curing patients thansingle drugs, the impact of such treatments on the evolution ofdrug resistance is unclear. In particular, very little is known abouthow the evolution of resistance is affected by the nature of theinteractions—synergy or antagonism—between drugs. Here wedirectly measure the effect of various inhibitory and subinhibitorydrug combinations on the rate of adaptation. We develop anautomated assay for monitoring the parallel evolution of hundredsof Escherchia coli populations in a two-dimensional grid of druggradients over many generations. We find a correlation betweensynergy and the rate of adaptation, whereby evolution in moresynergistic drug combinations, typically preferred in clinical set-tings, is faster than evolution in antagonistic combinations. Wealso find that resistance to some synergistic combinations evolvesfaster than resistance to individual drugs. The accelerated evolu-tion may be due to a larger selective advantage for resistancemutations in synergistic treatments. We describe a simple geomet-ric model in which mutations conferring resistance to one drug ofa synergistic pair prevent not only the inhibitory effect of that drugbut also its enhancing effect on the other drug. Future study of theprofound impact that synergy and other drug-pair properties canhave on the rate of adaptation may suggest new treatmentstrategies for combating the spread of antibiotic resistance.

adaptation " antagonism " synergy " antibiotics " antibiotic resistance

Challenged by rapid emergence of drug-resistant pathogensand limited supply of new antibiotics, clinicians increasingly

rely on multidrug treatments to combat infections (1–7). Whendrugs are applied together the effect of a drug can depend on thepresence or absence of the other drug. Such interactions betweendrugs are classified as additive, synergistic, or antagonisticdepending on whether their combined effect on bacterial growthis equal to, greater than, or less than expected based on theinhibitory abilities of the individual drugs (8, 9). Two main goalsof drug treatment are stopping bacterial growth and preventingthe evolution of drug resistance (5, 10–12). Although synergis-tically interacting drugs are often favored because of theirgreater combined ability to inhibit growth (13), little directevidence for their ability to suppress the evolution of resistanceexists, and some studies even suggest the contrary (14–18).

Examining the evolution of resistance in the context of asimple geometric model of drug–drug fitness landscapes, we findthat mutations conferring full or partial resistance to one of theindividual drugs may be more beneficial to bacteria in synergisticthan in antagonistic drug treatments [Fig. 1; the situation formutations conferring simultaneous resistance to both drugs isillustrated in supporting information (SI) Fig. S1]. This deduc-tion is based on the simplifying assumption, demonstrated inprevious work, that mutations conferring resistance to a singledrug are effectively equivalent to a reduction in that drug’sconcentration (16, 17, 19, 20). When drugs amplify each other’seffects (synergy) (9), this effective reduction in the concentration

of one of the drugs not only relieves the effect associated withthat drug but also reduces its enhancing influence on the otherdrug. In contrast, when drugs partially inhibit one another(antagonism), resistance mutations that remove some of theeffect of one of the drugs will actually reveal the previouslysuppressed effect of the other drug (Fig. 1). This scenario hasrecently been experimentally observed for a hyperantagonisticdrug pair in which horizontally transferred alleles that conferresistance to one of the drugs can actually be deleterious in thecombined drug environment (17). This intuition applies whetherthe starting concentration is above or below an organism’sminimal inhibitory concentration (MIC). Such expected differ-ences in the selective advantage of resistant mutants in two-drug

Author contributions: M.H., N.S., D.H., and R.K. designed research; M.H. performed re-search; M.H., N.S., D.D., D.H., and R.K. analyzed data; and M.H., N.S., and R.K. wrote thepaper.


This article is a PNAS Direct Submission.§To whom correspondence may be addressed. E-mail: [email protected].!To whom correspondence may be addressed at: Systems Biology Department, HarvardMedical School, 200 Longwood Ave, Warren Alpert 519, Boston, MA 02115. E-mail:[email protected].

This article contains supporting information online at www.pnas.org/cgi/content/full/0805965105/DCSupplemental.


[Drug B]

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Fig. 1. A simple geometric model shows that a mutation conferring resis-tance to a single drug is most advantageous in a synergistic drug combination.Shown are isoboles, or lines of equal bacterial growth rate, in the plane ofconcentrations of drugs A with either drug B (where B interacts with drug Asynergistically), drug C (additively), or drug D (antagonistically). The arrowsshown on the isobolograms for the three types of interaction all correspondto the exact same mutation (indicated by a thin arrow along the axis of drugA’s concentration), which confers partial resistance to drug A by reducing theeffective concentration of drug A felt by the resistant mutant. The threearrows’ origins represent environments that have the same initial concentra-tion of drug A and the same fitness inhibition (10%, dotted line). Although themutation changes the effective concentration of drug A by the same amountin all environments, the fitness gain conferred by the mutation is greatest inthe synergistic case (it crosses more fitness contour lines).

www.pnas.org#cgi#doi#10.1073#pnas.0805965105 PNAS " September 16, 2008 " vol. 105 " no. 37 " 13977–13981

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The increase in bacterial fitness due to a single DR mutation is greater when synergistic combinations are used.

And the math?

And the math?

Can we pose the ‘optimal drugdeployment protocol’ as an actualoptimisation problem?

If so, what will we learn?

Kishony et al.’s experimental protocol:

environments suggest the hypothesis that the rate of adaptation,the speed with which lineages carrying such mutations spreadwithin evolving populations, might be greater for synergistic thanfor antagonistic drug combinations.

To experimentally explore the relation between drug inter-action and the rate of adaptation, we compared a drug pair thatexhibits strong antagonism [doxycycline (DOX), a tetracyclineantibiotic, and ciprofloxacin (CIP), a fluoroquinolone] to an-other pair showing strong synergy [DOX and a macrolideantibiotic, erythromycin (ERY)] (5, 17, 21, 22). For each pair,drugs were mixed in a two-dimensional array of wells in whichthe concentration of each of the single drugs varied from zero toabove its MIC. Populations derived from clonal expansion of asingle wild-type, drug-sensitive E. coli bacterium were intro-duced to all wells and propagated through daily serial transfers(see Materials and Methods) (23–25). The rates at which bacterialpopulations developed residual resistance to the various drugcombinations were measured by tracking the evolution of thesepopulations over !170 generations (Fig. 2). The degree ofantibiotic resistance acquired by each population is manifest inthe increase of its growth rate over time (The changes in MICthat accompanied these accelerations of growth were relativelymild, smaller than a factor of 2 in some cases and up to an 8-foldincrease in others; data not shown). From daily growth curves(Fig. 2A) we estimated how the growth rate changed for eachpopulation as it evolved (Fig. 2B). Typically, we see a saturationcurve with a relatively fast initial increase in fitness followed bya plateau with little or no additional adaptation in later times.We combined the increase in growth rate of each populationduring evolution, "r, and the time it took the population to reachthe half-way mark of that increase, tadapt, to define the rate ofadaptation, ! # ("r/2)/tadapt (Fig. 2B). This adaptation rate

shows large variability among the different drug treatments,reflecting variability in both initial growth rates and adaptationtimes (Fig. 2C). In contrast, much less variability was manifest inthe final growth rates attained by the populations, and by the endof the experiment most of the populations were growing at a ratesimilar to that in the drug-free environment (Fig. 2C).

ResultsOur data show that drug combinations have a strong effect onthe evolution of drug resistance (Fig. 3). Different drug pairs,however, have profoundly different impacts on the rate ofadaptation. For ERY-DOX, which is a strongly synergistic drugpair, we see accelerated adaptation when the drugs are used incombination (center of the 2-D drug grid, arrow in Fig. 3C)relative to drug treatments involving either of the drugs alone(the two edges lying on the drug concentration axes). For theantagonistic drug pair CIP-DOX, such an acceleration is absentin the combinations that we tested. Moreover, the oppositeeffect—a depression of the rate of adaptation relative to thesingle-drug environments—is apparent for some CIP-DOXcombinations (Fig. 3D). Related to these observations is the factthat resistance to the synergistic drug pair evolves rapidly, notonly compared to each drug separately, but also compared to theantagonistic pair. This link between the way drugs interact andthe rate of adaptation is consistent with the hypothesis describedin Fig. 1, and further exploration of this relation was achieved bythe additional experiments and analyses described below.

We expanded on the comparison of strongly synergistic andstrongly antagonistic drug combinations by including two addi-tional drug pairs in our study—CIP with the aminoglycosideamikacin (AMI) and AMI with DOX—which interact synergis-tically at some dose combinations but antagonistically at others.

0 20 40 60 80 100 1200

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3#10!4 3#10!3 3#10!210!1

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2/ ,adaptation of Ratetr

Fig. 2. Parallel quantitative measurement of the rate of adaptation in multidrug environments. (A) Example of growth in one particular dosage of ciprofloxacin(CIP) and doxycycline (DOX), showing measurements of optical density as a function of time (OD, black dots). Cells are propagated in media containing the drugsthrough daily serial transfers over 15 days (only the first 6 days are shown), resulting in alternating periods of growth and stationary phase (Inset). Best fit ofthe logistic growth curve (red lines; indicated equation) defines the growth rate (r) for this population in each day. The measurement error in the growth rateswas estimated to be !0.06/h (see Materials and Methods and Fig. S3). (B) Data points corresponding to daily growth rates show how the fitness in the populationfrom A increases over time. Time is measured in hours of growth (time in stationary phase is excluded). The total increase in growth rate of the population isdenoted by "r, and the adaptation time, tadapt, is defined as the time at which the population crosses the midpoint between its initial and final growth rates(see Materials and Methods for more details). Measured "r and tadapt are used for determining the rate of adaptation of each population (!, equation shown).(C) Scatter plot of rates of adaptation and final growth rates for CIP-DOX and ERY-DOX. The point highlighted in magenta corresponds to the population shownin A and B. Most populations that evolve recover the growth rate in a drug-free environment (dashed horizontal line).

13978 ! www.pnas.org"cgi"doi"10.1073"pnas.0805965105 Hegreness et al.

Very simple culturing experiment: serial dilutions, antibiotics erythromycin and doxycycline, E.coli, M9 minimal media, glucose limitation

24h







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rate

Basic model of growth in one flask:

optical density increases but its rate of increase is reduced by ery and dox

Ery and dox non-competitively target ribosomal subunits (translational inhibitors): we assume growth rate inhibition is proportional to reduction in activity.

combinationparameter

Michaelis-Menten forms for uninhibited uptake and growth.

Assume ery & dox transported passively into cell.

Parameterise the model in no-drug and two single-drug environments, separately.

Aim to predict drug interactions and inhibition curves.

In the model:

0 5 10 15 20 250

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[Rif]/[3H rif] and [Rfb]/[3H rif]

competitive RNAP binding of {Rif,Rfb} v. 3H rif

rela

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fract

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of R

NA

Pbo

und

3 Hrif

rifampicin (Rif) datarifabutin (Rfb) data1 param Rif fit (0.98106)1 param Rfb fit (0.98444)

It depends on the drug target, but for rif drugswhere data is available,

‘relative activity’ behaves like

where p is a parameter.

If ‘complete inhibition’ cannot be achieved, then we’d get

Basic model of growth in one flask:

Ery and dox non-competitively target ribosomal subunits (translational inhibitors): we assume growth rate inhibition is proportional to reduction in activity.

combinationparameter

sugar uptake and growth

inhibition by erythromycin

inhibition by doxycycline

sugaruptake

eryuptake

doxuptake

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dox:

ery:

This model captures 12-hour ery and dox inhibition:

Chose 50% inhibition levels for basal drug

concentrations, check again for synergy:

ERY 0.2 0.4 0.6 0.8 DOX

75

80

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Popula

tion!

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%)

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=0.15, [ERY]max

=5

DataModel

optimal combination

The drug interaction is indeed

synergistic:

not a datafit

Take the same model, but include SD and MDresistant alleles, assuming resistance costs:

Allow n transfers:

genetics/adaptation

Over a finite horizon we have a finite dimensional optimisation problem:

Defining our state variable

is our model.

Of greater biological relevance are ...

The optimal combination problem:

s.t.

The optimal sequential problem:

s.t.

4

Figure 4: Optimal drug proportion as a function of the number of transfers per-

formed. Darker colours represent a lower payoff while lighter colours denote that

in average there is a low pathogen density at the end of each transfer. Circles de-

note the optimal drug proportion for an experiment with the corresponding number

of transfers. Note that for short-term experiments the optimal drug proportion cor-

responds roughly with the drug ratio that maximises the synergistic effect. But as

the number of transfers in the experiment increases and consequently bacteria start

adapting to the fixed environment and therefore the population structure changes,

the optimal drug ratio also changes. This figure illustrates that the optimal drug

combination is a dynamic property of the system that depends on the population

structure and the length of the experiment.

MDR evolution ⇒ the optimal combination can shift

N

4

Figure 4: Optimal drug proportion as a function of the number of transfers per-

formed. Darker colours represent a lower payoff while lighter colours denote that

in average there is a low pathogen density at the end of each transfer. Circles de-

note the optimal drug proportion for an experiment with the corresponding number

of transfers. Note that for short-term experiments the optimal drug proportion cor-

responds roughly with the drug ratio that maximises the synergistic effect. But as

the number of transfers in the experiment increases and consequently bacteria start

adapting to the fixed environment and therefore the population structure changes,

the optimal drug ratio also changes. This figure illustrates that the optimal drug

combination is a dynamic property of the system that depends on the population

structure and the length of the experiment.

3

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quenci

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SusceptibleDOX!resistantERY!resistantMultidrug resistant

(c)

Figure 3: Simulations of a serial transfer experiment designed to test the optimal

combination protocol. (a) Optical densities of a population of bacteria treated with

a fixed combination of erythromycin and doxycycline. At the beginning of each

transfer fresh medium is deployed at concentration S = 2000µg/ml, as well as a

fixed dose of antibiotic with a drug ratio of θ = 0.57. Cells are grown for 12 hours

before propagating a fraction of the end-population into the next transfer. The

dotted line illustrates the moment in time that the population enters the stationary

phase and shaded areas represent the densities of each bacterial phenotype. (b)

Rate of adaptation as a function of the number of transfers. Note how the fitness

of the population increases over time. (c) Frequencies of resistance to each drug in

the population as a function of the number of transfers performed. At the end of

the first transfer the population is composed mainly by susceptible bacteria but at

the end of the experiment more than eighty percent of the population is multidrug

resistant.

3

0 20 40 60 80 100 120 1400

0.05

0.1

0.15

0.2

0.25

0.3

OD

at 600 n

m

Time (hours)

(a)

1 2 3 4 5 6 7 8 9 10 11 12

0.05

0.1

0.15

0.2

0.25

0.3

Number of transfers

Ra

te o

f a

da

pta

tion

(b)

0 1 2 3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

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0.9

1

Number of transfers

Fre

qu

en

cie

s


(c)














resistant.

12h per transfer

Interesting, but it matters little as by 150 hours, most cells are MDR in this model anyway.

Dynamics across multiple transfers:

5

0 20 40 60 80 100 120 1400

0.05

0.1

0.15

0.2

0.25

OD

at 600 n

m

Time (hours)

(a)

1 2 3 4 5 6 7 8 9 10 11 12

0.05

0.1

0.15

0.2

0.25

0.3

Number of transfers

Rate

of adapta

tion

(b)

0 1 2 3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of transfers

Fre

quenci

es


(c)

Figure 5: Example of a serial transfer experiment where only one drug is deployedat the beginning of each transfer. (a) The antibiotic used in each transfer is denotedby the colour code at the bottom of the figure; blue denotes that doxycycline wasused at a concentration 0.7µg/ml while green denotes erythromycin at 3.5µg/ml.The optimal rotation protocol illustrated here can be represented with the vectorθ∗rot = (0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0) and was determined after simulating all pos-sible 12-transfer rotations. (b) Rate of adaptation as a function of the number oftransfers. It is important to notice that each time a switch between drugs is per-formed, there is a reduction in the overall fitness of the population. (c) Frequenciesof resistance as a function of the number of transfers. As opposed to the fixed-dosecombination treatment that selected for multidrug resistance, in this case even afterseveral dilutions the population is still mainly composed of susceptible bacteria.

5

0 20 40 60 80 100 120 1400

0.05

0.1

0.15

0.2

0.25

OD

at 600 n

m

Time (hours)

(a)

1 2 3 4 5 6 7 8 9 10 11 12

0.05

0.1

0.15

0.2

0.25

0.3

Number of transfers

Rate

of adapta

tion

(b)

0 1 2 3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of transfers

Fre

qu

enci

es


(c)


3

0 20 40 60 80 100 120 1400

0.05

0.1

0.15

0.2

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0.3

OD

at

60

0 n

m

Time (hours)

(a)

1 2 3 4 5 6 7 8 9 10 11 12

0.05

0.1

0.15

0.2

0.25

0.3

Number of transfers

Rate

of adapta

tion

(b)

0 1 2 3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of transfers

Fre

qu

en

cie

s


(c)














resistant.

3

0 20 40 60 80 100 120 1400

0.05

0.1

0.15

0.2

0.25

0.3

OD

at

60

0 n

m

Time (hours)

(a)

1 2 3 4 5 6 7 8 9 10 11 12

0.05

0.1

0.15

0.2

0.25

0.3

Number of transfers

Rate

of adapta

tion

(b)

0 1 2 3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of transfers

Fre

quenci

es


(c)














resistant.

optimal combination

optimal rotation

Comparing the two suboptimal treatments:

rotation has fewer MDR types

6

1 2 3 4 5 6 7 8 9 10 11 120

0.05

0.1

0.15

0.2

0.25

0.3

Number of transfers

OD

at 600 n

m

Combination

Rotation

Figure 6: Optimal densities at the end of each transfer under two different drug

deployment regimes: the rotation protocol illustrated in Figure 5 and the fixed-

proportion combination protocol shown in Figure 3. At the beginning of the ex-

periment the combination protocols minimises the density of bacteria considerably

more than the rotation protocol. Interestingly, this trend is reversed at the end of

the experiment, when the treatment protocol that minimises bacterial density is the

one that deploys both synergistic antibiotics sequentially and not in combination.

For treatments of longer duration, this

simple model predicts that combination is the less effective of

the two:

5

0 20 40 60 80 100 120 1400

0.05

0.1

0.15

0.2

0.25

OD

at 600 n

m

Time (hours)

(a)

1 2 3 4 5 6 7 8 9 10 11 12

0.05

0.1

0.15

0.2

0.25

0.3

Number of transfers

Rate

of adapta

tion

(b)

0 1 2 3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of transfers

Fre

qu

enci

es


(c)


3

0 20 40 60 80 100 120 1400

0.05

0.1

0.15

0.2

0.25

0.3

OD

at

60

0 n

m

Time (hours)

(a)

1 2 3 4 5 6 7 8 9 10 11 12

0.05

0.1

0.15

0.2

0.25

0.3

Number of transfers

Rate

of adapta

tion

(b)

0 1 2 3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of transfers

Fre

quenci

es


(c)














resistant.

optimal rotation optimal combination

100hrs

• We’re testing these predictions in the lab...




















MIC

ROBI

OLO

GY

Recall...




















MIC

ROBI

OLO

GY

How should we treat to minimise selection for drug resistance?

hit early and hard, empirical, rotation, de-escalation, sequential, combination, tapering, pulsing, probiotic, surveillance-based, periodic monitoring,...,random!

MG

B –

Can

ada-

UK

Wor

ksho

p –

Lond

on, E

ngla

nd, F

ebru

ary

6, 2

008

-1

Centre de recherche en infectiologieUniversité Laval

Michel G. BergeronFebruary [email protected]

“Finding the Bug: Controlling Resistance Through Rapid (<1h) DNA-Based Diagnostics”

Michel G. Bergeron, MD, FRCPC

!"#$%&&#"'()*'+,(-".()

/-0-&-#)'#$'1-2"#3-#4#56'()*

+%)7"%'*%'"%2,%"2,%'%)'-)$%27-#4#5-%'8+9:;'<)-0%"&-7='>(0(4

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+()(*(

!,#)%J 8IGK;'LBIM?@AB

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>#)*#)D'N)54()*'Y Z%3"C("6'LM@D'?AAK

MG

B –

Can

ada-

UK

Wor

ksho

p –

Lond

on, E

ngla

nd, F

ebru

ary

6, 2

008

-1

Centre de recherche en infectiologieUniversité Laval

Michel G. BergeronFebruary [email protected]

“Finding the Bug: Controlling Resistance Through Rapid (<1h) DNA-Based Diagnostics”

Michel G. Bergeron, MD, FRCPC

!"#$%&&#"'()*'+,(-".()

/-0-&-#)'#$'1-2"#3-#4#56'()*

+%)7"%'*%'"%2,%"2,%'%)'-)$%27-#4#5-%'8+9:;'<)-0%"&-7='>(0(4

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+()(*(

!,#)%J 8IGK;'LBIM?@AB

NM.(-4J 1-2,%4OFOP%"5%"#)Q2"2,C4OC4(0(4O2(

+()(*(M<R'S)7-3-#7-2'9%&-&7()2%'T#"U&,#V&J'W P%(7-)5'7,%'PC5& X

>#)*#)D'N)54()*'Y Z%3"C("6'LM@D'?AAK

But treatment duration is, apparently, still not well

understood.

Maximising drug appropriateness: the right drug for right bug is a modern treatment paradigm:

April MMEMS meeting:

Thanks: MRC, EPSRC, NSF/Nescent, MMEMS

Ivana Gudelj, Rafael Pena-Miller, Laurence Hurst, David Laenermann, Martin Ackermann, Hinrich Schuelenberg, Vahid Shahrezaei

Antibiotics and Mathematics: some observations...two of which are truly novel—i.e., defined as...

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Transcript of Antibiotics and Mathematics: some observations...two of which are truly novel—i.e., defined as...