Controlling the evolution of antibiotic resistance

208 Pages·2011·4.73 MB·English

Controlling the evolution of antibiotic resistance
Athesispresentedforthedegreeof
DoctorofPhilosophyofImperialCollege
by
Rafael Pena-Miller
DepartmentofMathematics
ImperialCollege
180Queen’sGate,LondonSW72BZ
JANUARY 21, 2011
2
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andthatanyideasorquotationsfromtheworkofotherpeople,publishedorotherwise,are
fullyacknowledgedinaccordancewiththestandardreferencingpracticesofthediscipline.
RafaelPena-Miller
DepartmentofMathematics
ImperialCollegeLondon
3
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5
Abstract
Modellingantibioticresistanceevolutionisinherentlyamultiscaleproblem: fromthephys-
ical interactions between drug molecules and their targets to the epidemiology of drug re-
sistance in clinical settings. Although predicting the evolution of resistance is a difficult
and ongoing problem, it is known that pathogens are continually adapting to our drug pre-
scription patterns. For this reason, as well as the continual downturn in the discovery of
newdrugs,thequestionofhowtobestdeployantibioticshasneverbeenmorepressing.
The purpose of this thesis is to use tools from control and systems theory to ask the fol-
lowingfundamentalquestion: Howcanwedesignrationalantibioticdeploymentstrategies
thatdonotpromotetheevolutionofantimicrobialresistance?
By re-examining epidemiological models from the literature, in the first part of this thesis
weshowthattheoptimaldrugdeploymentprotocolhasauniversalstructurenotdetermined
by biological detail. This class of epidemiological models, however, provide insight into
the underlying mechanisms that influence the spread of disease at the population level but
fail to capture the complex molecular interactions between different antibiotics and bacte-
ria, as well as to provide an experimental system to test the efficacy of different treatment
protocols. Therefore in the second part of the thesis we pose an evolutionary model of an
experimental microbial system that allows us to study drug interactions and the effect that
combinationtreatmentshaveontheevolutionofmultidrugresistance. Again,usingoptimal
control theory we design drug deployment protocols that minimise conditions promoting
theevolutionofantimicrobialresistanceinasinglehost.
Finally, in the last part of the thesis we propose an epidemiological model where patients
are considered as individual agents receiving antimicrobial treatment in a clinical setting.
This stochastic and spatially explicit model allows us the possibility to evaluate the effi-
cacy of different drug usage strategies. We conclude with a general principle: the best
performingdrugusagepoliciesutilisethehighestqualityofavailableinformation.
OnExactitudeinScience
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deliveredituptotheInclemenciesofSunandWinters. IntheDesertsoftheWest,stilltoday,there
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Acknowledgements
First of all I would like to thank my supervisor, Rob, for the countless beers he has bought
me whilst explaining me the rules of cricket. Working with Rob has been a highlight of
my life and I cannot overstate how much I have learned from his enthusiastic, creative and
innovativeapproachtowardsresearch.
ManythankstoMartinwhosefriendlyandhelpfulcharacterencouragedmanyinspirational
conversations throughout my PhD. I would also like to thank Hinrich, David and Gunther
forthedaataandforbeingsopatientwiththecrazyenglishmathematicianandhismexican
studentgatecrashingtheirlab.
In addition, I would like to thank the members of the BioMaths group at Imperial College
for all the lively discussions we’ve had, in particular to Ivana and Vahid. I also wish to
acknowledge the contributions, advice and suggestions of Alex Hall, Gabe Perron, Craig
MacLeanandSylvainGandon.
Because not everything in life is science (there is also football), I would like to thank
everybodywhosharedafootballpitchwithmeduringmystayinLondon,eitherafriendly
kickabout in Hyde Park or a competitive match under the A4... ¡Que bien que juega el
AcapulcoTropical!
IalsowanttothankallmymatesfromtheDepartmentofMathematicsthatmadeImperial
College and its grim grey corridors a lovely place to work. In particular I would like to
thank David, Ed, Flor, Kahn, Ewan, Chris and Jack. My carnales from the photonics lab
deserve a special mention too: Pavel, Mac, Ren and Matt. The mexican crowd has also
been very helpful on those long and dark London nights: Ana, Ioscani and Pablo, but
speciallyAldoandNatathatmanagedtomakemefeelathomefromthemomentIarrived
toHeathrow.
Of course, a special acknowledgement to my family, and in particular to José and JoAnn,
thathavebeenverycaringandsupportivenotonlyduringmyPhDbutthroughoutmyentire
life. Thisthesisbelongstothemasmuchasitdoestome.
But above all I would like to thank Ayari for sharing this journey with me. Every morning
I consider myself lucky to wake up next to someone that encourages and understands me
thewayshedoes.
(andbothCONACYTandSEPforfundingmyPhD)
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Table of contents
Abstract 5
Introduction 16
I Epidemiology of drug resistance 21
1 Emergenceandspreadofantibioticresistance 22
1.1 Torotate,ornottorotate? . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2 Mathematicalmodelsofantibioticuse . . . . . . . . . . . . . . . . . . . . 28
1.2.1 Bonhoeffer,LipsitchandLevin(1997) . . . . . . . . . . . . . . . . 28
1.2.2 Bergstrom,LoandLipsitch(2004) . . . . . . . . . . . . . . . . . . 32
1.2.3 Chow,WangandCastillo-Chavez(2007) . . . . . . . . . . . . . . . 34
2 Acontrol-theoreticapproach 36
2.1 Parametervaluesforsimulations: theimportanceofasymmetry . . . . . . . 37
2.2 Statementofthecontrolproblem . . . . . . . . . . . . . . . . . . . . . . . 39
2.3 Whenismixingoptimal? . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4 Optimalprotocols: bang-bangcontrols . . . . . . . . . . . . . . . . . . . . 54
2.5 Theoptimalmixingprotocol . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.6 Numericalexamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.6.1 Drugrotationoutperformsmixing . . . . . . . . . . . . . . . . . . 62
2.6.2 Adaptiverotationprotocols . . . . . . . . . . . . . . . . . . . . . . 64
2.6.3 Releasingthemust-treatconstraint . . . . . . . . . . . . . . . . . . 67
9
3 Ingeneral,whichisoptimal: mixingorcycling? 72
3.1 Optimalcyclingandmixing: twoimpracticalprotocols . . . . . . . . . . . 73
3.2 Cyclingversusmixing: atheoremconcerningtheirstatistics . . . . . . . . 75
II Optimal antibiotic deployment into a single-host 83
4 Controllingtheevolutionofresistance 84
4.1 Apossiblecontrol-theoreticformulation . . . . . . . . . . . . . . . . . . . 85
4.1.1 Optimalityofantibioticpulsing . . . . . . . . . . . . . . . . . . . . 86
4.2 Othertherapeuticallyrelevantcontrols . . . . . . . . . . . . . . . . . . . . 89
4.2.1 Optimaldurationofantibiotictherapy . . . . . . . . . . . . . . . . 90
4.2.2 Taperingdosagestrategies . . . . . . . . . . . . . . . . . . . . . . 91
4.2.3 Adaptivepulsing . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3 Colonisationresistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5 Modellingbacteriostaticantibiotics 95
5.1 TheGrowthInhibitionCoefficientγ(A) . . . . . . . . . . . . . . . . . . . 95
5.2 Evolutionarydynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 Competitiveadvantageandfitnesscostofresistance . . . . . . . . . . . . . 105
6 Designingeffectivesingle-drugdeploymentprotocols 108
6.1 Chemostatmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Evaluatingtheefficacyofdifferentstrategies . . . . . . . . . . . . . . . . . 113
7 Antibioticinteractions 120
7.1 Classifyingdruginteractions . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2 Synergisticinteractionbetweentwoantibioticswiththesametarget . . . . 122
7.3 Predictingthedose-responsesurface . . . . . . . . . . . . . . . . . . . . . 127
8 Ongoingwork: Evolutionofresistanceinmultidrugenvironments 131
8.1 Optimaldrugproportion . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
10
8.2 Modellingserialtransfers . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8.3 Designingoptimalmultidrugcombinations . . . . . . . . . . . . . . . . . . 139
9 Optimaldeploymentofsynergisticantibioticsintoachemostat 148
9.1 Incorporatingantibioticsintoacontinuousculturedevice . . . . . . . . . . 148
9.2 Completecompetitiveadvantage . . . . . . . . . . . . . . . . . . . . . . . 149
9.3 Controllingthechemostatoptimally . . . . . . . . . . . . . . . . . . . . . 151
9.4 Supportingcommensalbacteriawithrotationalprotocols . . . . . . . . . . 156
III Selecting against antibiotic resistance in clinical settings 161
10 Anindividual-basedmodelofahospitalward 162
10.1 Stewardshipprogramstocontrolresistanceinhealthcarecentres . . . . . . 162
10.2 Modellingpatientsassingle-hosts . . . . . . . . . . . . . . . . . . . . . . 165
10.3 Anon-deterministic,spatiallyexplicitmodelofahospitalward . . . . . . 168
10.4 Evaluatingtheefficacyofdifferenthospital-wideusagestrategies . . . . . . 171
10.5 Communitystructureandtheefficacyoftreatmentprotocols . . . . . . . . 176
Conclusion 182
Appendix 185
A Modelparameters 185
B EntropicRegularisation 189
C Geneticalgorithm 192
D Experimentalmethods 194
References 196