Theoretical and Experimental Studies of the Pharmaco-, Population and Evolutionary Dynamics of Single- and Multi-Drug Therapy for Bacterial Infections Open Access

Abstract

The discovery of antibiotics and their use for the treatment of bacterial infections represents one of the major advances of modern medicine. However, despite being available for decades, it is not clear that these drugs are being used in a manner that maximizes their clinical utility; treatment of some bacterial infections is beset by substantial morbidity and high likelihoods of recrudescence and mortality. The goal of this dissertation, in its broadest sense, is to provide quantitative insights to facilitate the design and evaluation of optimal treatment regimens that minimize the likelihood of mortality, the magnitude and term of morbidity and the likelihood of antibiotic resistant bacteria emerging and being transmitted during therapy. To accomplish this, we use a combination of in vitro pharmacodynamic experiments, mathematical models and computer simulations to explore the pharmaco-, population and evolutionary dynamics of bacteria under single and multi-drug treatment regimens. As measures of efficacy for different regimens, we examine the relative rates at which they clear infections and their ability to prevent the emergence and ascent of single- and multi-drug resistant bacteria. We conduct these assessments for Mycobacterium marinum, a time- and cost-effective surrogate organism for Mycobacterium tuberculosis (Chapter 2), Staphylococcus aureus and Escherichia coli (Chapter 3). We find that for drug combinations, the type of interaction between the component drugs, synergy, additivity or antagonism, can substantially affect the time to clearance of an infection. Save for scenarios in which patients are non-adherent to therapy, the evolutionary advantage of combination therapy in preventing treatment failure due to single-drug resistance, however, prevails regardless of the type of drug interaction. In Chapter 4, we extend the within-host mathematical models of antibiotic therapy developed in the previous chapters by incorporating the contribution of host innate and adaptive immune responses. We explore the properties of this model to determine the relationship between antibiotic dose, dosing frequency and term of therapy on treatment success. We find that under most conditions, high dose treatment for extended periods is more effective than more moderate regimens in increasing the rate of cure, preventing the emergence and ascent of resistance and minimizing potential immunopathology.

Table of Contents

Table of Contents

1. Chapter 1: Introduction

1.1 Bacterial infections and treatment: a brief history . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Bacterial Resistance to antibiotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Epidemiology of bacterial infections and resistance . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Design of antibiotic treatment regimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4.1 The Pharmacokinetic-Pharmacodynamic (PK-PD) approach . . . . . . . . . 10

1.4.2 Mathematical modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.5 Combination antibiotic therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.6 The questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.7 Outline of the thesis and chapter summaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2. Chapter 2: Two-Drug Antimicrobial Therapy: A Mathematical Model and Experiments with Mycobacterium marinum

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.2 Materials and Methods

2.2.1 Bacteria and Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2.2 Antibiotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2.3 Time-kill experiments for generating single-antibiotic Hill functions . . . 32

2.2.4 MIC determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2.5 Antibiotic-kill experiments for generating two-drug pharmacodynamic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2.6 Drug interaction modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2.7 Estimation of drug interaction parameter . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.2.8 Numerical Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3 Results

2.3.1 Single drug pharmacodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3.2 Two-drug pharmacodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.3.3 Asymmetric antibiotic concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.3.4 Predicted dynamics of treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.3.5 The evolution of multiple resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.3.6 Non-adherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.3.6.1 Random non-adherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.3.6.2 Thermostat non-adherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.3.6.3 Drug Holidays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3. Chapter 3: The Pharmaco-, Population and Evolutionary Dynamics of Multi-drug Therapy: Experiments with S. aureus and E. coli and Computer Simulations

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.2 Materials and Methods

3.2.1 Bacterial strains and growth/sampling media . . . . . . . . . . . . . . . . . . . . . 69

3.2.2 Antibiotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.2.3 MIC determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.2.4 Antibiotic time-kill experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.2.5 Level of persistence experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.2.6 Pharmacodynamic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.3 Results

3.3.1 Multi-drug pharmacodynamics in theory . . . . . . . . . . . . . . . . . . . . . . . . 72

3.3.2 Multi-drug pharmacodynamics in practice . . . . . . . . . . . . . . . . . . . . . . . 74

3.3.3 Persistence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.3.4 Potential clinical implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.3.4.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.3.4.2 Single and multi-drug therapy and the contribution of persistence levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.3.4.3 The contribution of a spatial refuge . . . . . . . . . . . . . . . . . . . . . 86

3.4 Discussion

3.4.1 Pharmacodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.4.2 Population and evolutionary dynamics and potential implications for treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.4.5 Caveats and limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4. Chapter 4: Pharmacokinetics and Pharmacodynamics Meet Population Dynamics Meet Immunology: Predictions and hypotheses for the design and evaluation of antibiotic treatment regiments

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.2 Methods

4.2.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.2.2 Population growth and maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.2.3 Bacterial Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

4.2.4 Pharmacodynamics and Pharmacokinetics . . . . . . . . . . . . . . . . . . . . . . 112

4.2.5 The innate and adaptive immune responses

4.2.5.1 The innate immune response . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.2.5.2 The adaptive immune response . . . . . . . . . . . . . . . . . . . . . . 114

4.2.6 Bacterial population dynamics under immune action . . . . . . . . . . . . . 114

4.2.7 Computer simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.3 Results

4.3.1 Self-limited infection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.3.2 Non-self-limited infection that would be lethal in the absence of exogenous antimicrobial intervention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5. Chapter 5: Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

About this Dissertation

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School	Laney Graduate School
Department	Biological and Biomedical Sciences
Subfield / Discipline	Population Biology, Ecology & Evolution
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Biology, Microbiology
Keyword	evolution of antibiotic resistance mathematical modeling antibiotic pharmacodynamics
Committee Chair / Thesis Advisor	Levin, Bruce, Emory University
Committee Members	Shafer, William M, Emory University Antia, Rustom, Emory University Klugman, Keith P, Emory University Shinnick, Thomas M, Emory University

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