Research Collection

Doctoral Thesis

Within-host population dynamics and the evolution of drug resistance in bacterial infections

Author(s): Cadosch, Dominique Richard

Publication Date: 2016

Permanent Link: https://doi.org/10.3929/ethz-a-010795126

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ETH Library DISS. ETH NO. 23499

WITHIN-HOSTPOPULATIONDYNAMICSANDTHEEVOLUTION OFDRUGRESISTANCEINBACTERIALINFECTIONS

A thesis submitted to attain the degree of DOCTOR OF SCIENCES of ETH ZÜRICH (Dr. sc. ETH Zürich)

presented by

DOMINIQUERICHARDCADOSCH M.Sc. ETH Zürich, Switzerland

born on 30.05.1984

citizen of Vaz/Obervaz GR, Switzerland

accepted on the recommendation by Prof. Dr. Sebastian Bonhoeffer, examiner Prof. Dr. Theodore H. Cohen, co-examiner PD Dr. Roland Regoes, co-examiner

2016

To my parents, Ruth and Edgar Cadosch, for their sedulous support and guidance.

“I have a friend who’s an artist and has sometimes taken a view which I don’t agree with very well. He’ll hold up a flower and say "look how beautiful it is," and I’ll agree. Then he says "I as an artist can see how beautiful this is but you as a scientist take this all apart and it becomes a dull thing," and I think that he’s kind of nutty. First of all, the beauty that he sees is available to other people and to me too, I believe. Although I may not be quite as refined aesthetically as he is ... I can appreciate the beauty of a flower. At the same time, I see much more about the flower than he sees. I could imagine the cells in there, the complicated actions inside, which also have a beauty. I mean it’s not just beauty at this dimension, at one centimeter; there’s also beauty at smaller dimensions, the inner structure, also the processes. The fact that the colors in the flower evolved in order to attract insects to pollinate it is interesting; it means that insects can see the color. It adds a question: does this aesthetic sense also exist in the lower forms? Why is it aesthetic? All kinds of interesting questions which the science knowledge only adds to the excitement, the mystery and the awe of a flower. It only adds. I don’t understand how it subtracts.”

Richard Feynman

v

CONTENTS summary1 zusammenfassung3

1 general introduction5 2 the role of adherence and retreatment in de novo emer- gence of mdr-tb 11 3 alternative treatment strategies for tuberculosis 39 4 considering antibiotic stress-induced mutagenesis 61 5 general discussion 77 acknowledgements 103 curriculum vitae 105

vii

SUMMARY

This thesis investigates the influence of population dynamics of bacterial infections and their treatment on the probability of the emergence of drug resistance. In partic- ular the study of the effects of suboptimal patient compliance, various treatment reg- imens and the possibility of antibiotic stress-induced mutagenesis call for a deeper understanding of the mechanisms at play. The work presented in this study uses mathematical models that incorporate pharmacokinetics and -dynamics, as well as the effect of bacterial traits to make predictions about the evolution of drug resistance. All dynamics are being simulated at the within-host level. Chapter 1 is a general introduction of the central themes of this thesis. It gives a short overview over the advent of the study of population dynamics as a field of research. The global significance of tuberculosis and the problems that arise due to the frequent occurrence of drug resistance are being explained. I also address the issue of suboptimal treatment adherence and rationalize the value of mathematical modeling to tackle the questions in the following chapters. In Chapter 2, we investigate how adherence to the treatment regimen and the use of a standard retreatment regimen are involved in the emergence of multidrug- resistant tuberculosis (MDR-TB). MDR-TB is characterized by its resistance against isoniazid and rifampicin, two important first-line drugs. To answer the question whether there is a considerable probability for the de novo emergence of MDR-TB we simulate patients with various degrees of adherence to a standard treatment regimen containing a combination of four drugs. Patients who do not achieve complete clear- ance of the infection undergo a prolonged retreatment regimen with an additional fifth drug. Chapter 3 explores proposed alternative strategies for the treatment of pulmonary tuberculosis. We extend the previously established model and introduce more de- tailed absorption pharmacokinetics. This extension of the model enables us to inves- tigate the potential benefit and effects of extended-release formulations of rifampicin. Extended-release formulations show a much lower absorption and thus exhibit a lower but longer time-concentration profile. Such formulations are compared in daily or intermittent treatment regimens with conventional rifampicin formulations and their influence on the probability of treatment failure and the emergence of drug resistance are recorded. Furthermore, we also tested the advantage and risks involved with increased rifampicin doses. Chapter 4 then deals with the concept of antibiotic stress-induced mutagenesis (ASIM). The concept of stress-induced mutagenesis describes the increase of the bacterial mutation rate in response to a stress, such as the exposure to certain an- tibiotics. We propose a model to simulate the increase of the mutation rate in a drug concentration-dependent manner. With this ASIM model we then investigate how much a model with a fixed mutation rate would underestimate the risk for the emergence of a drug resistance mutation. Lastly, we study whether the regimen of administering a stress-inducing drug and a non-stress-inducing drug has an influ- ence on the emergence of resistance if we consider ASIM. 1 2 summary

Finally, in Chapter 5 I put the results and conclusions from the preceding chapters in a bigger perspective. Furthermore, I present some future directions that could be explored with further research. ZUSAMMENFASSUNG

Diese Dissertation untersucht den Einfluss von Populationsdynamik in bakteriel- len Infektionen und deren Behandlung auf die Wahrscheinlichkeit des Auftretens von Medikamentenresistenz. Im Besonderen die Analyse der Effekte suboptimaler Patienten-Adhärenz, die Anwendung unterschiedlicher Behandlungsstrategien und die Möglichkeit stress-bedingter Mutagenese durch Antibiotika verlangen nach ei- nem tiefgreifenderem Verständnis für die zugrundeliegenden Wirkmechanismen. Die Arbeit, welche in dieser Dissertation vorgestellt wird nutzt mathematische Model- le, welche Pharmakokinetik und Pharmakodynamik, sowie Effekte von bakteriellen Merkmalen beinhalten, um Prognosen in Bezug auf die Evolution von Medikamen- tenresistenz aufstellen zu können. Alle Dynamiken werden dabei jeweils auf der Ebene eines einzelnen Patienten simuliert. Kapitel 1 ist eine allgemeine Einführung in die zentralen Themen dieser Disserta- tion. Das Kapitel gibt einen kurzen Überblick über die Ursprünge der Erforschung von Populationsdynamiken. Die globale Bedeutung von Tuberkulose sowie die Pro- bleme, welche durch das häufige Auftreten von Medikamentenresistenz entstehen, werden erklärt. Ich spreche auch die Thematik von suboptimaler Adhärenz an sowie den Wert von mathematischer Modellierung, um die Fragestellungen der folgenden Kapitel anzupacken. In Kapitel 2 untersuchen wir, wie Adhärenz während der Behandlung und die An- wendung einer standardisierten Nachbehandlung involviert sind in das Auftreten von multiresistenter Tuberkulose (engl. multi-drugresistant tuberculosis; MDR-TB). MDR-TB ist gekennzeichnet durch die Resistenz gegenüber Isoniazid und Rifampi- cin, zwei wichtigen standardmässig eingesetzten Antibiotika. Um die Frage zu beant- worten, ob es eine nennenswerte Wahrscheinlichkeit gibt für das Auftreten de novo MDR-TB, simulieren wir Patienten mit unterschiedlichen Adhärenzen gegenüber ei- ner Behandlungsstrategie mit einer Kombination von vier Medikamenten. Patienten, in denen die Infektion nicht vollständig sterilisiert wurde, werden einer längeren Nachbehandlung mit einem zusätzlichen fünften Medikament unterzogen. Kapitel 3 erforscht alternative Behandlungsvorschläge für Lungentuberkulose. Wir erweitern das zuvor etablierte Modell und führen eine detailiertere Absorptions- Pharmakokinetik ein. Diese Erweiterung des Modells ermöglicht es uns, die poten- tiellen Vorteile und Auswirkungen eines Retard-Präparats von Rifampicin zu un- tersuchen. Retardarzneiformen zeichnen sich durch eine verlangsamte Absorption aus und weisen deshalb eine niedrigeres aber gestrecktes Konzentrationsprofil. Sol- che Arzeneiformen werden in täglichen und intermittierenden Behandlungsregimes verglichen mit konventionellen Rifampicin-Präparaten und die Wahrscheinlichkeiten für ein Behandlungsversagen sowie das Auftreten von Medikamentenresistenz wer- den ermittelt. Des Weiteren testen wir ebenfalls die Vorteile und Risiken die mit erhöhten Rifampicindosen verbunden sind. Kapitel 4 behandelt das Konzept von stressbedingter Mutagenese durch Antibio- tika (engl. antibiotic stress-induced mutagenesis; ASIM). Das Konzept von stressbe- dingter Mutagenese beschreibt den Anstieg der bakteriellen Mutationsrate als Reakti- 3 4 zusammenfassung

on auf einen äusseren Stressreiz, wie die Exposition gegenüber gewissen Antibiotika. Wir stellen ein Modell vor, um den Anstieg der Mutationsrate in Abhängigkeit zur Medikamentenkonzentration zu simulieren. Mit diesem ASIM-Modell untersuchen wir dann, wie stark ein Modell mit einer festen Mutationsrate das Risiko für das Auftreten von einer Mutation, die zu Medikamentenresistenz führt, unterschätzen würde. Schliesslich studieren wir ob ein Behandlungsregime, in dem ein stressauslö- sendes mit einem nicht-stressauslösenden Medikament kombiniert wird, einen Ein- fluss auf die Auftrittswahrscheinlichkeit von Medikamentenresistenz hat, wenn wir ASIM in Betracht ziehen. Zuletzt stelle ich in Kapitel 5 die Resultate und Schlussfolgerungen der voran- gegangenen Kapitel in einen grösseren Kontext. Des Weiteren stelle ich mögliche Richtungen vor, welche zukünftige Studien erforschen könnten. 1 GENERALINTRODUCTION

The advent of the scientific discussion of population dynamics is probably An Es- say on the Principle of Population [1] by Thomas Robert Malthus. In this book Malthus introduces the Malthusian growth model, which describes the exponential growth of a population over time. This growth is governed by the population growth rate r, sometimes called Malthusian parameter. While this model may seem rather simple it is still a basic component for most population dynamics models today. It is appli- cable to all scales of life - from large animals and plants down to tumor cells and bacteria. Since Thomas Robert Malthus the modeling of populations evolved further to reflect more complex relationships. The influence of density dependence on population growth can be achieved by introducing a carrying capacity parameter that turns the exponential growth model into a logistic function [2]. Further one could consider the mutual influence of two distinct populations that are either competing over the same resource or that are in a predator-prey relationship [3]. The complexity may increase even more if we consider migration and mutation as well as temporal and spatial dependencies of parameters. Particularly in the case of infectious diseases the study of population dynamics can be of great value. Historically this has been done predominantly on an epidemi- ological scale but scientific progress provided a more detailed picture of intra-host dynamics, which enables the development of models dealing with viral and bacterial populations. Among pathogens viruses represent a special case because they depend on the replication machinery of other living cells to proliferate. Bacteria on the other hand usually reproduce through binary fission. The study of population dynamics is of particular interest when we try to under- stand the underlying mechanisms of the emergence of drug resistance in bacterial infections. Here we can examine on an epidemiological scale the population dy- namics of patients who are at risk of being infected, actually infected or who have recovered from an infection [4] or we can study the population dynamics of bacte- ria (or viruses) inside a patient. In the first case we are interested in the relative spread of susceptible and resistant pathogens in a host population and in the later case we focus on the spread of individual bacteria and the evolution of drug resistant subgroups of the overall bacterial population within a single host. This thesis concentrates on the study of the within-host population dynamics of a bacterial infection with a particular interest in the corresponding mechanisms that may lead to drug resistance. These studies are performed with the help of stochas- tic computer simulations. Two chapters of this thesis deal with the influence of treatment and retreatment strategies on the emergence of drug resistance in pul- monary tuberculosis infections. The last chapter is a more conceptual work that investigates the impact of antibiotic stress-induced mutagenesis in any bacterial in- fection in which this may occur.

5 6 general introduction

1.1 tuberculosis

Two chapters of this thesis focus on the population dynamics and the treatment of pulmonary tuberculosis. For years the research funding for tuberculosis has only been a fraction of what is spent on HIV/AIDS [5]. Concerns about tuberculosis may be often less acute due to a reduced awareness among the population in de- veloped countries where incidence rates of TB are mostly rather low [6]. However, there are still about 2 billion people worldwide who are latently infected with TB [7], 9.6 million people have fallen ill and 1.5 million people died in 2014 due to a TB infection [6]. When in the middle of the 20th century effective antibiotics like streptomycin, isoniazid and rifampicin were discovered tuberculosis was thought to be under control [8]. Today we have to acknowledge that TB remains a global health problem. Even though the global incidence rates of TB started to decline the fre- quency of multidrug-resistant TB (MDR-TB) cases did not decline despite increased efforts for specialized MDR-TB treatments [6]. MDR-TB is characterized by its resis- tance against at least isoniazid and rifampicin, two important first-line drugs [6]. In some countries MDR-TB and extensively drug-resistant TB (XDR-TB) have become a growing epidemic [9; 10; 11]. Besides resistance against isoniazid and rifampicin XDR-TB is also resistant against at least one fluoroquinolone and either kanamycin, amikacin or capreomycin [12]. The standard short-course therapy for TB lasts six months. During the intensive phase of the first two months isoniazid, rifampicin, pyrazinamide and ethambutol are administered as a combination therapy. In the following two months of the con- tinuation phase only isoniazid and rifampicin are given [13]. The reasoning behind the application of a combination therapy is based on concerns regarding the loss of efficacy due to the pre-existence or de novo emergence of mono-resistant subpopula- tions [13]. During monotherapy it could be possible for bacteria that already carry a corresponding resistance mutation to gain a selective advantage, eventually replace the susceptible bacteria and render the therapy ineffective. In combination therapy there should always be another drug against which mono-resistant bacteria are still susceptible and are subsequently eradicated.

1.2 adherence

Non-adherence to treatment has always been considered a major risk factor for the emergence of de novo drug resistance [14; 15]. One of the main goals of the directly observed treatment, short course strategy (DOTS) by the WHO is to ensure a suffi- ciently high level of adherence to ensure treatment success [16]. The actual monitor- ing of DOTS in resource-limited settings is often provided by community members [17]. However, the actual degree of adherence by patients under such community- base programs has not been assessed [17] and these programs are often beyond direct control of health care providers. It is generally often difficult to obtain accurate es- timates of patient adherence. Patients may not truthfully answer in a survey and more sophisticated measures like a Medication Event Monitoring System (MEMS) [17] may only be conducted on a small scale. It is also imaginable that it not nec- essarily patient compliance that jeopardizes treatment success, discontinuous drug 1.3 methodology 7 supply or other factors that may occasionally prevent physical access to drugs (e.g. unreliable means of transport, armed conflicts etc.) and influence overall adherence negatively. Problems that may arise due to suboptimal patient adherence can be relatively conveniently examined with the help of mathematical models. Mathematical models allow us to assess the implications of reduced adherence. We are able to gather estimates about what levels of adherence are still reasonably safe and when do we face serious consequences. When we assume suboptimal adherence and simulate the corresponding population dynamics we get predictions about possible negative treatment outcomes like treatment failure and the emergence of resistance and we also gather estimates about the strength of association between different adherence levels and those outcomes.

1.3 methodology

In all chapters of this thesis we are applying mathematical models that are being simulated in silico. Mathematical models in evolutionary biology serve generally two purposes that are also relevant for the conclusions of this thesis. Firstly, mathematical models can be used to do "proof-of-concept" tests [18]. Verbal or theoretical concepts can be translated into a mathematical model and it can be assessed whether the hypothesized results of the theory coincide with the predictions of the model. This is particularly useful for concepts that are difficult to prove in vivo or in vitro because of experimental constraints or because of ethical reasons. The second purpose of mathematical models becomes evident when their validity has been confirmed by real-life observations. Then they can be used to explore new directions and make predictions about the natural world. The two purposes of com- putational modeling therefore engage in an ideally mutually stimulating interaction with empirical sciences: The theory about empirical observations can be tested in computational models, which then again may extend the currently existing theory and inspire new empirical investigations. A crucial point of contact between empiricism and modeling are assumptions. A hypothesis that is verbalized to explain an empirically observed phenomenon con- tains specific assumptions. These assumptions also have to be the foundation of a mathematical model. If the model is then not able to corroborate the hypothesis with- out violating the basic assumptions the hypothesis may have to be reconsidered or reformulated. The reformulation of the hypothesis may be supported by the model because the model allows to test whether changing one or a few assumptions might be sufficient to explain the observed phenomenon. In this thesis we use computational modeling for both scopes. On one hand, the mathematical model with which we simulate the course of infection and treatment of pulmonary tuberculosis is able to replicate patient outcomes that other studies observed previously. It is further able to confirm hypotheses about the progression to higher levels of drug resistance and the risks and chances involved with suboptimal and alternative treatment strategies. On the other hand, our mathematical model allows us to make qualitative predictions about the potential benefits of retreatment 8 general introduction

regimens and alternative treatment strategies. These results hopefully fuel further research in these directions.

1.4 overview of chapters

This thesis contains three studies that I conducted during my doctoral studies (Chap- ters 2–4). Chapters 2 and 3 explore how treatment of a pulmonary tuberculosis infection affects the probabilities for the emergence of drug resistance. Chapter 4 is a more conceptual work and examines how increased mutation rates due to stress elicited by the exposure to antibiotics changes the risk for the emergence of drug resistance. The thesis then concludes with a general Discussion (Chapter 5). In Chapter 2 we present a model framework that simulates the intra-host pathogen- esis during an acute pulmonary tuberculosis (TB) infection and its treatment. The population dynamics of M. tuberculosis is modeled in three distinct compartments within the lung: macrophages, granulomas and open cavities [19]. The treatment that we apply and the retreatment, in case the first treatment is not able to clear the infection, correspond to standard regimens recommended by the WHO [20; 21]. The stochastic model simulates patient that differ in several pharmacodynamic and pharmacokinetic parameters and they adhere to the treatment regimen to various degrees. Eventually after treatment and retreatment, patients are diagnosed as either successfully treated, if they do not harbor any M. tuberculosis bacteria anymore, failed patients, if there are any bacteria left, failed patients with multi-drug resistant TB, if 10% or more of the remaining bacteria are at least resistant against isoniazid and rifampicin, or failed patients with fully resistant TB, if 10% or more of the remaining bacterial population is resistant against all drugs that have been applied. Chapter 3 considers alternative treatment strategies for pulmonary tuberculosis. To study these strategies we extend the model framework that we used in Chapter 2 with a more detailed pharmacokinetic model. Besides the elimination of the drug in the patient due to excretion the pharmacokinetics model now also simulates the absorption of the drugs after administration. This enables us to test the efficacy of drug formulations that have lower absorption rate constants. Low absorption rate constants are a characteristic feature of extended-release formulations [22]. In pa- tient simulations we examine how combinations of intermittent and daily treatment regimens with and without the use of extended-release formulations of rifampicin influence the probabilities for a successful treatment outcome and for the emergence of resistance. Lastly, we also test what the effect of a net increase of the rifampicin dosage yields for the patient [23]. In Chapter 4 we then explore the influence of antibiotic stress-induced mutagene- sis (ASIM) on the probability for the emergence of resistance. In the model that we present the mutation rate of bacteria increases in a concentration-dependent manner when the bacteria are exposed to a drug that triggers a specific stress response [24]. We compare the ASIM model with a model that does not consider a change of the mutation rate and show the relative differences regarding the probabilities for the occurrence of resistance mutations. We also show the relative dependence of the observed effects on the underlying parameters. Eventually, we test whether the in- 1.4 overviewofchapters 9 clusion of ASIM causes a difference in the effectiveness of combination therapy or a cycling regimen for a single patient. Chapter 5 is a general discussion of this thesis. There I explore possible future directions in which research could expand. I also put the results and observations that have been made in this thesis in a bigger perspective.

2 THEROLEOFADHERENCEANDRETREATMENTINDENOVO EMERGENCEOFMDR-TB

Published as: D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (2016). The Role of Ad- herence and Retreatment in De Novo Emergence of MDR-TB. PLOS Computational Biology 12(3):e1004749. abstract

Treatment failure after therapy of pulmonary tuberculosis (TB) infections is an impor- tant challenge, especially when it coincides with de novo emergence of multi-drug- resistant TB (MDR-TB).We seek to explore possible causes why MDR-TB has been found to occur much more often in patients with a history of previous treatment.We develop a mathematical model of the replication of Mycobacterium tuberculosis within a patient reflecting the compartments of macrophages, granulomas, and open cavi- ties as well as parameterizing the effects of drugs on the pathogen dynamics in these compartments. We use this model to study the influence of patient adherence to ther- apy and of common retreatment regimens on treatment outcome. As expected, the simulations show that treatment success increases with increasing adherence. How- ever, treatment occasionally fails even under perfect adherence due to interpatient variability in pharmacological parameters. The risk of generating MDR de novo is highest between 40% and 80% adherence. Importantly, our simulations highlight the double-edged effect of retreatment: On the one hand, the recommended retreatment regimen increases the overall success rate compared to re-treating with the initial regimen. On the other hand, it increases the probability to accumulate more resis- tant genotypes. We conclude that treatment adherence is a key factor for a positive outcome, and that screening for resistant strains is advisable after treatment failure or relapse.

11 12 the role of adherence and retreatment in de novo emergence of mdr-tb

2.1 author summary

Our ability to treat and control acute pulmonary tuberculosis (TB) is threatened by the increasing occurrence of multi-drug-resistant tuberculosis (MDR-TB) in many countries around the globe. It is not clear whether MDR-TB occurs predominantly due to transmission, or whether there is a substantial contribution due to de novo emergence during treatment. Understanding the underlying mechanisms that are involved in the emergence of MDR-TB is important to develop countermeasures. We use a computational model of within-host TB infection and its subsequent treatment to qualitatively assess the risks of treatment failure and resistance emergence under various standard therapy regimes. The results show that especially patients with a history of previous TB treatment are at risk of developing MDR-TB. We conclude that de novo emergence of MDR-TB is a considerable risk during treatment. Based on our findings, we strongly recommend widespread implementation of drug sensitivity tests prior to the initiation of TB treatment.

2.2 introduction

Tuberculosis (TB) is a key challenge for global health [25; 26]. At present about one third of the global population is latently infected [27] and every year about 1.7 million people die of tuberculosis. A large number of patients live in resource-limited settings with restricted access to health-care. It is imperative that standard treatment measures are assessed for their efficacy and reliability. Understanding the driving forces behind therapy failures is challenging. This is to a large extent the case because of the complex life cycle and population structure of TB: The typical sequence of events leading to acute pulmonary tuberculosis occurs as follows [25; 28; 19; 29; 30]. Upon inhalation, TB bacilli reach the pulmonary alveoli of the lung. There they are assimilated by phagocytic macrophages. In most cases the bacteria are being killed continuously by phagocytosis while the cell-mediated immunity develops. More rarely, they may persist in an inactive state, which is considered a latent infection. Infected macrophages may aggregate and form gran- ulomas by recruiting more macrophages and other cell types. Inside granulomas, increased necrosis of macrophages can lead to the formation of a caseous core. In la- tently infected hosts, an equilibrium establishes where the immune system prevents further growth but the bacteria persist in a dormant state [31; 32]. However, espe- cially in patients with a compromised immune system, the bacteria may continue or resume growth [28; 29]. In this case, the bacterial population steadily increases until the granuloma bursts into the bronchus forming an open cavity. Mycobacterium tuberculosis is an aerobic organism and depends on the availability of oxygen to pro- mote its growth. Because the oxygen levels inside macrophages and granulomas are low, the growth rate is reduced [29; 32; 33; 34; 35]. In open cavities, oxygen supply is not limiting anymore and the population size increases rapidly. The extracellular bacteria in the cavities may also spread to other locations in the lung where they are again combated by the dendritic cells of the immune system. Some bacteria can be expelled with sputum and be transmitted to other individuals or they may enter a blood vessel and cause lesions in other organs. 2.2 introduction 13

The standard treatment is a six-month short-course regimen [25; 36; 37; 38; 13], consisting of two months of combination therapy with isoniazid, rifampicin, pyrazi- namide and ethambutol followed by a continuation phase of four months with iso- niazid and rifampicin only [39]. According to tuberculosis treatment guidelines all drugs are taken daily during the first two months. During the following four months isoniazid and rifampicin are administered three times a week with a 3-fold increased isoniazid dose [37]. For patients with previous TB treatments the WHO recommends a 8-month retreatment regimen containing additionally streptomycin [13]. In recent years, the problem of drug resistance has increased in severity due to the emergence and spread of multi-drug-resistant tuberculosis (MDR-TB) [40; 41; 42], where MDR-TB is defined as infection by M. tuberculosis strains conferring resistance to at least isoniazid and rifampicin. Resistant TB is assumed to emerge at least in part due to inappropriate treatment or suboptimal adherence to the treatment regimen [43]. Poor compliance has been associated with treatment failure and the emergence of resistance in previous studies [44; 45; 46; 47; 48]. Multi-drug-resistance usually develops in a step-wise manner. These steps are thought to include func- tional monotherapy; either due to different drug efficacies among certain bacterial populations or due to different pharmacokinetics [49; 50]. Prevalence data of MDR- TB in Europe (see Fig 2.1) show that patients who have previously received treatment are on average six times more likely to suffer from MDR-TB than patients who are newly diagnosed. There are several possible explanations for this observation. Indi- viduals who are infected with MDR-TB are more likely to have a treatment failure or a later relapse [51; 20; 52; 53], especially if they are not properly diagnosed. These pa- tients could then come under more accurate scrutiny and eventually be reported as MDR-TB patients with previous treatment history. Another more direct possibility is that a considerable fraction of patients who have contracted susceptible TB develop de novo MDR-TB during the first therapy [54]. The goal of this study is to assess the factors that determine the de novo acquisition of drug resistance and to get a better insight in the underlying dynamics. Specif- ically, we want to study the contribution of imperfect compliance and retreatment regimens. In some areas, second-line drugs are not easily accessible. Moreover, drug-susceptibility tests may not be performed due to the lack of required infrastruc- ture or questionable reliability of patient treatment history [55]. Hence, we assess the impact of a retreatment that is identical to the first therapy as well as a retreatment that follows the WHO recommendation [13]. To achieve this goal we develop a com- putational model of a within-host TB infection and its consecutive treatment with currently recommended first-line regimens. The model framework encompasses the population dynamics of various M. tuberculosis genotypes with different resistance patterns in three pulmonary compartments as well as the pharmacodynamics and the pharmacokinetics of the drugs that are used for treatment. The aim is to provide qualitative insights into the infection dynamics of tuberculosis. The parameterization is based on the most recent concepts and individual experimental results found in the literature. Given the current lack of a good animal or in vitro model for TB, a computational model,may help to bridge the gaps arising from the inaccessibility of TB in experimental model systems and allow the hypothetical assessment of treat- ment scenarios, which would be otherwise ethically inadmissible in patient trials. 14 the role of adherence and retreatment in de novo emergence of mdr-tb

Figure 2.1: The prevalence of multidrug-resistant tuberculosis (MDR-TB) in most Euro- pean countries is higher among previously treated patients than among newly diagnosed patients. The data on the percentage of newly diagnosed and previ- ously treated patients with MDR-TB where taken from reference [56] for 2009 and from reference [57] for 2010. Countries with incomplete data were omitted.

In particular, problems resulting from imperfect therapy adherence can be usefully addressed with a computational model.

2.3 methods

In the following section we present the basic framework of the computational model, the parameterization and key aspects of our simulations. In essence, our model consists of coupled logistic-growth models that are connected such that they capture the basic population structure (compartments) of TB (see Fig 2.2). The action of TB- drugs is included in this model via realistic pharmacokinetics / pharmacodynamics functions. Resistance to these drugs is modelled by distinguishing between up to 32 genotypes (all combinations of 5 mutations) with varying resistance patterns. Since mutations are generated at low frequencies and numbers (due to the low bacterial mutation rate), chance events are essential in the dynamics of this system and hence we consider a stochastic version of the model. In the following we provide a detailed 2.3 methods 15 description of the model; the model equations and further details can be found in S1 Text.

2.3.1 Model

Our model describes pulmonary tuberculosis and assesses the emergence of resis- tance during multi-drug therapy. A graphical illustration of the model is provided in Fig 2.2. The model reflects the compartmentalization of the bacteria into three distinct subpopulations as described by Grosset [19] intracellular bacteria within macrophages (M), bacteria within the caseating tissue of granulomas (G) and ex- tracellular bacteria which mostly reside in open cavities (OC). The compartments differ in their maximum population sizes as well as the bacterial replication rates that they allow. The base replication rate r is modified by a factor γ, which reflects the compartment specific conditions that influence the replication rate. Bacteria have a natural density-dependent death rate in each compartment. The constant replica- tion rate and the density-dependent death rate constitute a logistic growth model that was assumed to describe the basic population dynamics. Bacteria also migrate unidirectionally at a rate m from one compartment to another. Offspring bacteria have a certain chance to acquire or lose a mutation that confers resistance to one out of up to five drugs that may be administered during treatment. Every resistance mutation confers a fitness cost which affects the reproductive success of its carrier. This means that the bacterial population inside a compartment comprises of up to 32 genotypes, which differ in their drug resistance pattern as well as their relative fitness. To outline the population dynamics within a single compartment we describe them first in the form of a deterministic differential equation. The dynamical equation is given by

dNc,g Nc Nc0 = r · γc · ωg · Nc,g − mc · · Nc,g + mc0 · · Nc0,g − (dc + κc,g) · Nc,g (2.1) dt Kc Kc0

Here Nc,g is the number of bacteria of a specific genotype g in a specific compart- ment c. The parameter r is the base replication rate of M. tuberculosis and γc is a factor, which modifies the replication rate according to the different metabolic activities in each compartment. ωg represents the relative fitness of the specific genotype. mc is the rate with which bacteria migrate to the subsequent compartment. The migration rate is multiplied by the ratio between the total population size Nc and the carrying capacity Kc. This reflects the increased migratory activity that takes place during an acute infection. Nc0 , Kc0 and mc0 correspond to the overall bacterial population including all genotypes of the supplying compartment, its carrying capacity and its migration rate, respectively. The last term reflects the density-dependent death rate dc and the drug induced genotype specific killing rate κc,g. The bactericidal effects of the drugs contribute additively to the killing rate κc,g (see 2.A for further details). The dynamics of the bacterial population in the model are actually simulated as stochastic processes. For this reason we translated the underlying deterministic dif- ferential equations into a corresponding stochastic framework by applying Gillespie's τ -leap method [58]. 16 the role of adherence and retreatment in de novo emergence of mdr-tb

Figure 2.2: Diagram of model for the pathogenesis during acute pulmonary tuberculosis infection. We consider three different physiological compartments for the loca- tion of TB bacteria: host macrophages (M), granulomas (G) and open cavities (OC). The base replication rate r of the bacteria is modified by a compartment spe- cific parameter γ. The bacteria die with a density-dependent rate d and migrate from one compartment to another at a rate m. 2.3 methods 17

2.3.2 Parameterization

The parameter estimates used in this model are whenever possible drawn or derived from experimental results in the literature. To account for the diversity of infection and treatment courses in different patients we allow some parameters to vary within a certain range. Parameters are summarized in Table 2.1. The basic growth dynamics rest upon the replication rate and the carrying capac- ity of the compartments. Based on recent studies [59; 60; 61] we assume a maximum bacterial load between 105 and 107 bacteria each for the macrophage and the granu- loma compartment and 108 to 1010 bacteria for the extracellular compartment. Under optimal conditions M. tuberculosis has a replication time of 20 h, hence we set the maximum replication rate in the model to 0.8 d−1 [19]. Every new bacteria cell has at birth the chance to acquire or lose one or multi- ple resistance mutations and therefore get a genotype, which is different from the mother cell. The frequency of specific resistance mutations and therefore the mu- tation rate for the main first-line drugs have been first estimated by David in 1970 [62] to be around 10−7–10−10. However, more recent observations suggest consid- erably higher frequencies in the order of 10−6 to 10−8 [29; 63]. A possible reason for this discrepancy between these estimates are varying mutation rates in in vitro experiments compared to the conditions encountered in vivo due to stress-induced mutagenesis mechanisms or variations among strains [64; 65; 66]. Furthermore, we assume that mutations only occur during proliferation while mutations during the stationary phase could serve as an additional source of resistance mutations [67]. Therefore, we choose to allow for patients with the more recent higher mutation rates because this will yield more conservative estimates (see 2.2). Our model incor- porates backwards mutations from the resistant to the sensitive phenotype, which also restore the reproductive fitness. However, we consider a reversion to be ten times less likely than the original forward mutation because the occurrence of any additional mutation within a gene to be an exact reversion is more infrequent. When assessing the prevalence of certain genotypes, fitness costs that come with resistance mutations have to be considered. The cost of resistance against anti- tuberculosis drugs appears generally to be low [88; 84; 85; 86]. Drug-resistant mu- tants isolated in patients have even been found to be on par with susceptible wild type strains regarding their infectivity and replicative potential. Since cost-free resis- tance mutations are rather rare, the high fitness of resistant strains that have been found in clinical isolates [48,49] is assumed to arise due to the acquisition of sec- ondary site mutations which minimize the fitness costs (so-called compensatory mu- tations) [85]. However, there is evidence that at least initially newly acquired drug resistance confers some physiological cost [89]. Because our model simulates the de novo acquisition of resistance mutations and because the time frame of a single patient treatment is rather short we assign a small fitness cost to every possible mu- tation and neglect the counterbalance of fitness costs by compensatory mutations. The effect of administered drugs depends on the pharmacokinetics and pharma- codynamics of these drugs (see Table 1). Both influence the killing rate κc,g at any given time point during treatment. While pharmacokinetic parameters describe the course of the drug concentration in the target tissue, pharmacodynamic parame- 18 the role of adherence and retreatment in de novo emergence of mdr-tb

Table 2.1: Compartment characteristics Macrophages Granulomas Open cavities Compartmental characteristics 5 7 5 7 8 10 Carrying capacity (Kc) 10 –10 10 –10 10 –10

Growth modifier (γc) 0.5 0.1 1 −1 a a a Migration rate (mc,m’,d ) 0–0.1 0–0.1 0–0.1 Relative drug efficacies Isoniazid 0–1 [68; 69; 70] 0.01 [71] 1 Rifampicin 0.01 [69] 0.01 [29] 1 Pyrazinamide 0 [72; 73] 1 [29] 0 [74] Ethambutol 1 [69] 0–1 [29; 75; 76] 1 Streptomycin 0.1 [77; 68] 0.01 [29] 1 The provided references support the order of magnitude of the parameters, not the exact value. a estimation

ters characterize the effect the drugs have at a given concentration. The minimal inhibitory concentration (MIC) describes the minimal drug concentration at which bacterial growth is reduced by at least 99%. Additionally, the EC50 describes at which drug concentration the half-maximal effect (commonly, bacterial killing) is observed, while the Emax indicates the maximal effect of the drug. These pharmacodynamic parameters are obtained by fitting the drug action model to killing curves found in the literature [90; 82] (see S1 Text). The specific efficacy of most drugs in the differ- ent compartments is typically not quantified. There are several studies that tried to assess the bactericidal activity inside macro- phages [77; 68; 72; 69]. Unfortunately, these estimates are highly variable and sometimes even contradictory [91; 72]. In addition to these experimental difficulties, it is possible that the pharmacodynamics of anti-tuberculosis drugs are again different in the human body [92; 93; 94; 95; 96]. To reflect this uncertainty we assign compartment efficacies from a range of values which cor- responds to the most recent estimates [77; 68; 72; 69; 75; 73; 74; 70; 71; 76].

2.3.3 Simulations

To investigate the role of treatment adherence on patient outcome, we followed dis- ease progression starting with the infection of macrophages until all compartments approximately reached their maximum bacterial load. For each parameter set, we simulate the outcome of 10,000 patients who vary both in their pharmacokinetic and -dynamic characteristics as well as compartmental attributes. Parameters are gener- ally picked from a normal distribution. If only a range is known the parameters are chosen from a uniform distribution. To measure the actual treatment efficacy we let every patient develop an acute tuberculosis infection during 360 days. This allows 2.3 methods 19 c ], 62 [ 7 − ] 10 81 – ] ] 8 ; ] − 85 77 36 ; ; [ 81 10 ; · d d 84 82 [ [ 45 80 – [ c 95 1 5 32 31 . . . . . 2 0 3 35 0 0 1 1 ] 83 [ ] ] 87 13 ] ] ] . ; 62 [ 1 d d 79 79 68 – 36 7 c [ [ [ − 96 1 6 0 0 92 20 ...... 0 0 0 2 5 1 0 10 ] ] 81 [ 83 ] [ 78 35 [ . 8 76 . 4 − 8 . ] 24 ] 1 ± 10 – d – 84 74 9 [ ± d [ 21 60 . . − 1 94 6 . . . 0 40 28 1 29 13 10 9 ] 63 ; 62 [ 8 ] − 81 [ 10 : Model parameters – 2 ] 96 . 10 . 2 − 3 86 ] ] ; ] 10 ± 83 78 d · d [ [ 85 68 [ [ Table 61 . 1 4 51 25 82 34 46 ...... 0 0 0 13 1 2 0 2 ] ] ] ] 81 63 81 ] [ [ ; ] 78 ] 78 b b [ [ 62 83 [ 83 [ [ 94 59 71 30 7 . . . . 0 0 − 0 0 69 88 . . 5 5 10 ± ± ± ± – – – 8 ] 26 68 37 54 80 74 − ...... 4 3 1 1 2 1 ] 68 10 [ d : : : : : : · d 84 a a a a a a [ 1 025 033 56 86 . . . . . 0 0 0 IsoniazodFA FA SA Rifampicin Pyrazinamide2 Ethambutol Streptomycin SA 1 SA FA e ) ) ρ 1 ( ) − ) ) h Serum mg/L mg/L mg/L ( /C 50 FA = fast acetylators, SA = fast acetylators see text If isoniazid is administered three times a week instead of daily the dosage is three times higher [ ELF = epithelial lining fluid estimation ELF max Resistance cost c d e Half-life ( Dose ( MIC ( Resistance frequency Some of the provided referencesa support the order of magnitudeb of the parameters, not the exact value. C EC E 20 the role of adherence and retreatment in de novo emergence of mdr-tb

for the emergence of mutants prior to treatment initiation and provides enough time for the establishment of an equilibrium in the bacterial population composition. Af- ter this period we start the standard short course therapy regimen with four drugs being taken daily for two months followed by four months in which just isoniazid and rifampicin are taken three times per week. If the infection is not completely ster- ilized after the first treatment we schedule a retreatment. Since the model does not cover the possibility of dormant bacteria the population recovers rather quickly after an unsuccessful treatment. Hence, we begin the retreatment 30 days after completion of the previous treatment. After such a time span the population reaches a bacterial load where acute symptoms would be again suspected. If not stated otherwise the retreatment corresponds to the WHO recommendation for retreatments [20; 21]. The WHO recommendations include streptomycin, which is used together with the origi- nal four first-line drugs during the first two months. Afterwards the therapy is being continued for another month without streptomycin and during the last five months only isoniazid, rifampicin and ethambutol are administered. All drugs are being taken daily during the whole retreatment. The 95% confidence intervals (CI) of patient outcomes in the figures is calculated by picking the value for a two-sided 95% confidence limit with n − 1 degrees of freedom from a t-distribution table where n is the number of patients. This value is then multiplied with the standard deviation σ and divided by the square root of n. The resulting value is then added and subtracted from the mean to get the actual confidence interval.

t95% · σ CI = n√−1 (2.2) n

2.4 results

2.4.1 Treatment efficacy in single compartments against wild-type TB and MDR-TB

The impact of treatment on the net growth rate of wild-type or MDR bacteria dif- fers strongly between compartments (Fig 2.3): Before treatment starts, the growth rates in macrophages and granulomas are lower than in the open lung cavities due to hypoxia and a generally adverse environment for bacterial growth in these com- partments. Since we assume that the drug concentration immediately reaches the maximum the impact of combination therapy on growth rate is immediately appar- ent after the administration of the first dose of drugs. In all compartments the drugs are able to keep the wild-type populations from regrowth during the following days. Especially in granulomas pyrazinamide is able to diminish the population over a long period due to its relatively long half-life. MDR-TB is substantially less affected by the combination therapy because only pyrazinamide and ethambutol are effec- tive. This means that in macrophages or open lung cavities the multi-drug-resistant population remains constant at best or is even able to slowly grow. Only in the gran- ulomas where mostly pyrazinamide is active (see Table 1) the loss of effectiveness of isoniazid and rifampicin is less prominent. 2.4 results 21

Macrophages

10 0 ] 1 − 8 −2 6 −4 LogCFU 4

Growth rate [d rate Growth wild type wild type −6 MDR−TB MDR−TB 2 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0 Days Days

Granulomas

10 0 ] 1 − 8 −2 6 −4 LogCFU 4

Growth rate [d rate Growth wild type wild type −6 MDR−TB MDR−TB 2 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0 Days Days

Open cavities

10 0 ] 1 − 8 −2 6 −4 LogCFU 4

Growth rate [d rate Growth wild type wild type −6 MDR−TB MDR−TB 2 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0 Days Days

Figure 2.3: Net growth rates and population dynamics of wild-type and MDR bacteria in the modeled compartments after two days of treatment with the four first line drugs. All parameters for which a range of values exist have been set to the median value. On day 1 and day 2 all four drugs are applied simultaneously. 22 the role of adherence and retreatment in de novo emergence of mdr-tb

2.4.2 The role of adherence

The compliance of a patient with the prescribed drug regimen is a key factor for a successful treatment outcome. For the assessment of treatment success we mon- itor for every patient three different nested treatment outcomes. Firstly, we define treatment failure as the incomplete sterilization of the lung at the end of the ther- apy. Secondly, the emergence of MDR-TB is defined in our simulations as 10% or more [97] of the remaining bacterial population after treatment failure being resis- tant against at least isoniazid and rifampicin. Finally, emergence of full resistance (FR) is defined as 10% or more of the population being resistant against all drugs that were used in the treatment regimen (either 4 drugs for first treatment or up to 5 drugs for retreatment). Adherence in our simulations refers to the probability with which the patient takes the prescribed drugs at any given day. We assume that failure to take drugs on a given day always affects all drugs of the prescribed regimen. In our simulations, the level of adherence has a strong but complex impact on treatment success (Fig 2.4 A). Under perfect adherence the model shows a very low failure rate. However, if adherence decreases the probability for treatment failure increases rapidly. Between 40% and 80% adherence there is also a small fraction of patients that fail treatment due to the emergence of MDR-TB. Furthermore, at these adherence levels the model also shows only limited treatment success. Thus, failure decreases monotonically with adherence while MDR is maximized at intermediate levels. Patients who fail on the first treatment and who undergo retreatment (Fig 2.4 B) have a failure rate of 20% at 80% adherence. However, the probability for treatment failure increases to about 50% under perfect adherence. Patients who fail the first treatment despite high adherence may often have disadvantageous combina- tions of PK/PD parameters, which also decrease their success probabilities during the retreatment. In Fig 2.4 B, 2.4C and 2.4 D the number of patients per adherence level undergoing retreatment decreases strongly as can be seen from the frequency of treatment failure in Fig 2.4 A. When comparing Fig 2.4 A and 2.4 E, which shows the combined outcome probabilities for both treatments, we see that the retreatment reduces the probability of failure over the upper half of the adherence spectrum.

2.4.3 The role of retreatment

The additional treatment success of retreatment regimens depends on adherence and the addition of streptomycin to the regimen (Fig 2.4 B). In our model, even under perfect adherence the chance of treatment failure remains substantial, and in the majority of patients who fail under retreatment MDR-TB emerged de novo. Furthermore, at suboptimal adherence levels a considerable proportion of patients even carry strains that are not susceptible to any of the five administered drugs. The outcome of retreatment depends crucially on whether MDR was acquired during initial treatment: Because the majority of patients who fail the first treatment do not carry MDR-TB their outcome probabilities for the retreatment are almost identical to the overall cohort of failed patients (Fig 2.4 C). Even though the vast majority of patients who failed the first treatment did not develop MDR-TB, a substantial fraction 2.5 discussion 23 of patients who also failed the second treatment harbor MDR or FR strains. This occurs due to increased subpopulations of monoresistant bacteria that accumulate during the first treatment and that are by itself not sufficient to be diagnosed as MDR-TB. When comparing patients who are diagnosed with MDR-TB after the first treatment (Fig 2.4 D) and those who are not (Fig 2.4 C) we see that patients who develop MDR-TB are very likely to fail the retreatment as well. At higher adherence levels the majority of those patients develops full resistance against all five drugs (Fig 2.4 D). When considering the outcome for both treatments combined (Fig 2.4 E) it becomes more evident that the addition of streptomycin and the more intense retreatment has a beneficial effect on the overall success rate but patients who also fail the retreatment are more likely to carry multi-drug-resistant TB strains. When second-line drugs are not available or susceptibility test are not performed, it may occur frequently that a previously treated patient is retreated with the first line treatment. Our results in Fig 2.5 show that such a retreatment with the first line drugs has almost no additional treatment success beyond the initial treatment. Patients all across the spectrum of adherence experience treatment failure. The identical first- line retreament only increases the chances for the bacteria to accumulate resistance mutations and leads between 50% to 100% adherence to nearly all uncleared patients harboring MDR-TB or worse. This outcome is standing out when comparing the cumulative treatment success in Fig 2.5 D with the results after the first treatment. While the overall success curve did not change the fraction of MDR-TB patients over a large adherence range increased substantially.

2.5 discussion

The aim of this study is to elucidate the effects of treatment adherence and retreat- ment on the emergence of resistance in TB. The model explicitly incorporates the pharmacodynamics and pharmacokinetics of all drugs that are used for standard therapy and the WHO retreatment recommendation. Depending on the compart- ment in the lung in which the bacteria reside (macrophages, caseous centers of granulomas or open cavities), M. tuberculosis has different stages of infection and drug-susceptibilities. Therefore, we explicitly include these different compartments to be able capture the effect of heterogeneous selection pressure. Because not all of the parameters used in our model have been quantified with high accuracy, we do not claim that the model has quantitative predictive power. Rather, it aims to qualitatively demonstrate the underlying dynamics of a tuberculosis infection. Our results suggest that poor adherence is a major cause for treatment failure.When considering the predicted rates of treatment failure one also has to take into account that our definition of treatment failure is probably rather conservative. We do not include the possibility of remaining dormant bacteria, which might increase the like- lihood of treatment failure or relapse. On the other hand, we also neglect the pos- sibility of the infection being contained at a later time point by the immune system, thus probably underestimating the chance of success. It is also noteworthy that even at perfect adherence some patientsmay have a negative treatment outcome. This is most likely due to a random aggregation of very adverse pharmacokinetic param- eters and unfavorable infection attributes in some patients. Such outcomes due to 24 the role of adherence and retreatment in de novo emergence of mdr-tb

Treatment outcome after Treatment outcome after retreatment A first treatment B among failed patients 1.0 1.0

0.8 0.8

0.6 0.6 Treatment failure Emergence of MDR 0.4 0.4

Probability Emergence of FR Probability

0.2 0.2

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

Treatment outcome after retreatment Treatment outcome after retreatment C among failed patients without MDR D among failed patients with MDR 1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4 nodata Probability Probability

0.2 0.2

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

Treatment outcome for E both treatments combined 1.0

0.8

0.6

0.4 Probability

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence

Figure 2.4: Probabilities for treatment failure (blue), emergence of MDR-TB (green) and the emergence of a fully resistant strain (FR, red). (A) Treatment outcome prob- abilities based on the assessment of 10,000 simulated patients undergoing six month short course therapy at different levels of adherence. (B) Outcome proba- bilities of the standard retreatment regimen containing streptomycin for patients failing the previous treatment. (C and D) Retreatment outcome probabilities for patients failing the first treatment without or with MDR-TB respectively. (E) The overall probabilities for treatment outcome when both treatment regimens are considered. The width of the dark colored areas indicate the 95% confidence in- terval. Please note that the colored areas overlap and share a common baseline. Therefore, FR is a subcategory of MDR and FR and MDR are subcategories of treatment failure. The confidence intervals for the retreatment tend to widen at higher adherence levels due to the lower number of patients failing the previous treatment. The area with no data in panel (D) arises because patients with low adherence do not harbor MDR-TB after the first treatment. 2.5 discussion 25

Treatment outcome after retreatment Treatment outcome after retreatment A among failed patients B among failed patients without MDR 1.0 1.0

0.8 0.8

0.6 0.6 Treatment failure Emergence of MDR 0.4 0.4

Probability Emergence of FR Probability

0.2 0.2

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

Treatment outcome after retreatment Treatment outcome for C among failed patients with MDR D both treatments combined 1.0 1.0

0.8 0.8

0.6 0.6

0.4 nodata 0.4 Probability Probability

0.2 0.2

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

Figure 2.5: Corresponding treatment outcomes after two rounds of identical six-month short course therapy. (A) Treatment outcome probabilities after two rounds of identical first line therapy for treatment failure (blue), the emergence of MDR-TB (green) and the emergence of a fully resistant strain (FR, red). (B) Probabilities for patients who did not complete the first therapy successfully but who also did not harbor MDR-TB. (C) Treatment outcome probabilities for patients who failed the first treatment with MDR-TB. (D) The overall probabilities for treatment outcome when both treatment regimens are considered. There is no data available in panel (C) for patients with a lower adherence than 25% because such patients did not harbor MDR-TB after the first treatment. 26 the role of adherence and retreatment in de novo emergence of mdr-tb

pharmacokinetic variability and despite good adherence have been predicted in an in vitro study [98]. Furthermore, our results show that over a certain range of ad- herence a small fraction of patients develop MDR-TB. At intermediate adherence these patients also have a low likelihood of being treated successfully. Thus, good adherence to therapy is crucial: Not only does it increase treatment success, it also decreases the probability for the emergence of MDR-TB. According to our model, the WHO recommendation for retreatment is somewhat of a double-edged sword. While at high adherence levels the recommended treat- ment is able to cure the majority of patients who failed the first line therapy, it also increases the fraction of patients harboring drug resistant strains across almost the whole spectrum of adherence. Previous studies already raised concerns about the possible amplification of resistance [21; 99; 100; 101; 102]. In the WHO treatment guidelines it is recommended that drug susceptibility test results should be taken into account when deciding upon the retreatment regimen [17]. However, the vast majority of patients in our model would probably not have been diagnosed with MDR-TB after the first regimen even though they may still harbor increased subpop- ulations of monoresistant bacteria. Therefore it is conceivable that many would have been treated with the WHO recommended regimen. A large fraction of patients who failed this retreatment eventually developed MDR-TB. Considering the results from our model further clinical studies are needed which analyze the treatment success rates and the accompanying risks of the standard retreatment regimen. Retreating failed patients with an identical short course therapy leads to poor out- come in our simulations. A lower success rate for MDR-TB patients treated with the standard short- course therapy has been confirmed in a large cohort study [55]. In our simulations it is rare that patients who failed the previous treatment are cured af- ter undergoing the same therapy again provided that adherence remains unchanged. Retreatment with the same regimen only generates more opportunities for single resistant mutants that emerged during the first treatment to accumulate further mu- tations, thus minimizing the number of future treatment options. These findings are in accordance with previous studies which found a positive correlation between previous treatment and the occurrence of resistance [103; 104; 105; 106]. This might be an indicator that de novo resistance on an epidemiological scale occurs at a significant frequency and that the main contributor to the frequency of MDR-TB is not necessarily the mere transmission of such strains. In summary our data show that patient adherence is a crucial component of treat- ment success. The probably cheapest and most effective way to ensure a positive treatment outcome while also minimizing the risk for the emergence of MDR-TB is to maintain proper patient compliance with the treatment. This supports the Directly Observed Treatment, Short-Course (DOTS) strategy of the WHO, which includes healthcare workers or community health workers who directly monitor patient med- ication. If treatment fails, thorough tests of drug susceptibility of the remaining infecting population, would be of considerable value. According to our results a retreatment regimen including streptomycin has the potential to increase the overall cure rate, but also increases the fraction of patients who carry drug-resistant strains. A common principle of physicians is to “never add a single drug to a failing regime” [107] this principle is often not followed in retreatment. A preceding drug sensitiv- 2.6 acknowledgments 27 ity test might show existing drug resistances and the retreatment regimen could be adapted accordingly. Nonetheless the standard retreatment regimen is still superior to a retreatment with the identical first-line drugs. Such a retreatment is unlikely to achieve a higher overall cure rate and dramatically increases the probability for the emergence of MDR-TB, which reduces further treatment options. This shows that a dependable patient treatment history that is available to the responsible health professional is also important before initiating a treatment regimen.

2.6 acknowledgments

We thank Florian Marx and Ted Cohen for reviewing the manuscript and stimulating discussions.

2.7 author contributions

Conceived and designed the experiments: DC PAzW RK SB. Performed the experi- ments: DC. Analyzed the data: DC PAzW. Contributed reagents/materials/analysis tools: SB. Wrote the paper: DC PAzW RK SB.

APPENDIX

2.a supplementary material

2.a.1 Model equations

The following descriptions contain further details about the model mechanics and specifications of the equations that comprise the mathematical basis in addition to the explanations in the main article (see 2.3.1). The model is based on the τ-leap approximation [58]. In our case we do the simu- lations with a temporal resolution of 10−2 d. If in a time step a new bacterium is born it mutates and gains or loses resistance to one or several drugs with a likelihood that is equal to the corresponding mutation rate. For every patient and every drug we initially randomly pick a rate from a uniform distribution with the indicated mini- mum and maximum values in Table 2.1. The probability for a backward mutation is ten times lower than the corresponding picked rate. We assume that (uncompensated) resistance alleles confer a fitness disadvantage in the absence of drugs. In our model we restrict the effect of resistance costs cl to the reduction of the reproductive success. If multiple alleles involve a cost, the fitness of the corresponding genotype is given by

n wg = (1 − cl) (2.3) l=1 Y where cl is the cost of a resistance allele at the locus l and n is the number of resistance loci. The susceptible wild-type alleles have no cost and therefore the fully susceptible strain has a fitness of 1. The death rate dc of the bacterial population depends on the population density in the compartment among all genotypes.

Nc dc = r · γc (2.4) Kc

where r is the maximal replication rate of M. tuberculosis and γc is a factor, which modifies the maximal growth rate according to the different metabolic activities in each compartment. Nc is the combined population size of all genotypes in the com- partment and Kc is the carrying capacity of that specific compartment. The higher the population density is, the more increases the death rate. Together with the basic growth function this results in the conventional model for logistic growth:

  dNc,g Nc = r · Nc,g · 1 − (2.5) dt Kc The bactericidal activity of the antituberculosis drugs is accounted for by the sig- moid Emax model [108]. This leads to an adapted version of the enhanced death model 29 30 the role of adherence and retreatment in de novo emergence of mdr-tb

by Czock et al. [108] which we extend to reflect the use of multiple distinct drugs . The bactericidal effects of the drugs in a compartment are reflected in the killing rate variable κc,g.

n   1 κc,g = Emax,d · 1 − · νg,d (2.6) Cd·δc,d·ρd d=1 + 1 X EC50,d The killing rate depends on the genotype. Here we assume that a resistant mutant allele confers full resistance to the bactericidal activity of the corresponding drug. The resistance of a given genotype against an antibiotic drug is represented by the boolean variable νg,d with νg,d = 0 indicating resistance. For simplicity we assumed that the drug effects are additive. n is the number of drugs and EC50,d describes the concentration at which the half-maximal kill rate of a specific drug is reached. Emax is the maximal death rate. Together with the MIC and the EC50 it determines the antibacterial potency of a drug. Cd is the current drug concentration while δc,d and ρd are the efficacy of the drug in the specific compartment and the ratio between plasma and epithelial lining fluid concentration, respectively. We assume that immediately after the uptake of a drug the concentration increases instantaneously by an amount Cmax,d, followed by a exponential decay according to the following function,

−a(t−t0) Cd(t) = Cd(t0) · e (2.7)

where t0 is the last time point where the drug has been taken and

ln(2) a = d (2.8) t1/2

d where t1/2 is the half-life of drug d within the patient. For simplicity we assume that if the patient is non-adherent on a specific day all due drugs are missed simultaneously. Allowing the drugs to be missed inde- pendently caused only a marginally lower chance of a treatment failure (data not shown).

2.a.2 Fitting of anti-tuberculosis drug action

The Emax and EC50 values as we use them in our model were not readily available in the literature. In order to obtain them we use again an equation from the enhanced- death constant-replication model [108].

dN C = r · N − Emax · · N (2.9) dt EC50 + C 2.A supplementary material 31

If we assume that the population has no net growth and therefore the drug con- centration C is equal to the MIC we get the following relation

r · (MIC + EC50) E = (2.10) max MIC

The different Emax and EC50 values are collected by fitting equation 2.10 to the kill curves that were recorded in vitro by de Steenwinkel et al. and Marcel et al. [90; 82]. These papers report the in vitro effects of constant drug concentrations of isoniazid, ri- fampicin, ethambutol and streptomycin on the density of a M. tuberculosis suspension over the course of six or seven days, respectively. In Figure 2.6 we show simulations of this experimental setup using our model by assuming a single compartment in which all four available drugs have unimpaired efficacy. The data points were ex- tracted from the original figures as far as the data points were distinguishable. In order to prevent the unpredictable stochastic influence of rescue mutations we re- move the possibility of emerging resistance from the model. From the growth curves in the absence of any drug we estimate the average growth rate to be 1.95. This comparably high growth rate is likely due to the adapted phenotypes of regular lab strains of M. tuberculosis. The carrying capacity in the assays of de Steenwinkel et al. [90] we estimated to be 108.5 and 1013 in the assay of Marcel et al. [82]. The MIC concentrations from the literature [82; 77; 68] which are also confirmed in the experimental kill curves serve as reference points at which the bacterial growth and the bactericidal activity of the drug would cancel each other out and the pop- ulation would stay constant. The EC50 concentrations and the interdependent Emax values are derived by linear least-square fitting. The best fit values are calculated by averaging over all the available concentrations. The experimental data for isoniazid shows a recovery of population growth after day 2. The authors claim that this effect appears due to the development of a isoniazid-resistant subpopulation [90]. Because we do not consider such rescue mutations we decide to include only the first two days for the fitting of the bactericidal activity of isoniazid. To validate the quality of the fitting we calculate the average coefficient of determi- nation R2 for every drug. Isoniazid and ethambutol show a satisfactory R2 of 0.67 and 0.70 respectively and a very good 0.90 for streptomycin. The coefficient of determi- nation for the fitting of rifampicin is rather low with 0.36. Our model overestimates the bactericidal activity of rifampicin at high concentrations and underestimates the activity at low concentrations. Apparently a single drug action model as we use it does not provide the same descriptive quality for every first line drug. No kill curves were available for pyrazinamide hence we estimate an appropriate EC50 value from other studies [74; 109].

2.a.3 Robustness analysis

In order to obtain a better understanding of the influences of different parameter es- timates in the model we performed a robustness analysis in which we vary them and looked at their impact on the treatment outcome. In the following results we moni- tor the likelihood of treatment failure and the emergence of MDR-TB after a single 32 the role of adherence and retreatment in de novo emergence of mdr-tb

treatment with the four standard first-line drugs. As in the main text treatment fail- ure is again defined as incomplete sterilization after the completion of therapy and emergence of MDR-TB is defined as 10% or more [97] of the remaining population being resistant against at least isoniazid and rifampicin.

2.a.3.1 Carrying capacity

There is a large variance in reports about the maximum population size of M. tuber- culosis in a human lung during acute infection. This is also based on the fact that this number depends on the host immune defense and the course of infection. Many studies report 109 bacilli per open cavity and therefore an overall population size of 1010 or above. Thus, to study the effect of varying carrying capacity we ran simu- lations with compartmental carrying capacities that are 10-fold higher or lower for every compartment (see Figure 2.7 A and B). With 10-fold higher carrying capacities the probability for treatment failure increases substantially. The increased number of bacilli in each compartment also increases the standing variation in the bacterial population. This means that there are more bacteria that carry single or even dou- ble resistance mutations. Therefore, an increased carrying capacity also favors the emergence of MDR-TB.

2.a.3.2 Resistance costs

The cost of resistance in M. tuberculosis is generally assumed to be low [88; 84; 85; 86]. However, those estimates are mostly based on observations of clinically isolated strains. It is possible that these fitness costs are alleviated by compensatory mu- tations, which occur later during a chronic infection or during the chain of transmis- sion events. Since we assumed de novo emergence of resistance we assigned a 10% fitness cost on reproductive success for every mutation. We ran simulations in which we increased as well as decreased the fitness costs per resistance mutations. As we can see in Figure 2.7 C and D the results with slightly lower fitness costs still provide reasonable results. Although, if the costs are lower than 5% the probability of treatment failure and the likelihood of MDR emergence are unrealistically high. Thus, we conclude that resistance mutations are do very likely carry some fitness costs. Otherwise treatment outcomes would be expected to be much worse than what is generally observed in studies. This conclusion is partially confirmed in a previous study [89].

2.a.3.3 Migration rates

The rate with which M. tuberculosis migrates among the three compartments has to our knowledge not been quantified. We follow the assumptions made by Lipsitch and Levin [50]. The migration has only a pronounced influence if it increases (see Figure 2.7 C and D). This is most likely due to the increased density-dependent bacterial killing in the small compartments of macrophages and granulomas. With higher migration rates these compartments are flooded with bacteria from the open cavities. However, the influence on the emergence of MDR-TB is still small. Even though our estimates for the migration rate are not well established and we consider 2.A supplementary material 33 them to be already rather high we think that its minor influence does not severely affect the validity of our model.

2.a.3.4 EC50

We also investigate the influence of the EC50 parameter, i.e. the efficiency of the drug. In Figure 2.7 G and H we vary the EC50 values of every drug simultaneously between 1/10, 5/10 and the five- and tenfold of the standard parameter setting. An increased EC50 is predicted to cause a guaranteed treatment failure even at perfect adherence. On the other hand a decreased EC50 may dramatically improve the likeli- hood of a successful treatment at adherence levels, which are far below the optimum. Figure 7 F indicates that an elevated EC50 only promotes the selection of MDR-TB at intermediate levels of adherence, i.e. if the drugs are able to exert a certain selective pressure.

2.a.3.5 Missing drugs

In resource-limited settings, the drug supply is not always guaranteed, such that therapy might only comprise a subset of the four drugs. To investigate the impact of a missing drug, we test all four possible standard treatments that each lack one of the first-line drugs and assess the effect (see Figure 2.7 I and J). The lack of isoniazid, rifampicin or ethambutol always leads to treatment failure irrespective of the level of adherence. The explanation for this is as follows: The extracellular compartment harbors the largest number of bacteria. Here, isoniazid rifampicin and ethambutol most efficiently reduce bacterial load. Because of the high bacterial load we would expect that mutants resistant to either of these drugs pre-exist at treatment initiation. However, double-resistant mutants that could evade two drugs are expected to pre- exist only in a small fraction of drug-naive patients. If one of these main drugs is missing the mutants that are resistant against the remaining drug immediately take over and spread. Compared to isoniazid, rifampicin and ethambutol pyrazinamide is less essential for treatment success. This is probably because it does not affect the large extracellular compartment. However, it is important for clearing bacteria resid- ing in the caseous centers of granulomas, where it is the most active drug. Therefore, its usage favors a positive treatment outcome. However, its absence does not affect the outcome as much as the other drugs. Because the lack of isoniazid and rifampicin does not select for resistance against these drugs it is also unlikely that MDR occurs at a substantial frequency. The pre- viously observed minor influence of pyrazinamide is also evident as its absence does not substantially increase the risk of MDR emergence. Only a regimen with- out ethambutol drastically increases the probability for MDR to occur. This shows how important the role of ethambutol as a third extensively effective bactericidal drug is. Ethambutol is needed to prevent widespread treatment failure due to the development of MDR-TB.

2.a.3.6 Transmitted resistance

In Figure 2.8 we examine the possible effect of an infection with an M. tuberculosis strain that is already resistant at transmission. To model this, we exchange the bacte- 34 the role of adherence and retreatment in de novo emergence of mdr-tb

rial inoculum at the beginning of the infection with a strain that is resistant to one or two drugs. It is known that patients with active TB are highly infectious and even a small inoculum of one hundred bacilli or less that comprises primarily resistant mu- tants might establish an infection in a susceptible host. As in every simulation the infection is simulated for one year to reach its full potential and equilibrate. During this year random reversion mutations may occur which give rise to sensitive strains. These strains may slowly outcompete resistant strains and become more frequent due to their higher fitness in absence of drugs. The pre-existence of rifampicin or isoniazid resistance increases the risk of treat- ment failure the most among the single mutants at perfect adherence. This could be due to the potency of these drugs and the competitive advantage that such resistance mutations grant. Not surprisingly, a isoniazid- or rifampicin-resistant inoculum also increases the risk of MDR-TB. Pre-existing pyrazinamide or ethambutol-resistance has almost no effect on treatment outcome. Most likely due to their minor bacteri- cidal effectivity during the therapy. A double-resistant inoculum as in Figure 2.8 C and D has a fatal impact. Treatment failure is almost inevitable and MDR-TB occurs especially at higher levels of adherence. 2.A supplementary material 35

Experimental data Fitted model

Isoniazid Isoniazid 9 9 Control Control 8 8 2 0.015 mg/L R : 0.67 0.015 mg/L 7 0.031 mg/L 7 0.031 mg/L 0.062 mg/L 0.062 mg/L 6 0.125 mg/L 6 0.125 mg/L 5 0.25 mg/L 5 0.25 mg/L 0.5 mg/L 0.5 mg/L

4 1 mg/L LogCFU 4 1 mg/L LogCFU/ml 2 mg/L 2 mg/L 3 3 4 mg/L 4 mg/L 2 8 mg/L 2 8 mg/L 16 mg/L 16 mg/L 1 32 mg/L 1 32 mg/L 0 64 mg/L 0 64 mg/L 128 mg/L 128 mg/L 0 1 2 3 4 5 6 0 1 2 3 4 5 6 256 mg/L 256 mg/L Time (days) Time (days)

Rifampicin Control Rifampicin Control 9 9 0.0005 mg/L 0.0005 mg/L 8 0.001 mg/L 8 R2: 0.36 0.001 mg/L 0.0019 mg/L 0.0019 mg/L 7 0.0038 mg/L 7 0.0038 mg/L 6 0.0075 mg/L 6 0.0075 mg/L 0.015 mg/L 0.015 mg/L 5 0.031 mg/L 5 0.031 mg/L 0.062 mg/L 0.062 mg/L

4 LogCFU 4

LogCFU/ml 0.25 mg/L 0.25 mg/L 3 0.5 mg/L 3 0.5 mg/L 1 mg/L 1 mg/L 2 2 mg/L 2 2 mg/L 1 8 mg/L 1 8 mg/L 16 mg/L 16 mg/L 0 32 mg/L 0 32 mg/L 0 1 2 3 4 5 6 64 mg/L 0 1 2 3 4 5 6 64 mg/L 128 mg/L 128 mg/L Time (days) Time (days) 256 mg/L 256 mg/L

Ethambutol Ethambutol 9 9 Control Control 8 8 2 0.125 mg/L R : 0.70 0.125 mg/L 7 0.25 mg/L 7 0.25 mg/L 0.5 mg/L 0.5 mg/L 6 1 mg/L 6 1 mg/L 5 2 mg/L 5 2 mg/L 4 mg/L 4 mg/L

4 8 mg/L LogCFU 4 8 mg/L LogCFU/ml 16 mg/L 16 mg/L 3 3 32 mg/L 32 mg/L 2 64 mg/L 2 64 mg/L 128 mg/L 128 mg/L 1 256 mg/L 1 256 mg/L 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Time (days) Time (days)

Streptomycin Streptomycin 11 11 10 10 R2: 0.90 9 0.01 mg/L 9 0.01 mg/L 0.125 mg/L 0.125 mg/L 8 0.25 mg/L 8 0.25 mg/L 7 0.5 mg/L 7 0.5 mg/L 6 1 mg/L 6 1 mg/L 2 mg/L 2 mg/L 5 5

4 mg/L LogCFU 4 mg/L LogCFU/ml 4 8 mg/L 4 8 mg/L 3 16 mg/L 3 16 mg/L 32 mg/L 32 mg/L 2 2 1 1 0 0 001234567 1 2 3 4 5 6 001234567 1 2 3 4 5 6 Time (days) Time (days)

Figure 2.6: Comparison of the concentration- and time-dependent effects of isoniazid, ri- fampicin, ethambutol and streptomycin on sensitive M. tuberculosis. The plots in the left column are experimentally obtained killing curves for anti-tuberculosis drugs by de Steenwinkel et al. [90] and Marcel et al. [82] and originate from a metabolically highly active strain of Mtb H37Rv cultured in vitro at 37°C [90]. The plots on the right show the simulated killing curves that were calculated by fitting the pharmacodynamic model to the experimental data. The fitting was done by minimizing the sum of least squares over all curves. The coefficient of determi- nation (R2) indicates the average goodness of fit for each drug. Greyed out lines were not used for fitting. Modified from [90]. 36 the role of adherence and retreatment in de novo emergence of mdr-tb

A B

Carrying Capacity Standard 10−fold decreased 10−fold increased ProbabilityMDR Strain of Probability of Treatment Failure ProbabilityTreatment of 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Adherence Adherence C D

Resistance Costs 0.00 0.02 0.05 0.08 0.10 0.15 ProbabilityMDR Strain of Probability of Treatment Failure ProbabilityTreatment of 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Adherence Adherence E F

Migration Rates 10% 50% 100% 500% 1000% ProbabilityMDR Strain of Probability of Treatment Failure ProbabilityTreatment of 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Adherence Adherence G H

EC 50 10% 50% 100% 500% 1000% ProbabilityMDR Strain of Probability of Treatment Failure ProbabilityTreatment of 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Adherence Adherence I J

Missing Drug no drug missing Isoniazid Rifampicin Pyrazinamide Ethambutol ProbabilityMDRStrain of Probability of Treatment Failure ProbabilityTreatment of 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Adherence Adherence

Figure 2.7: Sensitivity analysis of the probability of treatment failure and emergence of resistance. In the left column are the plots for the probability of treatment failure due to incomplete clearance and in the right column are the plots for the proba- bility of the emergence of an MDR-TB strain, which accounts for at least 10% of the overall population. (A and B) Effect of different carrying capacities. (C and D) Effect of different fitness costs per resistance mutation. (E and F) Effect of dif- ferent migration rates among compartments. (G and H) Effect of lower or higher EC50 values. (I and J) Effect of treatment consisting of only three drugs. 2.A supplementary material 37

A B

Single Mutants wt INH RMP PZM EMB Probability of MDR Strain MDR of Probability Probability of Treatment Failure ProbabilityTreatment of 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Adherence Adherence C D

Double Mutants wt INH + RMP INH + PZM RMP + PZM INH + EMB RMP + EMB PZM + EMB Probability of MDR Strain MDR of Probability Probability of Treatment Failure ProbabilityTreatment of 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Adherence Adherence

Figure 2.8: Influence of pre-existing resistance mutations on treatment outcome after a reg- ular six-month therapy. In the left column are the plots for the probability of treatment failure due to incomplete clearance and in the right column are the plots for the probability of the emergence of an MDR-TB strain, which accounts for at least 10% of the overall population. (A and B) Effect of a homogeneous inoculum consisting of genotypes resistant to one drug. (C and D) Effect of a homogeneous inoculum consisting of genotypes resistant to two drugs.

3 ALTERNATIVETREATMENTSTRATEGIESFORTUBERCULOSIS

D Cadosch, P Abel zur Wiesch, S Bonhoeffer abstract

The standard six-month short-course therapy for pulmonary tuberculosis has been established in the 1970s. Since then there have not been major changes in the reg- imen that still requires considerable effort and dedication from the patient as well as from the health care system. In this study we explore the potential benefits and disadvantages of intermittent therapy as well as extended-release formulations and dose escalations of rifampicin. These alternative treatment strategies are tested for varying levels of patient adherence. Intermittent therapy is shown to have a reduced probability for a positive treatment outcome as well as a lower risk for the emer- gence of de novo MDR-TB. Extended-release formulations of rifampicin can mitigate the lower chances of successful treatment associated with intermittency but they also increase the probability for the emergence of resistance at suboptimal adherence lev- els. In contrast to the other strategies the absolute drug exposure is increased when we test for the effects of dose escalation of rifampicin. Dose escalation of rifampicin shows the same or lower probabilities for treatment failure at equal adherence levels but the probability of de novo MDR-TB increases for intermediate levels of adher- ence. We conclude that intermittent regimens could potentially lower the time and organizational burden for patients and the health care system but they show lower success rates. Extended-release formulations of rifampicin are a feasible strategy to mitigate the potential weaknesses of intermittent regimens. Dose escalation is also a promising alternative strategy. However, dose escalation as well as extended-release formulations of rifampicin depend on a very good patient compliance to be effective, otherwise the risks associated with the stronger selection for resistant genotypes may outweigh the benefits.

39 40 alternative treatment strategies for tuberculosis

3.1 introduction

The treatment of pulmonary tuberculosis (TB) with a six-month short-course che- motherapy was developed in the 1970s by the British Medical Research Council and its partners [110; 111]. This treatment regimen containing four antituberculo- sis drugs is still the current standard recommended by the WHO [13]. Adherence to the treatment regimen is considered to be a crucial factor influencing the success- ful completion of treatment and for preventing emergence of drug-resistant TB. The improvement of adherence was one of the goals of the directly observed treatment, short course (DOTS) strategy launched in the mid-90s. Since then, the case detec- tion increased and case prevalence decreased in countries where DOTS was applied [27]. However, the effort and organization that is needed to maintain a successful TB control program is substantial. TB patients are usually administered their drugs on a daily basis by a local health care worker during at least the first two months of the treatment. Also the long treatment period and the effort of the patient who in some countries has to travel long distances to see his supervising health worker may prevent him or her from uninterrupted attendance [13]. Another reason for patients to discontinue therapy may be the high pill burden or uncomfortable side effects [13; 112]. Given the difficulties with the current treatment strategy possible improvements of the standards could be of interest. In this study we are discussing three al- ternative strategies that address the problems outlined above: intermittent treat- ment, extended-release drug formulations and dose escalation. Intermittent regi- mens could facilitate the task of treatment supervision. Some studies found intermit- tent regimens to have equally good success rates when compared to daily treatment [21; 38]. Large-scale tuberculosis control programs that used simplified intermittent treatment regimes were considered to be sufficiently successful [113; 114]. However, intermittent treatment has also been found to be associated with a greater risk of acquired drug resistance [21] and with higher incidence rates of side effects from isoniazid and rifampicin [13; 38; 115; 116], the two most important first-line drugs. Another possible concern in intermittent treatment regimens is the possible phar- macokinetic mismatch that could lead to prolonged phases of mono-therapy [117]. Because the concerns of intermittent therapy are thought to outweigh the potential benefits the WHO recommends daily administration of antituberculosis drugs if pos- sible [13]. However, some of the issues mentioned with intermittent regimens could be al- leviated with the use of extended-release formulations. Such formulations cause a slower absorption of the drug and consequentially provide a more steady suppres- sive drug concentration over time [22]. Intermittently extended-release formulations should keep the antibiotic concentration above the minimum inhibitory concentra- tion (MIC) long enough to prevent a substantial regrowth of the bacterial population. The more long-lasting presence of rifampicin for example could decrease the prob- ability for side effects such as flu-like symptoms. These symptoms are assumed to be at least partially caused by the formation of anti-rifampicin antibodies and the development of a more potent immune reaction which may be triggered during al- ternating prolonged phases of high and low rifampicin concentrations that occur 3.2 methods 41 with intermittent therapy and standard rifampicin formulations [115; 116; 81; 92]. The benefits of an intermittent regimen with extended release drugs could prove to be at least as successful as daily treatment, decrease the work effort and operating expenses for monitoring programs as well as lower the pill burden and incidence of side effects for the patient and hence increase adherence and herewith the probability for a positive treatment outcome. Another point of improvement of the conventional treatment strategy would be the increase of the rifampicin dose (dose escalation). An increase of the rifampicin dose has been considered a promising direction because rifampicin is known to cause side effects less frequently than other first-line drugs [115; 63]. Furthermore, higher doses are more likely to prevent sub-target plasma concentrations due to malabsorption or reduced bioavailability in certain patients [115; 118; 119]. A study looked at the early bactericidal activity of an increased rifampicin dose in 14 patients and found promising results but concluded that further studies are warranted [120]. A more extensive clinical study that looked at increasing rifampicin doses found that higher doses were well tolerated and had a stronger bactericidal effect while also reducing resistance [23]. In this study we investigate the possible benefits of extended-release formulations in a daily or intermittent treatment regimen by means of extending a mathematical model used in a previous study [121]. We further test how big the impact of increased rifampicin doses is on treatment outcome. We evaluate the effects of these regimens over a range of patient adherence. We focus here exclusively on rifampicin since it is considered to have the biggest untapped potential in terms of sterilizing capacity [115; 63].

3.2 methods

3.2.1 Model

Our model is based on the extension of a framework of an acute pulmonary TB infection from an earlier study [121]. The mathematical model of the population dynamics of Mycobacterium tuberculosis considers three different compartments: macrophages, granulomas and open cavities. The compartments differ in their size, which limits the maximal population size and in the growth rate at which bacteria may replicate. Bacteria may migrate from macrophages to granulomas, from gran- ulomas to open cavities and from there again to macrophages. This represents an abstraction of the pathogenic cycle during an acute pulmonary TB outbreak in a pa- tient. The bacterial populations are assumed to consist of up to 16 genotypes, which represent all possible combinations of the four considered resistance mutations – one for each first-line drug. During replication bacteria may acquire resistance mutations with a certain probability. To reflect variations in the phenotype of bacteria as well as in the physiology of patients parameters are picked randomly from a specified range of values. Bacteria differ in their migration rates, maximal population densities and mutation rates for resistances against each drug. Patients may absorb and excrete drugs at variable rates, vary in their efficacy to absorb drugs, have different ratios between the blood serum drug concentration and the concentration in the epithelial 42 alternative treatment strategies for tuberculosis

lining fluid inside the lungs as well as varying drug penetrations for the three com- partments. The precise description of the model as well as its parametrization can be found in the previous study by Cadosch et al. [121]. Newly introduced parameters and parameter values that differ from the previous study are in Table 3.1. Beyond the previously established model framework we extended the pharmacokinetics to also include a first order absorption reaction. All simulations are stochastic and use the τ-leap method by Gillespie [58].

3.2.2 Pharmacokinetics

In the model the blood serum drug concentration in a patient is governed by a first order absorption reaction and a first-order excretion reaction. The first order absorp- tion reaction in our case reflects the uptake of drug from the digestive tract to the blood stream while the first order excretion reaction reflects the elimination of drug primarily by the kidneys or the biliary tract [126]. Upon drug administration the amount of unabsorbed drug U in the digestive tract instantaneously increases by the administered dose D. The amount of unabsorbed drug U then decreases according to the following differential equation:

dU = −k · U (3.1) dt a

where ka is absorption rate constant. Besides the absorption rate constant the drug concentration in the blood serum C is also influenced by the excretion rate constant ke.

dC = k · U − k · C (3.2) dt a e

The absorption rate constant ka is related to the time tmax until the peak blood serum concentration is reached on the absorption and excretion rate constant as

ln(ka) − ln(ke) tmax = (3.3) ka − ke

By transforming equation 3.3 we can calculate the absorption rate constant ka for known tmax and ke.

−k ·t W−1(−e e max · ke · tmax) ka = − (3.4) tmax

Here W−1 denotes the lower branch of the Lambert function. The excretion rate constant depends on the concentration half-life t1/2.

ln(2) ke = (3.5) t1/2 3.2 methods 43 ] ] 124 ; 124 ; 79 ; 79 ; ] 123 ; 123 ; 124 ; 115 [ 115 ] [ 5 . 115 68 [ 5 3 [ – – 4 0 5 0 – . . . 2 1 1 1 ] ] 79 ] 125 ; ; 125 78 78 ; ; ; 79 123 ; 123 ; ; 123 122 ; 122 ; ] ; 122 98 115 ; ; [ 115 [ 6 95 . 115 [ [ 9 50 – 5 – 2 . 5 . – 5 20 1 12 ] ] 79 125 ; ; 78 79 ] ; ; 123 123 123 ; ; ; 122 122 122 : Drug parameterization ; ; ; 1 . 23 3 [ 115 115 ] [ [ 9 . 68 3 9 3 [ – – – Table 6 1 3 4 . . . . 1 6 1 0 ] ] ] 125 125 ; 79 ; ; 79 79 ; 78 ; ; 123 123 ; 123 ; ; 122 122 ; 122 ; ; ] 115 115 [ [ 115 68 [ [ 1 . 2 4 7 – – – 5 9 75 025 . . . . 1 Isoniazid Rifampicin Pyrazinamide Ethambutol 1 0 0 ) 1 − ) ) h ) mg/l mg/L ( h ( max max Half-life ( Some of the provided references support the order of magnitude of the parameters, not the exact value. C t MIC ( 44 alternative treatment strategies for tuberculosis

To calculate the required dose D that has to be administered in order to achieve a maximum blood serum concentration Cmax after a time tmax we can look at the Bateman equation [127; 128], which is used to calculate the drug concentration C at time t depending on the underlying absorption and excretion rate constants.

D · ka C(t) = · (e−ke·t − e−ka·t) (3.6) ka − ke From equation 3.6 we can then derive a formula with which we can calculate the dose D that is needed to reach the specified concentration Cmax.

Cmax · (ka − ke) D = −k ·t −k ·t (3.7) ka · (e e max − e a max ) The different concentration-time curves of rifampicin between the standard absorp- tion rate constant of 16.3 d−1 and a fixed absorption rate constant of 1 d−1, represent- ing an extended-release formulation, can be seen in Figure 3.1. Both curves are based on a half-life of 2.3 h [115; 122; 123; 78; 79] and the same amount of drug is adminis- tered but the fast standard absorption rate constant results from a tmax that is set to 2.15 h [10,26,27,29,30]. In the simulations involving extended-release formulations of rifampicin the standard fast absorption rifampicin formulation with an absorption rate constant ka that is dependent on tmax and ke is compared to an extended-release formulation of rifampicin that has a fixed slow absorption rate constant of 1 d−1 or an intermediate absorption rate constant of 5 d−1.

3.2.3 Patient simulations

In order to capture a wide range of combinations of bacterial and patient parameters we simulate every treatment scenario for 1000 independent patients. Every patient is initially inoculated with 1000 wild-type bacteria. Because we assume that the pa- tients are immunocompromised, we allow bacteria to replicate and mutate freely for 360 days. During this time all three compartments harbor bacteria up to their carrying capacity and in the compartment of open cavities small subpopulations of monoresistant bacteria emerge and reach equilibrium sizes. The compartment of open cavities is the only compartment that is large enough for such low frequency genotypes to establish. The size of these subpopulations in the absence of any drug is determined by the carrying capacity, the mutation rate and the fitness cost, which is imposed by the de novo mutations. After the first 360 days a six months short-course therapy starts. The treatment involves the four standard first-line drugs isoniazid, rifampicin, pyrazinamide and ethambutol. In our standard regimen all drugs are administered daily during the first two months (intensive phase) and during the last four months isoniazid and rifampicin are administered three times a week (contin- uation phase) [13]. If the simulation involves intermittent therapy then rifampicin is administered every second or third day during the intensive phase and 1.5 times or once per week during the continuation phase respectively. To ensure compara- ble drug exposure the rifampicin doses are doubled or tripled in an intermittent regimen. 3.2 methods 45

Rifampicin

8 8 6 6 4 4 2 2 0 0 Concentration [mg/l] Concentration [mg/l] Concentration 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0

Time [days] Time [days]

Figure 3.1: Comparison of serum concentration profiles of rifampicin between the stan- dard absorption rate constant and the extended-release formulation. In the left panel are the pharmacokinetic profiles for a single administration of a rifampicin dose with the midpoint standard absorption rate constant of 16.3 d−1 (solid line) and with an absorption rate constant of 1 d−1 representing the extended-release formulation (dashed red line). The dotted line is the MIC of rifampicin for M. tuberculosis (see Table 3.1)[68]. The right panel shows the profiles for three con- secutive daily administrations with the standard absorption rate constant (solid line) or a single three-fold higher dose with the extended-release pharmacokinet- ics. The drug concentration profiles in each panel have within the computational accuracy the same AUC. 46 alternative treatment strategies for tuberculosis

At the end of the six months of therapy a patient is diagnosed with treatment failure if there are any Mtb bacteria left in any compartment. Among treatment failures besides patients with predominantly drug susceptible bacteria we further differentiate between patients with bacterial populations of which 10% or more [97] are resistant against at least isoniazid, resistant against at least rifampicin or those that are resistant against at least both isoniazid and rifampicin, which is the defini- tion of MDR-TB [99; 107]. Please note that MDR-TB is a subset of our definitions of isoniazid or rifampicin resistance and that it is the exact intersection of these two resistance definitions.

3.2.4 Pharmacodynamics simulations

In the pharmacodynamics simulations we have four genotypically distinct subpop- ulations: a fully susceptible wild-type, two populations that are either isoniazid- or rifampicin-resistant and a multidrug-resistant population that is resistant to isoni- azid and rifampicin. As we are interested in the relative population dynamics of the four genotypes, we start all populations from an arbitrary initial size that does not necessarily reflect their size in any patient at any time point. All drugs are administered only every second time that they are prescribed which corresponds to an enforced adherence level of exactly 50%, which has for all considered treat- ment regimens a high relative probability to favor the emergence of MDR-TB (see Results). The growth conditions and the drug efficacies are identical to the ones we attribute to the open cavities compartment, which we consider due to its size to be the most influential. In contrast to other simulations all patient-specific parameters are based on the midpoint of the parameter intervals (see Table 3.1 and [121]). For the pharmacodynamic simulations of intermittent therapy rifampicin is prescribed to be administered every three days in a triple-dose — but effectively it is taken only every six days due to the lowered adherence.

3.3 results

3.3.1 Treatment efficacy of an extended-release formulation of rifampicin in a daily or inter- mittent treatment regimen

The comparison between treatment regimens of different intermittencies with and without extended-release rifampicin formulations reveals that intermittency gener- ally has a negative effect on the probability of treatment failure while extended- release formulations have a positive effect (see Figure 3.2). We perform this compari- son over the full range of patient adherence. The standard daily administration of all drugs with rifampicin that has the standard fast absorption rate constant achieves a successful treatment outcome in almost all patients under perfect adherence (Figure 3.2 A). The success rate drops substantially below 90% adherence and at less than 40% adherence we find that the infection is not cleared in almost all patients. If an extended-release formulation of rifampicin is administered the curve shifts further to the left the slower the absorption is, indicating that such formulations provide a similar or higher likelihood of treatment success at the same adherence level. If 3.3 results 47 rifampicin with the standard absorption rate constant is administered at intervals of two or even three days in a double or triple-dose respectively, a positive treat- ment outcome at the same adherence level becomes less likely. However, the treat- ment success rate of high-dose intermittent administration of rifampicin increases if rifampicin is given as an extended-release formulation with lower absorption rate constants. The relative increase of benefit of the extended-release formulations is higher in high-dose intermittent regimens as is shown by the spread of the treatment failure curves within a group of equal absorption rate constants. While the treatment failure curves in the upper half of the adherence range between treatments with the same standard absorption rate constant but varying intermittency differ substantially from each other, the curves for the lowest absorption rate constant are rather close together. When we look at the probability for the emergence of MDR-TB we see that there is a substantial increase in the middle of the adherence spectrum for daily treatment regimens if we lower the absorption rate constant (Figure 3.2 B). For the intermit- tent regimens the probability of MDR-TB emergence is almost zero if we administer rifampicin with the standard absorption rate. The probability of MDR emergence when we intermittently use a rifampicin formulation with an intermediate absorp- tion rate constant is equal or lower than the daily administration of the fast absorp- tion formulation. When we use rifampicin formulations with the lowest absorption rate constant the risk of MDR-TB increases substantially for both intermittent thera- pies. We also compare the probabilities for the occurrence of genotypes that are at least resistant against against isoniazid or rifampicin for the different treatment regimens (see Figure 3.2 C and D). The slopes of all curves for isoniazid-resistance between about 30% and 100% adherence are almost identical to the curves indicating the prob- ability of treatment failure (Figure 3.2 C). This implies that at adherence levels above 30% treatment failure is generally due to the remaining bacterial population being resistant to at least isoniazid. The frequency of isoniazid-resistance decreases rapidly below 30% adherence. The probability for the occurrence of rifampicin-resistance on the other hand almost exactly mirrors the probability for the emergence of MDR-TB over the whole adherence spectrum (Figure 3.2 D). This indicates that rifampicin- resistance almost exclusively occurs in the context of MDR-TB. These results are confirmed when we exclusively consider isoniazid- or rifampicin-monoresistance. The probabilities for the emergence of isoniazid-monoresistance (Figure 3.2 E) are almost identical to Figure 3.2 C. Only when the adherence levels are low enough for MDR-TB to occur in regimens with slowly absorbed extended-release formulations of rifampicin does the probability for isoniazid-resistance decrease more than in Fig- ure 3.2 C. The low probability for the emergence of rifampicin-monoresistance for all regimens along the whole spectrum of adherence except for a narrow band between 10% and 40% adherence supports the prior observation that rifampicin-resistance is almost exclusively associated with MDR-TB (Figure 3.2 F). 48 alternative treatment strategies for tuberculosis

A Probability of treatment failure B Probability of MDR−TB emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

C Probability of isoniazid− D Probability of rifampicin− resistance emergence resistance emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

E Probability of isoniazid− F Probability of rifampicin− monoresistance emergence monoresistance emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

Figure 3.2: Probabilities of treatment failure and the emergence of MDR-TB, isoniazid- and rifampicin-resistance with 10% fitness costs per resistance mutation for different treatment intervals and varying absorption rate constants. We distin- guish the risk of incomplete infection clearance (A), the emergence of MDR-TB (B), the emergence of any isoniazid-resistant genotype (C), the emergence of any rifampicin-resistant genotype (D), the emergence of isoniazid-monoresistance (E) and the risk of the emergence of rifampicin-monoresistance (F). In every panel are the probabilities for a regime with the standard dose daily administration of all drugs (black lines), a regime where a double-dose of rifampicin is administered only on every second occasion (blue lines) and a regime in which rifampicin is given every third time in a triple-dose (red lines). Within a regime the pharma- cokinetics of rifampicin have a standard fast absorption rate constant (solid lines), a fixed intermediate absorption rate constant of 5 d−1 (dotted lines) or a fixed low absorption rate constant of 1 d−1 (dashed lines). The intermediate and low absorption rate constants represent two different extended-release formulations of rifampicin. Emergence of resistance is defined as at least 10% of the bacterial population in the open cavities compartment being resistant. 3.3 results 49

3.3.2 Pharmacodynamics of an extended-release formulation of rifampicin in a daily or in- termittent treatment regimen at intermediate adherence

To better understand the underlying population dynamics during daily or intermit- tent treatment regimens with slowly absorbed extended-release formulations of ri- fampicin we performed additional pharmacodynamics simulations shown in Figure 3.3. Under the daily treatment regimen with the standard formulation of rifampicin (see Figure 3.3 A) we observe that the wild-type population declines rapidly every time after the antibiotics are being taken but the decline slows down and the popu- lation is even able to recover somewhat before the next administration every other day. The time until extinction for this initial population size is approximately 12 days. The isoniazid-resistant subpopulation also declines after every drug adminis- tration but the regrowth of the population after the drug concentrations declined to sub-MIC is more pronounced than the initial decline and the population is therefore able to persist and even increases over time. The rifampicin-resistant subpopulation on the other hand is more strongly affected by the remainder of effective drugs and declines similar to the wild-type population — just with a slightly slower rate. Since pyrazinamide is not expected to be effective in the pH-neutral environment of open cavities the MDR-TB population is only influenced by ethambutol. Ethambutol is not potent enough to control the MDR-TB population, which equally increases in all shown scenarios. If we administer rifampicin intermittently and in a triple-dose the picture looks similar (see Figure 3.3 B). The rifampicin-resistant population declines at the same rate here as well as in every other situation because the only difference between regimens is the formulation and frequency of rifampicin administrations. The wild- type population declines at a slower rate than if it is administered daily which may partially explain the lower success rates of intermittent therapies with standard ri- fampicin formulations. Isoniazid-resistant bacteria as well as the wild-type show a more distinct drop of their population size every sixth day when rifampicin is ad- ministered. These rare events as well as the smaller declines in population size in between rifampicin administrations are however not strong enough to diminish the population size in the long term. The overall growth rate is even higher than with the daily regimen. The extended-release formulation with a lower absorption rate constant in Fig- ure 3.3 C and D is able to suppress the isoniazid-resistant subpopulation in a daily regimen and in an intermittent regimen with a higher dosage. Extended-release ri- fampicin also seems to be more effective against wild-type TB as the population goes extinct after approximately 8 days in contrast to 12 or 15 days with the standard ri- fampicin formulation. The influence of different assumptions of fitness costs for resistance mutations on these results is described in the Supplementary Material 3.A.

3.3.3 Treatment efficacy of a regimen with increased rifampicin doses

A dose escalation of rifampicin decreases the probability for treatment failure but increases the risk of MDR-TB (see Figure 3.4). In the clinical study [23] that we re- 50 alternative treatment strategies for tuberculosis

A B

106 106 105 105 104 104

CFU 103 CFU 103 102 102 101 wild type 101 rINH 0 5 10 15 20 0 5 10 15 20 rRMP MDR−TB time [days] time [days]

C D

106 106 105 105 104 104

CFU 103 CFU 103 102 102 101 101

0 5 10 15 20 0 5 10 15 20

time [days] time [days]

Figure 3.3: Pharmacodynamics at 50% adherence of four subpopulations with different drug susceptibilities under treatment regimens with different rifampicin ad- ministrations. The four panels all show the bactericidal effect of the standard regimen on four different M. tuberculosis subpopulations. The subpopulations are either fully susceptible to all drugs (wild type), fully resistant to isoniazid (rINH), fully resistant to rifampicin (rRMP) or resistant to both isoniazid and rifampicin (MDR-TB). The environmental conditions correspond to the extracellular compart- ment in a patient. All patient-specific variable parameters are set to their midpoint value. The initial population sizes are arbitrarily chosen and do not necessarily reflect the population composition in any patient at any time point. The absorp- tion rate constant for rifampicin in the panels A and B is at the standard midpoint value of 16.3 d−1. In the panels C and D rifampicin is given as an extended- release formulation with a slow absorption rate constant of 1 d−1. The treatment regimen for the panels A and C prescribes all drugs to be administered daily. The regimen for the panels B and D prescribes a three-fold higher rifampicin dose every third day under perfect adherence. In all panels every second prescribed drug administration is missed corresponding to an enforced adherence level of 50%. 3.4 discussion 51

Probability of treatment failure Probability of MDR−TB emergence

1.0 1.0 0.8 Rifampicin 0.8 10 mg/kg 0.6 20 mg/kg 0.6 0.4 25 mg/kg 0.4

Probability 30 mg/kg Probability 0.2 0.2 35 mg/kg 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

Figure 3.4: Probabilities of treatment failure and the emergence of MDR for increasing doses of rifampicin. The parametrization of the increased rifampicin doses is derived from a clinical study [23]. produce in our model the 10 mg/kg dose that we use as our standard dose and which is the recommended dosage by the WHO [13] reaches a mean Cmax concentration of 8 mg/l. For the 20 mg/kg rifampicin dose the clinical study we get a mean Cmax of 23.95 mg/l. Therefore, unsurprisingly we find that the 20 mg/kg dose achieves a substantially higher treatment success rate than 10 mg/kg at least for adherence levels between 40% and 100%. The mean Cmax concentration correlates well with the applied dosage. However, the additional benefit of an increased rifampicin dose becomes smaller with higher doses. When we look at the probability for MDR emer- gence we see that 10 mg/kg bears the lowest risk at any level of adherence. This risk increases for intermediate adherence levels with higher rifampicin dosages.

3.4 discussion

In this study we investigated the feasibility of applying extended-release formula- tions of rifampicin in daily or intermittent treatment regimens as well as increasing the rifampicin dosing to improve TB therapies. We tested these alternative treatment strategies in a previously established mathematical model [121]. The mathematical model simulates the population dynamics of various genotypes with different drug susceptibilities during an acute pulmonary tuberculosis infection within a patient. Furthermore, the model also encompasses the pharmacodynamics and pharmacoki- netics during the treatment with first-line drugs. Many parameter values that are being used in our model have been established in in vitro studies or are based on estimates with limited accuracy. Because of the intrinsic uncertainty with these pa- rameter values we have to stress that the results we are presenting are of a qualitative kind and do not provide accurate quantitative predictions. From our results we see that in general the application of extended-release formu- lations increases or maintains the probability of a successful treatment for the same dosing regimen. This is most probably attributed to the fact that slowly absorbed extended-release formulations keep the rifampicin concentration above the growth suppression threshold for a longer time (see Figure 3.1). Furthermore, extended- release formulations may maintain suppressive concentrations even if the drug is 52 alternative treatment strategies for tuberculosis

occasionally not taken. On the other hand, according to our results intermittency is expected to work less well if formulations are used that are given at higher doses but with the standard absorption kinetics. An intuition for this observation can be found if we consider that the half-life of rifampicin is between 1.6 and 3 h [115; 122; 123; 78; 79] and the bactericidal activity does not necessarily linearly cor- relate with the concentration [121; 90]. Therefore, even if we double or triple the dose the rifampicin concentration stays above the MIC for only a few more hours which is too small of a benefit if the administration interval is two or three days. However, if we combine an intermittent treatment regimen with extended-release formulations the negative consequences are somewhat mitigated and we see com- parable or even better results than with the daily administration of the standard rifampicin formulation. Thus, the application of extended-release formulations has the potential to decrease the possible negative aspects of intermittent treatment and make it a more promising strategy. An intermittent dosing strategy is attractive be- cause it is expected to be less time-consuming for the responsible health care worker and therefore less costly. It also decreases the pill burden for the patient and es- pecially in combination with extended-release formulations, that induce lower peak concentrations, may cause fewer side effects. These patient-specific benefits may in- crease compliance and decrease the likelihood of defaulting, which in turn makes the whole control program more effective. Extended-release formulations potentially have a negative effect if adherence is suboptimal. At intermediate adherence levels our simulations showed a higher like- lihood for the emergence of MDR-TB in regimens that use extended-release formu- lations especially for formulations with the lower absorption rate constant. To un- derstand this phenomenon we have to look at the prevalence of subpopulations that are resistant against either isoniazid or rifampicin. We notice that treatment failure except for very low adherence levels (between 0% and 30%) almost always coincides with the presence of isoniazid-resistance. The association of isoniazid-resistance and a lower probability for a positive treatment outcome has been described previously in epidemiological studies [55; 53]. In our simulations rifampicin-resistance is less common and predominantly occurs in the context of MDR-TB. This confirms the rationale for the GeneXpert MTB/RIF assay to be used to diagnose the presence of MDR-TB [129]. The answer to the question why in our simulations isoniazid- resistance correlates with treatment failure and why extended-release formulations of rifampicin may increase the likelihood of MDR-TB to emerge can be found in the pharmacodynamics. There we see that in regimens that do not use extended-release formulations the isoniazid-resistant subpopulation is not sufficiently suppressed at suboptimal adherence and can grow. In comparison a rifampicin-resistant subpopu- lation is expected to go extinct. The pre-existence of isoniazid-resistance even before the treatment starts is expected in a small fraction of the overall bacterial population. This population would be strongly selected for its competitive advantage over the wild-type and rifampicin-resistant populations during treatment and would even- tually dominate the composition of the overall population. Besides the higher fre- quency of isoniazid-resistance mutations relative to rifampicin-resistance mutations [63; 62] this may also contribute to the higher prevalence of clinical isoniazid-resistant samples among all clinically diagnosed first-line drug monoresistances [130; 105]. An 3.4 discussion 53

MDR subpopulation would be even less suppressed than the isoniazid-resistant one. However, MDR-TB is not expected to be initially present in a treatment-naïve patient who gets infected with wild-type TB. It most probably emerges from an isoniazid- resistant bacterium at a later stage of treatment and due to the rather low repro- ductive rate of Mycobacterium tuberculosis it would need some time before it could reach a detectable frequency. If we would continue an unsuccessful treatment that is not able to suppress the infection but still exerts a sufficiently high selection pres- sure we would expect MDR-TB to eventually dominate the overall population. This has been suggested previously in a computational model, in which unsuccessfully treated patients underwent again the standard first-line therapy and accumulated further resistance mutations [121]. This step-wise accumulation of resistance has also been confirmed by clinical studies [100; 48; 131]. If we use extended-release for- mulations of rifampicin the isoniazid-resistant subpopulation is most probably not able to grow even if we miss half of all prescribed doses. It will decline while MDR- TB on the other hand is now at a clear competitive advantage, which means that it will outcompete all other monoresistant subpopulations rather quickly if it can arise in the first place. There are currently technical means developed that are able to reduce the absorption rate constant for drugs (unpublished data). In the example of rifampicin we see that such extended-release formulations are expected to be more effective in treating TB patients, and it is conceivable that the extension of this to all first-line drugs could increase the positive effects even more. However, if patient compliance drops low enough that more resistant genotypes have sufficient time and opportunity to arise they are more strongly selected. The relative order of the results in terms of treatment efficacy and risk of resis- tance emergence is rather robust to changes of the fitness of resistant genotypes (see Supplementary Material 3.A). Because the competitive advantage conferred by drug resistance is so strong the comparably low imposed fitness costs of 10% per mutation do not substantially influence the relative pharmacodynamics between genotypes. In contrast to the previous simulations in which the total amount of drug exposure remained constant we also tested treatment regimens in which we simply increased the amount of rifampicin that is being administered. Unsurprisingly, this strategy improves the success rate of treatment for intermediate to high adherence levels. However, according to our results an increased rifampicin dose is also more likely to promote the emergence of MDR-TB at intermediate adherence levels. This find- ing seems to contradict the results from a previous in vitro study [93]. In this study Gumbo et al. discovered that suppression of resistance was associated with a higher Cmax-to-MIC ratio. This makes sense if resistance is not absolute as in our model but variable. If we have in a population a diversity of genotypes that vary in their extent of resistance for a particular drug, e.g. their MIC, then it follows that higher doses are more likely to exceed the MIC of these moderately resistant subpopulations and are able to suppress them. For simplicity our model only considers absolute suscep- tibility or resistance and the level of resistance is not concentration dependent. We also do not simulate the emergence of higher resistance through step-wise acquisi- tion of intermediate resistance mutations for a single drug. Our model is therefore not able to capture this aspect of partial resistance emergence or suppression and may thus overestimate the occurrence of de novo MDR-TB. However, there are single 54 alternative treatment strategies for tuberculosis

point mutations that confer resistance that is high enough to enable its carrier to be virtually unaffected by clinically achievable rifampicin concentrations [132]. Hence, such genotypes may account for only a small fraction within the rifampicin-resistant subpopulation but they would be more strongly selected if they could arise. We can see that intermittent treatment could be a more feasible regimen option if extended-release formulations of rifampicin would be available. Intermittency itself has a number of benefits for care providers as well as for patients. Also higher rifampicin doses are a promising alternative treatment strategy. However, those more effective hypothetical treatment regimens might also bear an increased risk if they are suboptimally applied. If a potentially more effective regimen is inappropriately applied it could backfire due to its stronger selective pressure for drug resistance. We conclude that the guideline of ’hitting hard’ does yield a positive effect in that it is able to eradicate the infection more reliably. However, if a hard-hitting strategy is compromised by low enough adherence so that monoresistant genotypes may thrive it may actually increase the selective pressure on these genotypes and cause an amplification of resistance [133; 134].

3.5 acknowledgments

We thank Balázs Bogos for reviewing the manuscript. APPENDIX

3.a supplementary material

In order to investigate the influence of fitness costs on the probabilities for treatment failure and the emergence of drug resistance when testing daily and intermittent regimens with and without extended-release formulations of rifampicin we ran ad- ditional simulations in which we varied the relative fitness of genotypes. With our standard assumptions every mutation rate confers a fitness cost of 10% and the costs stack in a multiplicative manner with every additional mutation. That means that MDR-TB usually is assumed to have a relative fitness of 81%((1 − 0.1)2) if it does not carry any more resistance mutations. Instead of 10% fitness costs per mutation we assumed 5% fitness costs and repeat the simulation of 1’000 patients (see Figure 3.5). In comparison with Figure 3.2 we observe slightly increased probabilities for treatment failure above 50% adherence for all treatment regimens (Figure 3.5 A). The probability for the emergence of MDR-TB increased substantially relative to the simulations with 10% fitness costs per mutation (Figure 3.5 B). Even the daily treatment regimen with the standard formulations of rifampicin now bears a considerable risk for the emergence of MDR-TB from 20% up to 100% adherence. The occurrence of isoniazid- and rifampicin-resistance are comparable to the pattern observed in Figure 3.2. For the upper half of the adherence spectrum isoniazid-resistance (Figure 3.5 C) coincides with treatment failure and rifampicin-resistance almost exclusively occurs in the context of MDR-TB (Figure 3.5 D). If we completely neglect the any fitness costs inferred by resistance mutations the situation appears even more serious (see Figure 3.6). There is now a substantial chance for treatment failure even at perfect adherence and under the most effective treatment regimen (Figure 3.6 A). The comparison of Figure 3.6 A and B shows that treatment failure in regimens with extended-release formulations of rifampicin occurs almost always due to the emergence of MDR-TB at adherence levels of 75% and higher. The prevalence of isoniazid- and rifampicin-resistance are again very similar to the previous patterns. When we keep the fitness cost for monoresistance at 10% but increase the fitness of MDR-TB to the same level as the fully susceptible wild type the situation changes somewhat (see Figure 3.7). The probabilities for treatment failure are almost the same as with the original assumptions (Figure 3.7 A). However, treatment failure for patients with an adherence above 40% ensues almost always due to MDR-TB (Figure 3.7 B). Monoresistances of isoniazid an rifampicin are more rare than in any previous scenario (Figure 3.7 E and F) indicating that MDR-TB is outcompeting the monoresistant subpopulations. When we look at the pharmacodynamics with and without fitness costs we observe slight increases in growth rates if we neglect the costs inferred by resistance muta- tions (see Figure 3.8). However, neglecting the fitness costs does not affect the relative

55 56 alternative treatment strategies for tuberculosis

selective advantage of the different genotypes granted by the resistance mutations. Therefore, it is not surprising that we do not observe much of a change between the order of regimens in the Figures 3.2 and 3.5 – 3.7 in regard to the probability of treatment failure or the emergence of MDR-TB. 3.A supplementary material 57

A Probability of treatment failure B Probability of MDR−TB emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

C Probability of isoniazid− D Probability of rifampicin− resistance emergence resistance emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

E Probability of isoniazid− F Probability of rifampicin− monoresistance emergence monoresistance emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

Figure 3.5: Probabilities of treatment failure and the emergence of MDR-TB, isoniazid- and rifampicin-resistance with fitness costs of 5% per resistance mutation for different treatment intervals and varying absorption rate constants. We distin- guish the risk of incomplete infection clearance (A), the emergence of MDR-TB (B), the emergence of any isoniazid-resistant genotype (C), the emergence of any rifampicin-resistant genotype (D), the emergence of isoniazid-monoresistance (E) and the risk of the emergence of rifampicin-monoresistance (F). In every panel are the probabilities for a regime with the standard daily administration of all drugs (black lines), a regime where a double-dose of rifampicin is administered only on every second occasion (blue lines) and a regime in which rifampicin is given every third time in a triple-dose (red lines). Within a regime the pharma- cokinetics of rifampicin have a standard fast absorption rate constant (solid lines), a fixed intermediate absorption rate constant of 5 d−1 (dotted lines) or a fixed low absorption rate constant of 1 d−1 (dashed lines). The intermediate and low absorption rate constants represent two different extended-release formulations of rifampicin. Emergence of resistance is defined as at least 10% of the bacterial population in the open cavities compartment being resistant. 58 alternative treatment strategies for tuberculosis

A Probability of treatment failure B Probability of MDR−TB emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

C Probability of isoniazid− D Probability of rifampicin− resistance emergence resistance emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

E Probability of isoniazid− F Probability of rifampicin− monoresistance emergence monoresistance emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

Figure 3.6: Probabilities of treatment failure and the emergence of MDR-TB, isoniazid- and rifampicin-resistance with no fitness costs for any resistance mutation for different treatment intervals and varying absorption rate constants. We distin- guish the risk of incomplete infection clearance (A), the emergence of MDR-TB (B), the emergence of any isoniazid-resistant genotype (C), the emergence of any rifampicin-resistant genotype (D), the emergence of isoniazid-monoresistance (E) and the risk of the emergence of rifampicin-monoresistance (F). In every panel are the probabilities for a regime with the standard daily administration of all drugs (black lines), a regime where a double-dose of rifampicin is administered only on every second occasion (blue lines) and a regime in which rifampicin is given every third time in a triple-dose (red lines). Within a regime the pharma- cokinetics of rifampicin have a standard fast absorption rate constant (solid lines), a fixed intermediate absorption rate constant of 5 d−1 (dotted lines) or a fixed low absorption rate constant of 1 d−1 (dashed lines). The intermediate and low absorption rate constants represent two different extended-release formulations of rifampicin. Emergence of resistance is defined as at least 10% of the bacterial population in the open cavities compartment being resistant. 3.A supplementary material 59

A Probability of treatment failure B Probability of MDR−TB emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

C Probability of isoniazid− D Probability of rifampicin− resistance emergence resistance emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

E Probability of isoniazid− F Probability of rifampicin− monoresistance emergence monoresistance emergence

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4

Probability 0.2 Probability 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Adherence Adherence

Figure 3.7: Probabilities of treatment failure and the emergence of MDR-TB, isoniazid- and rifampicin-resistance with monoresistance conferring normal 10% fitness cost and MDR-TB with the same fitness as the wild type for different treatment intervals and varying absorption rate constants. We distinguish the risk of in- complete infection clearance (A), the emergence of MDR-TB (B), the emergence of any isoniazid-resistant genotype (C), the emergence of any rifampicin-resistant genotype (D), the emergence of isoniazid-monoresistance (E) and the risk of the emergence of rifampicin-monoresistance (F). In every panel are the probabilities for a regime with the standard daily administration of all drugs (black lines), a regime where a double-dose of rifampicin is administered only on every second occasion (blue lines) and a regime in which rifampicin is given every third time in a triple-dose (red lines). Within a regime the pharmacokinetics of rifampicin have a standard fast absorption rate constant (solid lines), a fixed intermediate absorption rate constant of 5 d−1 (dotted lines) or a fixed low absorption rate con- stant of 1 d−1 (dashed lines). The intermediate and low absorption rate constants represent two different extended-release formulations of rifampicin. Emergence of resistance is defined as at least 10% of the bacterial population in the open cavities compartment being resistant. 60 alternative treatment strategies for tuberculosis

A B

106 106 105 105 104 104

CFU 103 CFU 103 102 102 101 wild type 101 rINH 0 5 10 15 20 0 5 10 15 20 rRMP MDR−TB time [days] time [days]

C D

106 106 105 105 104 104

CFU 103 CFU 103 102 102 101 101

0 5 10 15 20 0 5 10 15 20

time [days] time [days]

Figure 3.8: Pharmacodynamics at 50% adherence of four subpopulations with different drug susceptibilities, with and without fitness costs under treatment regimens with different rifampicin administrations. The four panels all show the bacte- ricidal effect of the standard regimen on four different M. tuberculosis subpopu- lations. The subpopulations are either fully susceptible to all drugs (wild type), fully resistant to isoniazid (rINH), fully resistant to rifampicin (rRMP) or resistant to both isoniazid and rifampicin (MDR-TB). Fitness costs are either 10% per re- sistance mutation (dashed lines) or resistance mutations do not confer any costs at all (solid lines). The environmental conditions correspond to the extracellular compartment in a patient. All patient-specific variable parameters are set to their midpoint value. The initial population sizes are arbitrarily chosen and do not necessarily reflect the population composition in any patient at any time point. The absorption rate constant for rifampicin in the panels A and B is at the stan- dard midpoint value of 16.3 d−1. In the panels C and D rifampicin is given as an extended-release formulation with a slow absorption rate constant of 1 d−1. The treatment regimen for the panels A and C prescribes all drugs to be admin- istered daily. The regimen for the panels B and D prescribes a three-fold higher rifampicin dose every third day under perfect adherence. In all panels every second prescribed drug administration is missed corresponding to an enforced adherence level of 50%. 4 CONSIDERINGANTIBIOTICSTRESS-INDUCEDMUTAGENESIS

D Cadosch, P Abel zur Wiesch, S Bonhoeffer abstract

The mutation rate is a key parameter in the assessment of the risk of drug resistance. Mutation rates of resistance mutations are usually measured in absence of antibiotics and are assumed to be constant rates. Environmental stress elicited by antibiotic ex- posure has been shown to transiently increase the mutation rate in pathogenic bac- teria. In this study we explore the implications for the emergence of drug resistance that arise due to antibiotic stress-induced mutagenesis (ASIM). With a computational model we simulate the effect of ASIM on bacterial population dynamics. We show the magnitude by which models with a constant mutation rate underestimate the probability for the emergence of drug resistance. In a within-host model that also incorporates pharmacokinetics we further demonstrate that a cycling regimen of two drugs is less likely to cause multidrug-resistance compared to a combination regi- men if ASIM is taken into account. We conclude that ASIM is likely to substantially increase the risk of drug resistance and reveals drug interaction dynamics that could improve treatment efficacy. Our study shows that the measurement of parameters involved in ASIM is crucial for reliable estimates about the occurrence of drug resis- tance.

61 62 considering antibiotic stress-induced mutagenesis

4.1 introduction

Resistance to antibiotics has been a concern for almost as long as the history of an- tibiotic usage and will likely continue to be a major threat to public health in the foreseeable future [135; 136; 137; 138]. A large body of literature describes the un- derlying factors that lead to drug resistance in many pathogen/drug combinations. One of the key factors for the emergence of antibiotic resistance is the mutation rate [139; 140; 141]. The mutation rate is typically measured by culturing bacteria in the absence of drugs and then measuring the frequency of spontaneously emerged re- sistant mutants in this population on selective media [142; 143]. However, in recent years there has been mounting evidence that phenotypic mutation rates in bacteria are influenced by various stresses [24]. Importantly, these stresses include many an- tibiotics [144]. Most of the stresses are directly or indirectly linked to an increased abundance of reactive oxygen species (ROS) [24; 145]. Higher ROS concentrations, which can also be caused by certain antibiotics, may inflict DNA damage and lead to a change in the regulation of genes that are involved in DNA repair and replication. These genes control the induction of the SOS stress response, the methyl-directed mismatch repair pathway, the activation of double-strand break repair proteins or the expression of error-prone DNA polymerases [24; 146]. All of these responses increase the probability of introducing mutations. It has been argued that the abil- ity to transiently increase the mutation rate is a trait that has been established in many bacteria due to a second-order selection for increased mutability under ad- verse circumstances [24; 147; 148]. The existence of stress-induced mutagenesis has been controversially discussed [149; 150]. However, it may be still worth investigat- ing how a phenotypic alteration of mutation rates in response to antibiotic exposure affects resistance evolution. Here, we focus on the transient mutagenic effect of antibiotic exposure. We ex- pect that the resulting stress response has a positive feedback on the emergence of resistance mutations against the drug that is mutagenic as well as other drugs. Most mathematical models investigating the emergence of drug resistance assume stable mutation rates [151; 152; 153; 154]. By not taking into account the possibility of chang- ing mutation rates they may fail to describe a possible effect of pharmacokinetics on mutation rate and misjudge the overall likelihood of the emergence of resistance, es- pecially when more than one antibiotic is used. The aim of this study is to assess the influence of antibiotic stress-induced mutagenesis (ASIM) on the emergence of drug resistance. We find that ASIM does not only alter the expected frequency of de novo emergence of resistance, but also changes our expectations regarding the success of different treatment strategies.

4.2 methods

4.2.1 Mathematical model

The detailed description of the mathematical model is available in the Supplementary Material 4.A. In brief, we model bacterial population biology by assuming logistic growth and adding a drug-dependent death rate (Suppl Mat 4.A.1). The relationship 4.2 methods 63 between drug concentration and antibiotic-induced killing is described by a sigmoid Emax model [108] extended to multiple drugs (Suppl Mat 4.A.2). Additionally, we model the emergence of resistance mutations and assume that the mutation rate de- pends on the drug concentration (Suppl Mat 4.A.3). Pharmacokinetics are described by translating the values of the maximally achievable peak concentration, Cmax, the time until the peak concentration is reached, tmax, and the excretion half-life, t1/2, from the literature to a time-dependent concentration profile in patients (Suppl Mat 4.A.5). The bacterial population dynamics are simulated as stochastic processes by applying the Gillespie τ-leap method [58].

4.2.2 Assumptions and parameterization

4.2.2.1 Bacterial growth

The modeling of the bacterial growth is described in detail in Suppl Mat 4.A.1. We assume that the bacteria have a growth rate of 2 d−1, corresponding to a doubling time of approximately 15.1 h. The initial population size for the simulations with constant drug concentrations is assumed to be 107 fully susceptible bacteria. The maximum population size (carrying capacity) is 109 bacteria.

4.2.2.2 Resistance mutations

The model assumptions for the emergence of resistance are described in detail in Suppl Mat 4.A.4. The central part of this study is the introduction of a drug concen- tration dependent mutation rate. We assume that bacterial mutation rates increase with drug concentration in a sigmoidal fashion [155]. We make this assumption be- cause the mutagenic effect of antibiotics has been argued to arise due to the increased expression of more error prone DNA polymerases and repair proteins [144; 156; 157]. The expression levels of such polymerases and repair proteins are likely to eventually saturate and their error rate is expected to be constant at high drug concentrations. The sigmoidal curve is defined by three parameters: a minimum corresponding to the base mutation rate in absence of drugs, a maximum corresponding to the satura- tion of the mutation rate at high drug concentration, and a parameter termed mut50, which corresponds to the drug concentration at which the mutation rate reaches the half-point between minimum and maximum. As an estimate for the minimum mu- tation rate to become resistant to a single drug we conservatively assumed a rate of 10−9 per cell doubling [62]. The maximum mutation rate varies widely between studies [158; 159; 160; 161; 162; 163; 164; 165; 166]. The differences are probably due to both differences between combinations of bacteria and drugs and differences in ex- perimental designs and measuring methods. Here we assume a maximum ten-fold increase of the mutation rate for high drug concentrations. Most of the aforemen- tioned studies did not look at the concentration-dependent increase of the mutation rate. The few studies that measured the increase of the mutation rate at more than one drug concentration did this mostly at sub-MIC concentrations [158; 162; 165; 166]. Therefore, it is difficult to estimate whether and how far ASIM extends beyond the MIC. In our default parameter setting, we assume that the turning point of the mut50 parameter coincides with the MIC. 64 considering antibiotic stress-induced mutagenesis

Furthermore we assume that if a resistance mutation is acquired, it grants absolute resistance and the drug becomes completely ineffective. For every drug we assume that there is on such resistance mutation and the corresponding allele confers a fit- ness cost of 10% on the growth rate. Multiple resistance mutations are assumed to contribute multiplicatively to the overall fitness costs.

4.2.2.3 Pharmacokinetics

During the simulations the drug concentrations are either kept constant or they in- crease and decrease according to a pharmacokinetic model that is described in detail in Suppl Mat 4.A.5. Firstly, we investigate the effect of ASIM in a situation where a patient is treated with two equally bactericidal drugs, only one of which elicits ASIM. Secondly, we explore the dosing regime and compare situations where pa- tients are taking the two drugs combined every day (combination) and situations where patients alternate between the drugs every day (cycling). In order to be able to compare the two regimens the efficacy of the two regimens is equalized by ad- justing the dosage of the drugs in both cases so that patient clearance is achieved on average after 28 days. The exact dosages can be found in the Suppl Mat. Before treat- ment starts every patient harbors 5 × 107 fully susceptible wild-type bacteria and the simulation is repeated 1’000 times for every treatment scenario and drug type in Figures 4.1 and 4.2. In order to decrease the confidence intervals in the Figures 4.3 and 4.4 we performed these simulations 10’000 times each.

4.3 results

To get an overview over the basic parameters and their effects we first study a ba- sic model of ASIM. In Figure 4.1 a homogeneous population of sensitive bacteria is exposed to various constant drug concentrations. The net growth rate (red line), i.e. the difference of the natural replication rate and the drug-induced bactericidal killing rate, declines with increasing drug concentrations in a sigmoidal manner. In addition to the drug concentration, the net growth rate is affected by the replication rate, the KC50, the Emax value and the MIC of the drug (see Equations 4.4–4.4 and Table 4.1). At the MIC the drug-induced killing and the replication rate cancel each other out and the net growth rate is zero. The mutation rate (black line) without considering ASIM stays constant and is independent of the drug concentration (grey line). When ASIM is taken into account the mutation rate increases sigmoidally with higher drug concentrations (black line). The mutation rate increase depends on the mut50 and the maximum fold change Md. Here, mut50 is set to the MIC. These parameters are assumed constant during the simulations shown in Figure 4.1. We get three possible treatment outcomes: (i) complete sterilization, i.e. the drug concentration is suffi- cient to eradicate the bacterial population and the treatment is deemed successful; (ii) treatment failure, here defined as the treatment being unable to clear the bacterial population after 20 days (green line); (iii) emergence of resistance, defined here as the population containing at least 50 resistant bacteria after 20 days (dark blue line). Emergence of resistance implies treatment failure and is therefore a subset of the pre- vious category. We show the emergence of resistance with ASIM (dark blue line) and without ASIM (light blue line). Unsurprisingly, the risk for treatment failure drops 4.3 results 65

Table 4.1: Compartment characteristics Replication rate (r) 2 d−1 7 Initial population size (N0) 5 × 10 CFU Carrying capacity (K) 109 CFU a Drug half-life (t1/2) 3 h a Absorption time (tmax) 1 h c Dosage (D0) 3.18 / 8.80 MIC a 1 b a b KC50 5 a −9 Base mutation rate (md) 10 per replication d b mut50 0.25

Maximum fold increase of mutation rate (Md) 10 a b Resistance cost (cl) 0.1 a for all used drugs b arbitrary concentration unit c combination / cycling d only for mutagenic drug

from 100% at sub-inhibitory drug concentrations rapidly if the drug concentrations are above the MIC. Beyond the MIC in about 5% of all simulations the bacterial pop- ulation is rescued by the emergence of a resistant mutant under ASIM. Below the MIC resistant genotypes occur in up to 60% of all populations. This is substantially more frequent than in a model without ASIM. Next we assess how the emergence of resistance depends on mut50 (see Figure 4.2). To do so we repeat the simulations shown above for a wide range of drug concentrations and additionally vary the mut50 concentration. For each pair of drug concentration and mut50 value we count the frequency of the emergence of resistant mutants. The remaining parameters and the criteria for scoring the outcome of the simulations are the same as above. Resistant genotypes emerge rarely if the mut50 value is high and the drug concentration is either very low or very high. The risk for the emergence of resistance generally increases with lower mut50. It is highest at the lowest mut50 that we tested and at a drug concentration of 1/4 × MIC. Interestingly, 1/4 × MIC is the drug concentration at which the frequency of drug resistance is highest for every mut50. We conclude that the mut50 concentration has a substantial influence on the probability of emergence of resistance. To estimate the influence of ASIM on the emergence of resistance we repeated the above simulations 10’000 times for each parameter set with and without ASIM (see Figure 4.3). At low drug concentrations the frequency of emergence of resistance only differs marginally. However, at the MIC the risk of emergence of resistance increases about five-fold increasing to an about ten-fold risk at high drug concentrations. In Figure 4.1 we see that a considerable fraction of bacterial populations are rescued 66 considering antibiotic stress-induced mutagenesis 8 1.0 − 5 1.0 10 0.9 4 0.9 9 0.8 − 3 0.8 10 ×

0.7 8 2 0.7 9 0.6 − 1 0.6 10 ×

0.5 6 0 0.5

0.4 9 −1 0.4 − 10 Treatment failure rate failure Treatment 0.3 × −2 0.3 4 Mutation rate per generation Mutation rate

0.2 −3 strain of sensitive rate Net growth 0.2 9 Frequency of resistance emergence −

0.1 10 −4 0.1 × 2 9 0.0 − −5 0.0 10

IC IC IC IC IC IC IC IC IC IC IC IC M M M M M × M × M × M × × × × M × M × M × M × × 64 32 16 1 1 1 1/8 1/4 1/2 1 2 4 8 16 32 Concentration

Figure 4.1: Antibiotic stress-induced mutagenesis (ASIM) increases the risk of drug resis- tance over a large concentration range. A population of 107 bacteria is exposed to a range of constant drug concentrations. The outcome of 1000 simulations of treatment per parameter set is collected and the lines show the average. Treat- ment failure (green line) is defined as incomplete clearance after 20 days. The frequency of resistance emergence under ASIM is given in dark blue and without ASIM in light blue. At least 50 drug resistant bacteria have to be present in the population for a strain to be classified as resistant. Without considering ASIM resistance evolves in fewer populations. The mutation rate per generation in pres- ence of ASIM is given in black and increases in a sigmoidal manner with higher drug concentrations. The base mutation rate (without ASIM) is given in grey. The inflection point where the mutation rate reaches the half maximal increase (mut50) is at the MIC. The net growth rate (red line) is composed of the natural growth rate and the killing due to the bactericidal drug activity. 4.3 results 67

8 0.8 4

2 0.6 1 50 0.5 mut 0.4 0.25

0.125 0.2

0.0625 Probability of emergence resistance

IC IC C IC MICM MICM MICMICMICMICMI M MICMIC × × × × × × × × × × × × 64 32 16 1 1 1 1/8 1/4 1/2 1 2 4 8 16 32 Concentration

Figure 4.2: Emergence of drug resistance depends on drug concentration and mutation rate. The mut50 concentration is the antibiotic concentration at which the half maximal mutation rate is reached. To predict the influence of the mut50 value on the 7 probability of resistance emergence 10 bacteria with varying mut50 values are exposed to a wide range of drug concentrations. The color scale indicates the fraction of 1000 simulations per parameter set in which at least 50 drug resistant bacteria evolved after 20 days. 68 considering antibiotic stress-induced mutagenesis

due to the emergence of resistance even at very high drug concentrations. This is a much higher fraction than with a constant mutation rate. The simulations thus suggest that the underestimation of the risk of emergence of resistance due to AISM increases with higher drug concentrations. Next we investigate the implications of ASIM for the treatment of patients. To this end we are introducing a model that incorporates the pharmacokinetics as would be observed in a human patient treated with two bactericidal drugs simultaneously (see Figure 4.4). Four cases are studied: Patients receive both drugs either simultaneously or alternatingly every day and the drugs either do not elicit ASIM or only one of them elicits ASIM. The dosage of the drugs is adjusted to achieve complete clearance after 28 days on average if no double-resistance emerges. The simulation is stopped after 50 days and the frequency of patients harboring double-resistant bacteria is counted. Thus, if the bacterial population is not eradicated after 50 days, it is always due to the emergence of resistance. In accordance with the previous results the risk of emergence of double-resistant genotype is substantially lower if both drugs are not mutagenic. The two treatment strategies also do not differ from each other if no drug elicits ASIM. However, if one drug is mutagenic combination treatment seems to be significantly worse than an alternating regimen. The advantage of the alternating treatment is a direct consequence of ASIM.

4.4 discussion

Mathematical models are a useful tool to investigate the expected outcome of antibi- otic treatment strategies before costly and time consuming experimental and clinical studies are performed. Moreover, they aid in identifying gaps in our current knowl- edge that preclude quantitative predictions of treatment success and resistance evolu- tion. It is well known that at least some antibiotics increase bacterial mutation rates and thereby the rate of resistance evolution in a dose-dependent fashion. In this study we present a population dynamic model that addresses how dose-dependent antibiotic stress induced mutagenesis (ASIM) affects the probability of emergence of drug resistance in a single patient. Our study indicates that ASIM changes both our quantitative expectations regard- ing the frequency of resistance emergence as well as our qualitative expectations which treatment strategy is least likely to lead to treatment failure due to resis- tance. This is in agreement with previous expectations and results from other studies [160; 162; 167; 168]. Previous models, which do not take ASIM into account, under- estimate the probability for the emergence of resistance. The degree to which those models underestimate resistance evolution depends on the drug concentration to which the bacteria are exposed. High drug concentrations do not necessarily reduce the risk of drug resistance if fully resistant mutants rescue the bacterial population before it is completely eradicated. We find that the probability of resistance emer- gence peaks at approximately 1/4 × MIC independent from the exact relationship of drug concentration and mutation rates. Sub-MIC concentrations have been demon- strated to be associated with elevated occurrences of drug resistance [164; 166]. There are several factors which we would expect to drive resistance evolution: i) the size of the susceptible population that gives rise to resistant mutants, ii) the number of gen- 4.4 discussion 69

15

10

5

1 0 fold change of resistance emergence with ASIM fold C C C C C IC C C C C C C MI MI MI MI MI M MI MI MI MI MI MI × × × × × × × × × × × × 8 4 2 1 2 4 8 64 32 16 16 32 1 1 1 1 1 1 drug concentration

Figure 4.3: ASIM increases the emergence of drug resistance at higher drug concentrations. A population is classified as resistant when at least 50 bacteria became drug re- sistant after 20 days of treatment. The panel shows the fold change in emergence of drug resistance with ASIM compared to a model with a fixed mutation rate. In the ASIM model the mutation rate increases with higher drug concentrations assuming mut50 equals the MIC. The fixed mutation rate model assumes a mu- tation rate that is equal to that of the ASIM model at drug concentration zero. Each data point summarizes 10’000 simulations. The error bars indicate the 95% confidence interval. The increasing size of the confidence intervals is due to the increasingly rare occurrence of drug resistant bacteria at high drug concentrations without ASIM. 70 considering antibiotic stress-induced mutagenesis

Figure 4.4: ASIM changes theoretical predictions for optimal drug therapy. This graph shows the emergence of drug resistance within single patients that are treated with two bactericidal drugs, either administered every day simultaneously (com- bination, red bars) or given alternately on consecutive days (cycling, blue bars) Patients harbor a homogeneous population of 5 × 107 wild-type bacteria. For the simulations assuming fixed mutation rates neither drug is mutagenic (i.e. resis- tance mutations arise irrespective of the applied drug concentration), while with ASIM one of the two drugs induces mutagenesis. The mut50 concentration for the ASIM drug is 1/4 × MIC. Every parameter set is simulated 10’000 times and the fraction of patients that developed multidrug-resistance is given. The drug dosages are adjusted to achieve complete clearance after 28 days of treatment as- suming no emergence of multidrug-resistant strains. The error bars indicate the 95% confidence interval. In this case, the emergence of resistance is equivalent to treatment failure, i.e. patients who develop resistance are still infected after 28 days and all patients who fail treatment do so because of resistance evolution. 4.5 acknowledgments 71 erations before the population is eradicated, iii) the rate per replication with which resistance mutations emerge and iv) the fitness difference between susceptible and resistant bacteria. When keeping the initial population size constant, there seems to be an optimum for the last three factors to favor a high frequency of populations containing drug resistant bacteria. Patients who are treated with a mixture of drugs usually receive them in com- bination [169; 170]. Our results show that this strategy might not be optimal in preventing the emergence of resistance if one of the drugs elicits ASIM. This effect probably arises due to the lower number of drug applications that is compensated by higher doses. If a drug is less often administered the drug concentration is less of- ten at subinhibitory concentrations, which have previously been shown to favor the emergence of drug resistance. The advantage of a cycling regimen over combination therapy on an epidemiological scale has previously been shown to be advantageous in a hospital setting [168]. To the best of our knowledge, this study is the first that addresses the effects of dose-dependent ASIM. Our main limitation is the scarcity of experimentally obtained parameters. Depending on the study the increase of mutation rates varies widely, from 2-fold [164; 166] up to 10’000-fold [160]. Most studies report increases in the order of a few- up to 100-fold [158; 159; 161; 162; 163; 165]. Furthermore, most stud- ies showed an increase of the mutation rate only qualitatively, but did not establish a quantitative relationship between the drug concentration and the increase of the mutation rate. Due to the insufficient data from the literature we apply conservative parameter estimates. This also means that we are potentially over- or underestimat- ing the magnitude of the effects that we found. We therefore have to point out that the focus should be on the qualitative aspects of our results. We further have to point out that we look specifically at the influence of changing probabilities on the emer- gence of de novo rescue mutations [171]. That means, mutations that are involved in preventing the population from eradication and which appear when the stress is already present. We assume that none of these mutations occur in the population before the introduction of antibiotics and that the population is therefore genetically homogeneous. Here, we show that that ASIM has a profound effect on resistance evolution. One of the main messages of this work is therefore that dose-dependent ASIM should be investigated experimentally in more detail, especially at antibiotic concentrations above the MIC. The negative consequences of ASIM could be prevented by the intro- duction of drugs that specifically inhibit the intracellular mechanisms that increase the mutation rate of bacteria. Such drugs have been proposed previously as an ef- fective instrument to reduce the evolvability of pathogens [161; 172; 173; 174]. We find that ASIM increases the probability of treatment failure by up to 10-fold. Thus, drugs that prevent stress-induced mutagenesis might have a major impact on treat- ment outcome and warrant further investigation.

4.5 acknowledgments

We thank Antoine Frénoy for reviewing the manuscript.

APPENDIX

4.a supplementary material

4.a.1 General model

The bacterial population dynamics are simulated as stochastic processes by applying the Gillespie τ-leap method [58] with a temporal resolution of 10−2 d. The underlying processes can be described in differential equations that are explained below.

4.a.2 Bacterial growth and death

The general population dynamics are based on a classic logistic growth model.

dNg = r · ω · N − (d + κ ) · N (4.1) dt g g g g g

Here Ng is the number of bacteria of a specific genotype. r is the replication rate of the bacteria, which is modified by the fitness ωg of the strain. The population is reduced by the natural death rate dg and the drug-induced killing κg. The fitness of a specific genotype is influenced by the fitness costs that are imposed by resistance mutations.

n ωg = (1 − cl) (4.2) l=1 Y cl is the cost of a resistance allele at the locus l and n is the number of resistance loci. Susceptible wild-type alleles do not confer any costs. The death rate dg depends on the overall population density that is influenced by bacteria of every genotype.

N d = r · (4.3) g K Here K is the carrying capacity.

4.a.3 Pharmacodynamics

The killing rate κg is calculated by using the sigmoid Emax model by Czock et al. [108]. We extend it to include the effects of multiple drugs.

n   1 κg = Emax d · 1 − · νg d (4.4) ,  Cd  , d=1 KC + 1 X 50,d 73 74 considering antibiotic stress-induced mutagenesis

The killing rate depends on the additive effects of all drugs to which the specific bacterial strain is susceptible. The potency of a drug is governed by Emax,d, which is the maximal death rate. It is modified by the drug concentration Cd and the KC50,d concentration, which represents the concentration at which the drug exerts its half- maximal bactericidal potential. The Boolean parameter νg,d determines whether the drug is effective or whether the bacteria strain is resistant against the drug. Drug resistance is assumed to be absolute. The Emax value is obtained by adopting the equation from the enhanced-death con- stant replication model [108].

dN C = r · N − Emax · N · (4.5) dt KC50 + C When the drug concentration C is equal to the minimum inhibitory concentration (MIC) growth and killing cancel each other out and we get the following equation that determines the Emax value.

r · (MIC + KC50) E = (4.6) max MIC

4.a.4 Resistance mutations

The increase of the mutation rate m by a stress-inducing drug follows a curve that is defined by a sigmoid function [155].

n !! Md − 1 m(t) = m · Md − (4.7) Cd d=1 mut + 1 Y 50 If we assume that resistance to a drug is granted by the mutation of a single allele, then the number of drugs n is the number of resistance loci. m is the base mutation rate and M is the maximum increase of this rate that is achievable by a drug. The turning point of the sigmoid curve is defined by the mut50 concentration.

4.a.5 Pharmacokinetics

If the drug concentration in the simulation is not kept constant, classic absorption and excretion kinetics are applied to the drug concentration. Two drug compartments are simulated in the model: At the time point of drug ad- ministration, the whole dosage is instantly added to the compartment of unabsorbed drug D. From the first compartment D the drug is absorbed into the compartment C of the pharmacodynamically effective drug. From compartment C the drug concen- tration constantly decays due to excretion. The decrease of the drug concentration in compartment D is calculated according to the following equation:

dD = −k · D (4.8) dt a 4.A supplementary material 75

ka here is the absorption rate constant. The dynamics in compartment C are gov- erned accordingly:

dC = k · D − k · C (4.9) dt a e

ke is the excretion constant of the drug. To calculate the absorption rate constant ka we use the following equation that describes the relationship between the absorp- tion rate constant, the excretion rate constant ke and the time until the maximum concentration peak is reached tmax:

ln(ka) − ln(ke) tmax = (4.10) ka − ke From this we can derive an equation that enables us to calculate the absorption rate constant for a known tmax and ke.

−k ·t W−1(−e a max · ke · tmax) ka = − (4.11) tmax

W−1 denotes the lower branch of the Lambert function. The excretion rate constant ke is derived by from the concentration half-life t1/2.

ln(2) ke = (4.12) t1/2

To calculate the initial amount of drug D0 that has to be administered in order to reach a predefined peak concentration Cmax, we use the Bateman equation [127; 128], which is also the solution to equation 4.9 to calculate the drug concentration at any given time point considering drug absorption and excretion:

D · ka C(t) = · (e−ke·t − e−ka·t) (4.13) ka − ke

From this we derive a formula that calculates the required D0.

C · (k − k ) D = max a e 0 −k −k ·t (4.14) ka · (e e·tmax − e a max )

5 GENERALDISCUSSION

5.1 conclusions

5.1.1 Treatment of pulmonary tuberculosis

The initiation of the directly observed treatment, short course (DOTS) strategy im- plemented by the WHO had five main components: increasing government commit- ment, case detection by sputum smear microscopy, the standardization of treatment by the application of a short course treatment regimen under professional supervi- sion, providing sufficient drug supply and a standardized recording and reporting system [16]. While DOTS was reported to be very successful [27] there were also studies that showed the inadequacy of DOTS in areas with a high prevalence of drug resistance [175; 55]. It was argued that the incautious application of treatment reg- imens within the DOTS program could lead to an amplification of drug resistance among patients due to the undetected preexistence of mono- or multi-drug resistance [176; 177]. In Chapter 3 we see that there is a substantial likelihood that treatment failure coincides frequently with at least mono-resistance against isoniazid. Even if drug susceptibility testing with a GeneXPert MTB/RIF test [129] would be performed such patients would probably not be diagnosed as harboring MDR-TB (M. tuberculo- sis that is resistance against at least isoniazid and rifampicin). In Chapter 2 we find that the retreatment of patients with a treatment history indeed bears the risk of ac- cumulating additional resistance mutations if patients also fail the retreatment. This confirms the concerns mentioned above that the application of standard treatment for patients who are suspected to harbor Mtb with low resistance could lead to an amplification of the resistance. The DOTS-Plus strategy aims specifically at the diagnosis and optimal treatment of MDR-TB patients [178]. Based on our results we argue that this might aim too low. A thorough drug susceptibility testing that also screens for isoniazid-resistance could help to prevent a potentially detrimental administration of ineffective drugs. Not only is the patient more likely to fail the treatment if not all drugs are effective, he or she could also be forced to suffer later through retreatment regimens that have a lower success rate and are associated with more severe side-effects. Besides the per- sonal disadvantages for the patient, MDR-TB or XDR-TB (extensively drug-resistant TB: resistance against at least isonazid and rifampicin, a fluoroquinolone, and either amikacin, kanamycin or capreomycin [179]) treatments are also considerably more time-consuming and expensive [180; 181].

77 78 general discussion

5.1.2 Antibiotic stress-induced mutagenesis

Mutation rates are commonly assessed under ideal growth conditions for bacteria [62]. When any other influences can be excluded the mutation rate for a specific locus can be assumed to be dependent solely on the fidelity of the DNA replication machinery. However, in different environments there exist factors that may change mutation rates. The concept that mutation rates are not constant but can vary under certain circumstances has not been discussed in the literature for a long time. It is therefore not surprising that it is not customarily incorporated into within-host mod- els that deal with mutation rates. Mutation rates are a key parameter for models about the probability for the emergence of resistance [151; 182]. Several environmen- tal stresses have been shown to increase mutation rates in bacteria. Among those stresses is also the exposure to certain antibiotics [144]. In Chapter 4 we conceptually show what the implications of antibiotic stress-induced mutagenesis (ASIM) may be for the evolution of drug resistance in bacteria. When we compare the probabilities for the emergence of resistance between a model that assumes a static mutation rate and a model in which the antibiotic increases the mutation rate in a concentration- dependent manner, we observe a substantial increase of the probability for the emer- gence of drug resistance. This leads us to the conclusion that the concept of ASIM should at least be considered in future models that attempt to quantify the probabil- ities for the emergence of mutations. When we take ASIM into account we are also able to discover novel implications for combination therapy. In a scenario in which a patient is treated with two drugs against a bacterial infection we observe that it could be beneficial to administer the drugs alternately rather than simultaneously if one of the drugs increases mutage- nesis and the other does not. To my knowledge this study is the first to assess the potential benefits of a cycling drug administration regimen for an individual regard- ing the emergence of resistance.

5.2 future directions

When one is engaged in the business of modeling one has to accept the intrinsic shortcomings of models. Models try to represent actual systems in an abstract and simplified form. The human mind constantly constructs models to get a grasp on the reality around it and they help it to see and understand relationships and causalities. Because models are a simplification of reality they are also never absolutely true because they cannot fully capture the nature of reality. However, models are not meant to replicate the real world. Their task is to show whether certain assumptions are sufficient or necessary to give a reasonably accurate representation of the natural world. Still, one has to constantly answer the question whether a model reflects reality accurately enough to provide a sufficiently trustworthy answer to the specific question one is trying to tackle. In this section I would like to talk about aspects that we could not implement in our projects. There are various reasons for why we did not include certain things but it generally left me behind with some unrest. For the aforementioned reasons I have to constantly question my confidence in my models and their predictions because 5.2 future directions 79 not considering some aspects of the disease dynamics may open up the door for unjust conclusions. At the same time this attitude also helps me to maintain a critical eye on my own work and that of my colleagues and to think about possibilities for improvements of current models and future directions to explore.

5.2.1 Pharmacodynamics

Antibacterial drugs are commonly divided in two main classes: bacteriocidal drugs and bacteriostatic drugs. Bacteriocidal drugs are characterized by their ability to kill bacteria while bacteriostatic drugs merely inhibit the proliferation of bacteria. If you try to put an antimicrobial drug in one of these two categories you may discover that this is not always a straightforward task. Many antibiotics have a predominantly bac- teriostatic effect at low concentrations but may actually exhibit bacteriocidal activity at higher concentrations. It could even be taken into question whether a drug is bac- teriostatic at low concentrations if one could just observe that a colony does not grow anymore. The classification of bacteriostatic and bacteriocidal drugs is usually done at a population level. Hence, if one would examine the drug efficacy at a cellular level it is conceivable that the bacteriocidal activity of a drug and the bacterial pro- liferation just about cancel each other out and therefore no net growth of the colony is observed. Therefore, a bacteriocidal drug could at low concentrations be mistaken for being bacteriostatic. In fact one of the simplifications that we did in all chapters of this thesis is to assume that the activity of antimicrobial drugs is exclusively bacteriocidal. This simplification may lead to an overestimation of the probability of resistance emer- gence. If a drug is also at least partially bacteriostatic it would reduce the number of cell divisions and thereby the number of opportunities for mutations to arise. In early stages of the development we experimented with a pharmacodynamic model that also incorporated bacteriostatic activity. When we tried to fit this model to in vitro time-kill curves of anti-tuberculosis drugs [90] we observed negative growth inhibition at some concentrations (data not shown) and other unrealistic behavior. Eventually we settled for a pharmacodynamic model that only considered the bacte- riocidal effect of drugs. This simplified model allowed us to achieve reasonably good fits to the in vitro time-kill curves for most drugs (see Supplementary Material 2.A). However the effects of rifampicin, at least for higher concentrations, could not be fit very well. This is an indication that a single pharmacodynamic model is probably not sufficient to capture the activity of all drugs accurately. To further improve the pharmacodynamic model it would be desirable if drug actions could be experimen- tally observed at the cellular level. Eventually, we would be able develop a tailored function for every drug that describe their action more accurately. Another simplification of our pharmacodynamic model is the omission of the post- antibiotic effect [183]. The post-antibiotic effect inhibits growth for a certain time period even when the drug is not present anymore [184; 80]. The presence of the post-antibiotic effect has been reported in in vitro studies for most first-line drugs against M. tuberculosis [111]. It is reasonable to assume that it may last for several hours [185]. Neglecting the post-antibiotic effect may overestimate the risks in con- 80 general discussion

nection to intermittent therapy (see Chapter 3) and the risk for the emergence of drug resistance.

5.2.2 Pharmacokinetics

One factor that may be highly influential in the transferability of in vitro experiments to in vivo models is bioavailability. I am using here the pharmacological definition of bioavailability, which states that the bioavailability is a measurement of the rate and extent to which a drug reaches the site of action [186]. In this thesis the concept of bioavailability is embodied in the TB model as the ratio between the serum drug concentration and the concentration in the epithelial lining fluid within the lung [83] and it also influenced the relative drug efficacy parameters. For example, the relative drug efficacy parameters were assumed to be lower in macrophages if the drugs were reported to have a low cell-penetration [69; 68; 70; 77]. The ratio between the serum concentration and the epithelial lining fluid on the other hand is a global parameter because it changes the drug exposure in all simulated compartments. While in vitro data suggests that isoniazid and rifampicin have comparable bacte- riocidal activity at clinically relevant serum concentrations [90] the picture changes when we also consider the amount of drug that actually reaches the bacteria. Be- cause the rifampicin concentration in the epithelial lining fluid is only about a third as high as in the serum [83] it loses a substantial amount of its potency relative to isoniazid that actually is more concentrated in the epithelial lining fluid than in the blood serum [83]. This phenomenon also partially explains the strong survival bene- fit of isoniazid-resistance for M. tuberculosis relative to rifampicin-resistance that we observed in the results of Chapter 3. Somewhat related to that issue is the limited certitude about the conditions inside granulomas. Because the pathogenesis of a tuberculosis infection is different from the progression in animal models [187; 188] the knowledge about processes inside granulomas remains vague. The population growth dynamics inside granulomas as well as the pharmacokinetics and pharmacodynamics are largely based on assump- tions, less on actual measurements. It is not known whether the bioavailability of drugs is similar to the one in the epithelial lining fluid, and the premises about the efficacy of drugs is largely based on the assumptions of low bacterial growth and a low pH [19]. Furthermore, it is debatable whether all granulomas develop similarly and progress into open cavities during an acute infection. It is possible that the bac- terial populations in single granulomas remain dormant and are mostly unaffected by a treatment. Such granulomas could then at a later time point cause a relapse — probably with fully susceptible bacteria. Although, one has to keep in mind that the possibility of relapse, caused either by the regrowth of previously dormant bacteria or by reinfection, is anyway excluded in our model. If we included these possibilities they would decrease our net treatment success rate.

5.2.3 Immune system and life history traits

In our TB model apart from the role of macrophages as a compartment we do not ex- plicitly simulate the effect of the immune system on the progression of the infection. 5.2 future directions 81

We assume that the immune system of the patients is weak enough for the infection to become acute and are therefore neglecting any contributions of it to contain the infection. This is a reasonable assumption for an untreated infection, however, it is possible that after the initiation of treatment the infection is suppressed well enough that the immune system becomes less overwhelmed and is able to suppress the last remains of an infection even if patient adherence is suboptimal. This would imply that the treatment success rate could be underestimated. A classic simplification in our model is the absence of a natural death rate of bacteria. Bacteria may only die because of the limited population density inside the compartments or because of bacteriocidal drug actions. Such an assumption is a classical logistic growth model [2]. If we assumed a natural unconditional death rate and a correspondingly increased birth rate we could achieve the same net growth rate that we originally assumed. The difference would be that we would have a higher turnover of bacteria. With a higher turnover we would get more birth events and therefore more opportunities for resistance mutations to emerge. This means that our model may underestimate the probability for the emergence of resistance. Unfortunately, the growth rate of M. tuberculosis in vivo can only be estimated with limited certainty [189] and measurements of the natural birth and death rate in vitro do not exist in the literature. The definition of drug resistance that we apply in the models of this thesis is rather absolute. We assume that a particular mutation in a locus confers complete resistance to the corresponding drug. This definition is more strict than the common concep- tion that states that drug resistance is characterized by a reduction in effectiveness of a drug [190]. Measurements of the mutation frequency usually determine the ratio of bacteria that are able to grow or at least persist at drug concentrations above the MIC [62; 93; 191]. Such measurements are at risk to also include bacteria that are phenotypically drug tolerant. Drug tolerance has been described in M. tuberculosis and attributed to a slow down of metabolism [192] or an increased expression of efflux pumps [96]. Drug tolerance may serve as a stepping stone for the evolution of higher genetic drug resistance [192]. Genotypes with low levels of drug resistance may then accumulate further mutations that grant higher levels of drug mutation. In our model we do not simulate the stepwise acquisition of resistance mutations that render their carrier increasingly more drug resistant because currently available data does not allow for more accurate modeling. A more detailed model may also not provide much additional benefit because resistance mutations that grant low levels of resistance or that infer high fitness costs are not particularly relevant for the evo- lution of resistance. In a previous study it has been found that of several rifampicin resistance mutations the one that conferred the least fitness costs is predominantly found in clinical isolates [193]. It could therefore be justified to not consider the emergence of all resistance mutations but only the ones that provide a sufficient protection from drug actions without affecting the fitness too much. The mutation rate for drug resistance mutations itself is also less certain than what would be desirable to improve the predictions of models. There has been a debate about whether there are M. tuberculosis strains (e.g. Beijing strain) that have a genotypically higher mutation rate than other strains [131; 194; 66]. Furthermore, there are even discussions whether mutation rates could change transiently due to 82 general discussion

environmental influences. While some excluded the possibility for the induction of mutations by oxidative stress [195; 196] others still consider this as a possible explanation for the the observation of high mutation frequencies during latency [197; 189]. It has also been observed that genes for DNA repair and DNA stability were down regulated in clinical multi-drug resistant isolates of M. tuberculosis [192]. This could be an indication that M. tuberculosis is able under the influence of stress to increase its mutation rate and faster adapt to averse conditions. BIBLIOGRAPHY

[1] Thomas Robert Malthus. An Essay on the Principle of Population. J, Johnson, London, 1798.

[2] Pierre François Verhulst. Notice sur la loi que la population suit dans son accroissement. Correspondance mathématique et physique, 10:113–121, 1838.

[3] Alfred James Lotka. Elements of Physical Biology. Williams and Wilkins, 1925.

[4] Nikolaos I Stilianakis, Alan S Perelson, and Frederick G Hayden. Emergence of Drug Resistance during an Influenza Epidemic: Insights from a Mathematical Model. Journal of Infectious Diseases, 177(April):863–873, 1998.

[5] Treatment Action Group. 2014 Report on Tuberculosis Research Funding Trends, 2005-2013. Number November. Treatment Action Group, New York, 2nd edi- tion, 2015.

[6] WHO. WHO Global Tuberculosis Report 2015. Technical report, WHO, 2015.

[7] WHO. Global Tuberculosis Control Report 2009. Technical report, Geneva, 2009.

[8] D E Griffith and C M Kerr. Tuberculosis: Disease of the Past, Disease of the Present. Journal of PeriAnesthesia Nursing, 11(4):240–245, 1996.

[9] Helen S Cox, Cheryl McDermid, Virginia Azevedo, Odelia Muller, David Coet- zee, John Simpson, Marinus Barnard, Gerrit Coetzee, Gilles van Cutsem, and Eric Goemaere. Epidemic Levels of Drug Resistant Tuberculosis (MDR and XDR-TB) in a High HIV Prevalence Setting in Khayelitsha, South Africa. PLoS ONE, 5(11):e13901, jan 2010.

[10] Neel R Gandhi, Paul Nunn, Keertan Dheda, H Simon Schaaf, Matteo Zignol, Dick van Soolingen, Paul Jensen, and Jaime Bayona. Multidrug-resistant and extensively drug-resistant tuberculosis: a threat to global control of tuberculo- sis. Lancet, 375(9728):1830–1843, may 2010.

[11] Shenjie Tang, Qing Zhang, Jinming Yu, Yidian Liu, Wei Sha, Hua Sun, Lin Fan, Jin Gu, Xiaohui Hao, Lan Yao, and Heping Xiao. Extensively drug-resistant tuberculosis at a tuberculosis specialist hospital in Shanghai, China: clinical characteristics and treatment outcomes. Scandinavian Journal of Infectious Dis- eases, 43(4):280–285, apr 2011.

[12] Alistair D Calver, Alecia A Falmer, Megan B Murray, Odelia J Strauss, Eliz- abeth M Streicher, Madelene Hanekom, Thelma Liversage, Mothusi Masibi, Paul D van Helden, Robin M Warren, and Thomas C Victor. Emergence of Increased Resistance and Extensively Drug-Resistant Tuberculosis Despite

83 84 Bibliography

Treatment Adherence , South Africa. Emerging Infectious Diseases, 16(2):264– 271, 2010.

[13] WHO. Treatment of Tuberculosis: Guidelines, Fourth Edition. 4th edition, 2010.

[14] Stephen E Weis, Philip C Slocum, Francis X Blais, Barbara King, Mary Nunn, G Burgis Matney, Enriqueta Gomez, and Brian H Foresman. The Effect of Directly Observed Therapy on the Rates of Drug Resistance and Relapse in Tuberculosis. New England Journal of Medicine, 330(17):1179–1184, 1994.

[15] L M Wahl and Martin A Nowak. Adherence and drug resistance: predic- tions for therapy outcome. Proceedings of the Royal Society B: Biological Sciences, 267(1445):835–843, 2000.

[16] WHO. Tuberculosis. WHO Factsheet No. 104. Technical report, 1996.

[17] Jossy van den Boogaard, Ramsey A Lyimo, Martin J Boeree, Gibson S Kibiki, and Rob E Aarnoutse. Electronic monitoring of treatment adherence and vali- dation of alternative adherence measures in tuberculosis patients: a pilot study. Bulletin of the World Health Organization, 89(9):632–639, sep 2011.

[18] Maria R Servedio, Yaniv Brandvain, Sumit Dhole, Courtney L Fitzpatrick, Emma E Goldberg, Caitlin A Stern, Jeremy Van Cleve, and D Justin Yeh. Not Just a Theory - The Utility of Mathematical Models in Evolutionary Biology. PLoS biology, 12(12):1–5, 2014.

[19] Jacques Grosset. Bacteriologic Basis of Short-Course Chemotherapy for Tuber- culosis. Clinics in Chest Medicine, 1(2):231–241, 1980.

[20] Edward C Jones-López, Irene Ayakaka, Jonathan Levin, Nancy Reilly, Francis Mumbowa, Scott Dryden-Peterson, Grace Nyakoojo, Kevin Fennelly, Beth Tem- ple, Susan Nakubulwa, Moses L Joloba, Alphonse Okwera, Kathleen D Eise- nach, Ruth McNerney, Alison M Elliott, Jerrold J Ellner, Peter G Smith, and Roy D Mugerwa. Effectiveness of the standard WHO recommended retreat- ment regimen (category II) for tuberculosis in Kampala, Uganda: a prospective cohort study. PLoS Medicine, 8(3):e1000427, mar 2011.

[21] Dick Menzies, Andrea Benedetti, Anita Paydar, Sarah Royce, Madhukar Pai, William J Burman, Andrew Vernon, and Christian Lienhardt. Standardized Treatment of Active Tuberculosis in Patients with Previous Treatment and/or with Mono-resistance to Isoniazid: A Systematic Review and Meta-analysis. PLoS Medicine, 6(9):e1000150, sep 2009.

[22] Ping Gao, Xin Nie, Meijuan Zou, Yijie Shi, and Gang Cheng. Recent advances in materials for extended-release antibiotic delivery system. The Journal of An- tibiotics, 64(9):625–634, 2011.

[23] Martin J Boeree, Andreas H Diacon, Rodney Dawson, Kim Narunsky, Jeannine du Bois, Amour Venter, Patrick P J Phillips, Stephen H Gillespie, Timothy D. McHugh, Michael Hoelscher, Norbert Heinrich, Sunita Rehal, Dick van Soolin- gen, Jakko van Ingen, Cecile Magis-Escurra, David Burger, Georgette Plemper Bibliography 85

van Balen, Rob E Aarnoutse, and PanACEA Consortium. A dose-ranging trial to optimize the dose of rifampin in the treatment of tuberculosis. American Journal of Respiratory and Critical Care Medicine, 191(9):1058–65, 2015.

[24] R Craig MacLean, Clara Torres-Barceló, and Richard Moxon. Evaluating evo- lutionary models of stress-induced mutagenesis in bacteria. Nature Reviews: Genetics, 14(3):221–227, mar 2013.

[25] Stephen D Lawn and Alimuddin I Zumla. Tuberculosis. Lancet, 378(9785):57– 72, mar 2011.

[26] WHO. Global Tuberculosis Report 2014. Technical report, WHO, Geneva, 2014.

[27] WHO. Tuberculosis Fact Sheet (No. 104). Technical report, World Health Or- ganisation, Geneva, Switzerland, 2007.

[28] Barry R Bloom and C J Murray. Tuberculosis: commentary on a reemergent killer. Science, 257(5073):1055–1064, aug 1992.

[29] Jacques Grosset. Mycobacterium tuberculosis in the Extracellular Compart- ment: an Underestimated Adversary. Antimicrobial Agents and Chemotherapy, 47(3):833–836, 2003.

[30] Douglas B Young, Jaroslav Stark, and Denise E Kirschner. Systems biology of persistent infection: tuberculosis as a case study. Nature Reviews: Microbiology, 6(7):520–528, jul 2008.

[31] Clifton E Barry III, Helena I M Boshoff, Véronique Dartois, Thomas Dick, Sabine Ehrt, JoAnne L Flynn, Dirk Schnappinger, Robert J Wilkinson, and Dou- glas B Young. The spectrum of latent tuberculosis: rethinking the biology and intervention strategies. Nature Reviews: Microbiology, 7(12):845–855, dec 2009.

[32] Martin Gengenbacher and Stefan H E Kaufmann. Mycobacterium tuberculosis: success through dormancy. FEMS Microbiology Reviews, 36(3):514–32, may 2012.

[33] Denis A Mitchison. Basic Mechanisms of Chemotherapy. Chest, 76(6):771–781, 1979.

[34] Lawrence G Wayne and Charles D Sohaskey. Nonreplicating Persistence of Mycobacterium Tuberculosis. Annual Review of Microbiology, 55:139–163, 2001.

[35] Tige R Rustad, Ashley M Sherrid, Kyle J Minch, and David R Sherman. Hy- poxia: a window into Mycobacterium tuberculosis latency. Cellular Microbiol- ogy, 11(8):1151–1159, aug 2009.

[36] J B Bass Jr, L S Farer, Philip C Hopewell, R O’Brien, R F Jacobs, F Ruben, Dixie E Snider Jr, and G Thornton. Treatment of Tuberculosis and Tuberculosis Infection in Adults and Children. American Journal of Respiratory and Critical Care Medicine, 149(4):1359–1374, sep 1994. 86 Bibliography

[37] Julie L Gerberding, David W Fleming, Dixie E Snider Jr, Stephen B Thacker, John W Ward, Suzanne M Hewitt, C Kay Smith-Akin, Lynne McIntyre, Bev- erly J Holland, Malbea A Heilman, Quang M Doan, and Erica R Shaver. Treat- ment of Tuberculosis. American Thoracic Society, CDC, and Infectious Diseases Society of America. MMWR, 52(RR-11):1–84, 2003.

[38] WHO. Toman’s Tuberculosis - Case Detection, Treatment, and Monitoring. Geneva, 2nd edition, 2004.

[39] Lisa D Inge and John W Wilson. Update on the Treatment of Tuberculosis. American Family Physician, 78(4):457–465, aug 2008.

[40] Matteo Zignol, Mehran S Hosseini, Abigail Wright, Catharina Lambregts-van Weezenbeek, Paul Nunn, Catherine J Watt, Brian G Williams, and Christopher Dye. Global incidence of multidrug-resistant tuberculosis. The Journal of Infec- tious Diseases, 194(4):479–485, aug 2006.

[41] Neel R Gandhi, Anthony Moll, A Willem Sturm, Robert Pawinski, Thiloshini Govender, Umesh Lalloo, Kimberly Zeller, Jason R Andrews, and Gerald Fried- land. Extensively drug-resistant tuberculosis as a cause of death in patients co-infected with tuberculosis and HIV in a rural area of South Africa. Lancet, 368(9547):1575–1580, nov 2006.

[42] WHO. Global Tuberculosis Report 2013. World Health Organization, Geneva, 2013.

[43] Amita Jain and Pratima Dixit. Multidrug-resistant to extensively drug resistant tuberculosis: what is next? Journal of Biosciences, 33(4):605–16, nov 2008.

[44] Ariel Pablos-Méndez, Charles A Knirsch, R. Graham Barr, Barron H Lerner, and Thomas R Frieden. Nonadherence in tuberculosis treatment: Predictors and consequences in New York City. American Journal of Medicine, 102(2):164– 170, 1997.

[45] J P Zellweger and P Coulon. Outcome of patients treated for tuberculosis in Vaud County, Switzerland. The International Journal of Tuberculosis and Lung Disease, 2(5):372–377, may 1998.

[46] S. K. Sharma, K. K. Turaga, A. Balamurugan, P. K. Saha, R. M. Pandey, N. K. Jain, V. M. Katoch, and N. K. Mehra. Clinical and genetic risk factors for the development of multi-drug resistant tuberculosis in non-HIV infected patients at a tertiary care center in India: A case-control study. Infection, Genetics and Evolution, 3:183–188, 2003.

[47] I Y Gelmanova, S Keshavjee, Vera T Golubchikova, V I Berezina, Aivar K Strelis, Galina V Yanova, S Atwood, and Megan B Murray. Barriers to successful tuber- culosis treatment in Tomsk, Russian Federation: non-adherence, default and the acquisition of multidrug resistance. Bulletin of the World Health Organisation, 85(9):703–711, 2007. Bibliography 87

[48] Nigel J Saunders, Urmi H Trivedi, Marian L Thomson, Christine Doig, Ian F Laurenson, and Mark L Blaxter. Deep resequencing of serial sputum isolates of Mycobacterium tuberculosis during therapeutic failure due to poor compli- ance reveals stepwise mutation of key resistance genes on an otherwise stable genetic background. The Journal of Infection, 62(3):212–217, mar 2011.

[49] Denis A Mitchison. How drug resistance emerges as a result of poor com- pliance during short course chemotherapy for tuberculosis. The International Journal of Tuberculosis and Lung Disease, 2(1):10–15, 1998.

[50] Marc Lipsitch and Bruce R Levin. Population dynamics of tuberculosis treat- ment: mathematical models of the roles of non-compliance and bacterial het- erogeneity in the evolution of drug resistance. The International Journal of Tuber- culosis and Lung Disease, 2(3):187–199, 1998.

[51] H T W Quy, Frank G J Cobelens, Nguyen T N Lan, Tran N Buu, C S B Lam- bregts, and Martien W Borgdorff. Treatment outcomes by drug resistance and HIV status among tuberculosis patients in Ho Chi Minh City , Vietnam. The International Journal of Tuberculosis and Lung Disease, 10(1):45–51, 2006.

[52] Shama D Ahuja, David Ashkin, Monika Avendano, Rita Banerjee, Melissa Bauer, Jaime N Bayona, Mercedes C Becerra, Andrea Benedetti, Marcos Bur- gos, Rosella Centis, Eward D Chan, Chen-Yuan Chiang, Helen S Cox, Lia D’Ambrosio, Kathy DeRiemer, Nguyen Huy Dung, Donald A Enarson, Den- nis Falzon, Katherine Flanagan, Jennifer Flood, Maria L Garcia-Garcia, Neel R Gandhi, Reuben M Granich, Maria G Hollm-Delgado, Timothy H Holtz, Michael D Iseman, Leah G Jarlsberg, Salmaan Keshavjee, Hye-Ryoun Kim, Won-Jung Koh, Joey Lancaster, Christophe Lange, Wiel C M de Lange, Vaira Leimane, Chi Chiu Leung, Jiehui Li, Dick Menzies, Giovanni B Migliori, Sergey P Mishustin, Carole D Mitnick, Masa Narita, Philly O’Riordan, Mad- hukar Pai, Domingo Palmero, Seung-kyu Park, Geoffrey Pasvol, Jose Peña, Car- los Pérez-Guzmán, Maria I D Quelapio, Alfredo Ponce-de Leon, Vija Riekstina, Jerome Robert, Sarah Royce, H Simon Schaaf, Kwonjune J Seung, Lena Shah, Tae Sun Shim, Sonya S Shin, Yuji Shiraishi, José Sifuentes-Osornio, Giovanni Sotgiu, Matthew J Strand, Payam Tabarsi, Thelma E Tupasi, Robert van Al- tena, Martie Van der Walt, Tjip S Van der Werf, Mario H Vargas, Piret Viiklepp, Janice Westenhouse, Wing Wai Yew, and Jae-Joon Yim. Multidrug resistant pul- monary tuberculosis treatment regimens and patient outcomes: an individual patient data meta-analysis of 9,153 patients. PLoS Medicine, 9(8):e1001300, aug 2012.

[53] Mai N T Huyen, Tran N Buu, Edine W Tiemersma, Nguyen T N Lan, Nguyen Huy Dung, Kristin Kremer, Dick van Soolingen, and Frank G J Co- belens. Tuberculosis Relapse in Vietnam Is Significantly Associated With My- cobacterium tuberculosis Beijing Genotype Infections. The Journal of Infectious Diseases, 207(10):1516–1524, may 2013.

[54] L L Han, A Sloutsky, R Canales, V Naroditskaya, Sonya S Shin, Kwonjune J Seung, R Timperi, and Mercedes C Becerra. Acquisition of drug resistance 88 Bibliography

in multidrug-resistant Mycobacterium tuberculosis during directly observed empiric retreatment with standardized regimens. The International Journal of Tuberculosis and Lung Disease, 9(7):818–821, jul 2005.

[55] Marcos A Espinal, Sang Jae Kim, Pedro G Suarez, Kai Man Kam, Alexan- der G Khomenko, Giovanni B Migliori, Janette Baéz, Arata Kochi, Christopher Dye, and Mario C Raviglione. Standard Short-Course Chemotherapy for Drug- Resistant Tuberculosis Treatment: Treatment Outcomes in 6 Countries. JAMA: The Journal of the American Medical Association, 283(19):2537–2545, may 2000.

[56] European Centre for Disease Prevention and Control/WHO Regional Office for Europe. Tuberculosis surveillance in Europe 2009. Technical report, European Centre for Disease Prevention and Control, Stockholm, 2009.

[57] European Centre for Disease Prevention and Control/WHO Regional Office for Europe. Tuberculosis surveillance and monitoring in Europe 2012. Technical report, European Centre for Disease Prevention and Control, Stockholm, 2012.

[58] Daniel T Gillespie. Exact Stochastic Simulation of Coupled Chemical Reactions. The Journal of Physical Chemistry, 81(25):2340–2361, 1977.

[59] Timo Ulrichs, George A Kosmiadi, Vsevolod Trusov, Sabine Jörg, Lydia Pradl, Marina Titukhina, Vladimir Mishenko, Nadya Gushina, and Stefan H E Kauf- mann. Human tuberculous granulomas induce peripheral lymphoid follicle- like structures to orchestrate local host defence in the lung. The Journal of Pathology, 204(2):217–228, oct 2004.

[60] Justino Alavez-Ramírez, J Rogelio Avendano Castellanos, Lourdes Esteva, José Antonio Flores, José Luis Fuentes-Allen, Gisela García-Ramos, Guillermo Gómez, and Jesús López-Estrada. Within-host population dynamics of antibiotic-resistant M. tuberculosis. Mathematical Medicine and Biology, 24(1):35– 56, 2007.

[61] Jurriaan E M de Steenwinkel, Marian T ten Kate, Gerjo J de Knegt, Henri A Verbrugh, Rob E Aarnoutse, Martin J Boeree, Michael A den Bakker, Dick van Soolingen, and Irma A J M Bakker-Woudenberg. Consequences of noncompli- ance for therapy efficacy and emergence of resistance in murine tuberculosis caused by the Beijing genotype of Mycobacterium tuberculosis. Antimicrobial Agents and Chemotherapy, 56(9):4937–4944, sep 2012.

[62] Hugo L David. Probability distribution of drug-resistant mutants in unselected populations of Mycobacterium tuberculosis. Applied Microbiology, 20(5):810– 814, nov 1970.

[63] Denis A Mitchison. Role of individual drugs in the chemotherapy of tubercu- losis. The International Journal of Tuberculosis and Lung Disease, 4(9):796–806, sep 2000.

[64] Helena I M Boshoff, Michael B Reed, Clifton E Barry III, and Valerie Mizrahi. DnaE2 polymerase contributes to in vivo survival and the emergence of drug resistance in Mycobacterium tuberculosis. Cell, 113(2):183–193, apr 2003. Bibliography 89

[65] Indra L Bergval, Anja R J Schuitema, Paul R Klatser, and Richard M Anthony. Resistant mutants of Mycobacterium tuberculosis selected in vitro do not re- flect the in vivo mechanism of isoniazid resistance. The Journal of Antimicrobial Chemotherapy, 64(3):515–523, sep 2009. [66] Christopher B Ford, Rupal R Shah, Midori Kato Maeda, Sebastien Gagneux, Megan B Murray, Ted Cohen, James C Johnston, Jennifer Gardy, Marc Lipsitch, and Sarah M Fortune. Mycobacterium tuberculosis mutation rate estimates from different lineages predict substantial differences in the emergence of drug- resistant tuberculosis. Nature Genetics, (May), jun 2013. [67] Ponniah Karunakaran and Julian Davies. Genetic Antagonism and Hyper- mutability in Mycobacterium smegmatis. Journal of Bacteriology, 182(12):3331– 3335, 2000. [68] Nalin Rastogi, V Labrousse, and K S Goh. In Vitro Activities of Fourteen Antimicrobial Agents Against Drug Susceptible and Resistant Clinical Iso- lates of Mycobacterium tuberculosis and Comparative Intracellular Activities Against the Virulent H37Rv Strain in Human Macrophages. Current Microbiol- ogy, 33(3):167–175, sep 1996. [69] Ruben C Hartkoorn, Becky Chandler, Andrew Owen, Stephen A Ward, S Bertel Squire, David J Back, and Saye H Khoo. Differential drug susceptibility of intracellular and extracellular tuberculosis, and the impact of P-glycoprotein. Tuberculosis, 87(3):248–255, may 2007. [70] Ramesh Jayaram, Radha K Shandil, Sheshagiri Gaonkar, Parvinder Kaur, B L Suresh, B N Mahesh, R Jayashree, Vrinda Nandi, Sowmya Bharath, E Kantharaj, and V Balasubramanian. Isoniazid Pharmacokinetics-Pharmacodynamics in an Aerosol Infection Model of Tuberculosis. Antimicrobial Agents and Chemotherapy, 48(8):2951–2957, 2004. [71] Patrick J Brennan, Douglas B Young, Brian D Robertson, Peter Andersen, Clifton E Barry III, Warwick Britton, Phillip Butcher, Sang-Nae Cho, Ken Dun- can, Kathleen D Eisenach, Rajesh Gokhale, Glyn Hewinson, William R Jacobs, Gilla Kaplan, Stefan H E Kaufmann, Mark Perkins, Eric J Rubin, David G Rus- sell, and A Ginsberg. Handbook of Anti-Tuberculosis Agents. Tuberculosis, 88(2):85–170, 2008. [72] Leonid B Heifets, M Higgins, and B Simon. Pyrazinamide is not active against Mycobacterium tuberculosis residing in cultured human monocyte-derived macrophages. The International Journal of Tuberculosis and Lung Disease, 4(6):491– 495, 2000. [73] Nalin Rastogi, Marie-Christine Potar, and Hugo L David. Pyrazinamide Is Not Effective against Intracellularly Growing Mycobacterium tuberculosis. Antimi- crobial Agents and Chemotherapy, 32(2):287, 1988. [74] Ying Zhang and Denis A Mitchison. The curious characteristics of pyrazi- namide: a review. The International Journal of Tuberculosis and Lung Disease, 7(1):6–21, jan 2003. 90 Bibliography

[75] N A Kuck, E A Peets, and M Forbes. Mode of action of ethambutol on Mycobac- terium tuberculosis, strain H37Rv. The American Review of Respiratory Disease, 87:905–906, 1963.

[76] Giovanni Piccaro, Federico Giannoni, Perla Filippini, Alessandro Mustazzolu, and Lanfranco Fattorini. Activities of Drug Combinations against Mycobac- terium tuberculosis Grown in Aerobic and Hypoxic Acidic Conditions. Antimi- crobial Agents and Chemotherapy, 57(3):1428–1433, mar 2013.

[77] Jasvir Dhillon and Denis A Mitchison. Activity and Penetration of Antituber- culosis Drugs in Mouse Peritoneal Macrophages Infected with Mycobacterium microti OV254. Antimicrobial Agents and Chemotherapy, 33(8):1255–1259, aug 1989.

[78] Jacques Grosset and Baohong Ji. Experimental Chemotherapy of Mycobacte- rial Diseases. In Pattisapu R J Gangadharam and P Anthony Jenkins, editors, Mycobacteria: II Chemotherapy, chapter 3, pages 51–97. Chapman & Hall, New York, 1998.

[79] Helen McIlleron, Peter Wash, André Burger, Jennifer Norman, Peter I Folb, and Pete Smith. Determinants of Rifampin, Isoniazid, Pyrazinamide, and Ethambu- tol Pharmacokinetics in a Cohort of Tuberculosis Patients. Antimicrobial Agents and Chemotherapy, 50(4):1170–1177, 2006.

[80] J Graham Douglas and Mary-Joan McLeod. Pharmacokinetic Factors in the Modern Drug Treatment of Tuberculosis. Clinical Pharmacokinetics, 37(2):127– 146, aug 1999.

[81] Charles A Peloquin. What is the ’right’ dose of rifampin? International Journal of Tuberculosis and Lung Disease, 7(1):3–5, 2003.

[82] Nimi Marcel, Ajay Nahta, and Meenakshi Balganesh. Evaluation of Killing Kinetics of Anti-Tuberculosis Drugs on Mycobacterium tuberculosis Using a Bacteriophage-Based Assay. Chemotherapy, 54(5):404–411, jan 2008.

[83] Sungmin Kiem and Jerome J Schentag. Interpretation of Antibiotic Concen- tration Ratios Measured in Epithelial Lining Fluid. Antimicrobial Agents and Chemotherapy, 52(1):24–36, jan 2008.

[84] Ted Cohen, Ben Sommers, and Megan B Murray. The effect of drug resistance on the fitness of Mycobacterium tuberculosis. The Lancet - Infectious Diseases, 3(1):13–21, jan 2003.

[85] Dan I Andersson. The biological cost of mutational antibiotic resistance: any practical conclusions? Current Opinion in Microbiology, 9(5):461–465, oct 2006.

[86] Sebastien Gagneux, Clara Davis Long, Peter M Small, Tran Van, Gary K School- nik, and Brendan J M Bohannan. The Competitive Cost of Antibiotic Resistance in Mycobacterium tuberculosis. Science, 312(5782):1944–1946, jun 2006. Bibliography 91

[87] Ronald G Hall II, Richard E Leff, and Tawanda Gumbo. Treatment of Active Pulmonary Tuberculosis in Adults: Current Standards and Recent Advances. Pharmacotherapy, 29(12):1468–1481, 2010.

[88] Alexander S Pym, Brigitte Saint-Joanis, and Stewart T Cole. Effect of katG Mutations on the Virulence of Mycobacterium tuberculosis and the Implication for Transmission in Humans. Infection and Immunity, 70(9):4955–4960, 2002.

[89] A P Davies, O J Billington, B A Bannister, W R Weir, Timothy D McHugh, and Stephen H Gillespie. Comparison of Fitness of Two Isolates of Mycobacterium tuberculosis, one of Which had Developed Multi-drug Resistance During the Course of Treatment. The British Infection Society, 41(2):184–187, sep 2000.

[90] Jurriaan E M de Steenwinkel, Gerjo J de Knegt, Marian T ten Kate, Alex van Belkum, Henri A Verbrugh, Kristin Kremer, Dick van Soolingen, and Irma A J M Bakker-Woudenberg. Time-kill kinetics of anti-tuberculosis drugs, and emergence of resistance, in relation to metabolic activity of Mycobacterium tuberculosis. Journal of Antimicrobial Chemotherapy, 65(12):2582–2589, dec 2010.

[91] Alfred J Crowle, J A Sbarbaro, and M H May. Inhibition by Pyrazinamide of Tubercle Bacilli within Cultured Human Macrophages. The American Review of Respiratory Disease, 134(5):1052–1055, 1986.

[92] William J Burman, Keith Gallicano, and Charles A Peloquin. Compara- tive Pharmacokinetics and Pharmacodynamics of the Rifamycin Antibacterials. Clinical Pharmacokinetics, 40(5):327–341, 2001.

[93] Tawanda Gumbo, Arnold Louie, Weiguo Liu, David Brown, Paul G Ambrose, Sujata M Bhavnani, and George L Drusano. Isoniazid Bactericidal Activity and Resistance Emergence: Integrating Pharmacodynamics and Pharmacoge- nomics To Predict Efficacy in Different Ethnic Populations. Antimicrobial Agents and Chemotherapy, 51(7):2329–2336, jul 2007.

[94] Geraint R Davies and E L Nuermberger. Pharmacokinetics and pharmacody- namics in the development of anti-tuberculosis drugs. Tuberculosis, 88 Suppl 1:S65–S74, aug 2008.

[95] Tawanda Gumbo, Chandima S W Siyambalapitiyage Dona, Claudia Meek, and Richard E Leff. Pharmacokinetics-Pharmacodynamics of Pyrazinamide in a Novel In Vitro Model of Tuberculosis for Sterilizing Effect: a Paradigm for Faster Assessment of New Antituberculosis Drugs. Antimicrobial Agents and Chemotherapy, 53(8):3197–3204, aug 2009.

[96] Kristin N Adams, Kevin Takaki, Lynn E Connolly, Heather Wiedenhoft, Kathryn Winglee, Olivier Humbert, Paul H Edelstein, Christine L Cosma, and Lalita Ramakrishnan. Drug Tolerance in Replicating Mycobacteria Mediated by a Macrophage-Induced Efflux Mechanism. Cell, 145(1):39–53, apr 2011.

[97] S J Kim. Drug-susceptibility testing in tuberculosis: methods and reliability of results. The European Respiratory Journal, 25(3):564–569, mar 2005. 92 Bibliography

[98] Shashikant Srivastava, Jotam G Pasipanodya, Claudia Meek, Richard E Leff, and Tawanda Gumbo. Multidrug-Resistant Tuberculosis Not Due to Noncom- pliance but to Between-Patient Pharmacokinetic Variability. The Journal of Infec- tious Diseases, 204:1951–1959, 2011.

[99] Marcos A Espinal. The global situation of MDR-TB. Tuberculosis, 83(1-3):44–51, feb 2003.

[100] H T W Quy, Nguyen T N Lan, Martien W Borgdorff, Jacques Grosset, P D Linh, L B Tung, Dick van Soolingen, Mario C Raviglione, N V Cô, and J Broekmans. Drug resistance among failure and relapse cases of tuberculosis: is the standard re-treatment regimen adequate? The International Journal of Tuberculosis and Lung Disease, 7(7):631–636, 2003.

[101] Anton Mak, Adam Thomas, Mirtha Del Granado, Richard Zaleskis, Nigor Mouzafarova, and Dick Menzies. Influence of Multidrug Resistance on Tu- berculosis Treatment Outcomes with Standardized Regimens. American Journal of Respiratory and Critical Care Medicine, 178(3):306–312, aug 2008.

[102] Beth Temple, Irene Ayakaka, Sam Ogwang, Helen Nabanjja, Susan Kayes, Su- san Nakubulwa, William Worodria, Jonathan Levin, Moses Joloba, Alphonse Okwera, Kathleen D Eisenach, Ruth McNerney, Alison M Elliott, Peter G Smith, Roy D Mugerwa, Jerrold J Ellner, and Edward C Jones-López. Rate and ampli- fication of drug resistance among previously-treated patients with tuberculosis in Kampala, Uganda. Clinical Infectious Diseases, 47(9):1126–1134, nov 2008.

[103] Afranio L Kritski, Luis Sergio Rodrigues de Jesus, Monica K Andrade, Eduardo Werneck-Barroso, Maria Armanda Monteiro S Vieira, Alice Haffner, and Lee W Riley. Factors Associated With Drug Resistance and Adverse Outcomes. Chest, 111(5):1162–1167, 1997.

[104] G Abate, H Miörner, O Ahmed, and S E Hoffner. Drug resistance in Mycobac- terium tuberculosis strains isolated from re-treatment cases of pulmonary tu- berculosis in Ethiopia: susceptibility to first-line and alternative drugs. The International Journal of Tuberculosis and Lung Disease, 2(7):580–584, jul 1998.

[105] S Toungoussova, D A Caugant, P Sandven, A O Mariandyshev, and G Bjune. Drug resistance of Mycobacterium tuberculosis strains isolated from patients with pulmonary tuberculosis in Archangels, Russia. The International Journal of Tuberculosis and Lung Disease, 6(5):406–414, may 2002.

[106] S-E Ottmani, Matteo Zignol, N Bencheikh, L Laâsri, N Chaouki, and J Mahjour. Results of cohort analysis by category of tuberculosis retreatment cases in Mo- rocco from 1996 to 2003. The International Journal of Tuberculosis and Lung Disease, 10(12):1367–1372, 2006.

[107] Lawrence Peter Ormerod. Multidrug-resistant tuberculosis (MDR-TB): epi- demiology, prevention and treatment. British Medical Bulletin, 73-74:17–24, 2005. Bibliography 93

[108] David Czock and Frieder Keller. Mechanism-based pharmacokinetic- pharmacodynamic modeling of antimicrobial drug effects. Journal of Pharma- cokinetics and Pharmacodynamics, 34(6):727–751, dec 2007.

[109] Leonid B Heifets. Antituberculosis Drugs: Antimicrobial Activity In Vitro. In Leonid B Heifets, editor, Drug Susceptibility in the Chemotherapy of Mycobacterial Infections, chapter 1, pages 13–58. CRC Press, Boca Raton, 1 edition, 1991.

[110] East African/British Medical Research Councils. Controlled clinical trial of short-course (6-month) regimens of chemotherapy for treatment of pulmonary tuberculosis. Lancet, 299(May):1079–1085, 1972.

[111] Wallace Fox, Gordon A Ellard, and Denis A Mitchison. Studies on the treat- ment of tuberculosis undertaken by the British Medical Research Council Tu- berculosis Units, 1946-1986, with relevant subsequent publications. Interna- tional Journal of Tuberculosis and Lung Disease, 3(10):S231–S279, 1999.

[112] Niyi Awofeso. Anti-tuberculosis medication side-effects constitute major fac- tor for poor adherence to tuberculosis treatment. Bulletin of the World Health Organisation, 86(3):249–270, 2008.

[113] Zhao Feng-Zeng, Christopher Murray, Sergio Spinaci, Karel Styblo, Jaap Broek- mans, Zou Ji-Qian, Dai Yuang-Sheng, Chi Yan-Hua, Du Xin, Cao Ji-Ping, Chen Yan-Lin, Li Li-Mao, Li Ning-Wu, Liu Chuan-Jin, Liu Hong-Qiao, Lu Qiang, Tang Da-Rang, Wang Peng-Fei, Wang Zhen-Han, Wu Pu-Er, Zhang Fa-Da, Zhang Fu-Sheng, and Zhu Gui-Lin. Results of directly observed short-course chemotherapy in 112 842 Chinese patients with smear-positive tuberculosis. Lancet, 347(8998):358–362, 1996.

[114] G R Khatri and Thomas R Frieden. The status and prospects of tuberculosis control in India. International Journal of Tuberculosis and Lung Disease, 4(3):193– 200, 2000.

[115] Charles A Peloquin. Therapeutic Drug Monitoring in the Treatment of Tuber- culosis. Drugs, 62(15):2169–2183, jan 2002.

[116] M Aquinas, W G L Allan, P A L Horsfall, P K Jenkins, Wong Hung-Yan, David Girling, Ruth Tall, and Wallace Fox. Adverse reactions to daily and intermittent rifampicin regimens for pulmonary tuberculosis in Hong Kong. British Medical Journal, 1(5803):765–71, 1972.

[117] Jotam G Pasipanodya, Shashikant Srivastava, and Tawanda Gumbo. Meta- Analysis of Clinical Studies Supports the Pharmacokinetic Variability Hypoth- esis for Acquired Drug Resistance and Failure of Antituberculosis Therapy. Clinical Infectious Diseases, 55(2):169–177, jul 2012.

[118] Charles A Peloquin. Tuberculosis Drug Serum Levels. Clinical Infectious Dis- eases, 33(4):584–585, 2001. 94 Bibliography

[119] Reinout Van Crevel, B Alisjahbana, W C M de Lange, F Borst, H Danusantoso, J W M van der Meer, D Burger, and R H H Nelwan. Low plasma concentra- tions of rifampicin in tuberculosis patients in Indonesia. International Journal of Tuberculosis and Lung Disease, 6(6):497–502, 2002.

[120] P R Donald and A H Diacon. The early bactericidal activity of anti-tuberculosis drugs: a literature review. Tuberculosis, 88 Suppl 1:S75–83, aug 2008.

[121] Dominique Cadosch, Pia Abel zur Wiesch, Roger Kouyos, and Sebastian Bon- hoeffer. The Role of Adherence and Retreatment in De Novo Emergence of MDR-TB. PLOS Computational Biology, 12(3):e1004749, 2016.

[122] Erlina Burhan, Carolien Ruesen, Rovina Ruslami, Arum Ginanjar, Hadiarto Mangunnegoro, Purwantyastuti Ascobat, Rogier Donders, Reinout van Crevel, and Rob E Aarnoutse. Isoniazid, Rifampicin and Pyrazinamide Plasma Con- centrations in Relation to Treatment Response in Indonesian Pulmonary Tuber- culosis Patients. Antimicrobial Agents and Chemotherapy, 57(8):3614–3619, may 2013.

[123] A Tostmann, Charles M Mtabho, Hadija H Semvua, Jossy van den Boogaard, Gibson S Kibiki, Martin J Boeree, and Rob E Aarnoutse. Pharmacokinetics of First-Line Tuberculosis Drugs in Tanzanian Patients. Antimicrobial Agents and Chemotherapy, 57(7):3208–3213, apr 2013.

[124] M Zhu, W J Burman, J R Starke, J J Stambaugh, P Steiner, A E Bulpitt, D Ashkin, B Auclair, S E Berning, R W Jelliffe, G S Jaresko, and Charles A Peloquin. Phar- macokinetics of ethambutol in children and adults with tuberculosis. Interna- tional Journal of Tuberculosis and Lung Disease, 8(11):1360–1367, 2004.

[125] Charles A Peloquin, George S Jaresko, Chan-Loi Yong, Anther C F Keung, Amy E Bulpitt, and Roger W Jelliffe. Population Pharmacokinetic Modeling of Isoniazid, Rifampin, and Pyrazinamide. Antimicrobial Agents and Chemotherapy, 41(12):2670–2679, 1997.

[126] Marcos Abdo Arbex, Marília de Castro Lima Varella, Hélio Ribeiro de Siqueira, and Fernando Augusto Fiúza de Mello. Antituberculosis drugs: Drug interac- tions, adverse effects, and use in special situations. Part 1: First-line drugs. Jornal Brasileiro de Pneumologia, 36(June):626–640, 2010.

[127] Edward R Garrett. The Bateman Function Revisited: A Critical Reevaluation of the Quantitative Expressions to Characterize Concentrations in the One Compartment Body Model as a Function of Time with First-Order Invasion and First-Order Elimination. Journal of Pharmacokinetics and Biopharmaceutics, 22(2):103–128, 1994.

[128] Eugenio Roanes-Lozano, Alfonso González-Bermejo, Eugenio Roanes-Macías, and Justo Cabezas. An Application of Computer Algebra to Pharmacokinetics: The Bateman Equation. SIAM Review, 48(1):133–146, 2006. Bibliography 95

[129] Catharina C Boehme, Pamela Nabeta, Doris Hillemann, Mark P Nicol, Shub- hada Shenai, Fiorella Krapp, Jenny Allen, Rasim Tahirli, Robert Blakemore, Roxana Rustomjee, Ana Milovic, Martin Jones, Sean M O’Brien, David H Pers- ing, Sabine Ruesch-Gerdes, Eduardo Gotuzzo, Camilla Rodrigues, David Al- land, and Mark D Perkins. Rapid Molecular Detection of Tuberculosis and Rifampin Resistance. The New England Journal of Medicine, 363(11):1005–1015, 2010.

[130] A Trébucq, S Anagonou, M Gninafon, K Lambregts, and F Boulahbal. Preva- lence of primary and acquired resistance of Mycobacterium tuberculosis to antituberculosis drugs in Benin after 12 years of short-course chemotherapy. The International Journal of Tuberculosis and Lung Disease, 3(6):466–70, 1999.

[131] Matthias Merker, Thomas A Kohl, Andreas Roetzer, Leona Truebe, Elvira Richter, Sabine Rüsch-Gerdes, Lanfranco Fattorini, Marco R Oggioni, Helen Cox, Francis Varaine, and Stefan Niemann. Whole Genome Sequencing Re- veals Complex Evolution Patterns of Multidrug-Resistant Mycobacterium tu- berculosis Beijing Strains in Patients. PloS ONE, 8(12):e82551, jan 2013.

[132] Emma Huitric, Jim Werngren, Pontus Juréen, and Sven Hoffner. Resistance Levels and rpoB Gene Mutations among In Vitro-Selected Rifampin-Resistant Mycobacterium tuberculosis Mutants. Antimicrobial Agents and Chemotherapy, 50(8):2860–2862, 2006.

[133] Pia Abel zur Wiesch, Roger D Kouyos, Jan Engelstädter, Roland R Regoes, and Sebastian Bonhoeffer. Population biological principles of drug-resistance evolution in infectious diseases. The Lancet - Infectious Diseases, 11(3):236–247, 2011.

[134] Andrew F Read, Troy Day, and Silvie Huijben. The evolution of drug resis- tance and the curious orthodoxy of aggressive chemotherapy. Proceedings of the National Academy of Sciences, 108(Supplement_2):10871–10877, 2011.

[135] Cesar A Arias and Barbara E Murray. Antibiotic-Resistant Bugs in the 21st Century - A Clinical Super-Challenge. The New England Journal of Medicine, 360(5):439–443, 2009.

[136] Charles W Knapp, Jan Dolfing, Phillip A I Ehlert, and David W Graham. Evi- dence of Increasing Antibiotic Resistance Gene Abundances in Archived Soils since 1940. Environmental Science and Technology, 44(2):580–587, 2010.

[137] Ramanan Laxminarayan, Adriano Duse, Chand Wattal, Anita K M Zaidi, Heiman F L Wertheim, Nithima Sumpradit, Erika Vlieghe, Gabriel Levy Hara, Ian M Gould, Herman Goossens, Christina Greko, Anthony D So, Maryam Bigdeli, Göran Tomson, Will Woodhouse, Eva Ombaka, Arturo Quizhpe Per- alta, Farah Naz Qamar, Fatima Mir, Sam Kariuki, Zulfiqar A Bhutta, Anthony Coates, Richard Bergstrom, Gerard D Wright, Eric D Brown, and Otto Cars. An- tibiotic resistance - the need for global solutions. The Lancet Infectious Diseases, 13(12):1057–1098, 2013. 96 Bibliography

[138] Brad Spellberg, John G Bartlett, and David N Gilbert. The Future of Antibiotics and Resistance. New England Journal of Medicine, 368(4):299–302, 2013.

[139] Philip J Gerrish and J Gerardo García-Lerma. Mutation rate and the efficacy of antimicrobial drug treatment. The Lancet - Infectious Diseases, 3(1):28–32, 2003.

[140] María D Maciá, David Blanquer, Bernat Togores, Jaume Sauleda, José L Pérez, and Antonio Oliver. Hypermutation Is a Key Factor in Development of Multiple-Antimicrobial Resistance in Pseudomonas aeruginosa Strains Caus- ing Chronic Lung Infections. Antimicrobial Agents and Chemotherapy, 49(8):3382– 3386, 2005.

[141] Ana Sousa, Sara Magalhães, and Isabel Gordo. Cost of antibiotic resistance and the geometry of adaptation. Molecular Biology and Evolution, 2011.

[142] S E Luria and M Delbrück. Mutations of Bacteria from Virus Sensitivity to Virus Resistance. Genetics, 28(6):491–511, nov 1943.

[143] William A Rosche and Patricia L Foster. Determining Mutation Rates in Bacte- rial Populations. Methods, 20(1):617–638, 2010.

[144] Patricia L Foster. Stress-Induced Mutagenesis in Bacteria. Critical Reviews in Biochemistry and Molecular Biology, 42(5):373–397, 2007.

[145] Daniel J Dwyer, Michael A Kohanski, and James J Collins. Role of reactive oxy- gen species in antibiotic action and resistance. Current Opinion in Microbiology, 12(5):482–489, oct 2009.

[146] Rodrigo S Galhardo, P J Hastings, and Susan M Rosenberg. Mutation as a Stress Response and the Regulation of Evolvability. Critical Reviews in Biochem- istry and Molecular Biology, 42(5):399–435, 2007.

[147] Olivier Tenaillon, Erick Denamur, and Ivan Matic. Evolutionary significance of stress-induced mutagenesis in bacteria. Trends in Microbiology, 12(6):264–270, jun 2004.

[148] Yoav Ram and Lilach Hadany. The evolution of stress-induced hypermutation in asexual populations. Evolution, 66(7):2315–2328, 2012.

[149] John R Roth, Elisabeth Kugelberg, Andrew B Reams, Eric Kofoid, and Dan I Andersson. Origin of Mutations Under Selection: The Adaptive Mutation Con- troversy. Annual Review of Microbiology, 60:477–501, jan 2006.

[150] John R Roth. The joys and terrors of fast adaptation: new findings elucidate antibiotic resistance and natural selection. Molecular Microbiology, 79(2):279– 282, jan 2011.

[151] Marc Lipsitch and Bruce R Levin. The Population Dynamics of Antimicrobial Chemotherapy. Antimicrobial Agents and Chemotherapy, 41(2):363–373, 1997. Bibliography 97

[152] Sebastian Bonhoeffer, Marc Lipsitch, and Bruce R Levin. Evaluating treatment protocols to prevent antibiotic resistance. Proceedings of the National Academy of Sciences of the United States of America, 94(22):12106–12111, oct 1997.

[153] H. Allen Orr and Robert L. Unckless. Population Extinction and the Genet- ics of Adaptation. The American Naturalist, 172(2):160–169, 2008.

[154] Erik Gullberg, Sha Cao, Otto G Berg, Carolina Ilbäck, Linus Sandegren, Diar- maid Hughes, and Dan I Andersson. Selection of Resistant Bacteria at Very Low Antibiotic Concentrations. PLoS Pathogens, 7(7):e1002158, jul 2011.

[155] Ram Maharjan and Thomas Ferenci. Mutational Signatures Indicative of En- vironmental Stress in Bacteria. Molecular Biology and Evolution, 32(2):380–391, 2014.

[156] Phuong Pham, Savithri Rangarajan, Roger Woodgate, and Myron F Goodman. Roles of DNA polymerases V and II in SOS-induced error-prone and error-free repair in Escherichia coli. Proceedings of the National Academy of Sciences of the United States of America, 98(15):8350–8354, 2001.

[157] Meghna Patel, Qingfei Jiang, Roger Woodgate, Michael M Cox, and Myron F Goodman. A New Model for SOS-induced Mutagenesis: How RecA Protein Activates DNA Polymerase V. Critical Reviews in Biochemistry and Molecular Biology, 45(3):171–184, 2010.

[158] Joan Fung-Tomc, Benjamin Kolek, and Daniel P Bonner. Ciprofloxacin-Induced, Low-Level Resistance to Structurally Unrelated Antibiotics in Pseudomonas aeruginosa and Methicillin-Resistant Staphylococcus aureus. Antimicrobial Agents and Chemotherapy, 37(6):1289–1296, jun 1993.

[159] François Taddei, Ivan Matic, and Miroslav Radman. cAMP-dependent SOS induction and mutagenesis in resting bacterial populations. Proceedings of the National Academy of Sciences of the United States of America, 92(25):11736–11740, 1995.

[160] Ana Alonso, Ester Campanario, and José L Martínez. Emergence of multidrug- resistant mutants is increased under antibiotic selective pressure in Pseu- domonas aeruginosa. Microbiology, 145:2857–2862, oct 1999.

[161] Ryan T Cirz, Jodie K Chin, David R Andes, Valérie de Crécy-Lagard, William A Craig, and Floyd E Romesberg. Inhibition of Mutation and Combating the Evolution of Antibiotic Resistance. PLoS Biology, 3(6):e176, jun 2005.

[162] Stephen H Gillespie, Shreya Basu, Anne L Dickens, Denise M O’Sullivan, and Timothy D McHugh. Effect of subinhibitory concentrations of ciprofloxacin on Mycobacterium fortuitum mutation rates. The Journal of Antimicrobial Chemo- therapy, 56(2):344–348, aug 2005.

[163] Jesús Blázquez, José-María Gómez-Gómez, Antonio Oliver, Carlos Juan, Vivek Kapur, and Soledad Martín. PBP3 inhibition elicits adaptive responses in Pseu- domonas aeruginosa. Molecular Microbiology, 62(1):84–99, oct 2006. 98 Bibliography

[164] Stephanie K Henderson-Begg, David M Livermore, and Lucinda M C Hall. Effect of subinhibitory concentrations of antibiotics on mutation frequency in Streptococcus pneumoniae. The Journal of Antimicrobial Chemotherapy, 57(5):849– 854, may 2006.

[165] Emilia Varhimo, Kirsi Savijoki, Hanna Jefremoff, Jari Jalava, Antti Sukura, and Pekka Varmanen. Ciprofloxacin induces mutagenesis to antibiotic resistance independent of UmuC in Streptococcus uberis. Environmental Microbiology, 10(8):2179–2183, aug 2008.

[166] Michael A Kohanski, Mark A DePristo, and James J Collins. Sublethal Antibi- otic Treatment Leads to Multidrug Resistance via Radical-Induced Mutagene- sis. Molecular Cell, 37(3):311–320, feb 2010.

[167] Joseph F Petrosino, Rodrigo S Galhardo, Liza D Morales, and Susan M Rosen- berg. Stress-Induced beta-Lactam Antibiotic Resistance Mutation and Se- quences of Stationary-Phase Mutations in the Escherichia coli Chromosome. Journal of Bacteriology, 191(19):5881–5889, oct 2009.

[168] Uri Obolski and Lilach Hadany. Implications of stress-induced genetic varia- tion for minimizing multidrug resistance in bacteria. BMC Medicine, 10(89):1– 13, jan 2012.

[169] Scott T Micek, Emily C Welch, Junaid Khan, Mubashir Pervez, Joshua A Do- herty, Richard M Reichley, and Marin H Kollef. Empiric Combination An- tibiotic Therapy Is Associated with Improved Outcome against Sepsis Due to Gram-Negative Bacteria: a Retrospective Analysis. Antimicrobial Agents and Chemotherapy, 54(5):1742–1748, 2010.

[170] Pranita D Tamma, Sara E Cosgrove, and Lisa L Maragakis. Combination Ther- apy for Treatment of Infections with Gram-Negative Bacteria. Clinical Microbi- ology Reviews, 25(3):450–470, 2012.

[171] Stephanie M Carlson, Curry J Cunningham, and Peter A H Westley. Evolution- ary rescue in a changing world. Trends in Ecology & Evolution, 29(9):521–530, 2014.

[172] Andrew M Lee, Christian T Ross, Bu-Bing Zeng, and Scott F Singleton. A Molecular Target for Suppression of the Evolution of Antibiotic Resistance: In- hibition of the Escherichia coli RecA Protein by N6-(1-Naphthyl)-ADP. Journal of Medicinal Chemistry, 48(17):5408–5411, aug 2005.

[173] Ryan T Cirz and Floyd E Romesberg. Controlling Mutation: Intervening in Evo- lution as a Therapeutic Strategy. Critical Reviews in Biochemistry and Molecular Biology, 42(5):341–354, 2007.

[174] Thuy Do Thi, Elena López, Alexandro Rodríguez-Rojas, Jerónimo Rodríguez- Beltrán, Alejandro Couce, Javier R Guelfo, Alfredo Castañeda-García, and Jesús Blázquez. Effect of recA inactivation on mutagenesis of Escherichia coli exposed to sublethal concentrations of antimicrobials. The Journal of Antimicro- bial Chemotherapy, 66(3):531–538, mar 2011. Bibliography 99

[175] Helen Cox, Yared Kebede, Sholpan Allamuratova, Gabit Ismailov, Zamira Davletmuratova, Graham Byrnes, Christine Stone, Stefan Niemann, Sabine Rüsch-Gerdes, Lucie Blok, and Daribay Doshetov. Tuberculosis Recurrence and Mortality after Successful Treatment: Impact of Drug Resistance. PLoS Medicine, 3(10):e384, oct 2006. [176] Helen S Cox, Stefan Niemann, Gabit Ismailov, Daribay Doshetov, Juan Daniel Orozco, Lucie Blok, Sabine Rüsch-Gerdes, and Yared Kebede. Risk of acquired drug resistance during short-course directly observed treatment of tuberculosis in an area with high levels of drug resistance. Clinical infectious diseases : an official publication of the Infectious Diseases Society of America, 44(11):1421–1427, jun 2007. [177] Kwonjune J Seung, Irina E Gelmanova, Gennadiy G Peremitin, Vera T Gol- ubchikova, Vera E Pavlova, Olga B Sirotkina, Galina V Yanova, and Aivar K Strelis. The Effect of Initial Drug Resistance on Treatment Response and Ac- quired Drug Resistance during Standardized Short-Course Chemotherapy for Tuberculosis. Clinical Infectious Diseases, 39(9):1321–1328, nov 2004. [178] Rajesh Gupta and Marcos Espinal. A prioritised research agenda for DOTS- Plus for multidrug-resistant tuberculosis (MDR-TB). The International Journal of Tuberculosis and Lung Disease, 7(5):410–414, 2003. [179] Shenjie Tang, Shouyong Tan, Lan Yao, Fujian Li, Li Li, Xinzhi Guo, Yidian Liu, Xiaohui Hao, Yanqiong Li, Xiuxiu Ding, Zhanjun Zhang, Li Tong, and Jianan Huang. Risk Factors for Poor Treatment Outcomes in Patients with MDR-TB and XDR-TB in China: Retrospective Multi-Center Investigation. PloS ONE, 8(12):e82943, jan 2013. [180] S S Rajbhandary, S M Marks, and N N Bock. Costs of patients hospitalized for multidrug-resistant tuberculosis. Int J Tuberc.Lung Dis, 8(8):1012–1016, 2004. [181] N Sarita Shah, Abigail Wright, Gill-Han Bai, Lucia Barrera, Fadila Boulah- bal, Nuria Martín-Casabona, Francis Drobniewski, Christopher Gilpin, Marta Havelková, Rosario Lepe, Richard Lumb, Beverly Metchock, Françoise Por- taels, Maria Filomena Rodrigues, Sabine Rüsch-Gerdes, Armand Van Deun, Veronique Vincent, Kayla Laserson, Charles Wells, and J Peter Cegielski. World- wide emergence of extensively drug-resistant tuberculosis. Emerging Infectious Diseases, 13(3):380–387, mar 2007. [182] Yue Wu, Clare A Saddler, Frank Valckenborgh, and Mark M Tanaka. Dynamics of evolutionary rescue in changing environments and the emergence of antibi- otic resistance. Journal of Theoretical Biology, 340:222–31, jan 2014. [183] F M MacKenzie. The post-antibiotic effect. Journal of Antimicrobial Chemotherapy, 32(4):519–537, 1993. [184] Paul G Ambrose, Sujata M Bhavnani, Christopher M Rubino, Arnold Louie, Tawanda Gumbo, Alan Forrest, and George L Drusano. Pharmacokinetics- Pharmacodynamics of Antimicrobial Therapy: It’s Not Just for Mice Anymore. Clinical Infectious Diseases, 44(1):79–86, jan 2007. 100 Bibliography

[185] Chiu Yeung Chan, Carrie Au-Yeang, Wing Wai Yew, Chi Chiu Leung, and Augustine F B Cheng. In Vitro Postantibiotic Effects of Rifapentine, Isoniazid, and Moxifloxacin against Mycobacterium tuberculosis. Antimicrobial Agents and Chemotherapy, 48(1):340–343, 2004.

[186] L Shargel and A B Yu. Applied biopharmaceutics & pharmacokinetics. McGraw- Hill, New York, 4th edition, 1999.

[187] Michael C Chao and Eric J Rubin. Letting Sleeping dos Lie: Does Dormancy Play a Role in Tuberculosis? Annual Review of Microbiology, 64:293–311, oct 2010.

[188] E R Rhoades, A A Frank, and Ian M Orme. Progression of chronic pulmonary tuberculosis in mice aerogenically infected with virulent Mycobacterium tuber- culosis. The International Journal of Tuberculosis and Lung Disease, 78(1):57–66, 1997.

[189] David R Sherman and Sebastien Gagneux. Estimating the mutation rate of Mycobacterium tuberculosis during infection. Nature Genetics, 43(5):400–401, may 2011.

[190] WHO. "Antibmicrobial resistance" Fact sheet No 194. Technical report, 2015.

[191] Cassie F Pope, Denise M O’Sullivan, Timothy D McHugh, and Stephen H Gillespie. A practical guide to measuring mutation rates in antibiotic resistance. Antimicrobial Agents and Chemotherapy, 52(4):1209–1214, 2008.

[192] Anirvan Chatterjee, Dhananjaya Saranath, Purva Bhatter, and Nerges Mistry. Global Transcriptional Profiling of Longitudinal Clinical Isolates of Mycobac- terium tuberculosis Exhibiting Rapid Accumulation of Drug Resistance. PloS ONE, 8(1):e54717, jan 2013.

[193] O J Billington, Timothy D McHugh, and Stephen H Gillespie. Physiological Cost of Rifampin Resistance Induced In Vitro in Mycobacterium tuberculosis. Antimicrobial Agents and Chemotherapy, 43(8):1866–1869, aug 1999.

[194] Tran N Buu, Mai N T Huyen, H T W Quy, N V Hen, Matteo Zignol, Martien W Borgdorff, Frank G J Cobelens, and Dick van Soolingen. The Beijing genotype is associated with young age and multidrug-resistant tuberculosis in rural Viet- nam. The International Journal of Tuberculosis and Lung Disease, 13(7):900–906, 2009.

[195] Denise M O’Sullivan, Timothy D McHugh, and Stephen H Gillespie. Analysis of rpoB and pncA mutations in the published literature: an insight into the role of oxidative stress in Mycobacterium tuberculosis evolution? Journal of Antimicrobial Chemotherapy, 55(5):674–679, may 2005.

[196] Denise M O’Sullivan, Timothy D McHugh, and Stephen H Gillespie. The effect of oxidative stress on the mutation rate of Mycobacterium tuberculosis with im- paired catalase/peroxidase function. The Journal of Antimicrobial Chemotherapy, 62(4):709–712, oct 2008. Bibliography 101

[197] Christopher B Ford, Philana Ling Lin, Michael R Chase, Rupal R Shah, Oleg Iartchouk, James Galagan, Nilofar Mohaideen, Thomas R Ioerger, James C Sac- chettini, Marc Lipsitch, JoAnne L Flynn, and Sarah M Fortune. Use of whole genome sequencing to estimate the mutation rate of Mycobacterium tuberculo- sis during latent infection. Nature Genetics, 43(5):482–486, may 2011.

ACKNOWLEDGEMENTS

I would like to thank here all the people who contributed to my thesis and those who made my years here in the group of Theoretical Biology a great experience. First of all I am immensely grateful for having Sebastian Bonhoeffer as my supervisor. I could not wish for a more accommodating doctoral father. He provided a stimulat- ing environment and granted me the freedom to pursue the studies that interested me. By granting me the personal freedom to explore various directions and also occasionally divert from an originally chosen path I sometimes may have gotten lost but it also allowed me through introspection to learn to keep the bigger picture in perspective. At the same time he provided me always the support when I requested it. With this attitude and by his example he cultivated an environment that fostered a way of independent and critical thinking. It would be difficult to exaggerate the influence that Pia Abel zur Wiesch had on my doctoral studies. She is probably the single most responsible person for me choosing to pursue my doctoral studies. From my master’s thesis throughout my Ph.D. she fulfilled the role of my supervisor at least as much as Sebastian did. I think the mere fact that she was involved in every study in this thesis as well as a previous publication speaks volumes. I am forever grateful for all the knowledge and experience that she shared with me. It is a privilege to have collaborated with someone for whom I foresee an outstanding scientific career. Many thanks also go to Roger Kouyos who introduced me to the field of infectious disease modeling. He was my first mentor in the group of Theoretical Biology and much of what he taught me is still at the roots of all my mathematical models. I am always amazed by his capability to almost instantly capture concepts of rather com- plex issues that he is being confronted with. This was frequently highly appreciated when I called for his support or opinion. Special thanks go to Ted Cohen and Roland Regoes who kindly agreed to be in my examination committee. It humbles me to know that my work is being judged by people whose expertise I value greatly. Unfortunately, it would exceed the appropriate length of an acknowledgement section if I would express my heartfelt gratitude towards every former or current member in the group of Theoretical Biology, Experimental Ecology, Microbial Molec- ular Biology, Evolutionary Biology and Pathogen Ecology. I just want to state that I consider myself incredibly lucky to have been allowed to not only share office space but also share many stories and beers during countless hours of stimulating dis- cussions with people, none of which I would not consider a friend. Thanks for all the exhaustive runs up to the Waldhüsli, the beer brewing, hikes, skiing weekends and parties! I sincerely hope that we will stay in touch and that the procrastinating discussions continue. I definitely have to thank my sister, Eliane, with whom I shared a home for many years. Thank you for your patience and your leniency when I did not fully adhere to the house cleaning schedule!

103 104 Bibliography

Last but certainly not least I thank my parents, Ruth and Edgar. They spurred my ambition to always progress and develop further. Even when I diverted from my original path and they may have struggled initially to embrace my new goals I was absolutely sure that they would support me. Thank you very much for your confidence and your encouragement! CURRICULUMVITAE

Dominique Richard Cadosch

Institute of Integrative Biology CHN H76.1 Universitätstrasse 16 8092 Zürich Switzerland Phone: +41 44 632 89 22 Email: [email protected] url: http://www.tb.ethz.ch/people/person-detail.html?persid=130634

Birth date: 30 May, 1984 Nationality: Swiss

Language skills: German (native), English (full professional proficiency), French (limited working proficiency), Japanese (elementary proficiency) education

Mar. 2012 – May. 2016 Doctoral student in Theoretical Biology Thesis Title: Within-host population dynamics and the evolution of drug resistance in bacterial infections Supervisor: Prof. Sebastian Bonhoeffer Institute of Integrative Biology, D-USYS, ETH Zürich Zürich, Switzerland

Mar. 2010 – Nov. 2011 M.Sc. ETH in Ecology and Evolution Thesis Title: Modelling the within-host infection and therapy of pulmonary tubercu- losis Supervisor: Prof. Sebastian Bonhoeffer Institute of Integrative Biology, D-USYS, ETH Zürich Zürich, Switzerland

Sep. 2005 – Feb. 2010 B.Sc. ETH in Biology ETH Zürich Zürich, Switzerland

105 106 curriculum vitae

Jul. 2004 – May. 2005 Military service Mechanized infantry of the Swiss Army Switzerland

Aug. 2000 – Jun. 2004 Gymnasial Matura Alte Kantonsschule Aarau Aarau, Switzerland

other research experience

Jan. 2014 Participation in the Swiss Epidemiological Winter School Course: Applied Bayesian Statistics in Medical Research University of Bern Wengen, Switzerland

Sep. 2010 – Jun. 2011 Research project in Theoretical Biology at the ETH Zürich Title: Assessing the impact of adherence to anti-retroviral therapy on treatment failure and resistance evolution in HIV Supervisors: Roger Kouyos and Sebastian Bonhoeffer ETH Zürich Zürich, Switzerland

Sep. 2009 – Oct. 2011 Research project in the AI Lab of the University of Zürich Title: Attempt on Plant-Machine Interface: Towards Self-monitoring Plant Systems Supervisors: Dana Damian, Shuhei Miyashita, Rolf Pfeifer AI Lab, University of Zürich Zürich, Switzerland

teaching and supervisory experience

Sep. 2015 – Feb. 2016 Supervised seminar paper of a Master student Theoretical Biology group, ETH Zürich

Sep. 2014 – Apr. 2015 Supervised term paper of a Master student Theoretical Biology group, ETH Zürich

other professional activities

Referee or co-referee for: Nature Genetics, PLOS ONE, Infectious Diseases - Drug Targets. curriculum vitae 107 publications

D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (2016) The role of adherence and retreatment in de novo emergence of MDR-TB. PLOS Computational Biology 12(3): e1004749. doi: 10.1371/journal.pcbi.1004749 DD Damian, S Miyashita, S Aoyama, D Cadosch, PT Huang, M Ammann, R Pfeifer (2014) Automated physiological recovery of avocado plants for plant-based adaptive machines. Adaptive Behaviour 22(2): 109-122. doi:10.1177/1059712313511919 D Cadosch, S Bonhoeffer, R Kouyos (2012) Assessing the impact of adherence to anti-retroviral therapy on treatment failure and resistance evolution in HIV. Journal of the Royal Society Interface 9(74), 2309-2320. doi:10.1098/rsif.2012.0127 D Cadosch, HP Huang, DD Damian, S Miyashita, S Aoyama, R Pfeifer (2011) Attempt on Plant Machine Interface: Towards Self-monitoring Plant Systems. IEEE International Conference on Systems, Man and Cybernetics pp. 791-796. IEEE. doi:10.1109/ICSMC.2011.6083749 oral presentations

Sep. 2011 Attempt on Plant Machine Interface: Towards Self-monitoring Plant Systems. IEEE International Conference on Systems, Man and Cybernetics Anchorage AK, USA poster presentations

D Cadosch, S Bonhoeffer (Aug. 2015) Antibiotic stress-induced mutagenesis and the implications for the emergence of drug resistance. Gordon Research Conference on Microbial Population Biology Andover NH, USA D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (Aug. 2014) The role of adherence, retreatment and fitness costs for the emergence of MDR-TB. Gordon Research Conference on Drug Resistance Newry ME, USA D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (Aug. 2013) Modelling the within-host infection and therapy of pulmonary tuberculosis. Gordon Research Conference on Drug Resistance Easton MA, USA D Cadosch, HP Huang, DD Damian, S Miyashita, S Aoyama, R Pfeifer (Sep. 2011) Attempt on Plant Machine Interface: Towards Self-monitoring Plant Systems. IEEE International Conference on Systems, Man, and Cybernetics Anchorage AK, USA 108 curriculum vitae

D Cadosch, M Böller, M Ammann, DD Damian, S Miyashita, R Pfeifer (Jan. 2010) Attempt towards the cyborg-plant – Robotic response to water stress in avocados. 4th International Conference on Cognitive Systems, CogSys 2010 Zürich, Switzerland colophon

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