Contributions to the Mathematical Systems Medicine of Antimicrobial Therapy and Genotype-Phenotype Inference.

The following summary of my publications describes the main ideas in the corresponding research articles and clarfifies my contribution in multi-author publications. I decided to apply for habilitation according to x2.I.1.(c) of the Habilitationsordnung (this path is usually referred as Kumulative Habilitation"). I selected 13 first- or last author publications for this habilitation that concern contributions to the mathematical systems medicine of antiviral therapy [tMH10, tMS+11, FtK+11, tMMS12, DSt12, DWSt15, Dt16, DSt16, DDKt18, DSD+19, DDKt19], as well as inference of genotype-phenotype associations [SDH+15, SSJ+18]. The selected publications represent my major contributions in this research eld since submitting my doctoral thesis in September 2009

Mathematical Modelling of the Molecular Mechanisms of Interaction of Tenofovir with Emtricitabine against HIV

The combination of the two nucleoside reverse transcriptase inhibitors (NRTI) tenofovir disoproxil fumarate (TDF) and emtricitabine (FTC) is used in most highly active antiretroviral therapies for treatment of HIV-1 infection, as well as in pre-exposure prophylaxis against HIV acquisition. Administered as prodrugs, these drugs are taken up by HIV-infected target cells, undergo intracellular phosphorylation and compete with natural deoxynucleoside triphosphates (dNTP) for incorporation into nascent viral DNA during reverse transcription. Once incorporated, they halt reverse transcription. In vitro studies have proposed that TDF and FTC act synergistically within an HIV-infected cell. However, it is unclear whether, and which, direct drug–drug interactions mediate the apparent synergy. The goal of this work was to refine a mechanistic model for the molecular mechanism of action (MMOA) of nucleoside analogues in order to analyse whether putative direct interactions may account for the in vitro observed synergistic effects. Our analysis suggests that depletion of dNTP pools can explain apparent synergy between TDF and FTC in HIV-infected cells at clinically relevant concentrations. Dead-end complex (DEC) formation does not seem to significantly contribute to the synergistic effect. However, in the presence of non-nucleoside reverse transcriptase inhibitors (NNRTIs), its role might be more relevant, as previously reported in experimental in vitro studies.Peer Reviewe

Physiologically Based Pharmacokinetic Modelling: A Sub-Compartmentalized Model of Tissue Distribution

We present a sub-compartmentalized model of drug distribution in tissue that extends existing approaches based on the well-stirred tissue model. It is specified in terms of di®erential equations that explicitly account for the drug concentration in erythrocytes, plasma, interstitial and cellular space. Assuming, in addition, steady state drug distribution and by lumping the different sub-compartments, established models to predict tissue-plasma partition coe±cients can be derived in an intriguingly simple way. This direct link is exploited to explicitly construct and parameterize the sub-compartmentalized model for moderate to strong bases, acids, neutrals and zwitterions. The derivation highlights the contributions of the different tissue constituents and provides a simple and transparent framework for the construction of novel tissue distribution models

Physiologically Based Pharmacokinetic Modelling: A Sub-Compartmentalized Model of Tissue Distribution

We present a sub-compartmentalized model of drug distribution in tissue that extends existing approaches based on the well-stirred tissue model. It is specified in terms of di®erential equations that explicitly account for the drug concentration in erythrocytes, plasma, interstitial and cellular space. Assuming, in addition, steady state drug distribution and by lumping the different sub-compartments, established models to predict tissue-plasma partition coe±cients can be derived in an intriguingly simple way. This direct link is exploited to explicitly construct and parameterize the sub-compartmentalized model for moderate to strong bases, acids, neutrals and zwitterions. The derivation highlights the contributions of the different tissue constituents and provides a simple and transparent framework for the construction of novel tissue distribution models

Pharmacokinetics and Pharmacodynamics of the Reverse Transcriptase Inhibitor Tenofovir and Prophylactic Efficacy against HIV-1 Infection

Antiviral pre-exposure prophylaxis (PrEP) through daily drug administration can protect healthy individuals from HIV-1 infection. While PrEP was recently approved by the FDA, the potential long-term consequences of PrEP implementation remain entirely unclear. The aim of this study is to predict the efficacy of different prophylactic strategies with the pro-drug tenofovir- disoproxil-fumarate (TDF) and to assess the sensitivity towards timing- and mode of TDF administration (daily- vs. single dose), adherence and the number of transmitted viruses. We developed a pharmacokinetic model for TDF and its active anabolite tenofovir-diphosphate (TFV-DP) and validated it with data from 4 different trials, including 4 distinct dosing regimes. Pharmacokinetics were coupled to an HIV model and viral decay following TDF mono-therapy was predicted, consistent with available data. Subsequently, a stochastic approach was used to estimate the % infections prevented by (i) daily TDF-based PrEP, (ii) one week TDF started either shortly before, or -after viral exposure and (iii) a single dose oral TDF before viral challenge (sd-PrEP). Analytical solutions were derived to assess the relation between intracellular TFV-DP concentrations and prophylactic efficacy. The predicted efficacy of TDF was limited by a slow accumulation of active compound (TFV-DP) and variable TFV-DP half-life and decreased with increasing numbers of transmitted viruses. Once daily TDF-based PrEP yielded 80% protection, if at least 40% of pills were taken. Sd-PrEP with 300 mg or 600 mg TDF could prevent 50% infections, when given at least before virus exposure. The efficacy dropped to 10%, when given 1 h before 24 h exposure. Efficacy could not be increased with increasing dosage or prolonged administration. Post-exposure prophylaxis poorly prevented infection. The use of drugs that accumulate more rapidly, or local application of tenofovir gel may overcome the need for drug administration long before virus exposure

The utility of efavirenz-based prophylaxis against HIV infection. A systems pharmacological analysis

Pre-exposure prophylaxis (PrEP) is considered one of the five “pillars” by UNAIDS to reduce HIV transmission. Moreover, it is a tool for female self-protection against HIV, making it highly relevant to sub-Saharan regions, where women have the highest infection burden. To date, Truvada is the only medication for PrEP. However, the cost of Truvada limits its uptake in resource-constrained countries. Similarly, several currently investigated, patent-protected compounds may be unaffordable in these regions. We set out to explore the potential of the patent-expired antiviral efavirenz (EFV) as a cost-efficient PrEP alternative. A population pharmacokinetic model utilizing data from the ENCORE1 study was developed. The model was refined for metabolic autoinduction. We then explored EFV cellular uptake mechanisms, finding that it is largely determined by plasma protein binding. Next, we predicted the prophylactic efficacy of various EFV dosing schemes after exposure to HIV using a stochastic simulation framework. We predicted that plasma concentrations of 11, 36, 1287 and 1486ng/mL prevent 90% sexual transmissions with wild type and Y181C, K103N and G190S mutants, respectively. Trough concentrations achieved after 600 mg once daily dosing (median: 2017 ng/mL, 95% CI:445–9830) and after reduced dose (400 mg) efavirenz (median: 1349ng/mL, 95% CI: 297–6553) provided complete protection against wild-type virus and the Y181C mutant, and median trough concentrations provided about 90% protection against the K103N and G190S mutants. As reduced dose EFV has a lower toxicity profile, we predicted the reduction in HIV infection when 400 mg EFV-PrEP was poorly adhered to, when it was taken “on demand” and as post-exposure prophylaxis (PEP). Once daily EFV-PrEP provided 99% protection against wild-type virus, if ≥50% of doses were taken. PrEP “on demand” provided complete protection against wild-type virus and prevented ≥81% infections in the mutants. PEP could prevent >98% infection with susceptible virus when initiated within 24 h after virus exposure and continued for at least 9 days. We predict that 400 mg oral EFV may provide superior protection against wild-type HIV. However, further studies are warranted to evaluate EFV as a cost-efficient alternative to Truvada. Predicted prophylactic concentrations may guide release kinetics of EFV long-acting formulations for clinical trial design

Numerical approaches for the rapid analysis of prophylactic efficacy against HIV with arbitrary drug-dosing schemes

Pre-exposure prophylaxis (PrEP) is an important pillar to prevent HIV transmission. Because of experimental and clinical shortcomings, mathematical models that integrate pharmacological, viral- and host factors are frequently used to quantify clinical efficacy of PrEP. Stochastic simulations of these models provides sample statistics from which the clin- ical efficacy is approximated. However, many stochastic simulations are needed to reduce the associated sampling error. To remedy the shortcomings of stochastic simulation, we developed a numerical method that allows predicting the efficacy of arbitrary prophylactic regimen directly from a viral dynamics model, without sampling. We apply the method to var- ious hypothetical dolutegravir (DTG) prophylaxis scenarios. The approach is verified against state-of-the-art stochastic simulation. While the method is more accurate than stochastic simulation, it is superior in terms of computational performance. For example, a continuous 6-month prophylactic profile is computed within a few seconds on a laptop computer. The method’s computational performance, therefore, substantially expands the horizon of feasi- ble analysis in the context of PrEP, and possibly other applications.Pre-exposure prophylaxis (PrEP) is an important tool to prevent HIV transmission. However, experimental identification of parameters that determine prophylactic efficacy is extremely difficult. Clues about these parameters could prove essential for the design of next-generation PrEP compounds. Integrative mathematical models can fill this void: Based on stochastic simulation, a sample statistic can be generated, from which the prophylactic efficacy is estimated. However, for this sample statistic to be accurate, many simulations need to be performed. Here, we introduce a numerical method to directly compute the prophylactic efficacy from a viral dynamics model, without the need for sampling. Based on several examples with dolutegravir (DTG) -based short- and long-term PrEP, as well as post-exposure prophylaxis we demonstrate the correctness of the new method and its outstanding computational performance. Due to the method’s computational performance, a number of analyses, including formal sensitivity analysis, are becoming feasible with the proposed method.Peer Reviewe

S̲tochastic S̲imulation A̲lgorithm For Effective Spreading Dynamics On T̲ime-Evolving A̲daptive N̲etworX̲ (SSATAN-X)

Modelling and simulating of pathogen spreading has been proven crucial to inform containment strategies, as well as cost-effectiveness calculations. Pathogen spreading is often modelled as a stochastic process that is driven by pathogen exposure on time-evolving contact networks. In adaptive networks, the spreading process depends not only on the dynamics of a contact network, but vice versa, infection dynamics may alter risk behavior and thus feed back onto contact dynamics, leading to emergent complex dynamics. However, numerically exact stochastic simulation of such processes via the Gillespie algorithm is currently computationally prohibitive. On the other hand, frequently used ‘parallel updating schemes’ may be computationally fast, but can lead to incorrect simulation results. To overcome this computational bottleneck, we propose SSATAN-X. The key idea of this algorithm is to only capture contact dynamics at time-points relevant to the spreading process. We demonstrate that the statistics of the contact- and spreading process are accurate, while achieving ~100 fold speed-up over exact stochastic simulation. SSATAN-X’s performance increases further when contact dynamics are fast in relation to the spreading process, as applicable to most infectious diseases. We envision that SSATAN-X may extend the scope of analysis of pathogen spreading on adaptive networks. Moreover, it may serve to create benchmark data sets to validate novel numerical approaches for simulation, or for the data-driven analysis of the spreading dynamics on adaptive networks

An example with different dolutegravir prophylaxis schemes

To achieve the 90-90-90 goals set by UNAIDS, the number of new HIV infections needs to decrease to approximately 500,000 by 2020. One of the ‘five pillars’ to achieve this goal is pre-exposure prophylaxis (PrEP). Truvada (emtricitabine-tenofovir) is currently the only medication approved for PrEP. Despite its advantages, Truvada is costly and requires individuals to adhere to the once-daily regimen. To improve PrEP, many next-generation regimen, including long-acting formulations, are currently investigated. However, pre-clinical testing may not guide candidate selection, since it often fails to translate into clinical efficacy. On the other hand, quantifying prophylactic efficacy in the clinic is ethically problematic and requires to conduct long (years) and large (N>1000 individuals) trials, precluding systematic evaluation of candidates and deployment strategies. To prioritize- and help design PrEP regimen, tools are urgently needed that integrate pharmacological-, viral- and host factors determining prophylactic efficacy. Integrating the aforementioned factors, we developed an efficient and exact stochastic simulation approach to predict prophylactic efficacy, as an example for dolutegravir (DTG). Combining the population pharmacokinetics of DTG with the stochastic framework, we predicted that plasma concentrations of 145.18 and 722.23nM prevent 50- and 90% sexual transmissions respectively. We then predicted the reduction in HIV infection when DTG was used in PrEP, PrEP ‘on demand’ and post-exposure prophylaxis (PEP) before/after virus exposure. Once daily PrEP with 50mg oral DTG prevented 99–100% infections, and 85% of infections when 50% of dosing events were missed. PrEP ‘on demand’ prevented 79–84% infections and PEP >80% when initiated within 6 hours after virus exposure and continued for as long as possible. While the simulation framework can easily be adapted to other PrEP candidates, our simulations indicated that oral 50mg DTG is non-inferior to Truvada. Moreover, the predicted 90% preventive concentrations can guide release kinetics of currently developed DTG nano-formulations