A Novel Approach to Generate Hourly Photovoltaic Power Scenarios

Photovoltaic power is playing an ever-increasing role in the energy mix of countries worldwide. It is a stochastic energy source, and simulation models are needed to establish reliable risk management. This paper presents a novel approach for simulating hourly solar irradiation and—as a consequence—photovoltaic power based on easily accessible data such as wind, temperature, and cloudiness. Solar simulations are generated via a multiplication factor that scales the maximum possible solar irradiation. Photovoltaic simulations are then derived using formulas that approximate the physical interdependencies. The resulting simulations are unbiased on an annual level and reasonably reflect historic irradiation movements. Interpreting our approach as a descriptive model, we find that error values vary over the year and with granularity. Errors are highest when considering hourly values in wintertime, especially in the morning or late afternoon

Drug-Class Specific Impact of Antivirals on the Reproductive Capacity of HIV

Predictive markers linking drug efficacy to clinical outcome are a key component in the drug discovery and development process. In HIV infection, two different measures, viral load decay and phenotypic assays, are used to assess drug efficacy in vivo and in vitro. For the newly introduced class of integrase inhibitors, a huge discrepancy between these two measures of efficacy was observed. Hence, a thorough understanding of the relation between these two measures of drug efficacy is imperative for guiding future drug discovery and development activities in HIV. In this article, we developed a novel viral dynamics model, which allows for a mechanistic integration of the mode of action of all approved drugs and drugs in late clinical trials. Subsequently, we established a link between in vivo and in vitro measures of drug efficacy, and extract important determinants of drug efficacy in vivo. The analysis is based on a new quantity—the reproductive capacity—that represents in mathematical terms the in vivo analog of the read-out of a phenotypic assay. Our results suggest a drug-class specific impact of antivirals on the total amount of viral replication. Moreover, we showed that the (drug-)target half life, dominated by immune-system related clearance processes, is a key characteristic that affects both the emergence of resistance as well as the in vitro–in vivo correlation of efficacy measures in HIV treatment. We found that protease- and maturation inhibitors, due to their target half-life, decrease the total amount of viral replication and the emergence of resistance most efficiently

Hybrid stochastisch-determinstische Ansätze zur Simulation und Analyse von biochemischen Reaktionsnetzwerken

Traditionally, quantitative models of reaction networks are based on classical chemical kinetics. Under the assumption of the thermodynamic limit (infinite number of molecules/volume limit), reactions are modeled as continuous, deterministic processes. It has become evident, however, that discrete fluctuations play a crucial role in cellular processes like gene expression and signal transduction, where constituents are typically present in small numbers. In this case, a modeling approach based on stochastic reaction kinetics is required, where reactions are modeled as discrete stochastic processes. The temporal evolution of the probability density function of the number of molecules is given by the chemical master equation (CME), which, however, is impractical to solve in most applications due to its high dimensionality. Instead, it is common practice to approximate an indirect solution of the CME by computing realizations of the underlying Markov jump process. A major aim is the development of such indirect approaches that enable the simulation of complex multi-scale reaction networks. This thesis deals with the promising development of hybrid methods, where fast reactions associated with large numbers of molecules are continuously and deterministically approximated, and all other reactions are modeled as discrete stochastic processes. We demonstrate the benefit of such a hybrid system description on an integrative model of the replication dynamics of the human immunodeficiency virus (HIV). Based on hybrid simulations, we are able to design and validate in silico a novel treatment strategy for HIV-infected patients that can lead to significant improvements compared to conventional treatment strategies. While current hybrid methods almost exclusively rely on indirect approximations, a novel hybrid approach is presented in this thesis that allows to solve the CME directly. Based on a multi-scale expansion, evolution equations are derived that couple a CME on a reduced state space to evolution equations of deterministically approximated variables. Thus, the impact of changes in the probability distribution of the stochastic subsystem on the dynamics of the deterministic components becomes apparent and, in contrast to indirect hybrid methods, is taken into account explicitly. We illustrate and discuss the performance of this direct hybrid approaches in application to model systems of biological interest. In the last part of this thesis, we derive effective protein synthesis rates as typically incorporated in deterministic models of biochemical systems by reduction of a detailed stochastic model of gene expression. We use this approach to derive a protein interactions model of the flagellar gene regulation cascade in Escherichia coli. Based on the deduced functional relations between transcriptional and translational processes on the one hand and the synthesis rates on the other, we find that sensitivity with respect to effective rates does not directly carry over to the aggregated subprocesses.Traditionell beruhen quantitative Modelle von Reaktionsnetzwerken auf der Sicht der klassischen chemischen Kinetik. Unter der Annahme des thermodynamischen Grenzfalls (unendlicher Molekülanzahlen-/Volumenlimes) werden Reaktionen hierbei vereinfacht als kontinuierliche, deterministische Prozesse modelliert. In zellulären Systemen, die Prozesse wie Genexpression oder Signaltransduktion beinhalten, zeigt sich jedoch, dass zu beobachtende Fluktuationen bei geringen Molekülanzahlen von entscheidender Bedeutung sind. In diesen Fällen ist eine Modellierung basierend auf der stochastischen Reaktionskinetik erforderlich, in der Reaktionen als diskrete Zufallsprozesse beschrieben werden. Die zeitliche Entwicklung der Wahrscheinlichkeitsverteilung der Molekülanzahlen ist hierbei durch die chemische Mastergleichung (CME) gegeben, welche jedoch aufgrund ihrer hohen Dimensionalität im Allgemeinen nicht direkt gelöst werden kann. Stattdessen ist es üblich eine indirekte Lösung der CME durch Realisierungen des zugrundeliegenden Markov-Sprungrozesses zu approximieren. Ein weitverfolgtes Ziel ist nun die Entwicklung solcher indirekten Methoden, die die Simulation von komplexen, mehrskaligen Reaktionsnetzwerken ermöglichen. Gegenstand dieser Arbeit ist die vielversprechende Entwicklung von sogenannten hybriden Methoden, in denen schnelle Reaktionen assoziert mit hohen Molekülanzahlen kontinuierlich–deterministisch und komplementäre Reaktionen diskret–stochastisch modelliert werden. Wir demonstrieren den Nutzen einer hybriden Systembeschreibung an einem integrativen Modell der Replikationsdynamik des Humane Immundefizienz-Virus (HIV). Mithilfe hybrider Simulationen ist es uns möglich eine neuartige Behandlungsstrategie für HIV- Patienten zu entwerfen und zu validieren, die zu wesentlichen Verbesserungen gegenüber konventionellen Behandlungsstrategien führen kann. Während derzeitige hybride Methoden fast ausschließlich indirekte Näherungslösungen liefern, wird in dieser Arbeit ein neuer hybrider Zugang zur direkten Lösung der CME entwickelt. Anhand eines Mehrskalenansatzes werden Evolutionsgleichungen hergeleitet, die eine CME auf reduziertem Zustandsraum mit Evolutionsgleichungen der deterministisch approximierten Variablen koppeln. Hierdurch wird die Beeinflußung der Dynamik von deterministischen Komponenten durch Veränderungen in der Wahrscheinlichkeitsverteilung des stochastischen Teilsystems offensichtlich und kann, im Gegensatz zu indirekten hybriden Methoden, explizit berücksichtigt werden. Wir illustrieren und diskutieren unseren direkten hybriden Lösungsansatz an Modellsystemen von biologischem Interesse. Im letzten Teil dieser Arbeit leiten wir effektive Proteinsyntheseraten, wie sie üblicherweise in deterministischen Modellen genutzt werden, über Reduktion eines detaillierten, stochastischen Genexpressionsmodells her. Wir nutzen unseren Reduktionsansatz um ein Modell der Proteininteraktionen bei der flagellaren Genregulation in Escherichia coli abzuleiten. Die erhaltenen funktionalen Zusammenhänge zwischen einerseits Transkriptions- und Translationsprozessen und andererseits den Syntheseraten zeigen hierbei auf, dass sich eine hohe Sensitivität hinsichtlich effektiver Raten nicht zwangsläufig auf zugrundeliegende Subprozesse übertragt

Estimating HIV-1 Fitness Characteristics from Cross-Sectional Genotype Data

Despite the success of highly active antiretroviral therapy (HAART) in the management of human immunodeficiency virus (HIV)-1 infection, virological failure due to drug resistance development remains a major challenge. Resistant mutants display reduced drug susceptibilities, but in the absence of drug, they generally have a lower fitness than the wild type, owing to a mutation-incurred cost. The interaction between these fitness costs and drug resistance dictates the appearance of mutants and influences viral suppression and therapeutic success. Assessing in vivo viral fitness is a challenging task and yet one that has significant clinical relevance. Here, we present a new computational modelling approach for estimating viral fitness that relies on common sparse cross-sectional clinical data by combining statistical approaches to learn drug-specific mutational pathways and resistance factors with viral dynamics models to represent the host-virus interaction and actions of drug mechanistically. We estimate in vivo fitness characteristics of mutant genotypes for two antiretroviral drugs, the reverse transcriptase inhibitor zidovudine (ZDV) and the protease inhibitor indinavir (IDV). Well-known features of HIV-1 fitness landscapes are recovered, both in the absence and presence of drugs. We quantify the complex interplay between fitness costs and resistance by computing selective advantages for different mutants. Our approach extends naturally to multiple drugs and we illustrate this by simulating a dual therapy with ZDV and IDV to assess therapy failure. The combined statistical and dynamical modelling approach may help in dissecting the effects of fitness costs and resistance with the ultimate aim of assisting the choice of salvage therapies after treatment failure.ISSN:1553-734XISSN:1553-735

Estimating HIV-1 Fitness Characteristics from Cross-Sectional Genotype Data

<div><p>Despite the success of highly active antiretroviral therapy (HAART) in the management of human immunodeficiency virus (HIV)-1 infection, virological failure due to drug resistance development remains a major challenge. Resistant mutants display reduced drug susceptibilities, but in the absence of drug, they generally have a lower fitness than the wild type, owing to a mutation-incurred cost. The interaction between these fitness costs and drug resistance dictates the appearance of mutants and influences viral suppression and therapeutic success. Assessing <i>in vivo</i> viral fitness is a challenging task and yet one that has significant clinical relevance. Here, we present a new computational modelling approach for estimating viral fitness that relies on common sparse cross-sectional clinical data by combining statistical approaches to learn drug-specific mutational pathways and resistance factors with viral dynamics models to represent the host-virus interaction and actions of drug mechanistically. We estimate <i>in vivo</i> fitness characteristics of mutant genotypes for two antiretroviral drugs, the reverse transcriptase inhibitor zidovudine (ZDV) and the protease inhibitor indinavir (IDV). Well-known features of HIV-1 fitness landscapes are recovered, both in the absence and presence of drugs. We quantify the complex interplay between fitness costs and resistance by computing selective advantages for different mutants. Our approach extends naturally to multiple drugs and we illustrate this by simulating a dual therapy with ZDV and IDV to assess therapy failure. The combined statistical and dynamical modelling approach may help in dissecting the effects of fitness costs and resistance with the ultimate aim of assisting the choice of salvage therapies after treatment failure.</p></div

Two stage mechanistic model of <i>in vivo</i> HIV-1 infection dynamics [6].

<p>Target cells TU (T-cells) and MU (macrophages) can be infected by infective viruses (with effective infection rate constants and ), resulting in early stage infected cells and , respectively. Infection can also be unsuccessful after fusion of the virus, rendering the cell uninfected and thereby eliminating the virus (). and can also possibly return to uninfected states by destruction of essential viral proteins or DNA prior to integration (). cells can enter into a latent state (with probability ) that can get re-activated with a rate constant . Integration of viral DNA in the host genome proceeds with reaction rate constant in the T-cells and in the macrophages, resulting in late stage infected T-cells and macrophages , respectively. The infected cells release new viruses () and non-infective () viruses (with rate constants and , respectively) while the infected cells release new infective and non-infective viruses (with rate constants and , respectively). Target cells TU and MU are produced by the immune system at constant rate with rate constants and , respectively. , , , , and can be cleared by the immune system with reaction rate constants , , , , and , respectively. Viruses are cleared by the immune system with a rate constant . Mutations are modelled to occur at the stage of integration of the viral DNA. The incorporation of the various drug classes is indicated by the inhibition of corresponding processes: EI/FI - entry/fusion inhibitors, NRTI/NNRTI - nucleoside/non-nucleoside reverse transcriptase inhibitors, InI - integrase inhibitors, PI/MI - protease/maturation inhibitors.</p

Treatment outcome with ZDV+IDV dual therapy.

<p><b>A</b>. Genotypic reasons of treatment failure were assessed in terms of mutations present at point of virological failure. For different combinations of drug efficacies and , the different genotypic reasons of failure are shown in different colours. The treatment outcome could be a) failure with mutations resistant to both ZDV and IDV, (b) failure with mutations resistant only to ZDV, (c) failure with mutations resistant only to IDV, (d) failure with wild type, and (e) no detection of failure. <b>B</b>. Viral load (in copies RNA/ml) under ZDV+IDV therapy with  = 0.75 and  = 0.90. The blue line shows the total viral load, while the red dashed line depicts the wild type. The horizontal black dashed line represents the detection threshold used (500 copies/ml).</p

Estimated fitness costs for IDV mutants.

<p>Estimated resistance factors (on a logarithmic scale, log RF, column 2) and fitness costs (column 3) of mutants arising during IDV therapy. In parentheses, are the 95% confidence intervals for the estimates obtained from 200 bootstrap samples (where we resampled with replacement from the list of statistical waiting times and re-estimated fitness costs). Mutant types (column 4) are encoded by one ‘M’ for each major mutation and one ‘m’ for each minor mutation in the genotype.</p><p>Estimated fitness costs for IDV mutants.</p

Abundance of the 70R mutation and mutant genotypes with 70R under ZDV therapy.

<p><b>A</b>. Absolute abundance (in numbers) of the 70R mutation. <b>B</b>. Relative abundance of the 70R mutation in the viral population. The transient appearance and eventual fixation of the mutation 70R can be seen. <b>C</b>. Absolute abundance (in numbers) of mutant genotypes containing the mutation 70R. The absolute abundance of a certain mutation is calculated by adding all mutant genotypes containing the mutation.</p