@article{GopalakrishnanMontazeriMenzetal.2014, author = {Gopalakrishnan, Sathej and Montazeri, Hesam and Menz, Stephan and Beerenwinkel, Niko and Huisinga, Wilhelm}, title = {Estimating HIV-1 fitness characteristics from cross-sectional genotype data}, series = {PLoS Computational Biology : a new community journal}, volume = {10}, journal = {PLoS Computational Biology : a new community journal}, number = {11}, publisher = {PLoS}, address = {San Fransisco}, issn = {1553-734X}, doi = {10.1371/journal.pcbi.1003886}, pages = {14}, year = {2014}, abstract = {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.}, language = {en} } @article{MakaravaMenzThevesetal.2014, author = {Makarava, Natallia and Menz, Stephan and Theves, Matthias and Huisinga, Wilhelm and Beta, Carsten and Holschneider, Matthias}, title = {Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {90}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {4}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.90.042703}, pages = {6}, year = {2014}, abstract = {Amoebae explore their environment in a random way, unless external cues like, e. g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.}, language = {en} } @article{MenzLatorreSchuetteetal.2012, author = {Menz, Stephan and Latorre, Juan C. and Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Hybrid stochastic-deterministic solution of the chemical master equation}, series = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal}, volume = {10}, journal = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal}, number = {4}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1540-3459}, doi = {10.1137/110825716}, pages = {1232 -- 1262}, year = {2012}, abstract = {The chemical master equation (CME) is the fundamental evolution equation of the stochastic description of biochemical reaction kinetics. In most applications it is impossible to solve the CME directly due to its high dimensionality. Instead, indirect approaches based on realizations of the underlying Markov jump process are used, such as the stochastic simulation algorithm (SSA). In the SSA, however, every reaction event has to be resolved explicitly such that it becomes numerically inefficient when the system's dynamics include fast reaction processes or species with high population levels. In many hybrid approaches, such fast reactions are approximated as continuous processes or replaced by quasi-stationary distributions in either a stochastic or a deterministic context. Current hybrid approaches, however, almost exclusively rely on the computation of ensembles of stochastic realizations. We present a novel hybrid stochastic-deterministic approach to solve the CME directly. Our starting point is a partitioning of the molecular species into discrete and continuous species that induces a partitioning of the reactions into discrete-stochastic and continuous-deterministic processes. The approach is based on a WKB (Wentzel-Kramers-Brillouin) ansatz for the conditional probability distribution function (PDF) of the continuous species (given a discrete state) in combination with Laplace's method of integral approximation. The resulting hybrid stochastic-deterministic evolution equations comprise a CME with averaged propensities for the PDF of the discrete species that is coupled to an evolution equation of the related expected levels of the continuous species for each discrete state. In contrast to indirect hybrid methods, the impact of the evolution of discrete species on the dynamics of the continuous species has to be taken into account explicitly. The proposed approach is efficient whenever the number of discrete molecular species is small. We illustrate the performance of the new hybrid stochastic-deterministic approach in an application to model systems of biological interest.}, language = {en} } @article{SchaeferMenzJeltschetal.2017, author = {Sch{\"a}fer, Merlin and Menz, Stephan and Jeltsch, Florian and Zurell, Damaris}, title = {sOAR: a tool for modelling optimal animal life-history strategies in cyclic environments}, series = {Ecography : pattern and diversity in ecology ; research papers forum}, volume = {41}, journal = {Ecography : pattern and diversity in ecology ; research papers forum}, number = {3}, publisher = {Wiley}, address = {Hoboken}, issn = {0906-7590}, doi = {10.1111/ecog.03328}, pages = {551 -- 557}, year = {2017}, abstract = {Periodic environments determine the life cycle of many animals across the globe and the timing of important life history events, such as reproduction and migration. These adaptive behavioural strategies are complex and can only be fully understood (and predicted) within the framework of natural selection in which species adopt evolutionary stable strategies. We present sOAR, a powerful and user-friendly implementation of the well-established framework of optimal annual routine modelling. It allows determining optimal animal life history strategies under cyclic environmental conditions using stochastic dynamic programming. It further includes the simulation of population dynamics under the optimal strategy. sOAR provides an important tool for theoretical studies on the behavioural and evolutionary ecology of animals. It is especially suited for studying bird migration. In particular, we integrated options to differentiate between costs of active and passive flight into the optimal annual routine modelling framework, as well as options to consider periodic wind conditions affecting flight energetics. We provide an illustrative example of sOAR where food supply in the wintering habitat of migratory birds significantly alters the optimal timing of migration. sOAR helps improving our understanding of how complex behaviours evolve and how behavioural decisions are constrained by internal and external factors experienced by the animal. Such knowledge is crucial for anticipating potential species' response to global environmental change.}, language = {en} } @article{vonKleistMenzStockeretal.2011, author = {von Kleist, Max and Menz, Stephan and Stocker, Hartmut and Arasteh, Keikawus and Schuette, Christof and Huisinga, Wilhelm}, title = {HIV quasispecies dynamics during pro-active treatment switching impact on multi-drug resistance and resistance archiving in latent reservoirs}, series = {PLoS one}, volume = {6}, journal = {PLoS one}, number = {3}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0018204}, pages = {12}, year = {2011}, abstract = {The human immunodeficiency virus (HIV) can be suppressed by highly active anti-retroviral therapy (HAART) in the majority of infected patients. Nevertheless, treatment interruptions inevitably result in viral rebounds from persistent, latently infected cells, necessitating lifelong treatment. Virological failure due to resistance development is a frequent event and the major threat to treatment success. Currently, it is recommended to change treatment after the confirmation of virological failure. However, at the moment virological failure is detected, drug resistant mutants already replicate in great numbers. They infect numerous cells, many of which will turn into latently infected cells. This pool of cells represents an archive of resistance, which has the potential of limiting future treatment options. The objective of this study was to design a treatment strategy for treatment-naive patients that decreases the likelihood of early treatment failure and preserves future treatment options. We propose to apply a single, pro-active treatment switch, following a period of treatment with an induction regimen. The main goal of the induction regimen is to decrease the abundance of randomly generated mutants that confer resistance to the maintenance regimen, thereby increasing subsequent treatment success. Treatment is switched before the overgrowth and archiving of mutant strains that carry resistance against the induction regimen and would limit its future re-use. In silico modelling shows that an optimal trade-off is achieved by switching treatment at \& 80 days after the initiation of antiviral therapy. Evaluation of the proposed treatment strategy demonstrated significant improvements in terms of resistance archiving and virological response, as compared to conventional HAART. While continuous pro-active treatment alternation improved the clinical outcome in a randomized trial, our results indicate that a similar improvement might also be reached after a single pro-active treatment switch. The clinical validity of this finding, however, remains to be shown by a corresponding trial.}, language = {en} }