TY - JOUR A1 - Breitenbach, Tim A1 - Borzì, Alfio T1 - The Pontryagin maximum principle for solving Fokker–Planck optimal control problems JF - Computational Optimization and Applications N2 - The characterization and numerical solution of two non-smooth optimal control problems governed by a Fokker–Planck (FP) equation are investigated in the framework of the Pontryagin maximum principle (PMP). The two FP control problems are related to the problem of determining open- and closed-loop controls for a stochastic process whose probability density function is modelled by the FP equation. In both cases, existence and PMP characterisation of optimal controls are proved, and PMP-based numerical optimization schemes are implemented that solve the PMP optimality conditions to determine the controls sought. Results of experiments are presented that successfully validate the proposed computational framework and allow to compare the two control strategies. KW - Fokker–Planck equation KW - Pontryagin maximum principle KW - non-smooth optimal control problems KW - stochastic processes Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-232665 SN - 0926-6003 VL - 76 ER - TY - JOUR A1 - Kaltdorf, Martin A1 - Breitenbach, Tim A1 - Karl, Stefan A1 - Fuchs, Maximilian A1 - Kessie, David Komla A1 - Psota, Eric A1 - Prelog, Martina A1 - Sarukhanyan, Edita A1 - Ebert, Regina A1 - Jakob, Franz A1 - Dandekar, Gudrun A1 - Naseem, Muhammad A1 - Liang, Chunguang A1 - Dandekar, Thomas T1 - Software JimenaE allows efficient dynamic simulations of Boolean networks, centrality and system state analysis JF - Scientific Reports N2 - The signal modelling framework JimenaE simulates dynamically Boolean networks. In contrast to SQUAD, there is systematic and not just heuristic calculation of all system states. These specific features are not present in CellNetAnalyzer and BoolNet. JimenaE is an expert extension of Jimena, with new optimized code, network conversion into different formats, rapid convergence both for system state calculation as well as for all three network centralities. It allows higher accuracy in determining network states and allows to dissect networks and identification of network control type and amount for each protein with high accuracy. Biological examples demonstrate this: (i) High plasticity of mesenchymal stromal cells for differentiation into chondrocytes, osteoblasts and adipocytes and differentiation-specific network control focusses on wnt-, TGF-beta and PPAR-gamma signaling. JimenaE allows to study individual proteins, removal or adding interactions (or autocrine loops) and accurately quantifies effects as well as number of system states. (ii) Dynamical modelling of cell–cell interactions of plant Arapidopsis thaliana against Pseudomonas syringae DC3000: We analyze for the first time the pathogen perspective and its interaction with the host. We next provide a detailed analysis on how plant hormonal regulation stimulates specific proteins and who and which protein has which type and amount of network control including a detailed heatmap of the A.thaliana response distinguishing between two states of the immune response. (iii) In an immune response network of dendritic cells confronted with Aspergillus fumigatus, JimenaE calculates now accurately the specific values for centralities and protein-specific network control including chemokine and pattern recognition receptors. KW - cellular signalling networks KW - computer modelling Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-313303 VL - 13 ER - TY - JOUR A1 - Caliskan, Aylin A1 - Caliskan, Deniz A1 - Rasbach, Lauritz A1 - Yu, Weimeng A1 - Dandekar, Thomas A1 - Breitenbach, Tim T1 - Optimized cell type signatures revealed from single-cell data by combining principal feature analysis, mutual information, and machine learning JF - Computational and Structural Biotechnology Journal N2 - Machine learning techniques are excellent to analyze expression data from single cells. These techniques impact all fields ranging from cell annotation and clustering to signature identification. The presented framework evaluates gene selection sets how far they optimally separate defined phenotypes or cell groups. This innovation overcomes the present limitation to objectively and correctly identify a small gene set of high information content regarding separating phenotypes for which corresponding code scripts are provided. The small but meaningful subset of the original genes (or feature space) facilitates human interpretability of the differences of the phenotypes including those found by machine learning results and may even turn correlations between genes and phenotypes into a causal explanation. For the feature selection task, the principal feature analysis is utilized which reduces redundant information while selecting genes that carry the information for separating the phenotypes. In this context, the presented framework shows explainability of unsupervised learning as it reveals cell-type specific signatures. Apart from a Seurat preprocessing tool and the PFA script, the pipeline uses mutual information to balance accuracy and size of the gene set if desired. A validation part to evaluate the gene selection for their information content regarding the separation of the phenotypes is provided as well, binary and multiclass classification of 3 or 4 groups are studied. Results from different single-cell data are presented. In each, only about ten out of more than 30000 genes are identified as carrying the relevant information. The code is provided in a GitHub repository at https://github.com/AC-PHD/Seurat_PFA_pipeline. KW - single cell analysis KW - machine learning KW - explainability of machine learning KW - principal KW - feature analysis KW - model reduction KW - feature selection Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-349989 SN - 2001-0370 VL - 21 ER - TY - JOUR A1 - Kienle-Garrido, Melina-Lorén A1 - Breitenbach, Tim A1 - Chudej, Kurt A1 - Borzì, Alfio T1 - Modeling and numerical solution of a cancer therapy optimal control problem JF - Applied Mathematics N2 - A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer―a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero. KW - cancer KW - therapy KW - optimal control problem Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-177152 VL - 9 IS - 8 ER - TY - JOUR A1 - Breitenbach, Tim A1 - Lorenz, Kristina A1 - Dandekar, Thomas T1 - How to steer and control ERK and the ERK signaling cascade exemplified by looking at cardiac insufficiency JF - International Journal of Molecular Sciences N2 - Mathematical optimization framework allows the identification of certain nodes within a signaling network. In this work, we analyzed the complex extracellular-signal-regulated kinase 1 and 2 (ERK1/2) cascade in cardiomyocytes using the framework to find efficient adjustment screws for this cascade that is important for cardiomyocyte survival and maladaptive heart muscle growth. We modeled optimal pharmacological intervention points that are beneficial for the heart, but avoid the occurrence of a maladaptive ERK1/2 modification, the autophosphorylation of ERK at threonine 188 (ERK\(^{Thr188}\) phosphorylation), which causes cardiac hypertrophy. For this purpose, a network of a cardiomyocyte that was fitted to experimental data was equipped with external stimuli that model the pharmacological intervention points. Specifically, two situations were considered. In the first one, the cardiomyocyte was driven to a desired expression level with different treatment strategies. These strategies were quantified with respect to beneficial effects and maleficent side effects and then which one is the best treatment strategy was evaluated. In the second situation, it was shown how to model constitutively activated pathways and how to identify drug targets to obtain a desired activity level that is associated with a healthy state and in contrast to the maleficent expression pattern caused by the constitutively activated pathway. An implementation of the algorithms used for the calculations is also presented in this paper, which simplifies the application of the presented framework for drug targeting, optimal drug combinations and the systematic and automatic search for pharmacological intervention points. The codes were designed such that they can be combined with any mathematical model given by ordinary differential equations. KW - optimal pharmacological modulation KW - efficient intervention points KW - ERK signaling KW - optimal treatment strategies KW - optimal drug targeting KW - optimal drug combination Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-285164 SN - 1422-0067 VL - 20 IS - 9 ER - TY - JOUR A1 - Breitenbach, Tim A1 - Helfrich-Förster, Charlotte A1 - Dandekar, Thomas T1 - An effective model of endogenous clocks and external stimuli determining circadian rhythms JF - Scientific Reports N2 - Circadian endogenous clocks of eukaryotic organisms are an established and rapidly developing research field. To investigate and simulate in an effective model the effect of external stimuli on such clocks and their components we developed a software framework for download and simulation. The application is useful to understand the different involved effects in a mathematical simple and effective model. This concerns the effects of Zeitgebers, feedback loops and further modifying components. We start from a known mathematical oscillator model, which is based on experimental molecular findings. This is extended with an effective framework that includes the impact of external stimuli on the circadian oscillations including high dose pharmacological treatment. In particular, the external stimuli framework defines a systematic procedure by input-output-interfaces to couple different oscillators. The framework is validated by providing phase response curves and ranges of entrainment. Furthermore, Aschoffs rule is computationally investigated. It is shown how the external stimuli framework can be used to study biological effects like points of singularity or oscillators integrating different signals at once. The mathematical framework and formalism is generic and allows to study in general the effect of external stimuli on oscillators and other biological processes. For an easy replication of each numerical experiment presented in this work and an easy implementation of the framework the corresponding Mathematica files are fully made available. They can be downloaded at the following link: https://www.biozentrum.uni-wuerzburg.de/bioinfo/computing/circadian/. KW - computational biology and bioinformatics KW - systems biology Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-261655 VL - 11 IS - 1 ER -