The Impact of Time Delays on the Robustness of Biological Oscillators and the Effect of Bifurcations on the Inverse Problem

Differential equation models for biological oscillators are often not robust with respect to parameter variations. They are based on chemical reaction kinetics, and solutions typically converge to a fixed point. This behavior is in contrast to real biological oscillators, which work reliably under varying conditions. Moreover, it complicates network inference from time series data. This paper investigates differential equation models for biological oscillators from two perspectives. First, we investigate the effect of time delays on the robustness of these oscillator models. In particular, we provide sufficient conditions for a time delay to cause oscillations by destabilizing a fixed point in two-dimensional systems. Moreover, we show that the inclusion of a time delay also stabilizes oscillating behavior in this way in larger networks. The second part focuses on the inverse problem of estimating model parameters from time series data. Bifurcations are related to nonsmoothness and multiple local minima of the objective function

Modeling Non-Linear Dynamic Phenomena in Biochemical Networks

Facilitated by the development of high-throughput techniques, the focus of biological research has changed in the last decades from the investigation of single cell components to a system-level approach, which aims at an understanding of interactions between these cell components. This objective requires modeling and analysis methods for these regulatory networks. In this thesis, we investigate mechanisms causing qualitative dynamic behaviors of regulatory subsystems. For this purpose, we introduce a differential equation model based on underlying molecular binding reactions, whose parameters are estimated using time series concentration data. In the first part, the model is applied to subsystems with qualitatively different dynamic behaviors: The response of the Mycobacterium tuberculosis to DNA damages is described as the relaxation of a system to its steady state after external perturbation. Specific repression of genes in Escherichia coli by the global regulator protein H-NS is explained by the interrelation of feedback mechanisms. In order to prevent overfitting, a typical problem in network inference from experimental data, we introduce an approach based on Bayesian statistics, which includes prior knowledge about the system in terms of prior probability distributions. This approach is applied to simulated data and to the regulatory network of the Saccharomyces cerevisiae cell cycle. Motivated by results on the yeast cell cycle, the second part of this thesis investigates the robustness of periodic behavior in regulatory networks. The model presented belongs to a class of differential equations whose solutions tend to converge to a steady state. Accordingly, periodic behavior is not robust with respect to parameter variations. We explain this phenomenon by applying a bifurcation analysis and investigating the stability of steady states. It is shown that large time scale differences and an inclusion of time-delays can stabilize sustained oscillations, and we postulate that they are important to maintain oscillations in biological systems

RObust Sparse ensemble for outlIEr detection and gene selection in cancer omics data

We thank Peter Segaert for providing his adapted code of the enetLTS method. The results presented here are in whole or part based upon data generated by the TCGA Research Network: https://www.cancer.gov/tcga . Funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2075 390740016 (AJ and NR). Publisher Copyright: © The Author(s) 2022.The extraction of novel information from omics data is a challenging task, in particular, since the number of features (e.g. genes) often far exceeds the number of samples. In such a setting, conventional parameter estimation leads to ill-posed optimization problems, and regularization may be required. In addition, outliers can largely impact classification accuracy. Here we introduce ROSIE, an ensemble classification approach, which combines three sparse and robust classification methods for outlier detection and feature selection and further performs a bootstrap-based validity check. Outliers of ROSIE are determined by the rank product test using outlier rankings of all three methods, and important features are selected as features commonly selected by all methods. We apply ROSIE to RNA-Seq data from The Cancer Genome Atlas (TCGA) to classify observations into Triple-Negative Breast Cancer (TNBC) and non-TNBC tissue samples. The pre-processed dataset consists of (Formula presented.) genes and more than (Formula presented.) samples. We demonstrate that ROSIE selects important features and outliers in a robust way. Identified outliers are concordant with the distribution of the commonly selected genes by the three methods, and results are in line with other independent studies. Furthermore, we discuss the association of some of the selected genes with the TNBC subtype in other investigations. In summary, ROSIE constitutes a robust and sparse procedure to identify outliers and important genes through binary classification. Our approach is ad hoc applicable to other datasets, fulfilling the overall goal of simultaneously identifying outliers and candidate disease biomarkers to the targeted in therapy research and personalized medicine frameworks.publishersversionpublishe

The physics behind systems biology

Systems Biology is a young and rapidly evolving research field, which combines experimental techniques and mathematical modeling in order to achieve a mechanistic understanding of processes underlying the regulation and evolution of living systems. Systems Biology is often associated with an Engineering approach: The purpose is to formulate a data-rich, detailed simulation model that allows to perform numerical (‘in silico’) experiments and then draw conclusions about the biological system. While methods from Engineering may be an appropriate approach to extending the scope of biological investigations to experimentally inaccessible realms and to supporting data-rich experimental work, it may not be the best strategy in a search for design principles of biological systems and the fundamental laws underlying Biology. Physics has a long tradition of characterizing and understanding emergent collective behaviors in systems of interacting units and searching for universal laws. Therefore, it is natural that many concepts used in Systems Biology have their roots in Physics. With an emphasis on Theoretical Physics, we will here review the ‘Physics core’ of Systems Biology, show how some success stories in Systems Biology can be traced back to concepts developed in Physics, and discuss how Systems Biology can further benefit from ist Theoretical Physics foundation

Modeling sphingomyelin synthase 1 driven reaction at the Golgi apparatus can explain data by inclusion of a positive feedback mechanism

AbstractHere we present a minimal mathematical model for the sphingomyelin synthase 1 (SMS1) driven conversion of ceramide to sphingomyelin based on chemical reaction kinetics. We demonstrate via mathematical analysis that this model is not able to qualitatively reproduce experimental measurements on lipid compositions after altering SMS1 activity. We prove that a positive feedback mechanism from the products to the reactants of the reaction is one possible model extension to explain these specific experimental data. The proposed mechanism in fact exists in vivo via protein kinase D and the ceramide transfer protein CERT. The model is further evaluated by additional observations from the literature

Modeling of biocatalytic reactions: A workflow for model calibration, selection and validation using Bayesian statistics

We present a workflow for kinetic modeling of biocatalytic reactions which combines methods from Bayesian learning and uncertainty quantification for model calibration, model selection, evaluation, and model reduction in a consistent statistical framework. Our workflow is particularly tailored to sparse data settings in which a considerable variability of the parameters remains after the models have been adapted to available data, a ubiquitous problem in many real‐world applications. Our workflow is exemplified on an enzyme‐catalyzed two‐substrate reaction mechanism describing the symmetric carboligation of 3,5‐dimethoxy‐benzaldehyde to (R )‐3,3′,5,5′‐tetramethoxybenzoin catalyzed by benzaldehyde lyase from Pseudomonas fluorescens . Results indicate a substrate‐dependent inactivation of enzyme, which is in accordance with other recent studies

Periportal steatosis in mice affects distinct parameters of pericentral drug metabolism

Little is known about the impact of morphological disorders in distinct zones on metabolic zonation. It was described recently that periportal fibrosis did affect the expression of CYP proteins, a set of pericentrally located drug-metabolizing enzymes. Here, we investigated whether periportal steatosis might have a similar effect. Periportal steatosis was induced in C57BL6/J mice by feeding a high-fat diet with low methionine/choline content for either two or four weeks. Steatosis severity was quantified using image analysis. Triglycerides and CYP activity were quantified in photometric or fluorometric assay. The distribution of CYP3A4, CYP1A2, CYP2D6, and CYP2E1 was visualized by immunohistochemistry. Pharmacokinetic parameters of test drugs were determined after injecting a drug cocktail (caffeine, codeine, and midazolam). The dietary model resulted in moderate to severe mixed steatosis confined to periportal and midzonal areas. Periportal steatosis did not affect the zonal distribution of CYP expression but the activity of selected CYPs was associated with steatosis severity. Caffeine elimination was accelerated by microvesicular steatosis, whereas midazolam elimination was delayed in macrovesicular steatosis. In summary, periportal steatosis affected parameters of pericentrally located drug metabolism. This observation calls for further investigations of the highly complex interrelationship between steatosis and drug metabolism and underlying signaling mechanisms

Identification of models of heterogeneous cell populations from population snapshot data

Background: Most of the modeling performed in the area of systems biology aims at achieving a quantitative description of the intracellular pathways within a "typical cell". However, in many biologically important situations even clonal cell populations can show a heterogeneous response. These situations require study of cell-to-cell variability and the development of models for heterogeneous cell populations. Results: In this paper we consider cell populations in which the dynamics of every single cell is captured by a parameter dependent differential equation. Differences among cells are modeled by differences in parameters which are subject to a probability density. A novel Bayesian approach is presented to infer this probability density from population snapshot data, such as flow cytometric analysis, which do not provide single cell time series data. The presented approach can deal with sparse and noisy measurement data. Furthermore, it is appealing from an application point of view as in contrast to other methods the uncertainty of the resulting parameter distribution can directly be assessed. Conclusions: The proposed method is evaluated using artificial experimental data from a model of the tumor necrosis factor signaling network. We demonstrate that the methods are computationally efficient and yield good estimation result even for sparse data sets