Titel Deelnemers "Korte inhoud"
"Modeling enzyme controlled metabolic networks in rapidly changing environments by robust optimization" "H Lindhorst, S Lucia, R Findeisen, Steffen Waldherr" "© 2017 IEEE. Constraint-based methods, such as the flux balance analysis (FBA), are widely used to model cellular growth processes without relying on knowledge of regulatory features. Regulation is instead substituted by an optimization problem to maximize a biological objective such as biomass accumulation. A recent extension to these methods is called dynamic enzyme-cost FBA (deFBA). This fully dynamic modeling method allows to predict optimal enzyme levels and reaction fluxes under changing environmental conditions. However, this method was designed for well-defined deterministic settings in which dynamics of the environment are exactly known. In this letter, we present a theoretical framework called the robust deFBA which extends the deFBA to handle uncertainty in nutrient availability. We achieve this by combining deFBA with multi-stage model predictive control which explicitly captures the evolution of uncertainty by a scenario tree. The resulting method is capable of predicting robust optimal gene expression levels for rapidly changing environments. We apply these algorithms to a model of the core metabolic process in bacteria under alternating oxygen availability."
"Dynamic Density Estimation in Heterogeneous Cell Populations" "Armin Küper, Robert Dürr, Steffen Waldherr" "Multicellular systems play a key role in bioprocess and biomedical engineering. Cell ensembles encountered in these setups show phenotypic variability like size and biochemical composition. As this variability may result in undesired effects in bioreactors, close monitoring of the cell population heterogeneity is important for maximum production output, and accurate control. However, direct measurements are mostly restricted to a few cellular properties. This motivates the application of model-based online estimation techniques for the reconstruction of non-measurable cellular properties. Population balance modeling allows for a natural description of cell-to-cell variability. In this contribution, we present an estimation approach that, in contrast to existing ones, does not rely on a finite-dimensional approximation through grid based discretization of the underlying population balance model. Instead, our so-called characteristics based density estimator employs sample approximations. With two and three-dimensional benchmark examples we demonstrate that our approach is superior to the grid based designs in terms of accuracy and computational demand."
"Robustness and Information Transfer within IL-6-induced JAK/STAT Signalling" "Ulrike Billing, Tomasz Jetka, Lukas Nortmann, Nicole Wundrack, Michal Komorowski, Steffen Waldherr, Fred Schaper, Anna Dittrich" "Cellular communication via intracellular signalling pathways is crucial. Expression and activation of signalling proteins is heterogenous between isogenic cells of the same cell-type. However, mechanisms evolved to enable sufficient communication and to ensure cellular functions. We use information theory to clarify mechanisms facilitating IL-6-induced JAK/STAT signalling despite cell-to-cell variability. We show that different mechanisms enabling robustness against variability complement each other. Early STAT3 activation is robust as long as cytokine concentrations are low. Robustness at high cytokine concentrations is ensured by high STAT3 expression or serine phosphorylation. Later the feedback-inhibitor SOCS3 increases robustness. Channel Capacity of JAK/STAT signalling is limited by cell-to-cell variability in STAT3 expression and is affected by the same mechanisms governing robustness. Increasing STAT3 amount increases Channel Capacity and robustness, whereas increasing STAT3 tyrosine phosphorylation reduces robustness but increases Channel Capacity. In summary, we elucidate mechanisms preventing dysregulated signalling by enabling reliable JAK/STAT signalling despite cell-to-cell heterogeneity."
"A Novel Framework for Parameter and State Estimation of Multicellular Systems Using Gaussian Mixture Approximations" "Robert Duerr, Steffen Waldherr" "© 2018 by the authors. Multicellular systems play an important role in many biotechnological processes. Typically, these exhibit cell-to-cell variability, which has to be monitored closely for process control and optimization. However, some properties may not be measurable due to technical and financial restrictions. To improve the monitoring, model-based online estimators can be designed for their reconstruction. The multicellular dynamics is accounted for in the framework of population balance models (PBMs). These models are based on single cell kinetics, and each cellular state translates directly into an additional dimension of the obtained partial differential equations. As multicellular dynamics often require detailed single cell models and feature a high number of cellular components, the resulting population balance equations are often high-dimensional. Therefore, established state estimation concepts for PBMs based on discrete grids are not recommended due to the large computational effort. In this contribution a novel approach is proposed, which is based on the approximation of the underlying number density functions as the weighted sum of Gaussian distributions. Thus, the distribution is described by the characteristic properties of the individual Gaussians, like the mean and covariance. Thereby, the complex infinite dimensional estimation problem can be reduced to a finite dimension. The characteristic properties are estimated in a recursive approach. The method is evaluated for two academic benchmark examples, and the results indicate its potential for model-based online reconstruction for multicellular systems."
"Estimation methods for heterogeneous cell population models in systems biology" "Steffen Waldherr" "Heterogeneity among individual cells is a characteristic and relevant feature of living systems. A range of experimental techniques to investigate this heterogeneity is available, and multiple modelling frameworks have been developed to describe and simulate the dynamics of heterogeneous populations. Measurement data are used to adjust computational models, which results in parameter and state estimation problems. Methods to solve these estimation problems need to take the specific properties of data and models into account. The aim of this review is to give an overview on the state of the art in estimation methods for heterogeneous cell population data and models. The focus is on models based on the population balance equation, but stochastic and individual-based models are also discussed. It starts with a brief discussion of common experimental approaches and types of measurement data that can be obtained in this context. The second part describes computational modelling frameworks for heterogeneous populations and the types of estimation problems occurring for these models. The third part starts with a discussion of observability and identifiability properties, after which the computational methods to solve the various estimation problems are described."
"Optimization of bioprocess productivity based on metabolic-genetic network models with bilevel dynamic programming" "Banafsheh Jabarivelisdeh, Steffen Waldherr" "One of the main goals of metabolic engineering is to obtain high levels of a microbial product through genetic modifications. To improve the productivity of such a process, the dynamic implementation of metabolic engineering strategies has been proven to be more beneficial compared to static genetic manipulations in which the gene expression is not controlled over time, by resolving the trade-off between growth and production. In this work, a bilevel optimization framework based on constraint-based models is applied to identify an optimal strategy for dynamic genetic and process level manipulations to increase productivity. The dynamic enzyme-cost flux balance analysis (deFBA) as underlying metabolic network model captures the network dynamics and enables the analysis of temporal regulation in the metabolic-genetic network. We apply our computational framework to maximize ethanol productivity in a batch process with Escherichia coli. The results highlight the importance of integrating the genetic level and enzyme production and degradation processes for obtaining optimal dynamic gene and process manipulations."
"Hybrid simulation algorithm for efficient numerical solution of population balance equations" "Robert Dürr, Steffen Waldherr" "© 2018 Cell-to-cell variability of multicellular systems affects many processes from bioprocess engineering, systems biology and systems medicine. Multiscale modeling of these cellular heterogeneities with population balance equations is a valuable tool to understand the interplay of individual cell dynamics (intracellular level), interactions of cells with each other (population level) and interactions of cells with other molecular species (extracellular level). The resulting mathematical models represent high dimensional partial integro-differential equations which are rarely solvable analytically. As alternative to classical numerical solution methods which are not well suited for efficient solution, we propose a hybrid simulation algorithm in this contribution. This technique is based on a combination of the method of partial characteristics and approximate moment methods using monomial cubatures. The technique's efficiency and accuracy is shown for a multicellular system describing cell-to-cell signaling in osteochondro-switch models."
"Model Predictive Control of a Fed-batch Bioreactor Based on Dynamic Metabolic-Genetic Network Models" "Banafsheh Jabarivelisdeh, Rolf Findeisen, Steffen Waldherr" "© 2018 In this work, a model predictive control of a fed-batch bioreactor is presented, described by the dynamic enzyme-cost FBA model (deFBA). The deFBA model is employed within a bilevel optimization to obtain fed-batch operating policies including the substrate feeding and process-level regulation of metabolism for optimizing the productivity of a target product. The advantages of implementing the closed-loop control in order to compensate for modelling errors are evaluated by comparing with the performance of an open-loop control. A case study involving the fed-batch fermentation of Escherichia coli for ethanol production is considered to find optimal operating strategies for maximal productivity."
"Dynamic modeling of enzyme controlled metabolic networks using a receding time horizon" "H Lindhorst, AM Reimers, Steffen Waldherr" "© 2018 Microorganisms have developed complex regulatory features controlling their reaction and internal adaptation to changing environments. When modeling these organisms we usually do not have full understanding of the regulation and rely on substituting it with an optimization problem using a biologically reasonable objective function. The resulting constraint-based methods like the Flux Balance Analysis (FBA) and Resource Balance Analysis (RBA) have proven to be powerful tools to predict growth rates, by-products, and pathway usage for fixed environments. In this work, we focus on the dynamic enzyme-cost Flux Balance Analysis (deFBA), which models the environment, biomass products, and their composition dynamically and contains reaction rate constraints based on enzyme capacity. We extend the original deFBA formalism to include storage molecules and biomass-related maintenance costs. Furthermore, we present a novel usage of the receding prediction horizon as used in Model Predictive Control (MPC) in the deFBA framework, which we call the short-term deFBA (sdeFBA). This way we eliminate some mathematical artifacts arising from the formulation as an optimization problem and gain access to new applications in MPC schemes. A major contribution of this paper is a systematic approach for choosing the prediction horizon and identifying conditions to ensure solutions grow exponentially. We showcase the effects of using the sdeFBA with different horizons through a numerical example."
"Hybrid simulation algorithm for efficient numerical solution of population balance equations" "Robert Dürr, Steffen Waldherr" "Cell-to-cell variability of multicellular systems affects many processes from biopro- cess engineering, systems biology and systems medicine. Multiscale modeling of these cellular heterogeneities with population balance equations is a valuable tool to understand the interplay of individual cell dynamics (intracellular level), interactions of cells with each other (population level) and interactions of cells with other molecular species (extracellular level). The resulting mathematical models represent high dimensional partial integro-differential equations which are rarely solvable analytically. As alternative to classical numerical solution methods which are not well suited for efficient solution, we propose a hybrid simulation algorithm in this contribution. This technique is based on a combination of the method of partial characteristics and approximate moment methods using monomial cubatures. The technique’s efficiency and accuracy is shown for a multicellular system describing cell-to-cell signaling in osteochondro- switch models."