Klaus Mauch

Integration of Physiology and Fluid Dynamics

The purpose of strategies for the integration of fluid dynamics and physiology is the development of more reliable simulation tools to accelerate the process of scale-up. The rigorous mathematical modeling of the richly interactive relationship between the dynamic response of biosystems and the physical environment changing in time and space must rest on the link between coupled momentum, energy and mass balances and structured modeling of the biophase. With the exponential increase in massive computer capabilities hard- and software tools became available for simulation strategies based on such holistic integration approaches. The review discusses fundamental aspects of application of computational fluid dynamics (CFD) to three-dimensional two-phase turbulence flow in stirred tank bioreactors. Examples of coupling momentum and material balance equations with simple unstructured kinetic models for the behavior of the biophase are used to illustrate the application of these strategies to the selection of suitable impeller configurations. The examples reviewed in this paper include distribution of carbon and energy source in fed batch cultures as well as dissolved oxygen fields during aerobic fermentations. A more precise forecasting of the impact of the multitude of interactions must, however, rest upon a rigorous understanding of the response of the cell factory to the complex dynamic stimulation due to space- and time-dependent concentration fields. The paper also introduces some ideas for fast and very fast experimental observations of intracellular pool concentrations based on stimulus response methods. These observations finally lead to a more complex integration approach based on the coupling of CFD and structured metabolic models.

Bridging the layers: towards integration of signal transduction, regulation and metabolism into mathematical models

Mathematical modelling is increasingly becoming an indispensable tool for the study of cellular processes, allowing their analysis in a systematic and comprehensive manner. In the vast majority of the cases, models focus on specific subsystems, and in particular describe either metabolism, gene expression or signal transduction. Integrated models that are able to span and interconnect these layers are, by contrast, rare as their construction and analysis face multiple challenges. Such methods, however, would represent extremely useful tools to understand cell behaviour, with application in distinct fields of biological and medical research. In particular, they could be useful tools to study genotype-phenotype mappings, and the way they are affected by specific conditions or perturbations. Here, we review existing computational approaches that integrate signalling, gene regulation and/or metabolism. We describe existing challenges, available methods and point at potentially useful strategies.

Determination of in vivo kinetics of the starvation-induced Hxt5 glucose transporter of Saccharomyces cerevisiae

We have investigated the role and the kinetic properties of the Hxt5 glucose transporter of Saccharomyces cerevisiae. The HXT5 gene was not expressed during growth of the yeast cells in rich medium with glucose or raffinose. However, it became strongly induced during nitrogen or carbon starvation. We have constructed yeast strains constitutively expressing only Hxt5, Hxt1 (low affinity) or Hxt7 (high affinity), but no other glucose transporters. Aerobic fed-batch cultures at quasi steady-state conditions, and aerobic and anaerobic chemostat cultures at steady-state conditions of these strains were used for estimation of the kinetic properties of the individual transporters under in vivo conditions, by investigating the dynamic responses of the strains to changes in extracellular glucose concentration. The K(m) value and the growth properties of the HXT5 single expression strain indicate that Hxt5 is a transporter with intermediate affinity.

Quantification of statin effects on hepatic cholesterol synthesis by transient 13C-flux analysis

The present work is the first to deal with the determination of cholesterol synthesis rates in primary rat hepatocytes using transient (13)C-flux analysis. The effects of statins on cholesterol biosynthesis and central carbon fluxes were quantified at a therapeutic concentration of 50 nM atorvastatin using carbon-labeled glutamine. The flux through the cholesterol pathway decreased from 0.27 to 0.08 mmol/l(cv)h in response to the administration of the hypolipidemic drug. Isotopic steady state was reached within 4h in the central carbon metabolism but not in the cholesterol pathway, regardless of whether atorvastatin was administered or not. Marked channeling was observed for the symmetrical tricarboxylic acid cycle intermediates, succinate and fumarate. Non-stationary (13)C-based flux identification delivers both intracellular fluxes and intermediate levels, which was for the first time utilized for investigating systems-level effects of the administered drug by quantifying the flux control of the 3-hydroxy-3-methylglutaryl-coenzyme A reductase.

A multi-scale modeling framework for individualized, spatiotemporal prediction of drug effects and toxicological risk.

In this study, we focus on a novel multi-scale modeling approach for spatiotemporal prediction of the distribution of substances and resulting hepatotoxicity by combining cellular models, a 2D liver model, and whole body model. As a case study, we focused on predicting human hepatotoxicity upon treatment with acetaminophen based on in vitro toxicity data and potential inter-individual variability in gene expression and enzyme activities. By aggregating mechanistic, genome-based in silico cells to a novel 2D liver model and eventually to a whole body model, we predicted pharmacokinetic properties, metabolism, and the onset of hepatotoxicity in an in silico patient. Depending on the concentration of acetaminophen in the liver and the accumulation of toxic metabolites, cell integrity in the liver as a function of space and time as well as changes in the elimination rate of substances were estimated. We show that the variations in elimination rates also influence the distribution of acetaminophen and its metabolites in the whole body. Our results are in agreement with experimental results. What is more, the integrated model also predicted variations in drug toxicity depending on alterations of metabolic enzyme activities. Variations in enzyme activity, in turn, reflect genetic characteristics or diseases of individuals. In conclusion, this framework presents an important basis for efficiently integrating inter-individual variability data into models, paving the way for personalized or stratified predictions of drug toxicity and efficacy.

BioPreDyn-bench: a suite of benchmark problems for dynamic modelling in systems biology.

BackgroundDynamic modelling is one of the cornerstones of systems biology. Many research efforts are currently being invested in the development and exploitation of large-scale kinetic models. The associated problems of parameter estimation (model calibration) and optimal experimental design are particularly challenging. The community has already developed many methods and software packages which aim to facilitate these tasks. However, there is a lack of suitable benchmark problems which allow a fair and systematic evaluation and comparison of these contributions.ResultsHere we present BioPreDyn-bench, a set of challenging parameter estimation problems which aspire to serve as reference test cases in this area. This set comprises six problems including medium and large-scale kinetic models of the bacterium E. coli, baker’s yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The level of description includes metabolism, transcription, signal transduction, and development. For each problem we provide (i) a basic description and formulation, (ii) implementations ready-to-run in several formats, (iii) computational results obtained with specific solvers, (iv) a basic analysis and interpretation.ConclusionsThis suite of benchmark problems can be readily used to evaluate and compare parameter estimation methods. Further, it can also be used to build test problems for sensitivity and identifiability analysis, model reduction and optimal experimental design methods. The suite, including codes and documentation, can be freely downloaded from the BioPreDyn-bench website, https://sites.google.com/site/biopredynbenchmarks/.

Dynamics and Control of the Central Carbon Metabolism in Hepatoma Cells

BackgroundThe liver plays a major role in metabolism and performs a number of vital functions in the body. Therefore, the determination of hepatic metabolite dynamics and the analysis of the control of the respective biochemical pathways are of great pharmacological and medical importance. Extra- and intracellular time-series data from stimulus-response experiments are gaining in importance in the identification of in vivo metabolite dynamics, while dynamic network models are excellent tools for analyzing complex metabolic control patterns. This is the first study that has been undertaken on the data-driven identification of a dynamic liver central carbon metabolism model and its application in the analysis of the distribution of metabolic control in hepatoma cells.ResultsDynamic metabolite data were collected from HepG2 cells after they had been deprived of extracellular glucose. The concentration of 25 extra- and intracellular intermediates was quantified using HPLC, LC-MS-MS, and GC-MS. The in silico metabolite dynamics were in accordance with the experimental data. The central carbon metabolism of hepatomas was further analyzed with a particular focus on the control of metabolite concentrations and metabolic fluxes. It was observed that the enzyme glucose-6-phosphate dehydrogenase exerted substantial negative control over the glycolytic flux, whereas oxidative phosphorylation had a significant positive control. The control over the rate of NADPH consumption was found to be shared between the NADPH-demand itself (0.65) and the NADPH supply (0.38).ConclusionsBased on time-series data, a dynamic central carbon metabolism model was developed for the investigation of new and complex metabolic control patterns in hepatoma cells. The control patterns found support the hypotheses that the glucose-6-phosphate dehydrogenase and the Warburg effect are promising targets for tumor treatment. The systems-oriented identification of metabolite dynamics is a first step towards the genome-based assessment of potential risks posed by nutrients and drugs.

Metabolic engineering with multi-objective optimization of kinetic models.

Kinetic models have a great potential for metabolic engineering applications. They can be used for testing which genetic and regulatory modifications can increase the production of metabolites of interest, while simultaneously monitoring other key functions of the host organism. This work presents a methodology for increasing productivity in biotechnological processes exploiting dynamic models. It uses multi-objective dynamic optimization to identify the combination of targets (enzymatic modifications) and the degree of up- or down-regulation that must be performed in order to optimize a set of pre-defined performance metrics subject to process constraints. The capabilities of the approach are demonstrated on a realistic and computationally challenging application: a large-scale metabolic model of Chinese Hamster Ovary cells (CHO), which are used for antibody production in a fed-batch process. The proposed methodology manages to provide a sustained and robust growth in CHO cells, increasing productivity while simultaneously increasing biomass production, product titer, and keeping the concentrations of lactate and ammonia at low values. The approach presented here can be used for optimizing metabolic models by finding the best combination of targets and their optimal level of up/down-regulation. Furthermore, it can accommodate additional trade-offs and constraints with great flexibility.

Reconstruction of dynamic network models from metabolite measurements

One of the most ambitious and challenging goals of systems biology is the identification oftargets for reshaping biological systems based on quantitative predictions with the aid of mathematicalmodels. Whereas the potential and promise of biological systems modelling is substantial, severalobstacles are still encountered when addressing the issue of predictive design based on dynamic models.This is particularly because of the well known difficulties in assessing enzyme kinetics under in vivo conditions as a prerequisite for a sound quantitative analysis ofthe network via dynamic modelling. The article will describe developments and applications of toolsaimed at achieving sustained improvements within this important field. Our experience in using metabolitedata for reconstruction of dynamic models led to a dual approach. At the core of the modular conceptis the decomposition of the networks into manageable subunits. Furthermore, a new top down approachis presented for estimating kinetic parameters for the individual reactions in whole cell metabolicnetworks from time series data.

In Silico Modeling for the Prediction of Dose and Pathway-Related Adverse Effects in Humans From In Vitro Repeated-Dose Studies

Long-term repeated-dose toxicity is mainly assessed in animals despite poor concordance of animal data with human toxicity. Nowadays advanced human in vitro systems, eg, metabolically competent HepaRG cells, are used for toxicity screening. Extrapolation of in vitro toxicity to in vivo effects is possible by reverse dosimetry using pharmacokinetic modeling. We assessed long-term repeated-dose toxicity of bosentan and valproic acid (VPA) in HepaRG cells under serum-free conditions. Upon 28-day exposure, the EC50 values for bosentan and VPA decreased by 21- and 33-fold, respectively. Using EC(10) as lowest threshold of toxicity in vitro, we estimated the oral equivalent doses for both test compounds using a simplified pharmacokinetic model for the extrapolation of in vitro toxicity to in vivo effect. The model predicts that bosentan is safe at the considered dose under the assumed conditions upon 4 weeks exposure. For VPA, hepatotoxicity is predicted for 4% and 47% of the virtual population at the maximum recommended daily dose after 3 and 4 weeks of exposure, respectively. We also investigated the changes in the central carbon metabolism of HepaRG cells exposed to orally bioavailable concentrations of both drugs. These concentrations are below the 28-day EC(10) and induce significant changes especially in glucose metabolism and urea production. These metabolic changes may have a pronounced impact in susceptible patients such as those with compromised liver function and urea cycle deficiency leading to idiosyncratic toxicity. We show that the combination of modeling based on in vitro repeated-dose data and metabolic changes allows the prediction of human relevant in vivo toxicity with mechanistic insights.