Outer bounding of the specific growth rate and identification of growth phases.

<p>Depicted is the 1-sigma confidence interval of the specific growth rate for the bioreactor (left) and the shaker (right) experiment. Phase I: exponential cell growth. Phase II: decreasing cell growth. Phase III: declining cell concentration.</p

Statistical analysis of the measurement errors by validation assay.

<p>non-homogeneous variance. LOD: limit of detection. SD: standard deviation. % SD: relative standard deviation.</p

Uncertainty analysis and outlier detection.

<p>Reachable state sets are shaded, outliers are in a circle. Bioreactor: Glc-limitation, Shaker: pH-dependency.</p

Determining the influence of inter-individual variability during development of a urea cycle disorder.

<p>(<b>A</b>) Simulated venous plasma concentration profiles of ammonia in 100 individuals during development of a urea cycle disorder (single profiles and mean). (<b>B</b>) The distribution of ammonia concentrations as well as the cumulative sums in healthy and diseased individuals are significantly different (p<0.001).</p

Integrating Cellular Metabolism into a Multiscale Whole-Body Model

<div><p>Cellular metabolism continuously processes an enormous range of external compounds into endogenous metabolites and is as such a key element in human physiology. The multifaceted physiological role of the metabolic network fulfilling the catalytic conversions can only be fully understood from a whole-body perspective where the causal interplay of the metabolic states of individual cells, the surrounding tissue and the whole organism are simultaneously considered. We here present an approach relying on dynamic flux balance analysis that allows the integration of metabolic networks at the cellular scale into standardized physiologically-based pharmacokinetic models at the whole-body level. To evaluate our approach we integrated a genome-scale network reconstruction of a human hepatocyte into the liver tissue of a physiologically-based pharmacokinetic model of a human adult. The resulting multiscale model was used to investigate hyperuricemia therapy, ammonia detoxification and paracetamol-induced toxication at a systems level. The specific models simultaneously integrate multiple layers of biological organization and offer mechanistic insights into pathology and medication. The approach presented may in future support a mechanistic understanding in diagnostics and drug development.</p> </div

Identification of Growth Phases and Influencing Factors in Cultivations with AGE1.HN Cells Using Set-Based Methods

<div><p>Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-)validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN). We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell growth and metabolism under conditions of uncertainty.</p></div

Comparison of two specific liver functions (production of oleate and cysteine, respectively).

<p>Only fluxes which are nonzero at least in one of the three cases are compared. The number of fluxes which remain at their original values ( = ), become smaller or higher (<, >) or are non-zero (new) after application of 1 g and 15 g of paracetamol are indicated.. (<b>A</b>) Changes in fluxes after application of 1 g and 15 g paracetamol for production of oleate. (<b>B</b>) Changes in fluxes after application of 1 g and 15 g paracetamol for production of cysteine.</p

Specific growth rate hypotheses.

<p>Specific growth rate hypotheses.</p

Reduction of uric acid production following multiple allopurinol administrations.

<p>(<b>A</b>) Simulated venous plasma and intrahepatic concentration profiles of allopurinol and oxypurinol are in agreement with experimental PK data <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002750#pcbi.1002750-Turnheim1" target="_blank">[43]</a>. (<b>B</b>) Prediction of venous plasma and intrahepatic concentration profiles of allopurinol and oxypurinol after multiple dosing based on the single application model. (<b>C</b>) Relative enzyme activity of xanthine oxidase (XO) following inhibition by a single dose of allopurinol. (<b>D</b>) Relative enzyme activity of XO following inhibition by multiple administration of allopurinol. (<b>E</b>) Simulated venous plasma and intrahepatic concentration profiles of uric acid following a single dose of allopurinol. (<b>F</b>) Simulated venous plasma and intrahepatic concentration profiles of uric acid following multiple dosing of allopurinol. Experimentally-measured venous plasma concentrations quantifying the hyperuricemic state (*) and the healthy uricemic state (**) <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002750#pcbi.1002750-Lentner1" target="_blank">[48]</a> after treatment with allopurinol are indicated.</p

Pathogenesis of a urea cycle disorder in ammonia plasma concentrations and metabolic exchange rates.

<p>(<b>A</b>) Simulated venous plasma and intrahepatic concentration profiles of ammonia during development of a urea cycle disorder. The black dashed line represents the overall reduction in ornithine transcarbamylase activity. (<b>B, C</b>): Resulting exchange fluxes calculated with FBA during development of a urea cycle disorder. (B) Hepatic influx rates of the three substrates ammonia, oxygen and glucose. (C) Hepatic efflux rates of the three products urea, alanine and glutamine.</p