Model-based analysis of response and resistance factors of cetuximab treatment in gastric cancer cell lines.

Targeted cancer therapies are powerful alternatives to chemotherapies or can be used complementary to these. Yet, the response to targeted treatments depends on a variety of factors, including mutations and expression levels, and therefore their outcome is difficult to predict. Here, we develop a mechanistic model of gastric cancer to study response and resistance factors for cetuximab treatment. The model captures the EGFR, ERK and AKT signaling pathways in two gastric cancer cell lines with different mutation patterns. We train the model using a comprehensive selection of time and dose response measurements, and provide an assessment of parameter and prediction uncertainties. We demonstrate that the proposed model facilitates the identification of causal differences between the cell lines. Furthermore, our study shows that the model provides predictions for the responses to different perturbations, such as knockdown and knockout experiments. Among other results, the model predicted the effect of MET mutations on cetuximab sensitivity. These predictive capabilities render the model a basis for the assessment of gastric cancer signaling and possibly for the development and discovery of predictive biomarkers.

PESTO: Parameter EStimation TOolbox.

Summary: PESTO is a widely applicable and highly customizable toolbox for parameter estimation in MathWorks MATLAB. It offers scalable algorithms for optimization, uncertainty and identifiability analysis, which work in a very generic manner, treating the objective function as a black box. Hence, PESTO can be used for any parameter estimation problem, for which the user can provide a deterministic objective function in MATLAB. Availability and implementation: PESTO is a MATLAB toolbox, freely available under the BSD license. The source code, along with extensive documentation and example code, can be downloaded from https://github.com/ICB-DCM/PESTO/. Contact: jan.hasenauer@helmholtz-muenchen.de. Supplementary information: Supplementary data are available at Bioinformatics online.

iVUN: interactive Visualization of Uncertain biochemical reaction Networks.

BACKGROUND: Mathematical models are nowadays widely used to describe biochemical reaction networks. One of the main reasons for this is that models facilitate the integration of a multitude of different data and data types using parameter estimation. Thereby, models allow for a holistic understanding of biological processes. However, due to measurement noise and the limited amount of data, uncertainties in the model parameters should be considered when conclusions are drawn from estimated model attributes, such as reaction fluxes or transient dynamics of biological species. METHODS AND RESULTS: We developed the visual analytics system iVUN that supports uncertainty-aware analysis of static and dynamic attributes of biochemical reaction networks modeled by ordinary differential equations. The multivariate graph of the network is visualized as a node-link diagram, and statistics of the attributes are mapped to the color of nodes and links of the graph. In addition, the graph view is linked with several views, such as line plots, scatter plots, and correlation matrices, to support locating uncertainties and the analysis of their time dependencies. As demonstration, we use iVUN to quantitatively analyze the dynamics of a model for Epo-induced JAK2/STAT5 signaling. CONCLUSION: Our case study showed that iVUN can be used to perform an in-depth study of biochemical reaction networks, including attribute uncertainties, correlations between these attributes and their uncertainties as well as the attribute dynamics. In particular, the linking of different visualization options turned out to be highly beneficial for the complex analysis tasks that come with the biological systems as presented here.

Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems.

BACKGROUND: In quantitative biology, mathematical models are used to describe and analyze biological processes. The parameters of these models are usually unknown and need to be estimated from experimental data using statistical methods. In particular, Markov chain Monte Carlo (MCMC) methods have become increasingly popular as they allow for a rigorous analysis of parameter and prediction uncertainties without the need for assuming parameter identifiability or removing non-identifiable parameters. A broad spectrum of MCMC algorithms have been proposed, including single- and multi-chain approaches. However, selecting and tuning sampling algorithms suited for a given problem remains challenging and a comprehensive comparison of different methods is so far not available. RESULTS: We present the results of a thorough benchmarking of state-of-the-art single- and multi-chain sampling methods, including Adaptive Metropolis, Delayed Rejection Adaptive Metropolis, Metropolis adjusted Langevin algorithm, Parallel Tempering and Parallel Hierarchical Sampling. Different initialization and adaptation schemes are considered. To ensure a comprehensive and fair comparison, we consider problems with a range of features such as bifurcations, periodical orbits, multistability of steady-state solutions and chaotic regimes. These problem properties give rise to various posterior distributions including uni- and multi-modal distributions and non-normally distributed mode tails. For an objective comparison, we developed a pipeline for the semi-automatic comparison of sampling results. CONCLUSION: The comparison of MCMC algorithms, initialization and adaptation schemes revealed that overall multi-chain algorithms perform better than single-chain algorithms. In some cases this performance can be further increased by using a preceding multi-start local optimization scheme. These results can inform the selection of sampling methods and the benchmark collection can serve for the evaluation of new algorithms. Furthermore, our results confirm the need to address exploration quality of MCMC chains before applying the commonly used quality measure of effective sample size to prevent false analysis conclusions.

Lessons learned from quantitative dynamical modeling in systems biology.

Due to the high complexity of biological data it is difficult to disentangle cellular processes relying only on intuitive interpretation of measurements. A Systems Biology approach that combines quantitative experimental data with dynamic mathematical modeling promises to yield deeper insights into these processes. Nevertheless, with growing complexity and increasing amount of quantitative experimental data, building realistic and reliable mathematical models can become a challenging task: the quality of experimental data has to be assessed objectively, unknown model parameters need to be estimated from the experimental data, and numerical calculations need to be precise and efficient. Here, we discuss, compare and characterize the performance of computational methods throughout the process of quantitative dynamic modeling using two previously established examples, for which quantitative, dose- and time-resolved experimental data are available. In particular, we present an approach that allows to determine the quality of experimental data in an efficient, objective and automated manner. Using this approach data generated by different measurement techniques and even in single replicates can be reliably used for mathematical modeling. For the estimation of unknown model parameters, the performance of different optimization algorithms was compared systematically. Our results show that deterministic derivative-based optimization employing the sensitivity equations in combination with a multi-start strategy based on latin hypercube sampling outperforms the other methods by orders of magnitude in accuracy and speed. Finally, we investigated transformations that yield a more efficient parameterization of the model and therefore lead to a further enhancement in optimization performance. We provide a freely available open source software package that implements the algorithms and examples compared here.

Bayesian model selection validates a biokinetic model for zirconium processing in humans.

BACKGROUND: In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection. RESULTS: We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler. CONCLUSIONS: In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology.