Lessons Learned from Quantitative Dynamical Modeling in Systems Biology

Andreas Raue,Sabine Hug,Brian D Harms,Max Schelke,Jens Timmer,Fabian J Theis,Julie Bachmann,Marcel Schilling,Andrew Matteson,Ursula Klingmüller,Clemens Kreutz,Daniel Kaschek,Enrique Hernandez-Lemus

doi:10.1371/journal.pone.0074335

Abstract

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.

Highlights

Biological processes such as the regulation of cellular decisions by signal transduction pathways and subsequent target gene expression are governed by highly complex molecular mechanisms
In the context of Systems Biology, dynamical models consisting of ordinary differential equations (ODE) are a frequently used approach that facilitates to analyze the mechanism of action in a systematic manner
We presented a comprehensive discussion and comparison of methods used for quantitative dynamic modeling, employing two recent examples of relevant size and impact

Summary

Introduction

Biological processes such as the regulation of cellular decisions by signal transduction pathways and subsequent target gene expression are governed by highly complex molecular mechanisms. These intertwined processes are difficult to understand by interpreting experimental results directly since the underlying mechanism can be rather counter-intuitive. The advantage of building a mathematical model is that molecular mechanisms that are supposed to govern the respective process need to be formulated explicitly This allows to test hypothesis about the supposed network structure of the molecular interactions [1] and to predict systems behavior that is not accessible by experiments directly [2]. In the following we introduce quantitative dynamical modeling and subsequently present results on how challenges in the model building and calibration process were tackled

Objectives

Methods

Results

Conclusion