Lessons Learned from Quantitative Dynamical Modeling in Systems Biology

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.

Model-Based Hypothesis Testing in Biomedicine : How Systems Biology Can Drive the Growth of Scientific Knowledge

“…When it comes to the units for the states and parameters in the S6K-model (Figure 16), the following choices were made: The states have been implemented as arbitrary concentration units, also known as nondimensionalization [56,57]. This is because we for most components do not know, or can choose to ignore, the real concentrations of these states.…”

“…There are various ways of doing this. In systems biology, the two most common ways for doing these approximations are the Finite Difference Method (FDM), and the simultaneous simulation of the sensitivities equations [56,65]. For the first approach, FDM, which was already mentioned in a different context with regards to solving PDEs (Section 3.5, p. 23) the gradient is approximated using Taylor's theorem.…”

“…With regards to the second approach, the sensitivity equations, this involves formulating time derivatives for the sensitivities, i.e. the inner derivatives with respect to θ, as part of the ODE system to be solved [56,65].…”

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“…be the amount or concentrations of a molecule or metabolite, or the proportion of hemoglobin that is oxygenated could be one state while the deoxygenated proportion is another state. In the papers presented in this thesis, states are represented in a nondimensionalized manner, which means that the concentrations and amounts have arbitrary units [75] [76]. This is often used when we do not know the real values for the concentrations or amounts for most components in the system.…”

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“…to cellular signaling pathway models. For the implementation of the model and parameter estimation, the D2D software [42] was utilized.…”