Experimental Design for Parameter Estimation of Gene Regulatory Networks

Abstract

Systems biology aims for building quantitative models to address unresolved issues in molecular biology. In order to describe the behavior of biological cells adequately, gene regulatory networks (GRNs) are intensively investigated. As the validity of models built for GRNs depends crucially on the kinetic rates, various methods have been developed to estimate these parameters from experimental data. For this purpose, it is favorable to choose the experimental conditions yielding maximal information. However, existing experimental design principles often rely on unfulfilled mathematical assumptions or become computationally demanding with growing model complexity. To solve this problem, we combined advanced methods for parameter and uncertainty estimation with experimental design considerations. As a showcase, we optimized three simulated GRNs in one of the challenges from the Dialogue for Reverse Engineering Assessment and Methods (DREAM). This article presents our approach, which was awarded the best performing procedure at the DREAM6 Estimation of Model Parameters challenge. For fast and reliable parameter estimation, local deterministic optimization of the likelihood was applied. We analyzed identifiability and precision of the estimates by calculating the profile likelihood. Furthermore, the profiles provided a way to uncover a selection of most informative experiments, from which the optimal one was chosen using additional criteria at every step of the design process. In conclusion, we provide a strategy for optimal experimental design and show its successful application on three highly nonlinear dynamic models. Although presented in the context of the GRNs to be inferred for the DREAM6 challenge, the approach is generic and applicable to most types of quantitative models in systems biology and other disciplines.

Profile likelihood in systems biology

“…In the Systems Biology setting, the parameter profile likelihood has been proposed for the calculation of confidence intervals and in addition for the investigation of parameter identifiability [4,5]. It is increasingly applied in recent years [6][7][8][9][10][11][12].…”

Estimation and Identifiability of Model Parameters in Human Nociceptive Processing Using Yes-No Detection Responses to Electrocutaneous Stimulation

“…Future work could consider the choice of stimulus properties in order to resolve practical non-identifiability in a model-based study. In addition, one could choose a frequentist (Steiert et al, 2012) or adapt a Bayesian framework (Myung et al, 2013) in the exploration of stimulus settings.…”

Modeling the inflammatory response in the hypothalamus ensuing heat stroke: Iterative cycle of model calibration, identifiability analysis, experimental design and data collection

“…Therefore parameter sets having a negligible impact on the prior distribution are ignored from the beginning. Finding such a subset can be done with the help of the profile likelihoods as defined in [39]. θ(θ m ) = argmin θn =m χ 2 (ỹ|θ) (28) is one point on the profile likelihood PL(θ m ) which is represented by a parameter vector containing the re-optimized parameters θ n =m to the parameter value θ m .…”

“…The method has been described in detail in [39,10]. Briefly, a wide spread of trajectories corresponds to a very informative experiment to identify the respective parameter whereas small variability relates to a weak informative experiment.…”