Abstract
Logic models of signaling pathways are a promising way of building effective in silico functional models of a cell, in particular of signaling pathways. The automated learning of Boolean logic models describing signaling pathways can be achieved by training to phosphoproteomics data, which is particularly useful if it is measured upon different combinations of perturbations in a high-throughput fashion. However, in practice, the number and type of allowed perturbations are not exhaustive. Moreover, experimental data are unavoidably subjected to noise. As a result, the learning process results in a family of feasible logical networks rather than in a single model. This family is composed of logic models implementing different internal wirings for the system and therefore the predictions of experiments from this family may present a significant level of variability, and hence uncertainty. In this paper, we introduce a method based on Answer Set Programming to propose an optimal experimental design that aims to narrow down the variability (in terms of input–output behaviors) within families of logical models learned from experimental data. We study how the fitness with respect to the data can be improved after an optimal selection of signaling perturbations and how we learn optimal logic models with minimal number of experiments. The methods are applied on signaling pathways in human liver cells and phosphoproteomics experimental data. Using 25% of the experiments, we obtained logical models with fitness scores (mean square error) 15% close to the ones obtained using all experiments, illustrating the impact that our approach can have on the design of experiments for efficient model calibration.
Highlights
The recent development of high-throughput experimental technologies allows us to observe different cellular parts under multiple situations
We provide a precise characterization of the combinatorial problem related to the optimal selection of signaling perturbations, together with an Answer Set Programming (Gebser et al, 2012) based solution to this problem included within the open source python package caspo, which is freely available for download1
Experimental Design on Artificial and Real Case Studies We evaluate our approach using the workflow described in Section 4 for real-world signaling pathways in human liver cells, and both artificial and real phosphoproteomics datasets
Summary
The recent development of high-throughput experimental technologies allows us to observe different cellular parts under multiple situations This information is of great value to generate and validate computational models of the molecular processes happening within cells. Optimality Criteria in the Learning Step The above mentioned behavior of the learning MSE confirms that the space of optimal logic models returned by training procedures is very sensitive to the dataset under consideration. That is, it may constantly change when observations of new perturbations are being considered (see the toy example provided in Supplementary Material).
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