Integrating Quantitative Knowledge into a Qualitative Gene Regulatory Network

Despite recent improvements in molecular techniques, biological knowledge remains incomplete. Any theorizing about living systems is therefore necessarily based on the use of heterogeneous and partial information. Much current research has focused successfully on the qualitative behaviors of macromolecular networks. Nonetheless, it is not capable of taking into account available quantitative information such as time-series protein concentration variations. The present work proposes a probabilistic modeling framework that integrates both kinds of information. Average case analysis methods are used in combination with Markov chains to link qualitative information about transcriptional regulations to quantitative information about protein concentrations. The approach is illustrated by modeling the carbon starvation response in Escherichia coli. It accurately predicts the quantitative time-series evolution of several protein concentrations using only knowledge of discrete gene interactions and a small number of quantitative observations on a single protein concentration. From this, the modeling technique also derives a ranking of interactions with respect to their importance during the experiment considered. Such a classification is confirmed by the literature. Therefore, our method is principally novel in that it allows (i) a hybrid model that integrates both qualitative discrete model and quantities to be built, even using a small amount of quantitative information, (ii) new quantitative predictions to be derived, (iii) the robustness and relevance of interactions with respect to phenotypic criteria to be precisely quantified, and (iv) the key features of the model to be extracted that can be used as a guidance to design future experiments. Author Summary: Understanding the response of a biological system to a stress is of great interest in biology. This issue is usually tackled by integrating information arising from different experiments into mathematical models. In particular, continuous models take quantitative information into account after a parameter estimation step whereas much recent research has focused on the qualitative behaviors of macromolecular networks. However, both modeling approaches fail to handle the true nature of biological information, including heterogeneity, incompleteness and multi-scale features, as emphasized by recent advances in molecular techniques. The principle novelty of our method lies in the use of probabilities and average-case analysis to overcome this weakness and to fill the gap between qualitative and quantitative models. Our framework is applied to study the response of Escherichia coli to a carbon starvation stress. We combine a small amount of quantitative information on protein concentrations with a qualitative model of transcriptional regulations. We derive quantitative predictions about proteins, quantify the robustness and relevance of transcriptional interactions, and automatically extract the key features of the model. The main biological novelty is therefore the presentation of new knowledge derived from the combination of quantitative and qualitative multi-scale information in a single approach.