Despite recent molecular technique improvements, biological knowledge remains incomplete. Reasoning on living systems hence implies to integrate heterogeneous and partial informations. Although current investigations successfully focus on qualitative behaviors of macromolecular networks, others approaches show partial quantitative informations like protein concentration variations over times. We consider that both informations, qualitative and quantitative, have to be combined into a modeling method to provide a better understanding of the biological system. We propose here such a method using a probabilistic-like approach. After its exhaustive description, we illustrate its advantages by modeling the carbon starvation response in Escherichia coli. In this purpose, we build an original qualitative model based on available observations. After the formal verification of its qualitative properties, the probabilistic model shows quantitative results corresponding to biological expectations which confirm the interest of our probabilistic approach.
Deep Dive into Integrating heterogeneous knowledges for understanding biological behaviors: a probabilistic approach.
Despite recent molecular technique improvements, biological knowledge remains incomplete. Reasoning on living systems hence implies to integrate heterogeneous and partial informations. Although current investigations successfully focus on qualitative behaviors of macromolecular networks, others approaches show partial quantitative informations like protein concentration variations over times. We consider that both informations, qualitative and quantitative, have to be combined into a modeling method to provide a better understanding of the biological system. We propose here such a method using a probabilistic-like approach. After its exhaustive description, we illustrate its advantages by modeling the carbon starvation response in Escherichia coli. In this purpose, we build an original qualitative model based on available observations. After the formal verification of its qualitative properties, the probabilistic model shows quantitative results corresponding to biological expectations
The last decade has seen great successes in macromolecular network modeling. In particular, qualitative methods appear today as well-adapted for reasoning on biological systems, despite the current lack of quantitative informations (de Jong, 2002). Thus most of interesting and investigated knowledges concern local informations such as gene-gene or gene-protein interactions. They allow to build networks like on Figure 1 (A), that model the global qualitative behavior of a biological system. However, other experiments illustrated Figure 1 (B) give insights about various partial quantitative knowledges. They emphasize both molecular concentration variations and time-series.
These two related kinds of partial quantitative information, i.e., time and concentration, are well studied by other experiments (Wolfe, 2005) and reflect as well the overall system behavior. Both informations, qualitative and quantitative, have hence to be combined into a modeling method for giving a better understanding of the biological system. Due to the lack of quantitative informations, we propose a modeling approach that (i) spreads partial local informations through the qualitative network and (ii) gives insights about global behaviors. Probabilistic approaches are well adapted for bringing complementary quantitative or semi quantitative knowledges into a qualitative model. Among them, we suggest an original toll based approach that predicts various molecular productions combining both qualitative and partial quantitative knowledges. After an overview of our probabilistic approach (Sec. 2), we propose here to apply it on gene regulatory model of the carbon starvation response in Escherichia coli. In this purpose, we (Sec. 3.1) build a model based on a novel qualitative abstraction, validate its behavior using a formal verification approach, which (Sec. 3.2) allows us to accurately apply our probabilistic method. Such a protocol emphasizes several biological insights of interest. Figure 1: Biological informations concerning Escherichia coli carbon starvation system. (A) represents interactions between genes involved in the regulatory network (adapted from (Ropers et al., 2006)). (B) shows quantitative variations of macromolecules of interest (based on (Ball et al., 1992)). Note the linear relationship between fis RNA and Fis protein productions.
We consider biological networks as graphs that show transitions between various components of the system. Each transition is related to variations of characteristic quantities of the system and produces its own impact on the whole system behavior. In a gene regulatory network, a qualitative graph arrow is associated with a production or consumption of the corresponding protein.
In order to abstract qualitative biological behaviors, we represent a gene regulatory network by a qualitative graph where each state stands for a qualitative variation of a gene activity. We focus on the macromolecular transformation derivative, which is more tractable to model detailed macromolecular concentration variations. As illustration, following interactions describe the fact that (i) gene x activates gene y and (ii) x represses y:
Such a representation implies that gene x produces protein X that activates gene y. Thus (i) and (ii) represent respectively an overall increase of Y protein production and an overall decrease of Y . Note that such an abstraction neglects post-transcriptional regulations which is particularly unappropriated for modeling eukaryote gene regulatory network.
This biological abstraction allows us to model various qualitative interactions. Considering that a gene x activity is summarized by two qualitative states x + and x -, y activation by x might be described by the set of rules and its corresponding transitions:
A peak of gene x activity that activates y is represented by:
A minimal activity of gene x that activates y is symbolized by:
Gene y repressions by a gene x activity are modeled using similar rules that imply transitions toward y -. Such an abstraction gives the opportunity to focus on qualitative behaviors. Reasoning on quantities associated with qualitative rules allows us to emphasize quantitative states of the system despite concurrent qualitative rules.
We make the assumption that the biological system is associated with several quantities q 1 , . . . , q k that represent the current state of the system. For illustration, these quantities represent protein concentrations, or other non trivial quantities such as the number of times a particular pathway is taken by the living system. Studying the behavior of biological systems hence consists in understanding the evolution of these quantities. Note here that such quantities may not be experimentally measurable. Since the last decade, biological behaviors have been often described by qualitative graphs that abstract different component variations within the system. In our model, we consider that each transition of th
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