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Symbolic Representation and Inference of Regulatory Network Structures

Recent results have demonstrated the usefulness of symbolic approaches for addressing various problems in systems biology. One of the fundamental challenges in systems biology is the extraction of integrated signaling-transcriptional networks from experimental data. In this chapter, we present a general logic-based framework, called Abductive Regulatory Network Inference (ARNI), where we formalize the network extraction problem as an abductive inference problem. A general logical model is provided that integrates prior knowledge on molecular interactions and other information for capturing signal-propagation principles and compatibility with experimental data. Solutions to our abductive inference problem define signed-directed networks that explain how genes are affected during the experiments. Using in-silico datasets provided by the dialogue for reverse engineering assessments and methods (DREAM)) consortium, we demonstrate the improved predictive power and complexity of our inferred network topologies compared with those generated by other non-symbolic inference approaches, showing the suitability of our approach for computing complete realistic networks. We also explore how the improved expressiveness together with the modularity and flexibility of the logic-based nature of our approach can support automated scientific discovery where the validity of hypothesized biological ideas can be examined and tested outside the laboratory.

1.1. Introduction: logical modeling and abductive inference in systems biology

Systems biology is generally concerned with developing formal models that aim to describe the operation of various biological processes. Its study is based on the synthesis of a model or a theory from empirical experimental information. At the cellular level, systems biology aims to build models that describe, at some level of abstraction, the underlying operation of a cell at the genomic and/or protein level. The central challenge is then how to choose an appropriate framework that would (1) enable the construction of a model from experimental data and (2) empower such models with a predictive capability for new information beyond the one used to construct the model.

As in many cases of such scientific exploration, the choice of the framework under which we formulate the model depends on the type of experimental data that is available at the time of the development of the scientific model. In general, at the initial stages of an investigation the available data is usually descriptive and qualitative rather than quantitative. As such we set out to develop a first model, based on some principles that we believe underlie the phenomena, where we are primarily interested in capturing the overall and general interrelation between the concepts of interest. It is then important to require a framework that is (1) high-level close to the human description of the phenomena and thus close to the experimental language, and (2) modular and flexible so that the models can easily be adapted to new information and other changes that might come about.

Under these conditions and requirements for our language, a symbolic or logical framework is particularly suitable. A logical scientific theory normally offers a high-level declarative description that can be understood easily by the expert experimental scientists that provide the experimental data. Logical models are also highly modular where changes can often be isolated to parts of the model without the need for an overall complete reformulation of the model. Furthermore, within a logical approach we can employ abductive reasoning to help in the process of building a theory from experimental data. Abductive reasoning is a formalization of the explanatory scientific reasoning that is typically carried out by human scientists when they think about the phenomena they are studying, either when they are trying to understand their experimental findings, or when they are planning the next set of experiments to help them improve their understanding of the phenomena.

Hence, in choosing a logical approach, we provide a framework that not only responds well to the object level requirement of describing the phenomena, but also to the meta level task of reasoning about the models developed thus far and deciding on their further investigation through new experiments, or indeed new desirable properties and principles that the model must adhere to. For molecular biology, logic is particularly suited as, at least currently, in many cases the theoretical models and experimentation of cell biology are developed following a rationale at the qualitative rather than quantitative level. The nature of much of the experimental data is descriptive with the aim to first understand the qualitative interrelations between the various constituents and processes in the cell.

In this chapter, we have developed a logical model of regulatory cell networks, covering both transcriptional networks and upstream signaling regulatory networks. We have implemented a qualitative model that is based on general biological principles and which exploits current prior knowledge of molecular interactions that are already known. The approach, called ARNI, for abductive inference of regulatory networks, constructs causal signed-directed networks of interactions between genes from high-throughput experimental data. These networks rely on the simple and general underlying principles that signals from the environment propagate along paths of protein interactions to reach the regulatory components of cells (i.e. production of genes) and that genes are under the influence of multiple overlapping inputs, which might be compatible or competitive to each other. The networks also exhibit several important motifs including feedback loops (positive and negative), which allow a gene to control its own expression, and feed-forward loops (coherent or incoherent), whereby a gene has both direct and indirect connections to its target1. Each of these motifs governs fundamental properties of the overall dynamic behaviorof the network such as robustness, oscillations, memory and bistability [ALO 07, YEG 04].

Our construction of regulatory networks relies on abductive reasoning as an automated form of the scientific reasoning of rationalizing the high throughput experimental data. Indeed, the problem of signaling network reconstruction naturally maps to an abductive task. Specifically, (1) gene expression data constitutes the experimental data; (2) the given (partial) knowledge is a logic-based theory governing biological phenomena, as for instance the notions of gene regulation, interactive potential; (3) biological constraints like sign consistency between interacting gene expressions are captured via integrity constraints and (4) sentences about unknown compatible and competitive gene regulations are the abducible information that can be assumed to form a network. Thus, assuming the general possible structure of signaling networks an abductive computation results in the inference of possible signed-directed networks, in terms of compatible and competitive gene regulations, that conform to the available experimental observations.

As argued above, our logical approach offers a high-level declarative model with suitable and increased expressiveness for the wide applicability to a variety of signaling network problems and challenges. We demonstrate these properties of the approach through a series of evaluation experiments that test the effectiveness of the abductive networks and explore the expressiveness of the logical framework. We also examine the usefulness of our abductive approach in the meta-level scientific reasoning, as a scientific assistant and how this, together with the modularity of the approach, can support the further development and improvement of the initially constructed networks.

Our approach follows a series of works that rely on logical abduction for addressing various problems in systems biology. Abduction has been used to learn/revise metabolic pathways [RAY 10, TAM 06] and to hypothesize on the function of genes [RAY 08, KIN 04]. Abductive reasoning is also used in [TRA 09, LAZ 13] for meta-level reasoning over hypotheses but de-novo topology inference is not considered in these existing contributions. More directly related to our work is the approach in [PAP 05], which uses abductive logic programming to infer gene dependencies to explain the changes in the gene expression levels. Our work advances that in [PAP 05] in several ways, specifically by allowing the use of prior knowledge, modeling and reasoning about competitive gene influences and presenting a framework that can act as a scientific assistant to biologists for testing the validity of new hypotheses.

In comparison with non-symbolic approaches such as gene co-expression networks based on statistical principles [ROT 13, HE 09] and physical network models [YEA 04, OUR 07, HUA 09], logical approaches like ours offer improved expressiveness, as they enable the inference of networks with more complex regulatory structures, and added modularity that allows the logic model to be easily adapted to new available information (e.g. addition of new constraints).

This chapter is structured as follows. Section 1.2 presents the ARNI approach with its main key components. Section 1.3 describes the results on evaluating the predictive power of our approach and demonstrates the increased expressive power of ARNI. Section 1.4 explores ARNI as a scientific assistant for biological hypothesis testing and section 1.5 concludes the chapter with a discussion on related work and future directions.

1.2. Logical modeling of regulatory networks

In this...