Applications of a formal approach to decipher discrete genetic networks

Modeling Procedures

Being concerned by the understanding of the mechanism underlying chronic degenerative diseases , we presented in the previous chapter the medical systems biology conceptual framework that we present for that purpose in this volume. More specifically, we argued there the clear advantages offered by a state-space perspective when applied to the systems-level description of the biomolecular machinery that regulates complex degenerative diseases. We also discussed the importance of the dynamical interplay between the risk factors and the network of interdependencies that characterizes the biochemical, cellular, and tissue-level biomolecular reactions that underlie the physiological processes in health and disease. As we pointed out in the previous chapter, the understanding of this interplay (articulated around cellular phenotypic plasticity properties, regulated by specific kinds of gene regulatory networks) is necessary if prevention is chosen as the human-health improvement strategy (potentially involving the modulation of the patient's lifestyle). In this chapter we provide the medical systems biology mathematical and computational modeling tools required for this task.

Formal reasoning about systems biology using theorem proving

System biology provides the basis to understand the behavioral properties of complex biological organisms at different levels of abstraction. Traditionally, analysing systems biology based models of various diseases have been carried out by paper-and-pencil based proofs and simulations. However, these methods cannot provide an accurate analysis, which is a serious drawback for the safety-critical domain of human medicine. In order to overcome these limitations, we propose a framework to formally analyze biological networks and pathways. In particular, we formalize the notion of reaction kinetics in higher-order logic and formally verify some of the commonly used reaction based models of biological networks using the HOL Light theorem prover. Furthermore, we have ported our earlier formalization of Zsyntax, i.e., a deductive language for reasoning about biological networks and pathways, from HOL4 to the HOL Light theorem prover to make it compatible with the above-mentioned formalization of reaction kinetics. To illustrate the usefulness of the proposed framework, we present the formal analysis of three case studies, i.e., the pathway leading to TP53 Phosphorylation, the pathway leading to the death of cancer stem cells and the tumor growth based on cancer stem cells, which is used for the prognosis and future drug designs to treat cancer patients.

Boolean Dynamic Modeling Approaches to Study Plant Gene Regulatory Networks: Integration, Validation, and Prediction

Mathematical models based on dynamical systems theory are well-suited tools for the integration of available molecular experimental data into coherent frameworks in order to propose hypotheses about the cooperative regulatory mechanisms driving developmental processes. Computational analysis of the proposed models using well-established methods enables testing the hypotheses by contrasting predictions with observations. Within such framework, Boolean gene regulatory network dynamical models have been extensively used in modeling plant development. Boolean models are simple and intuitively appealing, ideal tools for collaborative efforts between theorists and experimentalists. In this chapter we present protocols used in our group for the study of diverse plant developmental processes. We focus on conceptual clarity and practical implementation, providing directions to the corresponding technical literature.

Molecular mechanisms underlying COPD-muscle dysfunction unveiled through a systems medicine approach

MOTIVATION

Skeletal muscle dysfunction is a systemic effect in one-third of patients with chronic obstructive pulmonary disease (COPD), characterized by high reactive-oxygen-species (ROS) production and abnormal endurance training-induced adaptive changes. However, the role of ROS in COPD remains unclear, not least because of the lack of appropriate tools to study multifactorial diseases.

RESULTS

We describe a discrete model-driven method combining mechanistic and probabilistic approaches to decipher the role of ROS on the activity state of skeletal muscle regulatory network, assessed before and after an 8-week endurance training program in COPD patients and healthy subjects. In COPD, our computational analysis indicates abnormal training-induced regulatory responses leading to defective tissue remodeling and abnormal energy metabolism. Moreover, we identified tnf, insr, inha and myc as key regulators of abnormal training-induced adaptations in COPD. The tnf-insr pair was identified as a promising target for therapeutic interventions. Our work sheds new light on skeletal muscle dysfunction in COPD, opening new avenues for cost-effective therapies. It overcomes limitations of previous computational approaches showing high potential for the study of other multi-factorial diseases such as diabetes or cancer.

CONTACT

jroca@clinic.ub.es or martacascante@ub.eduSupplementary information: Supplementary data are available at Bioinformatics online.

A Method to Identify and Analyze Biological Programs through Automated Reasoning

Predictive biology is elusive because rigorous, data-constrained, mechanistic models of complex biological systems are difficult to derive and validate. Current approaches tend to construct and examine static interaction network models, which are descriptively rich, but often lack explanatory and predictive power, or dynamic models that can be simulated to reproduce known behavior. However, in such approaches implicit assumptions are introduced as typically only one mechanism is considered, and exhaustively investigating all scenarios is impractical using simulation. To address these limitations, we present a methodology based on automated formal reasoning, which permits the synthesis and analysis of the complete set of logical models consistent with experimental observations. We test hypotheses against all candidate models, and remove the need for simulation by characterizing and simultaneously analyzing all mechanistic explanations of observed behavior. Our methodology transforms knowledge of complex biological processes from sets of possible interactions and experimental observations to precise, predictive biological programs governing cell function.

Logical Modeling and Dynamical Analysis of Cellular Networks

The logical (or logic) formalism is increasingly used to model regulatory and signaling networks. Complementing these applications, several groups contributed various methods and tools to support the definition and analysis of logical models. After an introduction to the logical modeling framework and to several of its variants, we review here a number of recent methodological advances to ease the analysis of large and intricate networks. In particular, we survey approaches to determine model attractors and their reachability properties, to assess the dynamical impact of variations of external signals, and to consistently reduce large models. To illustrate these developments, we further consider several published logical models for two important biological processes, namely the differentiation of T helper cells and the control of mammalian cell cycle.

A hybrid model of cell cycle in mammals

Time plays an essential role in many biological systems, especially in cell cycle. Many models of biological systems rely on differential equations, but parameter identification is an obstacle to use differential frameworks. In this paper, we present a new hybrid modeling framework that extends René Thomas' discrete modeling. The core idea is to associate with each qualitative state "celerities" allowing us to compute the time spent in each state. This hybrid framework is illustrated by building a 5-variable model of the mammalian cell cycle. Its parameters are determined by applying formal methods on the underlying discrete model and by constraining parameters using timing observations on the cell cycle. This first hybrid model presents the most important known behaviors of the cell cycle, including quiescent phase and endoreplication.

Descriptive vs. mechanistic network models in plant development in the post-genomic era

Network modeling is now a widespread practice in systems biology, as well as in integrative genomics, and it constitutes a rich and diverse scientific research field. A conceptually clear understanding of the reasoning behind the main existing modeling approaches, and their associated technical terminologies, is required to avoid confusions and accelerate the transition towards an undeniable necessary more quantitative, multidisciplinary approach to biology. Herein, we focus on two main network-based modeling approaches that are commonly used depending on the information available and the intended goals: inference-based methods and system dynamics approaches. As far as data-based network inference methods are concerned, they enable the discovery of potential functional influences among molecular components. On the other hand, experimentally grounded network dynamical models have been shown to be perfectly suited for the mechanistic study of developmental processes. How do these two perspectives relate to each other? In this chapter, we describe and compare both approaches and then apply them to a given specific developmental module. Along with the step-by-step practical implementation of each approach, we also focus on discussing their respective goals, utility, assumptions, and associated limitations. We use the gene regulatory network (GRN) involved in Arabidopsis thaliana Root Stem Cell Niche patterning as our illustrative example. We show that descriptive models based on functional genomics data can provide important background information consistent with experimentally supported functional relationships integrated in mechanistic GRN models. The rationale of analysis and modeling can be applied to any other well-characterized functional developmental module in multicellular organisms, like plants and animals.

Gene regulatory network models for floral organ determination

Understanding how genotypes map unto phenotypes implies an integrative understanding of the processes regulating cell differentiation and morphogenesis, which comprise development. Such a task requires the use of theoretical and computational approaches to integrate and follow the concerted action of multiple genetic and nongenetic components that hold highly nonlinear interactions. Gene regulatory network (GRN) models have been proposed to approach such task. GRN models have become very useful to understand how such types of interactions restrict the multi-gene expression patterns that characterize different cell-fates. More recently, such temporal single-cell models have been extended to recover the temporal and spatial components of morphogenesis. Since the complete genomic GRN is still unknown and intractable for any organism, and some clear developmental modules have been identified, we focus here on the analysis of well-curated and experimentally grounded small GRN modules. One of the first experimentally grounded GRN that was proposed and validated corresponds to the regulatory module involved in floral organ determination. In this chapter we use this GRN as an example of the methodologies involved in: (1) formalizing and integrating molecular genetic data into the logical functions (Boolean functions) that rule gene interactions and dynamics in a Boolean GRN; (2) the algorithms and computational approaches used to recover the steady-states that correspond to each cell type, as well as the set of initial GRN configurations that lead to each one of such states (i.e., basins of attraction); (3) the approaches used to validate a GRN model using wild type and mutant or overexpression data, or to test the robustness of the GRN being proposed; (4) some of the methods that have been used to incorporate random fluctuations in the GRN Boolean functions and enable stochastic GRN models to address the temporal sequence with which gene configurations and cell fates are attained; (5) the methodologies used to approximate discrete Boolean GRN to continuous systems and their use in further dynamic analyses. The methodologies explained for the GRN of floral organ determination developed here in detail can be applied to any other functional developmental module.

Time series dependent analysis of unparametrized Thomas networks

This paper is concerned with the analysis of labeled Thomas networks using discrete time series. It focuses on refining the given edge labels and on assessing the data quality. The results are aimed at being exploitable for experimental design and include the prediction of new activatory or inhibitory effects of given interactions and yet unobserved oscillations of specific components in between specific sampling intervals. On the formal side, we generalize the concept of edge labels and introduce a discrete time series interpretation. This interpretation features two original concepts: 1) Incomplete measurements are admissible, and 2) it allows qualitative assumptions about the changes in gene expression by means of monotonicity. On the computational side, we provide a Python script, erda.py, that automates the suggested workflow by model checking and constraint satisfaction. We illustrate the workflow by investigating the yeast network IRMA.

"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis

Background

In Thomas' formalism for modeling gene regulatory networks (GRNs), branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a) asynchrony, (b) incompletely specified behavior, and (c) interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulators, because infinitely many paths may appear, limiting ordinary simulators to statistical conclusions. Model checkers for branching time, by contrast, are able to prove properties in the presence of infinitely many paths.

Results

We have developed Antelope ("Analysis of Networks through TEmporal-LOgic sPEcifications", http://turing.iimas.unam.mx:8080/AntelopeWEB/), a model checker for analyzing and constructing Boolean GRNs. Currently, software systems for Boolean GRNs use branching time almost exclusively for asynchrony. Antelope, by contrast, also uses branching time for incompletely specified behavior and environment interaction. We show the usefulness of modeling these two phenomena in the development of a Boolean GRN of the Arabidopsis thaliana root stem cell niche.

There are two obstacles to a direct approach when applying model checking to Boolean GRN analysis. First, ordinary model checkers normally only verify whether or not a given set of model states has a given property. In comparison, a model checker for Boolean GRNs is preferable if it reports the set of states having a desired property. Second, for efficiency, the expressiveness of many model checkers is limited, resulting in the inability to express some interesting properties of Boolean GRNs.

Antelope tries to overcome these two drawbacks: Apart from reporting the set of all states having a given property, our model checker can express, at the expense of efficiency, some properties that ordinary model checkers (e.g., NuSMV) cannot. This additional expressiveness is achieved by employing a logic extending the standard Computation-Tree Logic (CTL) with hybrid-logic operators.

Conclusions

We illustrate the advantages of Antelope when (a) modeling incomplete networks and environment interaction, (b) exhibiting the set of all states having a given property, and (c) representing Boolean GRN properties with hybrid CTL.