Exhaustive analysis of dynamical properties of Biological Regulatory Networks with Answer Set Programming

International audienceThe combination of numerous simple influences between the components of a Biological Regulatory Network (BRN) often leads to behaviors that cannot be grasped intuitively. They thus call for the development of proper mathematical methods to delineate their dynamical properties. As a consequence , formal methods and computer tools for the modeling and simulation of BRNs become essential. Our recently introduced discrete formalism called the Process Hitting (PH), a restriction of synchronous automata networks, is notably suitable to such study. In this paper, we propose a new logical approach to perform model-checking of dynamical properties of BRNs modeled in PH. Our work here focuses on state reachability properties on the one hand, and on the identification of fixed points on the other hand. The originality of our model-checking approach relies in the exhaustive enumeration of all possible simulations verifying the dynamical properties thanks to the use of Answer Set Programming

Efficient parameter search for qualitative models of regulatory networks using symbolic model checking

Investigating the relation between the structure and behavior of complex biological networks often involves posing the following two questions: Is a hypothesized structure of a regulatory network consistent with the observed behavior? And can a proposed structure generate a desired behavior? Answering these questions presupposes that we are able to test the compatibility of network structure and behavior. We cast these questions into a parameter search problem for qualitative models of regulatory networks, in particular piecewise-affine differential equation models. We develop a method based on symbolic model checking that avoids enumerating all possible parametrizations, and show that this method performs well on real biological problems, using the IRMA synthetic network and benchmark experimental data sets. We test the consistency between the IRMA network structure and the time-series data, and search for parameter modifications that would improve the robustness of the external control of the system behavior

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

Methods for control strategy identification in Boolean networks

Understanding control mechanisms present in biological processes is crucial for the development of potential therapeutic applications, for instance cell reprogramming or drug target identification. Experimental approaches aimed at identifying possible control targets are usually costly and time-consuming. Mathematical modeling provides a formal framework to study biological systems and to predict potential successful candidate interventions. A common modeling framework is Boolean modeling, which stands out for its ability to capture the qualitative behavior of the system using coarse representations of the interactions between the components, overcoming the usual parametrization problem. The main goal of this thesis is the study of the control problems present in biological systems and the development of efficient and complete approaches for control strategy identification. In particular, we aim at developing methods to identify sets of minimal controls that are able to induce the desired states in biological systems modeled by Boolean networks. With the goal of making our approaches attractive for application, we establish two key factors: efficiency and diversity. We want our approaches to be able to deal with state-of-the-art networks in a reasonable amount of time while providing as many different optimal control sets as possible. With these factors in mind, we developed two different approaches. Our first method is based on value percolation, one of the most simple and efficient approaches to control strategy identification in Boolean networks. Percolation-based methods can be implemented efficiently but are limited and might miss many control strategies. Our approach introduces the use of trap spaces, regions of the state space closed under the dynamics. This allows us to increase the number of control strategies identified while still benefiting from an efficient implementation. Our second approach focuses on exhaustivity and flexibility. Based on model checking techniques, it allows us to identify all the minimal control strategies for a given target. This approach is also able to deal with more complex control problems, since it can handle any type of target. To overcome the higher computational costs associated with the comprehensiveness of the method, we also introduce several reduction techniques to improve its performance. In the last chapter, we show the applicability of our approaches to different biological systems. We study the control strategies obtained for a network modeling the epithelial-to-mesenchymal transition, considering different control targets and types of interventions. We also explore the relevance of the intervention strategies identified in the biological context. Finally, we compare our approaches to other current control methods in different Boolean networks.Das Verständnis von Kontrollmechanismen in biologischen Prozessen ist von entscheidender Bedeutung für die Entwicklung potenzieller therapeutischer Anwendungen, z. B. die Reprogrammierung von Zellen oder die Identifizierung von Zielstrukturen für Medikamente. Experimentelle Ansätze zur Identifizierung möglicher Kontrollziele sind in der Regel kostspielig und zeitaufwändig. Die mathematische Modellierung bietet einen formalen Rahmen zur Untersuchung biologischer Systeme und zur Vorhersage potenziell erfolgreicher Interventionskandidaten. Ein etablierter Formalismus ist die boolesche Modellierung, die sich durch ihre Fähigkeit auszeichnet, das qualitative Verhalten des Systems mit Hilfe grober Darstellungen der Wechselwirkungen zwischen den Komponenten zu erfassen und so das übliche Parametrisierungsproblem zu überwinden. Das Hauptziel dieser Arbeit ist die Untersuchung der Kontrollprobleme in biologischen Systemen und die Entwicklung von effizienten und vollständigen Ansätzen zur Identifikation von Kontrollstrategien. Insbesondere geht es um die Entwicklung von Methoden zur Identifizierung von Mengen minimaler Steuerungen, die in der Lage sind, die gewünschten Zustände in biologischen, durch boolesche Netzwerke modellierten Systemen zu induzieren. Um unsere Ansätze für die Anwendung attraktiv zu machen, legen wir zwei Schlüsselfaktoren fest: Effizienz und Vielfalt. Unsere Methoden sollen in der Lage sein, biologische Netzwerke von aktuellem Interesse in angemessener Zeit zu bearbeiten und dabei so viele verschiedene optimale Kontrollsätze wie möglich bereitzustellen. Mit Blick auf diese Faktoren haben wir zwei verschiedene Ansätze entwickelt. Unsere erste Methode basiert auf der Wertperkolation, einem der einfachsten und effizientesten Ansätze zur Berechnung von Steuerungen boolescher Netze. Auf Perkolation basierende Methoden können zwar effizient implementiert werden, lassen aber möglicherweise viele Kontrollstrategien außer Acht. Unser Ansatz führt die Verwendung von Trap-Spaces ein, d.h. Regionen des Zustandsraums, die unter der Dynamik abgeschlossen sind. Dadurch können wir die Anzahl der identifizierten Kontrollstrategien erhöhen und gleichzeitig von einer effizienten Implementierung profitieren. Unser zweiter Ansatz konzentriert sich auf Vollständigkeit und Flexibilität. Auf der Grundlage von Modellprüfungstechniken können wir alle minimalen Kontrollstrategien für ein bestimmtes Ziel identifizieren. Dieser Ansatz ist auch in der Lage, komplexere Steuerungsprobleme zu behandeln, da er mit jeder Art von Ziel umgehen kann. Um die mit der Vollständigkeit der Methode verbundenen höheren Rechenkosten zu überwinden, führen wir mehrere leistungsverbessernde Reduktionstechniken ein. Im letzten Kapitel zeigen wir die Anwendbarkeit unserer Ansätze auf verschiedene biologische Systeme. Wir untersuchen die Kontrollstrategien, die wir für ein Netzwerk erhalten, das den Übergang von Epithel- zu Mesenchymzellen modelliert, wobei wir verschiedene Kontrollziele und Arten von Eingriffen berücksichtigen. Wir untersuchen auch die Relevanz der ermittelten Interventionsstrategien im biologischen Kontext. Schließlich vergleichen wir unsere Ansätze mit anderen aktuellen Kontrollmethoden angewandt auf verschiedene boolesche Netzwerke

Analyzing Large Network Dynamics with Process Hitting

In this chapter, we introduce the Process Hitting framework, which provides the methodology of constructing the most permissive dynamics and then using successive refinements to fine tune the model. We present static analysis methods designed to identify fixed points or answer successive reachability questions, and introduce the stochastic semantics of Process Hitting too

The impact of cellular characteristics on the evolution of shape homeostasis

The importance of individual cells in a developing multicellular organism is well known but precisely how the individual cellular characteristics of those cells collectively drive the emergence of robust, homeostatic structures is less well understood. For example cell communication via a diffusible factor allows for information to travel across large distances within the population, and cell polarisation makes it possible to form structures with a particular orientation, but how do these processes interact to produce a more robust and regulated structure? In this study we investigate the ability of cells with different cellular characteristics to grow and maintain homeostatic structures. We do this in the context of an individual-based model where cell behaviour is driven by an intra-cellular network that determines the cell phenotype. More precisely, we investigated evolution with 96 different permutations of our model, where cell motility, cell death, long-range growth factor (LGF), short-range growth factor (SGF) and cell polarisation were either present or absent. The results show that LGF has the largest positive impact on the fitness of the evolved solutions. SGF and polarisation also contribute, but all other capabilities essentially increase the search space, effectively making it more difficult to achieve a solution. By perturbing the evolved solutions, we found that they are highly robust to both mutations and wounding. In addition, we observed that by evolving solutions in more unstable environments they produce structures that were more robust and adaptive. In conclusion, our results suggest that robust collective behaviour is most likely to evolve when cells are endowed with long range communication, cell polarisation, and selection pressure from an unstable environment