Sepinoud Azimi

Reaction System Models for the Heat Shock Response

Reaction systems are a formal framework for modeling processes driven by biochemical reactions. They are based on the mechanisms of facilitation and inhibition. A main assumption is that if a resource is available, then it is present in sufficient amounts and as such, several reactions using the same resource will not compete concurrently against each other; this makes reaction systems very different as a modeling framework than traditional frameworks such as ODEs or continuous time Markov chains. We demonstrate in this paper that reaction systems are rich enough to capture the essential characteristics of ODE-based models. We construct a reaction system model for the heat shock response in such a way that its qualitative behavior correlates well with the quantitative behavior of the corresponding ODE model. We construct our reaction system model based on a novel concept of dominance graph that captures the competition on resources in the ODE model. We conclude with a discussion on the expressivity of reaction systems as compared to that of ODE-based models.

Complexity of model checking for reaction systems

Reaction systems are a new mathematical formalism inspired by the living cell and driven by only two basic mechanisms: facilitation and inhibition. As a modeling framework, they differ from the traditional approaches based on ODEs and CTMCs in two fundamental aspects: their qualitative character and the non-permanency of resources. In this article we introduce to reaction systems several notions of central interest in biomodeling: mass conservation, invariants, steady states, stationary processes, elementary fluxes, and periodicity. We prove that the decision problems related to these properties span a number of complexity classes from P to NP- and coNP-complete to PSPACE-complete.

Dependency graphs and mass conservation in reaction systems

Reaction systems is a new mathematical formalism inspired by the biological cell, which focuses on an abstract set-based representation of chemical reactions via facilitation and inhibition. In this article we focus on the property of mass conservation for reaction systems. We show that conservation of sets gives rise to a relation between the species, which we capture in the concept of the conservation dependency graph. We then describe an application of this relation to the problem of listing all conserved sets. We further give a sufficient negative polynomial criterion which can be used for proving that a set is not conserved. Finally, we present a simulator of reaction systems, which also includes an implementation of the algorithm for listing the conserved sets of a given reaction system.

Multi-Stability, Limit Cycles, and Period-Doubling Bifurcation with Reaction Systems

Quantitative models may exhibit sophisticated behaviour that includes having multiple steady states, bistability, limit cycles, and period-doubling bifurcation. Such behaviour is typically driven by the numerical dynamics of the model, where the values of various numerical parameters play the crucial role. We introduce in this paper natural correspondents of these concepts to reaction systems modelling, a framework based on elementary set theoretical, forbidding/enforcing-based mechanisms. We construct several reaction systems models exhibiting these properties.

On the Implementation of Quantitative Model Refinement

The iterative process of adding details to a model while preserving its numerical behavior is called quantitative model refinement, and it has been previously discussed for ODE-based models and for kappa-based models. In this paper, we investigate and compare this approach in three different modeling frameworks: rule-based modeling, Petri nets and guarded command languages. As case study we use a model for the eukaryotic heat shock response that we refine to include the acetylation of the heat shock factor. We discuss how to perform the refinement in each of these frameworks in order to avoid the combinatorial state explosion of the refined model. We conclude that Bionetgen (and rule-based modeling in general) is well-suited for a compact representation of the refined model, Petri nets offer a good solution through the use of colors, while the PRISM refined model may be much larger than the basic model.

Generating the Logicome of a Biological Network

There has been much progress in recent years towards building larger and larger computational models for biochemical networks, driven by advances both in high throughput data techniques, and in computational modeling and simulation. Such models are often given as unstructured lists of species and interactions between them, making it very difficult to understand the logicome of the network, i.e. the logical connections describing the activation of its key nodes. The problem we are addressing here is to predict whether these key nodes will get activated at any point during a fixed time interval (even transiently), depending on their initial activation status. We solve the problem in terms of a Boolean network over the key nodes, that we call the logicome of the biochemical network. The main advantage of the logicome is that it allows the modeler to focus on a well-chosen small set of key nodes, while abstracting away from the rest of the model, seen as biochemical implementation details of the model. We validate our results by showing that the interpretation of the obtained logicome is in line with literature-based knowledge of the EGFR signalling pathway.

Directed Overlap-inclusion Graphs as Representations of Ciliate Genes

The simple intramolecular model for gene assembly in ciliates consists of three molecular operations based on local DNA manipulations. It was shown to predict correctly the assembly of all currently known ciliate gene patterns. Mathematical models in terms of signed permutations and signed strings proved limited in capturing some of the combinatorial details of the simple gene assembly process. A different formalization in terms of overlap-inclusion graphs, recently introduced by Brijder and Hoogeboom, proved well-suited to describe two of the three operations of the model and their combinatorial properties. We introduce in this paper an extension of the framework of Brijder and Hoogeboom in terms of directed overlap-inclusion graphs where more of the linear structure of the ciliate genes is described. We investigate a number of combinatorial properties of these graphs, including a necessary property in terms of forbidden induced subgraphs.

WEBRSIM: A Web-Based Reaction Systems Simulator

We introduce WEBRSIM, the first web-based simulator for reaction systems. The simulator has an easy-to-use interface where the input is a reaction system and four functionalities: the computation of the interactive process driven by a given context sequence, the behaviour graph of the reaction system, its conservation dependency graph, and all its conserved sets. WEBRSIM comes with a browser-based friendly interface and offers a fast software to support computational modeling with reaction systems.

Steady states of constrained reaction systems

Abstract Reaction systems, a mathematical formalism inspired by the mechanisms within a biological cell, focuses on an abstract set-based representation of chemical reactions via facilitation and inhibition. The simple yet elegant nature of reaction systems makes them ideal tools for analysing qualitatively the phenomena which typically are dealt with quantitatively. Steady states are one of the well studied and important subjects across various fields of science ranging from biology, to chemistry, to engineering and economics. Finding all steady states of an arbitrary reaction system has been shown to be an NP -complete problem. We study reaction systems with a small number of reactants and inhibitors and we propose an algorithm to list all steady states of such reaction systems. We also show that the complexity of such an algorithm is polynomial. This reduction in complexity opens a door to transform modelling with reaction systems from an abstract concept to a tool that can be used on real-life case studies.

An Excursion Through Quantitative Model Refinement

There is growing interest in creating large-scale computational models for biological process. One of the challenges in such a project is to fit and validate larger and larger models, a process that requires more high-quality experimental data and more computational effort as the size of the model grows. Quantitative model refinement is a recently proposed model construction technique addressing this challenge. It proposes to create a model in an iterative fashion by adding details to its species, and to fix the numerical setup in a way that guarantees to preserve the fit and validation of the model. In this survey we make an excursion through quantitative model refinement – this includes introducing the concept of quantitative model refinement for reaction-based models, for rule-based models, for Petri nets and for guarded command language models, and to illustrate it on three case studies (the heat shock response, the ErbB signaling pathway, and the self-assembly of intermediate filaments).