Ricardo Honorato-Zimmer

Reversible Sesqui-Pushout Rewriting

The paper proposes a variant of sesqui-pushout rewriting (SqPO) that allows one to develop the theory of nested application conditions (NACs) for arbitrary rule spans; this is a considerable generalisation compared with existing results for NACs, which only hold for linear rules (w.r.t. a suitable class of monos). Besides this main contribution, namely an adapted shifting construction for NACs, the paper presents a uniform commutativity result for a revised notion of independence that applies to arbitrary rules; these theorems hold in any category with (enough) stable pushouts and a class of monos rendering it weak adhesive HLR. To illustrate results and concepts, we use simple graphs, i.e. the category of binary endorelations and relation preserving functions, as it is a paradigmatic example of a category with stable pushouts; moreover, using regular monos to give semantics to NACs, we can shift NACs over arbitrary rule spans.

Approximations for Stochastic Graph Rewriting

In this note we present a method to compute approximate descriptions of a class of stochastic systems. For the method to apply, the system must be presented as a Markov chain on a state space consisting in graphs or graph-like objects, and jumps must be described by transformations which follow a finite set of local rules.

Annotation of rule-based models with formal semantics to enable creation, analysis, reuse and visualization.

Motivation: Biological systems are complex and challenging to model and therefore model reuse is highly desirable. To promote model reuse, models should include both information about the specifics of simulations and the underlying biology in the form of metadata. The availability of computationally tractable metadata is especially important for the effective automated interpretation and processing of models. Metadata are typically represented as machine-readable annotations which enhance programmatic access to information about models. Rule-based languages have emerged as a modelling framework to represent the complexity of biological systems. Annotation approaches have been widely used for reaction-based formalisms such as SBML. However, rule-based languages still lack a rich annotation framework to add semantic information, such as machine-readable descriptions, to the components of a model. Results: We present an annotation framework and guidelines for annotating rule-based models, encoded in the commonly used Kappa and BioNetGen languages. We adapt widely adopted annotation approaches to rule-based models. We initially propose a syntax to store machine-readable annotations and describe a mapping between rule-based modelling entities, such as agents and rules, and their annotations. We then describe an ontology to both annotate these models and capture the information contained therein, and demonstrate annotating these models using examples. Finally, we present a proof of concept tool for extracting annotations from a model that can be queried and analyzed in a uniform way. The uniform representation of the annotations can be used to facilitate the creation, analysis, reuse and visualization of rule-based models. Although examples are given, using specific implementations the proposed techniques can be applied to rule-based models in general. Availability and implementation: The annotation ontology for rule-based models can be found at http://purl.org/rbm/rbmo. The krdf tool and associated executable examples are available at http://purl.org/rbm/rbmo/krdf. Contact: anil.wipat@newcastle.ac.uk or vdanos@inf.ed.ac.uk

Moment Semantics for Reversible Rule-Based Systems

We develop a notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the ‘no-dangling-edge’ condition inherent in DPO rewriting. Our main result is that the linear span of marked graph occurrence-counting functions – or motif functions – form an algebra which is closed under the infinitesimal generator of (the Markov chain associated with) any such rewriting system. This gives a general procedure to derive the moment semantics of any such rewriting system, as a countable (and recursively enumerable) system of differential equations indexed by motif functions. The differential system describes the time evolution of moments (of any order) of these motif functions under the rewriting system. We illustrate the semantics using the example of preferential attachment networks; a well-studied complex system, which meshes well with our notion of marked graph rewriting. We show how in this case our procedure obtains a finite description of all moments of degree counts for a fixed degree.

Kappa Rule-Based Modeling in Synthetic Biology

Rule-based modeling, an alternative to traditional reaction-based modeling, allows us to intuitively specify biological interactions while abstracting from the underlying combinatorial complexity. One such rule-based modeling formalism is Kappa, which we introduce to readers in this chapter. We discuss the application of Kappa to three modeling scenarios in synthetic biology: a unidirectional switch based on nitrosylase induction in Saccharomyces cerevisiae, the repressilator in Escherichia coli formed from BioBrick parts, and a light-mediated extension to said repressilator developed by the University of Edinburgh team during iGEM 2010. The second and third scenarios in particular form a case-based introduction to the Kappa BioBrick Framework, allowing us to systematically address the modeling of devices and circuits based on BioBrick parts in Kappa. Through the use of these examples, we highlight the ease with which Kappa can model biological interactions both at the genetic and the protein-protein interaction level, resulting in detailed stochastic models accounting naturally for transcriptional and translational resource usage. We also hope to impart the intuitively modular nature of the modeling processes involved, supported by the introduction of visual representations of Kappa models. Concluding, we explore future endeavors aimed at making modeling of synthetic biology more user-friendly and accessible, taking advantage of the strengths of rule-based modeling in Kappa.

Chromar, a Rule-based Language of Parameterised Objects

Abstract Modelling in biology becomes necessary when systems are complex but the more complex the systems are the harder the models become to read. The most common ways of writing models are by writing reactions on discrete, typed objects (e.g. molecules of different species), or writing rate equations for the populations of such species. One problem (1) with those approaches is that the number of species and reactions is often so large that the model cannot be realistically enumerated. Another problem (2) is that the number of species and reactions is fixed, whereas biology often grows new compartments which means new reactions and species. Here we develop an extension to the representation of reactions where the objects carry variables that are defined by their type (for example objects of type Leaf all have a Mass variable). The dynamics are defined by rules about types, which means they work for all objects of that type. This compact representation solves problem 1. If we think of the object variables as the analogue of reaction/rate equation species, creating a new object of some type means we are also creating new species (solving problem 2). We also developed an embedding of Chromar in the programming language Haskell and showed its applicability to two examples. Having a more compact representation can help make models a tool for knowledge representation and exchange instead of just a simulation input. Embedding Chromar in a general purpose programming language lifts some of the constraints of modelling languages while still maintaining the naturalness of a domain-specific language.

Emergent Communities in Socio-cognitive Networks

We investigate a recent network model which combines social and cognitive features. Each node in the social network holds a (possibly different) cognitive network that represent its beliefs. In this internal cognitive network a node denotes a concept and a link indicates whether the two linked concepts are taken to be of a similar or opposite nature. We show how these networks naturally organise into communities and use this to develop a method that detects communities in social networks. How they organise depends on the social structure and the ratio between the cognitive and social forces driving the propagation of beliefs.

Mean Quantitative Coverability in Stochastic Graph Transformation Systems

Many classical problems for Petri nets, in particular reachability and coverability, have obvious counterparts for graph transformation systems. Similarly, many problems for stochastic Petri nets, seen as a model for chemical reaction networks, are special cases of corresponding problems in graph transformation. For example, the evolution of the counts of chemical species in a test tube over time is a typical phenomenon from chemistry, which can faithfully be modelled and analysed using stochastic Petri nets. The corresponding mean quantitative coverability problem for stochastic graph transformation is simple to describe – yet hard to solve. This extended abstract summarises the fundamental ideas and challenges.