An analysis of innocent interaction

We present two abstract machines for innocent interaction. The first, a rather complicated machine, operates directly on innocent strategies. The second, a far simpler machine, requires a “compilation” of the innocent strategies into “cellular” strategies before use. Given two innocent strategies, we get the same final result if we make them interact using the first machine or if we first cellularize them then use the other machine

A knowledge representation meta-model for rule-based modelling of signalling networks

The study of cellular signalling pathways and their deregulation in disease states, such as cancer, is a large and extremely complex task. Indeed, these systems involve many parts and processes but are studied piecewise and their literatures and data are consequently fragmented, distributed and sometimes--at least apparently--inconsistent. This makes it extremely difficult to build significant explanatory models with the result that effects in these systems that are brought about by many interacting factors are poorly understood. The rule-based approach to modelling has shown some promise for the representation of the highly combinatorial systems typically found in signalling where many of the proteins are composed of multiple binding domains, capable of simultaneous interactions, and/or peptide motifs controlled by post-translational modifications. However, the rule-based approach requires highly detailed information about the precise conditions for each and every interaction which is rarely available from any one single source. Rather, these conditions must be painstakingly inferred and curated, by hand, from information contained in many papers--each of which contains only part of the story. In this paper, we introduce a graph-based meta-model, attuned to the representation of cellular signalling networks, which aims to ease this massive cognitive burden on the rule-based curation process. This meta-model is a generalization of that used by Kappa and BNGL which allows for the flexible representation of knowledge at various levels of granularity. In particular, it allows us to deal with information which has either too little, or too much, detail with respect to the strict rule-based meta-model. Our approach provides a basis for the gradual aggregation of fragmented biological knowledge extracted from the literature into an instance of the meta-model from which we can define an automated translation into executable Kappa programs.Comment: In Proceedings DCM 2015, arXiv:1603.0053

Rule-based Modelling and Tunable Resolution

We investigate the use of an extension of rule-based modelling for cellular signalling to create a structured space of model variants. This enables the incremental development of rule sets that start from simple mechanisms and which, by a gradual increase in agent and rule resolution, evolve into more detailed descriptions

Categorical Combinatorics for Innocent Strategies

International audienceWe show how to construct the category of games and innocent strategies from a more primitive category of games. On that category we define a comonad and monad with the former distributing over the latter. Innocent strategies are the maps in the induced two-sided Kleisli category. Thus the problematic composition of innocent strategies reflects the use of the distributive law. The composition of simple strategies, and the combinatorics of pointers used to give the comonad and monad are themselves described in categorical terms. The notions of view and of legal play arise naturally in the explanation of the distributivity. The category-theoretic perspective provides a clear discipline for the necessary combinatorics

Biological signalling and causality

Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of differential equations quickly impractical, if not conceptually inappropriate. As an alternative, we propose an agent-based / concurrent language, named κ, which places causal reasoning front center. We illustrate how κ transparently represents biological knowledge, thereby making models easier to build, discuss, modify, and merge. By taming the combinatorial explosion, circumventing the frustrations of handling opaque systems of equations, and lowering the mathematical threshold for molecular biologists, κ holds promise for making modelling more widely available. The causal structure of processes, is largely absent from systems of differential equations, yet it deeply shapes the dynamical, and perhaps even evolutionary, characteristics of complex distributed biological systems. We illustrate the use of κ and its associated causal analysis by means of a model of EGFR signalling that would overwhelm any traditional approach. The model is obtained by refactoring two extant models based on differential equations. We formalize the colloquial concept of pathway in terms of a special kind of event structure and illustrate how the juxtaposition of it with relationships of conflict between rules can be used to dissect EGFR signalling dynamics

Models of Tet-On System with Epigenetic Effects

International audienceWe present the first results of ongoing work investigating two models of the artificial inducible promoter Tet-On that include epigenetic regulation. We consider chromatin states and 1D diffusion of transcription factors that reveal, respectively, stochastic noise and a memory effect

Intrinsic Information carriers in combinatorial dynamical systems

International audienceMany proteins are composed of structural and chemical features—“sites” for short—defined by definite inter- action capabilities, such as non-covalent binding or covalent modification of other proteins. This modularity allows for varying degrees of independence, as the behavior of a site might be controlled by the state of some but not all sites of the ambient protein. Independence quickly generates a startling combinatorial complexity that characterizes most biological networks, such as mammalian signaling systems, and effectively prevents their study in terms of kinetic equations—unless the complexity is radically trimmed. Yet, if combinatorial complexity is key to the system's behavior, eliminating it will prevent, not facilitate, understanding. A more adequate representation of a combinatorial system is afforded by a graph-based framework of rewrite rules where each rule specifies only the information that an interaction mechanism depends on. Unlike reactions, rules deal with patterns, i.e. sets of molecular species, rather than molecular species themselves. Although the stochastic dynamics induced by a set of rules on a mixture of molecules can be simulated, we aim at capturing the system's average or deterministic behavior. However, expansion of the rules into differential equations at the level of molecular species is not only impractical, but conceptually indefensible. If rules describe patterns of interaction, fully-defined molecular species are unlikely to constitute appropriate units of dynamics. Rather, we must seek aggregated variables reflective of the causal structure laid down by the mechanisms expressed by the rules. We call these variables “fragments” and the process of identifying them “fragmentation”. Ideally, fragments are aspects of the system's microscopic population that the set of rules can actually distinguish on average; in practice, it may only be feasible to identify an approximation to this. Most importantly, fragments are self-consistent descriptors of system dynamics in that their time evolution is governed by a closed system of kinetic equations. Taken together, fragments are endogenous distinctions that matter for the dynamics of a system, and this warrants viewing them as the carriers of information. Although fragments can be thought of as multi-sets of molecular species (an extensional view), their self-consistency suggests treating them as autonomous aspects cut off from their microscopic anchors (an intensional view). Fragmentation is a seeded process and plays out depending on the seed provided, which leaves open the possibility that different inputs cause distinct fragmentations, in effect altering the set of information carriers that govern the behavior of a system, even though nothing has changed in its microscopic constitution. We provide a mathematical specification of fragments, but not an algorithmic implementation. We have done so elsewhere in rather technical terms with specific biases that, although effective, were lacking an embed- ding into a more general conceptual framework. Our main objective in this contribution is to provide that framework

Totality in arena games

We tackle the problem of preservation of totality by composition in arena games. We first explain how this problem reduces to a finiteness theorem on what we call pointer structures, similar to the parity pointer functions of Harmer, Hyland & Melliès and the interaction sequences of Coquand. We discuss how this theorem relates to normalization of linear head reduction in simply-typed λ-calculus, leading us to a semantic realizability proof à la Kleene of our theorem. We then present another proof of a more combinatorial nature. Finally, we discuss the exact class of strategies to which our theorems apply