Periodic Reporting for period 1 - RaSiR (Rule-algebraic Simple Rewriting)
Reporting period: 2017-10-01 to 2019-09-30
The central aim of the RaSiR project has been to improve upon the existing theory of rewriting systems in order to permit the development of fundamentally new approaches to algorithm design in bioinformatics. Crucially, the simulations provided by the existing rule-based modeling platforms alone are not providing sufficient information in order to understand dynamical and functional behaviors of biological systems, since the core sources of these behaviors are given by pathways and their interactions rather than individual realizations of the systems. Despite the long history of rewriting theory with over 40 years of developments, we identified certain key aspects of the theory that had previously not been considered or understood. In particular, through a close analogy to the theory of combinatorics, re-focusing the analysis of rule-based systems upon sequential compositions of rules (rather than on sequential rewriting steps) revealed a fruitful new type of mathematical structure: sequential compositions of rules have a certain associativity property, which permits to encode the non-determinism in rule compositions within a mathematical structure of so-called rule algebras.
At a fundamental level, we addressed the question of how to extrapolate from customized formulations of rewriting theories to a universal framework, accessible also to practitioners outside the bioinformatics communities. Developing this general framework permitted us to discover interesting novel application areas of rewriting theories including the stochastic dynamics of social networks, random graph models and pattern counting problems in combinatorics. Our work was motivated by the possibility of achieving a deeper understanding of the origin of functional behavior of biological systems and of their pathway dynamics, with potential applications including the discovery of potential drug targets, as well as the discovery of a variant of statistical mechanics tailor-made for the study of stochastic network models and random graphs.
Currently, extending beyond the end of the funding period, we continue our joint work together with an extended team in order to address the problem of implementing algorithms based upon the tracelet framework. We aim to extend the open-source KAPPA platform for biochemical modeling as well as the MØD platform for analysis of organo-chemical reaction systems with modules that permit to perform tracelet-based pathway dynamics analysis tasks, as well as statically generating pathway data directly from the specification of the reaction systems.