MolFoundry automates analysis of graph rules in chemistry and biology
Automating Observable Closure Analysis for Graph Transformation Models with MolFoundry
Logic in Computer ScienceDiscrete Mathematics
Summary
Tracking how molecules change and interact can be very complex because there are countless possibilities. The authors created MolFoundry, a tool that helps analyze these changes by combining rules about how molecule parts behave without listing every possible state. This method makes predictions about molecular processes, like chemical reactions, in a way that is faster and more manageable. They showed it works on several real chemical problems by generating equations that describe molecule counts over time.
What this means in practice
- •For computational chemists: Generate precise mathematical models of chemical reactions directly from graph-based molecular rules to predict molecular behavior.
- •For synthetic polymer developers: Improve understanding and prediction of polymer formation dynamics through exact analysis of copolymerization reaction rules without exhaustive simulations.
Authors
Marcel Friedrichs, Addie Jordon, Juri Kolčák, Daniel Merkle
Abstract
Graph transformations model changing systems, with applications in software, biology and chemistry, among others. We introduce MolFoundry, a graph transformation framework, and present a workflow for observable analysis that tracks the dynamics of local patterns through rule composition. Analysing rule compositions avoids the need to enumerate a potentially infinite state space. Building on rule-algebraic stochastic rewriting, MolFoundry's kernel composes rules with nested application conditions, including missing-edge constraints. Given rules, rates and query patterns, the algorithms iteratively identify auxiliary pattern counts and search for closure. Using exact counting identities supplied by graph-family backends, successful searches yield closed ordinary differential equations for average counts or, with justified individual jumps, finite event models describing joint changes and rates. We evaluate conditional composition and automated discovery of auxiliary observables against published calculations and independent rule application. Applications to aldol addition, copolymerization and chlorination show how the framework yields quantitative predictions directly from molecular graph rules.