Rule-based modeling

• Faeder et al. "Rule-Based Modeling of Biochemical Networks," Complexity (2005)
• Hlavacek et al. "Rules for Modeling Signal-Transduction Systems," Science’s STKE (2006)
• Faeder, Blinov, Hlavacek. "Rule-based modeling of biochemical systems with BioNetGen," Systems Biology (2009)

Early work on rule-based modeling pointed out the need for a formal language for systems biology and simulating networks where combinations of binding and modification states lead to combinatorial explosion in traditional models.

The Kappa language

• Danos, Laneve. "Formal Molecular Biology," Theor. Comput. Sci. (2004)
• Danos et al. "Rule-Based Modelling and Model Perturbation," TCSB (2009)
• Boutillier, Cristescu, Feret. "Counters in Kappa: Semantics, Simulation, and Static Analysis," ESOP (2019)
• Boutillier. "The Kappa Simulator Made Interactive," CMSB (2019)
• Behr et al. "A High-Level Language for Rule-Based Modelling," PLOS ONE (2015)

Kappa is a formally defined language that has been extended in various ways, including to implement counters, user-initiated interventions during simulation, and higher-level rule-writing.

Modeling biological systems

• Danos et al. "Rule-Based Modelling of Cellular Signalling," CONCUR (2007)
• Wilson-Kanamori et al. "Kappa Rule-Based Modelling in Synthetic Biology," CMSB (2014)
• Bouguéon et al. "The Rule-based Model Approach: A Kappa Model for Hepatic Stellate Cells Activation by TGFB1," in Systems Biology Modelling and Analysis: Formal Bioinformatics Methods and Tools (2022)
• Boujakan et al. "A Rule-Based Modeling Approach for Studying Animal Thermotaxis-Driven Aggregation in Juvenile Honeybees," CMSB (2025)

Kappa has been used to model a variety of biological systems including synthetic gene circuits, cell signalling, and animal behavior.

Static and causal analysis

• Boutillier et al. "KaSa: A Static Analyzer for Kappa," CMSB (2018)
• Danos V et al. "Graphs, Rewriting and Causality in Rule-based Models" (2011)
• Laurent, Yang, Fontana. "Counterfactual Resimulation for Causal Analysis of Rule-Based Models," IJCAI (2018)

Theoretical work on Kappa has included causal analysis of simulations, and static analysis of rulesets to extract information about the behavior of systems prior to any simulation.

Tools

• Boutillier et al. "The Kappa Platform for Rule-Based Modeling," Bioinformatics (2018)
• Forbes et al. "Dynamic Influence Networks for Rule-based Models," IEEE Trans. Vis. Comput. Graph. (2017)
• Sorokin, Sorokina, Armstrong. "RKappa: Statistical Sampling Suite for Kappa Models," HSB (2014)
• Camporesi, Feret, Lý. "KADE: A Tool to Compile Kappa Rules into (Reduced) ODE Models," CMSB (2017)

Beyond stochastic simulation, tools have been developed for static analysis, causal story extraction, visualization, browser-based model development, and translation into differential equations.