Reaction systems were originally inspired by biological regulation and have been successfully applied to a variety of biological processes, ranging from gene regulation to cellular stress responses and molecular self-assembly.

T-Cell Receptor Signalling Network

T-cell receptor (TCR) signalling is a central process in the activation of the adaptive immune response. Reaction systems were used to model the protein-interaction network governing T-cell activation and to analyse causal dependencies within the network. Using slicing techniques and dependency analysis, the study identified which molecular interactions are responsible for specific signalling outcomes and how inhibitory effects propagate through the system. This case study demonstrates the use of reaction systems not only for modelling biological networks but also for explaining their behaviour and identifying the mechanisms underlying observed cellular responses.

Reference: Brodo, L., Bruni, R., Falaschi, M., Gori, R., & Milazzo, P. (2025). Slicing analyses for negative dependencies in reaction systems modeling gene regulatory networks. Natural Computing, 24(4), 1045–1074. https://doi.org/10.1007/s11047-025-10046-5

Distributed Predator–Prey Ecosystems

The Lotka–Volterra predator–prey model is one of the classical models of population dynamics in ecology. In this case study, reaction systems were used to develop the first distributed reaction-system model of interacting predator–prey ecosystems. Each ecosystem evolves according to its own local predator–prey dynamics, while communication between ecosystems allows populations to influence one another through different network topologies and communication policies. The study demonstrated how distributed reaction systems can model synchronization, communication, and emergent behaviour in networks of interacting ecological systems. 

Reference: Brodo, L., Bruni, R., Falaschi, M., & Petre, I. (2025). Simulation and analysis of distributed reaction systems. IEEE Access, 13, 119709–119725. https://doi.org/10.1109/ACCESS.2025.3586078

Oncogenic Signalling and Cancer Proliferation

This case study introduced a reaction-system model of oncogenic signalling based on a Boolean model of breast-cancer-related signalling pathways. The model captures the interactions between the RTK, MAPK, PI3K, AKT, mTORC1, and cell-cycle pathways, including feedback loops and cross-talk mechanisms. It was developed as a running example for studying controllability in reaction systems and demonstrates how external interventions can drive a system between proliferative, non-proliferative, and uncontrolled-proliferation states. The work introduced one of the first detailed cancer-signalling models formulated within the reaction-system framework. 

Reference: Ivanov, S., & Petre, I. (2020). Controllability of reaction systems. Journal of Membrane Computing, 2(4), 290–302. https://doi.org/10.1007/s41965-020-00055-x

Yeast Cell Cycle Regulatory Network

The cell cycle is one of the most fundamental regulatory processes in living organisms. In this case study, a well-known Boolean-network model of the budding yeast cell cycle was translated into a reaction system, enabling simulation and causal analysis within the reaction-system framework. The study demonstrated how reaction systems can model complex gene-regulatory dynamics and support investigations of dependencies among regulatory genes. 

Reference: Barbuti, R., Bove, P., Gori, R., Levi, F., & Milazzo, P. (2018). Simulating gene regulatory networks using reaction systems. In Proceedings of CS&P 2018, CEUR Workshop Proceedings, 2240. CEUR-WS.org. https://ceur-ws.org/Vol-2240/paper11.pdf

Self-Assembly of Intermediate Filaments

Intermediate filaments are essential components of the cellular cytoskeleton. This case study used reaction systems to model the self-assembly process of vimentin filaments, showing how complex biological structures can emerge from simple local interactions. The work demonstrated the suitability of reaction systems for representing biological assembly processes and structural organization within cells.

Reference: Azimi, S., Panchal, C., Czeizler, E., & Petre, I. (2015). Reaction systems models for the self-assembly of intermediate filaments. Annals of University of Bucharest, LXII(2), 9–24.

Heat Shock Response

The heat shock response is a cellular defense mechanism that protects proteins from damage caused by environmental stress. Reaction systems were used to develop a qualitative model of this process, capturing the interactions between heat shock factors, heat shock proteins, and environmental stimuli. The study demonstrated that reaction systems can reproduce key biological behaviors while relying only on facilitation and inhibition.

Reference: Azimi, S., Iancu, B., & Petre, I. (2014). Reaction system models for the heat shock response. Fundamenta Informaticae, 131(3–4), 299–312. https://doi.org/10.3233/FI-2014-1016

Lac Operon Regulation in Escherichia coli

The lac operon is one of the most extensively studied gene-regulatory systems in biology. Reaction systems were used to model how bacterial cells regulate lactose metabolism in response to environmental conditions. This example highlighted the natural ability of reaction systems to represent biological regulation through the presence and absence of molecular entities.

Reference: Corolli, L., Maj, C., Marini, F., Besozzi, D., & Mauri, G. (2012). An excursion in reaction systems: From computer science to biology. Theoretical Computer Science, 454, 95–108. https://doi.org/10.1016/j.tcs.2012.04.003

Although reaction systems were inspired by biological processes, their underlying principles have proven useful in a variety of other domains. These applications demonstrate the flexibility of the framework and its ability to model systems driven by context-dependent interactions.

Cryptographic Boolean Functions

Reaction systems have been applied to the design of cryptographic Boolean functions, fundamental building blocks of modern cryptographic systems. In this work, Boolean functions are represented as reaction systems and evolved using evolutionary optimization techniques to discover functions with strong cryptographic properties, such as high nonlinearity. The resulting framework, called EvoBRS, demonstrates that reaction systems can serve not only as modelling tools but also as an interpretable and effective representation for solving challenging combinatorial optimization problems in cryptography. 

Reference: Ascone, R., Mariot, L., Manzoni, L., & Pietropolli, G. (2025). Evolving cryptographic Boolean functions with reaction systems. In Proceedings of the Genetic and Evolutionary Computation Conference Companion, GECCO ’25 Companion, 195–198. Association for Computing Machinery. https://doi.org/10.1145/3712255.3726685

Comorbidity Treatment Strategies

This application extended reaction systems with guards and constraints to model treatment strategies for patients affected by multiple coexisting diseases. The framework was used to analyse interactions between clinical guidelines and therapies in the presence of multimorbidity. A case study involving atrial fibrillation and hypertension demonstrated how reaction systems can support reasoning about treatment plans, adverse interactions, and healthcare decision making in complex clinical scenarios.

Reference: Bowles, J., Brodo, L., Bruni, R., Falaschi, M., Gori, R., & Milazzo, P. (2024). Enhancing reaction systems with guards for analysing comorbidity treatment strategies. In R. Gori, P. Milazzo, & M. Tribastone (Eds.), Computational Methods in Systems Biology, Lecture Notes in Computer Science, 14971, 27–44. Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-71671-3_3

Transactions and Contracts

Reaction systems have been applied to the modelling of transactions and contracts between interacting parties. In this framework, contractual clauses, obligations, permissions, and actions are represented through reactions whose execution depends on the availability or absence of specific conditions. The resulting models make it possible to analyse contract execution, verify compliance with contractual requirements, and reason about the behaviour of interacting parties in a formally rigorous manner. This work demonstrates how the reaction-system paradigm can be extended beyond natural systems to support the modelling and analysis of complex socio-technical processes. 

Reference: Bottoni, P., & Labella, A. (2021). Transactions and contracts based on reaction systems. Theoretical Computer Science, 881, 25–61. https://doi.org/10.1016/j.tcs.2021.07.012

Tower of Hanoi

The Tower of Hanoi puzzle provided one of the earliest demonstrations of the expressive power of reaction systems outside biology. The puzzle was encoded as a reaction system in which legal moves correspond to reactions and the state of the puzzle is represented through the presence and absence of entities. This case study showed that reaction systems can model discrete algorithmic processes and combinatorial problems using the same facilitation and inhibition principles originally inspired by biological regulation. 

Reference: Corolli, L., Maj, C., Marini, F., Besozzi, D., & Mauri, G. (2012). An excursion in reaction systems: From computer science to biology. Theoretical Computer Science, 454, 95–108. https://doi.org/10.1016/j.tcs.2012.04.003

Binary Counter

One of the earliest examples used to demonstrate the computational capabilities of reaction systems was a binary counter. In this model, the presence and absence of entities encode the bits of a binary number, while reactions implement the increment and carry operations required for counting. The example showed that reaction systems can serve not only as models of biochemical interactions but also as a programming formalism capable of implementing non-trivial computational processes.

Reference: Ehrenfeucht, A., & Rozenberg, G. (2007). Reaction systems. Fundamenta Informaticae, 75(1–4), 263–280. https://doi.org/10.3233/FUN-2007-751-415