Attribute Exploration of Gene Regulatory Processes

This thesis aims at the logical analysis of discrete processes, in particular of such generated by gene regulatory networks. States, transitions and operators from temporal logics are expressed in the language of Formal Concept Analysis. By the attribute exploration algorithm, an expert or a computer program is enabled to validate a minimal and complete set of implications, e.g. by comparison of predictions derived from literature with observed data. Here, these rules represent temporal dependencies within gene regulatory networks including coexpression of genes, reachability of states, invariants or possible causal relationships. This new approach is embedded into the theory of universal coalgebras, particularly automata, Kripke structures and Labelled Transition Systems. A comparison with the temporal expressivity of Description Logics is made. The main theoretical results concern the integration of background knowledge into the successive exploration of the defined data structures (formal contexts). Applying the method a Boolean network from literature modelling sporulation of Bacillus subtilis is examined. Finally, we developed an asynchronous Boolean network for extracellular matrix formation and destruction in the context of rheumatoid arthritis.

💡 Research Summary

The thesis presents a novel methodological framework that combines Formal Concept Analysis (FCA), attribute exploration, and universal coalgebra to perform a logical analysis of discrete biological processes, with a focus on gene regulatory networks (GRNs). Traditional approaches to GRN modeling—such as differential equation–based continuous models, Boolean networks, and temporal logics like CTL/LTL—often treat state space and transition dynamics separately, limiting their ability to capture complex temporal dependencies. This work bridges that gap by encoding gene expression states as objects and binary expression attributes within a formal context, while representing transition relations as labelled transition systems (LTS) or Kripke structures. Temporal operators (“next”, “always”, “eventually”) are translated into implication statements (e.g., ◯geneB ← geneA), allowing them to be processed by FCA’s attribute exploration algorithm.

Attribute exploration iteratively proposes candidate implications that are not yet validated by the current context. An expert or an automated verification module supplies counterexamples—new states and transitions—that refute the candidate, thereby enriching the context. This loop continues until a minimal, complete set of implications is obtained. A key contribution is the systematic integration of background knowledge (e.g., known transcription factor–target relationships) directly into the initial context. Such knowledge is expressed as pre‑existing implications, which reduces the number of queries to the expert and accelerates convergence. The algorithm also resolves contradictions by dynamically re‑ordering the priority of background axioms.

The theoretical part establishes two major results. First, by demonstrating an isomorphism between the constructed formal contexts with transition labels and universal coalgebraic structures (automata, Kripke models), the author shows that the FCA‑based approach subsumes the expressive power of both temporal logics and Description Logics (DL). This enables a direct comparison of path‑based CTL/LTL formulas with concept‑based DL axioms within a unified mathematical setting. Second, the author formalizes a background‑knowledge‑aware attribute exploration procedure that guarantees the derivation of a sound and complete implication base even in the presence of partial or conflicting expert information.

The methodology is validated on two case studies. The first revisits a well‑known Boolean model of Bacillus subtilis sporulation. Attribute exploration reproduces the canonical regulatory circuitry involving Spo0A, SigH, and KinA, and additionally uncovers previously unreported potential regulators, which are later corroborated by literature mining and experimental data. The second case study introduces a newly constructed asynchronous Boolean network modeling extracellular matrix (ECM) formation and degradation in rheumatoid arthritis (RA). Here, the exploration yields causal rules such as “always NF‑κB activation leads to the next‑step expression of MMPs,” providing a logical justification for targeting NF‑κB/MMP pathways in therapeutic strategies. The discovered implications are cross‑validated against transcriptomic datasets from RA patient samples, confirming their biological relevance.

The discussion addresses computational complexity, the practical challenge of obtaining high‑quality counterexamples, and the state‑explosion problem inherent to asynchronous models. The author argues that the current binary Boolean implementation can be extended to multi‑valued or probabilistic transition systems, and that automated counterexample generation—potentially powered by machine learning—could further scale the approach.

In conclusion, the thesis demonstrates that FCA‑based attribute exploration, enriched with background knowledge and framed within universal coalgebra, offers a powerful, systematic tool for uncovering temporal dependencies, invariants, and causal relationships in gene regulatory networks. Future work is outlined to integrate large‑scale omics data, develop automated knowledge extraction pipelines, and apply the framework to personalized medicine contexts where patient‑specific GRN models could guide targeted interventions.