Weak Independence and Coupled Parallelism in Biological Petri Nets
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912775987527680 |
|---|---|
| author | Simao, Eugenio |
| author_facet | Simao, Eugenio |
| contents | Motivation: Biological Petri Nets (Bio-PNs) model biochemical pathways where multiple reactions simultaneously affect shared metabolites through convergent production or regulatory coupling. However, classical Petri net independence theory requires transitions to share no places -- a constraint that fails to capture biological reality. This mismatch prevents parallel simulation and incorrectly flags biologically valid models as structurally problematic.
Results: To resolve this fundamental limitation, we introduce weak independence -- a novel formalization distinguishing resource conflicts from biological coupling. Building on this theory, we extend the Bio-PN definition from a classical 5-tuple to a 12-tuple by adding regulatory structure, environmental exchange classification, dependency taxonomy, heterogeneous transition types, and biochemical formula tracking. This extended formalism enables systematic classification of three place-sharing modes: competitive (conflict), convergent (superposition), and regulatory (read-only). Validating our approach on 100 diverse BioModels (1,775 species, 2,234 reactions across metabolism, signaling, and gene regulation), we find that 96.93% of transition pairs exhibit weak independence -- confirming that biological networks inherently favor cooperation over competition. Our SHYpn implementation demonstrates the practical impact, achieving up to 2.6x speedup on 30% of evaluated models.
Availability and Implementation: Open-source at https://github.com/simao-eugenio/shypn (MIT License). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak Independence and Coupled Parallelism in Biological Petri Nets Simao, Eugenio Molecular Networks Quantitative Methods Motivation: Biological Petri Nets (Bio-PNs) model biochemical pathways where multiple reactions simultaneously affect shared metabolites through convergent production or regulatory coupling. However, classical Petri net independence theory requires transitions to share no places -- a constraint that fails to capture biological reality. This mismatch prevents parallel simulation and incorrectly flags biologically valid models as structurally problematic. Results: To resolve this fundamental limitation, we introduce weak independence -- a novel formalization distinguishing resource conflicts from biological coupling. Building on this theory, we extend the Bio-PN definition from a classical 5-tuple to a 12-tuple by adding regulatory structure, environmental exchange classification, dependency taxonomy, heterogeneous transition types, and biochemical formula tracking. This extended formalism enables systematic classification of three place-sharing modes: competitive (conflict), convergent (superposition), and regulatory (read-only). Validating our approach on 100 diverse BioModels (1,775 species, 2,234 reactions across metabolism, signaling, and gene regulation), we find that 96.93% of transition pairs exhibit weak independence -- confirming that biological networks inherently favor cooperation over competition. Our SHYpn implementation demonstrates the practical impact, achieving up to 2.6x speedup on 30% of evaluated models. Availability and Implementation: Open-source at https://github.com/simao-eugenio/shypn (MIT License). |
| title | Weak Independence and Coupled Parallelism in Biological Petri Nets |
| topic | Molecular Networks Quantitative Methods |
| url | https://arxiv.org/abs/2512.17106 |