Ecological and stochastic determinants of the growth and persistence of the oral pathogen Porphyromonas gingivalis
This repository contains the Jupyter Notebook(s) used in the study:
Ecological and stochastic determinants of the growth and persistence of the oral pathogen Porphyromonas gingivalis. npj Syst Biol Appl (2026). https://doi.org/10.1038/s41540-026-00662-x
By: Moemen Hussein, Arnab Barua, Mohammad Qasaimeh, Matthew Smardz, Patricia I. Diaz & Haralampos Hatzikirou
The work integrates quantitative growth experiments with deterministic and stochastic mathematical modeling to explain how Allee-type density dependence, facilitation by Veillonella parvula, and microenvironmental noise jointly enable under-threshold survival and, ultimately, dysbiotic configurations of the oral microbiome.
Periodontitis arises from a shift from a health-associated, commensal-dominated biofilm to a pathogen-enriched, inflammatory state. A key paradox is that P. gingivalis shows a clear Allee effect, it should go extinct below a quorum, yet it is repeatedly detected at low abundance in vivo. Our analysis shows that this paradox is resolved once we incorporate (i) Vp-mediated lowering of the Allee threshold and (ii) stochastic fluctuations that enable under-threshold survival.
This repository hosts code that reproduces the main modeling components in the manuscript:
- Deterministic cubic Allee-effect model fitted to Pg growth data to identify the critical density.
- Vp-spent-medium / facilitation module to re-fit the Allee threshold under metabolite supplementation.
- Stochastic extension + Fokker–Planck analysis to show noise-induced persistence and the stationary distribution observed in 32-day, subcritical Pg cultures.
- Two-species, game-theoretic / replicator model to map Pg–Vp interactions to extinction, coexistence, dominance, or bistability, constrained by the co-culture experiments (Day 0 vs Day 9 Vp addition).
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Pg_colonization_model.ipynb— main notebook implementing the pipeline:- Fit of the cubic Allee-effect growth model to single-species Pg data
- Re-fitting under V. parvula spent medium to quantify the shift in the Allee threshold
- Stochastic simulations (Euler–Maruyama) reproducing the heterogeneous 32-day outcomes
- Fokker–Planck–based stationary distribution to compare with replicate experiments
- Replicator-dynamics exploration of the (β, γ) plane for Pg–Vp interactions
Developed and tested with Python 3.10.
pip install numpy scipy matplotlib jupyter pandas- Quantified Allee threshold for P. gingivalis from fitted cubic model, showing negative growth below the quorum.
- Facilitation by V. parvula: spent/conditioned medium lowers the effective Allee threshold, enabling subcritical inocula to persist.
- Noise-enabled persistence: multiplicative microenvironmental noise shifts the effective saddle node and produces a truncated, power-law-like stationary distribution matching 32-day replicate cultures.
- Experiment-constrained phase space: because Vp saturates to (near) carrying capacity in co-culture, the reachable endpoints during the experimental horizon are effectively “Pg extinction” or “Pg–Vp coexistence,” which pins the relevant region of the (β, γ) plane.
If you use this code or analysis, please cite:
Hussein, M., Barua, A., Qasaimeh, M. et al. Ecological and stochastic determinants of the growth and persistence of the oral pathogen Porphyromonas gingivalis. npj Syst Biol Appl (2026). https://doi.org/10.1038/s41540-026-00662-x
For questions or collaborations:
- Corresponding author: haralampos.hatzikirou@ku.ac.ae
Permanent link to this notebook: https://github.com/Moemenhussein11/P.gingivalis-Colonization