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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.

📑 Overview

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).

📓 Contents

  • 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

🛠️ Requirements

Developed and tested with Python 3.10.

pip install numpy scipy matplotlib jupyter pandas

📊 Key Results

  • 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.

📘 Citation

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

📬 Contact

For questions or collaborations:

Permanent link to this notebook: https://github.com/Moemenhussein11/P.gingivalis-Colonization