# A scoping review of mathematical modeling techniques for gingival keratinization: A framework for periodontal research

## TL;DR

This paper reviews mathematical models for studying how gums protect against stress and disease, comparing their strengths for periodontal research.

## Contribution

A comparative framework for selecting mathematical models in periodontal research based on biological and computational criteria.

## Key findings

- Agent-Based Models (ABMs) best simulate spatial organization and mechanical stress responses in gingival keratinization.
- Gene Regulatory Networks (GRNs) excel in modeling gene expression, while ODEs are better for temporal dynamics.
- ABMs provide the highest perturbation coverage for inflammation and mechanical stress simulations.

## Abstract

Gingival keratinization is a critical physiological process that protects against mechanical stress and microbial invasion. Disruptions in this process contribute to periodontal diseases, affecting over 50% of adults worldwide. Despite its clinical significance, the molecular mechanisms of gingival keratinization remain poorly understood. This scoping review evaluates three predominant mathematical modeling paradigms—Gene Regulatory Networks (GRNs0, Ordinary Differential Equations (ODEs), and Agent-Based Models (ABMs)—to establish a framework for periodontal research.

A comprehensive literature search was conducted in PubMed, Web of Science, and IEEE Xplore, identifying 42 studies for analysis. Models were assessed across six dimensions: biological scale, spatial-temporal resolution, stochasticity, computational complexity, and perturbation response. Quantitative scoring was applied to compare capabilities in gene expression, temporal dynamics, and spatial modeling. Statistical analysis included one-way ANOVA and Tukey’s HSD test.

ABMs demonstrated superior versatility (total score: 75.0%) in simulating spatial organization and mechanical stress responses, while GRNs excelled in gene expression modeling (score: 9/10) and ODEs in temporal dynamics (score: 7/10). Perturbation coverage was highest for ABMs (87.5%), particularly for inflammation and mechanical stress. GRNs and ODEs scored 62.1% and 65.2%, respectively, with strengths in genetic and population-level dynamics.

ABMs are optimal for spatial and stochastic modeling, whereas GRNs and ODEs are better suited for molecular and temporal analyses. Integrating these approaches could provide a comprehensive understanding of gingival keratinization. This review offers guidelines for model selection based on research objectives and computational resources.

Key words:Gingival keratinization, Periodontal diseases, Gene regulatory networks, Differential equations, Computational biology, Systems biology.