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

Background: 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. Material and Methods: 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. Results: 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. Conclusions: 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.