"Computational Analysis of Phosphorylated Tau Protein Surfaces Using Geometric Descriptors: Reconstruction Strategies and Pattern Discovery in Molecular Dynamics Simulations"

Tau protein plays an essential role in maintaining the stability of neuronal microtubules. However, when excessively phosphorylated, particularly at serine and threonine residues, it is believed to contribute significantly to the development of Alzheimer’s disease. These post-translational modifications can lead to substantial changes in the three-dimensional conformation and physicochemical behavior of the protein. The present study investigates the hypothesis that different phosphorylation states of Tau generate distinct three-dimensional surface patterns, which can be identified and characterized through geometric descriptors and unsupervised clustering techniques. Two independent datasets were analyzed. The first dataset, used primarily for exploratory analysis, included nine progressively phosphorylated states of Tau protein, with modifications limited to serine residues. These configurations were generated through molecular dynamics (MD) simulations. The output structures were treated as point clouds and subsequently converted into triangulated 3D meshes using a variety of surface reconstruction techniques. After qualitative and quantitative comparisons, the Screened Poisson surface reconstruction method was selected due to its ability to preserve local surface detail while maintaining global structural coherence. Parameters for the reconstruction algorithm were tuned accordingly. Following mesh generation, geometric descriptors were extracted using a combination of MATLAB and Python-based tools. The focus of the analysis was to determine whether recurring surface patterns or geometric signals correlated with the level of phosphorylation. The second dataset was designed to better approximate biologically realistic conditions. It consisted of short frame sequences of Tau phosphorylated in vitro by specific kinases, each targeting different clusters of serine and threonine residues. Due to the limited number of frames available for each cluster, a more robust surface processing pipeline was implemented. In this case, mesh generation was performed using a two-pass Alpha Wrap method, chosen for its ability to handle incomplete or noisy point cloud data. Geometric descriptors with high numerical stability were prioritized, addressing convergence and noise-related issues observed during the processing of the first dataset with standard MATLAB tools. As with the exploratory dataset, the analysis remained purely structural, employing unsupervised clustering techniques to investigate potential groupings among phosphorylation states. The findings indicate that geometric descriptors, when carefully selected and interpreted, can provide valuable insights into protein surface morphology, even in the absence of supervised learning. This work represents a foundational step toward the use of geometric analysis and unsupervised machine learning techniques to explore the structural behavior of intrinsically disordered proteins under pathological conditions. It also sets the stage for future integration with more complex biological datasets and supervised learning approaches for predictive modeling.