Machine learning insights into calcium phosphate nucleation and aggregation

In this study, we utilized machine learning interatomic potentials (MLIPs) to investigate the nucleation mechanisms of calcium phosphate, a critical component of bone and teeth. Our analysis encompassed the process from pre-nucleation stage to the growth of amorphous calcium phosphate (ACP) in solution. We observed fluctuations in free calcium ion concentration and tracked the formation of uniform clusters in the early nucleation phases, confirming the existence of pre-nucleation clusters (PNCs). The PNCs are characterized by the composition Ca2[(PO4)1.6(HPO4)(H2PO4)0.4] and predominantly exhibit a triangular structure formed by phosphate groups. This structure is not only the core of the short-range ordered units in ACP but also exhibits the structural characteristics of the fundamental building blocks of HAP. Importantly, these clusters interact dynamically with water molecules through hydrogen bonding and proton exchange, which is essential for their stability and growth. The gradual growth of these clusters occurs via ion attachment and cluster adsorption. This work provides insights into calcium phosphate mineralization, with implications for materials science and biomedical engineering, particularly in biomaterial synthesis. The application of MLIPs demonstrates a high-accuracy, efficient approach for simulating complex systems may advance our understanding of crystallization and biomineralization processes. Statement of significance: Calcium phosphate nucleation is crucial in biological mineralization and the synthesis of biomaterials, serving as a key aspect in the design of hydroxyapatite (HAP)-based biomaterials. However, the mechanisms of early nucleation remain unclear due to the complex ion-water interactions, which lead to rapid nucleation rates and small cluster sizes. This study combines MLIP with MD simulations to explore the nucleation process of calcium phosphate, revealing the transition from pre-nucleation to the formation of ACP. It clarifies the relationship between PNCs and the crystalline structure of HAP. This work addresses the knowledge gap regarding early-stage calcium phosphate nucleation and highlights the potential of MLIP in simulating complex ionic solutions, laying a solid foundation for AI-guided research in biological and biomedical materials.