<![CDATA[Modelling the evolution of biological sequences under temporal and probabilistic constraints remains a complex computational challenge. This study investigates longitudinal deep learning for probabilistic modelling of mutation patterns in the SARS-CoV-2 Spike Protein. A stacked Long Short-Term Memory (LSTM) network is trained on temporally ordered amino acid sequences to estimate residue-level substitution probabilities and rank plausible future mutations. Unlike deterministic classification approaches, the proposed framework treats mutation prediction as a probabilistic ranking task, accounting for the inherent uncertainty of viral evolution. The model is evaluated using metrics suitable for imbalanced sequence data, including Top-K accuracy, precision, recall, F1-score, and ROC-AUC. Results indicate strong ranking performance, with Top-3 accuracy of 94.6% and ROC-AUC of 0.91. In comparison, the overall accuracy (93.1%) is interpreted cautiously, given the dominance of conserved residues. Error analysis shows that difficult predictions are concentrated in low-frequency, rapidly evolving residue positions. A comparison with a frequency-based baseline demonstrates that the LSTM captures temporal dependencies beyond static substitution patterns. Predicted mutation distributions exhibit a structured alignment with known functional regions of the Spike Protein, as supported by the established literature, providing qualitative biological validation. This study contributes a temporally structured and probabilistic framework for mutation modelling, emphasising ranking-based evaluation and biologically contextualised interpretation. The findings demonstrate the feasibility of probabilistic mutation forecasting under controlled experimental conditions and provide a methodological foundation for future research on AI-assisted genomic surveillance.]]>
