Hyper-Efficient Stochastic Polymer Folding Prediction via Adaptive Markov Chain Monte Carlo (AS-MCMC)

**Abstract:** Predicting protein folding remains a grand challenge in computational biology, crucial for drug discovery and understanding disease mechanisms. Current Monte Carlo (MC) methods, while powerful, suffer from slow convergence and scalability issues, particularly for larger polypeptides. This paper introduces Adaptive Stochastic Polymer Folding Prediction via Adaptive Markov Chain Monte Carlo (AS-MCMC), a novel approach optimizing the Metropolis-Hastings algorithm by dynamically adjusting proposal distributions based on real-time conformational landscape analysis. This enhances sampling efficiency, accelerates convergence, and improves the accuracy of protein folding predictions, demonstrably surpassing traditional MCMC methods in simulations of peptides ranging from 100-500 amino acids. The framework is immediately applicable for accelerating drug development pipelines and gaining deeper insights into protein structure-function relationships.