Direct Phasing of Protein Crystals with Hybrid Difference Map Algorithms.

Direct methods for solving protein crystal structures from X-ray diffraction data provide an essential approach for validating predicted models while avoiding external model bias. Nevertheless, traditional iterative projection algorithms, including the widely used Difference Map (DiffMap), are often limited by modest phase retrieval success rates. To address this limitation, we introduce a novel Hybrid Difference Map (HDM) algorithm that synergistically combines the strengths of DiffMap and the Hybrid Input-Output (HIO) method through six distinct iterative update rules. HDM retains an optimized DiffMap-style relaxation term for fine-grained density modulation in protein regions while adopting HIO's efficient negative feedback mechanism for enforcing the solvent flatness constraint. Using the transmembrane photosynthetic reaction center 2uxj as a test case, the first HDM formula, HDM-f1, successfully recovered an atomic-resolution structure directly from random phases under a conventional full-resolution phasing scheme, demonstrating the robust phasing capability of the approach. Systematic evaluation across 22 protein crystal structures (resolution 1.5-3.0 Å, solvent content ≥ 60%) revealed that all six HDM variants outperformed DiffMap, achieving 1.8-3.5× higher success rates (average 2.8×), performing on par with or exceeding HIO under a conventional phasing scheme. Further performance gains were achieved by integrating HDM with advanced strategies: resolution weighting and a genetic algorithm-based evolutionary scheme. The genetic evolution strategy boosted the success rate to nearly 100%, halved the median number of iterations required for convergence, and reduced the final phase error to approximately 35° on average across test structures through averaging of multiple solutions. The resulting electron density maps were of high interpretability, enabling automated model building that produced structures with a backbone RMSD of less than 0.5 Å when compared to their PDB-deposited counterparts. Collectively, the HDM algorithm suite offers a robust, efficient, and adaptable framework for direct phasing, particularly for challenging cases where conventional methods struggle. Our implementation supports all space groups providing an accessible tool for the broader structural biology community.