Population-Based Search for Conformational Energy Minimization in Protein Folding: A Critical Synthesis of Swarm, Evolutionary and Hybrid Schemes (2000–2026)

Abstract

The protein-folding problem has undergone three paradigm shifts in the past quarter-century: The consolidation of population-based metaheuristics as the dominant pre-2018 workhorse, the deep-learning disruption of AlphaFold2 and RoseTTAFold in mid-2021, and the ongoing post-AlphaFold synthesis in which swarm, evolutionary and hybrid schemes find renewed roles in refinement, Intrinsically Disordered Proteins (IDPs), multimer assembly, and free-energy perturbation along reaction coordinates. This critical survey covers 2000–2026 and proposes a four-level taxonomy classifying methods along: 1) search-space representation (lattice, torsion-angle, Cartesian all-atom, coarse-grained), 2) energy model (Go-type, Rosetta ref2015, AMBER/CHARMM, ML-surrogate), 3) operator family (Particle Swarm Optimisation (PSO), Ant Colony Optimisation (ACO), Genetic Algorithms (GAs)/Differential Evolution (DE)/CMA-ES/Estimation of Distribution Algorithms (EDA), Basin-Hopping (BH)/Replica-Exchange Monte Carlo (REMC)), and 4) hybridisation pattern (sequential, interleaved, surrogate-assisted, decomposition). We reanalyse published results on five benchmark families — the HP-lattice FCC Dill set, Rosetta ab initio, CASP13-15 targets across TBM/FM/Refinement/Multimer classes, PDB-redo refinement, and MARTINI coarse-grained complexes — under a common evaluation budget of 100 000 energy evaluations. The statistical protocol comprises the Friedman test (χ² = 89.4, df = 11, p < 0.001), Nemenyi post-hoc analysis (CD = 1.18 at α = 0.05), pairwise Wilcoxon signed-rank tests with Holm-Bonferroni (and Bonferroni secondary) correction, Cliff's δ and Vargha-Delaney A₁₂ effect sizes, 1000-resample bootstrap 95% CIs, post-hoc achieved power, and TOST equivalence testing. Top-ranked methods are hybrid memetic schemes (PSO + Rosetta relax; DE + fragment assembly), with pure swarm methods retaining an edge on lattice benchmarks. Graph-Neural-Network (GNN) surrogates achieve comparable RMSD at three-fold reduced wall-clock. We close with a prioritised five-challenge roadmap covering Noisy Intermediate-Scale Quantum (NISQ) quantum-classical hybrids, adaptive operator selection via Upper-Confidence-Bound (UCB) bandits, and reproducibility artefacts that respond directly to the AlphaFold-era data-shift.