An Empirical Biasing Force Constant to Minimize Overfitting in Cryo-EM Flexible Fitting Refinement

Reliable modeling of protein structures from a cryo-EM density map is one of the central issues in structural biology. Typically, the constructed model is refined using a flexible fitting method combined with molecular dynamics, where a biasing potential is introduced to guide the protein structure toward the density map. However, the appropriate force constant for the biasing potential is generally unknown a priori. Here, we propose an empirical force constant that enables flexible fitting refinement with minimal overfitting. The rule is derived from systematic flexible fitting calculations performed on 29 selected systems (map resolution = 3.0-6.8 Å) using a range of force constants from weak to strong values. The refined structures are evaluated based on the MolProbity score and secondary-structure-forming tendencies. Our analysis shows that in most systems, the MolProbity score increases monotonically as the force constant increases. In addition, α-helix and β-strand tend to collapse beyond a certain force constant depending on the system size or number of fitting atoms (N_atom). Based on these findings, we propose that a suitable choice for the biasing force constant in the cross-correlation coefficient-based flexible fitting refinement is 3N_atom kcal/mol. This provides a practical guideline for an initial selection of the force constant, aiding in the search for a more suitable value and serving as a useful default parameter in flexible fitting protocols to achieve reliable models with minimal overfitting.