Probing α/β Balances in Modified Amber Force Fields from a Molecular Dynamics Study on a ββα Model Protein (1FSD)

1FSD is a 28-residue designed protein with a ${\beta}{\beta}{\alpha}$ motif. Since this protein displays most essential features of protein structures in such a small size, this model protein can be an outstanding system for evaluating the balance in the propensity of the secondary structures and the quality of all-atom protein force fields. Particularly, this protein would be difficult to fold to its correct native structure without establishing proper balances between the secondary structure elements in all-atom energy functions. In this work, a series of the recently optimized five amber protein force fields [$ff03^*$, $f99sb^*$-ildn, ff99sb-${\phi}^{\prime}$-ildn, ff99sb-nmr1-ildn, ff99sb-${\Phi}{\Psi}$(G24, CS)-ildn] were investigated for the simulations of 1FSD using a conventional molecular dynamics (MD) and a biased-exchange meta-dynamics (BEMD) methods. Among those tested force fields, we found that ff99sb-nmr1-ildn and ff99sb-${\Phi}{\Psi}$(G24, CS)-ildn are promising in that both force fields can locate the native state of 1FSD with a high accuracy (backbone rmsd ${\leq}1.7{\AA}$) in the global free energy minimum basin with a reasonable energetics conforming to a previous circular dichroism (CD) experiment. Furthermore, both force fields led to a common set of two distinct folding pathways with a heterogeneous nature of the transition state to the folding. We anticipate that these force fields are reasonably well balanced, thereby transferable to many other protein folds.