Sparsity‐weighted outlier FLOODing (OFLOOD) method: Efficient rare event sampling method using sparsity of distribution

Abstract

As an extension of the Outlier FLOODing (OFLOOD) method [Harada et al., J. Comput. Chem. 2015, 36, 763], the sparsity of the outliers defined by a hierarchical clustering algorithm, FlexDice, was considered to achieve an efficient conformational search as sparsity-weighted "OFLOOD." In OFLOOD, FlexDice detects areas of sparse distribution as outliers. The outliers are regarded as candidates that have high potential to promote conformational transitions and are employed as initial structures for conformational resampling by restarting molecular dynamics simulations. When detecting outliers, FlexDice defines a rank in the hierarchy for each outlier, which relates to sparsity in the distribution. In this study, we define a lower rank (first ranked), a medium rank (second ranked), and the highest rank (third ranked) outliers, respectively. For instance, the first-ranked outliers are located in a given conformational space away from the clusters (highly sparse distribution), whereas those with the third-ranked outliers are nearby the clusters (a moderately sparse distribution). To achieve the conformational search efficiently, resampling from the outliers with a given rank is performed. As demonstrations, this method was applied to several model systems: Alanine dipeptide, Met-enkephalin, Trp-cage, T4 lysozyme, and glutamine binding protein. In each demonstration, the present method successfully reproduced transitions among metastable states. In particular, the first-ranked OFLOOD highly accelerated the exploration of conformational space by expanding the edges. In contrast, the third-ranked OFLOOD reproduced local transitions among neighboring metastable states intensively. For quantitatively evaluations of sampled snapshots, free energy calculations were performed with a combination of umbrella samplings, providing rigorous landscapes of the biomolecules.

Structural dissimilarity sampling with dynamically self-guiding selection

“…S2 and S4 in Supporting Information). In OFLOOD, initial structures (outliers) always located at edges of conformational distributions in our previous studies …”

“…Judging from the assessments for the different numbers of initial structures, one might need to confirm whether the total number of initial structures is sufficient for reproducing structural transitions of a given protein with reasonable computational costs. Although it is desirable to independently perform trials with different numbers of initial structures and assess their conformational sampling efficiencies, as far as we have experienced, N initial should be a set of no more than 100 for the actual applications of relevant protein dynamics including protein folding, large‐amplitude motions, and induced fit processes …”

Temperature–pressure shuffling outlier flooding method enhances the conformational sampling of proteins

“…As one of the representative enhanced conformational sampling techniques developed by us, outlier flooding method (OFLOOD), has been proposed as a rare event sampling technique by combining a physical science‐based method with an information science‐based method, that is, MD simulation with a hierarchical clustering method. Figure shows the concept of OFLOOD.…”

“…Although the detailed dynamics cannot be pursued, free energy landscapes (FEL) can be estimated by the umbrella sampling or a Markov state model (MSM) once the transition pathways among (meta-) stable structures are obtained. [23,24] As one of the representative enhanced conformational sampling techniques developed by us, outlier flooding method (OFLOOD), [30][31][32][33] has been proposed as a rare event sampling technique by combining a physical science-based method with an information science-based method, that is, MD simulation with a hierarchical clustering method. Figure 1 shows the concept of OFLOOD.…”

Common folding processes of mini-proteins: Partial formations of secondary structures initiate the immediate protein folding

“…Shaw et al have reported that the folding processes of these mini‐proteins might be relatively complicated and different from a simple two‐state folding between unfolded and their native states, indicating that there might exist multiple folding pathways. Actually, our previous studies have also reported a possibility that the mini‐proteins such as Trp‐cage and Villin have multiple folding routes, and there exist intermediate states during the folding pathways. Herein, it seems that the partial formations of secondary structures in the early process might play a major role in the fast‐folding of these mini‐proteins, because proteins have characteristic secondary structures as partial elements in their native structures.…”