Constructing Optimal Coarse-Grained Sites of Huge Biomolecules by Fluctuation Maximization

Abstract

Coarse-grained (CG) models are valuable tools for the study of functions of large biomolecules on large length and time scales. The definition of CG representations for huge biomolecules is always a formidable challenge. In this work, we propose a new method called fluctuation maximization coarse-graining (FM-CG) to construct the CG sites of biomolecules. The defined residual in FM-CG converges to a maximal value as the number of CG sites increases, allowing an optimal CG model to be rigorously defined on the basis of the maximum. More importantly, we developed a robust algorithm called stepwise local iterative optimization (SLIO) to accelerate the process of coarse-graining large biomolecules. By means of the efficient SLIO algorithm, the computational cost of coarse-graining large biomolecules is reduced to within the time scale of seconds, which is far lower than that of conventional simulated annealing. The coarse-graining of two huge systems, chaperonin GroEL and lengsin, indicates that our new methods can coarse-grain huge biomolecular systems with up to 10,000 residues within the time scale of minutes. The further parametrization of CG sites derived from FM-CG allows us to construct the corresponding CG models for studies of the functions of huge biomolecular systems.

Determining Optimal Coarse‐Grained Representation for Biomolecules Using Internal Cluster Validation Indexes

“…In order to search for the optimal number N , we developed the SLIO algorithm, which could be combined with ED‐CG for coarse‐graining biomolecules. SLIO is an accurate and efficient optimization algorithm, which has been demonstrated by tests performed by us . The detailed principle of the SLIO algorithm is described in the previous study …”

“…In this work, we coarse‐grain protein sequences by using the SLIO algorithm based on the ED‐CG method . In the ED‐CG method, a property function ƒ ED‐CG ( N ) is defined as the sum of the squared displacement difference of pairwise Cα atoms, as shown in eq.…”

“…The CG models could be constructed from the fine‐grained models such as all‐atom model by using the “bottom‐up” strategies . By resorting to the strategies, we could set up a connection between the statistical properties of fine‐grained ensembles and CG ensembles . Construction of CG models based on all‐atom models needs a preliminary definition of how to map fine‐grained models to CG models.…”

“…Coarse‐graining a protein with a given sequence composed of M residues into the number N ( N < M ) UCG beads involves two major optimization problems in mathematics . First, if the sequential M residues are CG into a specific number of N UCG beads, it means that the protein sequence needs to be divided into N clusters that are separated by N ‐1 boundaries along the protein backbone, which refers to the problem of boundary optimization.…”

“…In order to solve the problem of boundary optimization, Zhang et al proposed a combined algorithm composed of simulated annealing and steepest descent (SASD) to obtain the optimal N ‐1 boundaries dividing the protein sequence into N clusters, based on their proposed essential dynamics coarse‐graining (ED‐CG) method . Xia and coworkers developed two efficient and rapid algorithms, namely, the stepwise optimization imposed with boundary constraint (SOBC) and stepwise local iterative optimization (SLIO) for coarse‐graining. The further comparison of SASD, SOBC, and SLIO combined with ED‐CG demonstrates that SLIO is the most accurate and fast algorithm for coarse‐graining .…”