A coarse-grained Langevin molecular dynamics approach to de novo protein structure prediction

Takeshi N. Sasaki, Hikmet Cetin and Masaki Sasai

Department of Computational Science and Engineering, Nagoya University, Nagoya 464-8603, Japan

ABSTRACT De novo prediction of protein structures, the prediction of structures from amino-acid sequences which are not similar to those of hitherto resolved structures, has been one of the major challenges in molecular biophysics. In this paper, we develop a new method of de novo prediction, which combines the fragment assembly method and the simulation of physical folding process: Structures which have consistently assembled fragments are dynamically searched by Langevin molecular dynamics of conformational change. The benchmarking test shows that the prediction is improved when the candidate structures are cross-checked by an empirically derived score function.

KEY WORDS protein structure prediction, Langevin dynamics, fragment assembly

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INTRODUCTION Prediction of protein structure from amino-acid sequence is a major challenge in biophysics. As the number of determined structures increases, fairly precise prediction has become possible if the sequence of the target protein is close to the sequence of a known structure [1]. Such prediction utilizing homologous proteins is called template based modeling (TBM). For targets whose sequences do not resemble those of hitherto resolved structures, however, the prediction becomes a harder problem [2], which is known as de novo prediction or template free modeling (FM). It is important to develop a reliable de novo prediction technique not only to solve previously unseen structures but also to understand the principles of structure formation. In recent experiment of the 7th critical assessment of techniques for protein structure prediction (CASP7), results of both TBM and FM have been intensively discussed [3]. From this discussion, we can see that we still do not have a reliable consistent technique for de novo prediction in spite of the much effort devoted to this problem [4-12].
Following Anfinsen’s thermodynamic hypothesis [13], native structures should have low free energy. In de novo prediction, many research groups have developed sampling techniques to find such low free energy structures by applying various types of effective energy functions. Relatively successful methods among them are the fragment assembly
method [4-8] and the Threading/Assembly/Refinement (TASSER) method [9-12], which have employed the strategy to assemble the candidates of local structures such as 9-residue length fragments [4-8] or longer chain configurations [9-12]. In these methods, local structural candidates are selected at first by utilizing the local sequential similarity between target and database proteins, and then the whole chain structure is predicted by finding the consistent combination of local structural candidates to form the whole structure of the low effective energy. Success of these methods implies that consistency [14] and minimal frustration [15] among local and whole structures are the guidelines for structural formation in proteins.
Another strategy for de novo prediction is to use Monte Carlo [16-18] or Langevin molecular dynamics (MD) methods [19-22] to simulate the folding process. Merits of simulating physical folding process are in multiple ways. First, the method developed in the prediction problem should give insights on folding process, second, the method could be applied outside of the prediction problem to the large scale conformational change in protein functioning, and last but not least, the structure generation mimicking the process existing in nature should be a reasonable way to resolve the complex conformation. In the present paper we discuss a newly developed de novo prediction method which 2

incorporates both of above two strategies at the same time. In this method a coarse-grained energy function consisting of several terms of potentials is constructed. Some of those potentials express structural tendency for fragments to take in the target protein, and other multi-residue potentials express how the fragments are assembled through hydrophobic interactions and hydrogen-bonding. In this way, both the local structure prediction and the minimally frustrated assembly of local structures should be realized at the same time when this total energy function is lowered enough. Using thus defined energy function, Langevin MD simulations are performed to search structures of low energy. A benchmarking test of this method is performed by targeting proteins used in the TBM and FM categories of CASP7.

METHODS Peptide chain is expressed by the connected beads of α carbons, whose coordinates are denoted by {ri}. Folding of a peptide chain is simulated by numerically solving an overdamped Langevin equation,

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