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Elastic model for proteins (polymers)

There has been a lot of attention on the study of mechanics of proteins and/or single molecules. Such study was typically implemented by using classical molecular dynamics (MD) simulation. In spite of ability to describe the dynamics of biological macromolecules (e.g. proteins), MD simulation exhibits the computational restriction in the spatial and temporal scale. In order to overcome such computational limitation, the coarse-grained model has recently been taken into account. In this review, I would take a look at a couple of coarse-grained models of protein molecules.

Proteins perform the biological functions through conformational changes that are well described by low-frequency normal modes of protein structures. For low-frequency normal modes, the normal mode analysis (NMA) for molecular structure of proteins was typically utilized. However, such NMA possesses the computational difficulties, because of anharmonic potential field prescribed to whole atoms of protein structures. Recently, M.M. Tirion (Phys. Rev. Lett., 1996) provided the coarse-grained model, which revolutionize the protein dynamics studies [for details, see Ref]. In her work, the alpha carbon atoms (dominant carbon atom in backbone chain) were prescribed by a harmonic potential field in such a way that alpha carbons in neighborhood (defined by a cut-off distance) were connected by elastic harmonic springs (with only one single stiffness parameter). One may regard this simple model as mass-spring model to protein structures. This simple model was surprisingly able to describe the conformational fluctuation of protein structures. Moreover, this simple model (referred to as Tirion's model) allows one to describe the conformational transition of protein structures by using low-frequency normal modes from Tirion's model. For instance, several researchers (C.L. Brooks, I. Bahar, R.L. Jernigan, M. Karplus, A. Kidera, et al.) have successfully described the biological function of viruses, motor proteins, and protein kinase, and protein folding core predictions based on the Tirion's model. Recently, I have deveoped the coarse-graining scheme of protein structures, that is, the model reduction of elastic network model (for details, click here). It was reported that reduced elastic model is sufficient for Normal Mode studies of proteins for understanding the protein dynamics related to biological functions.

Proteins are renowned as a strong molecule that exhibits the remarkable mechanical strength. For instance, spider silk protein exhibits the high mechanical strength upon mechanical loading. Such remarkable mechanical strength is ascribed to protein structures, that is, the folded structure of proteins is unfolded upon mechanical loading. For computational experiment of protein unfolding, the protein structural change upon mechanical loading was well described by steered MD simulation developed by Schulten and coworkers. For computational tractability for study of correlation between folding topology and mechanical response, I and my former advisors developed the coarse-grained model of cross-linked polymer molecules, which reveals the relationship between folding topology (cross-link topology) and mechanical unfolding behavior (mechanical strength) of proteins (For details, see here). In this work, it is shown that specific folding topology such as parallel strand is responsible for remarkable mechanical strength of proteins.

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