Abstract
The elastic network model (ENM) is a widely used method to study native protein dynamics by normal mode analysis (NMA). In ENM we need information about all pairwise distances, and the distance between contacting atoms is restrained to the native value. Therefore ENM requires O(N2) information to realize its dynamics for a protein consisting of N amino acid residues. To see if (or to what extent) such a large amount of specific structural information is required to realize native protein dynamics, here we introduce a novel model based on only O(N) restraints. This model, named the ‘contact number diffusion’ model (CND), includes specific distance restraints for only local (along the amino acid sequence) atom pairs, and semi-specific non-local restraints imposed on each atom, rather than atom pairs. The semi-specific non-local restraints are defined in terms of the non-local contact numbers of atoms. The CND model exhibits the dynamic characteristics comparable to ENM and more correlated with the explicit-solvent molecular dynamics simulation than ENM. Moreover, unrealistic surface fluctuations often observed in ENM were suppressed in CND. On the other hand, in some ligand-bound structures CND showed larger fluctuations of buried protein atoms interacting with the ligand compared to ENM. In addition, fluctuations from CND and ENM show comparable correlations with the experimental B-factor. Although there are some indications of the importance of some specific non-local interactions, the semi-specific non-local interactions are mostly sufficient for reproducing the native protein dynamics.
Highlights
The biological function of a protein cannot be completely understood unless roles of the structure and its dynamics are characterized
1) Low-frequency Modes are More Dominant in contact number diffusion’ model (CND) than in elastic network model (ENM) and molecular dynamics (MD)
We compared the distribution of eigenvalues of the covariance matrices obtained from CND and ENM as well as a MD trajectory of ligand-free adenylate kinase from Escherichia coli (Figure 1)
Summary
The biological function of a protein cannot be completely understood unless roles of the structure and its dynamics are characterized. One method to obtain dynamic characteristic of a protein around its native structure is the normal mode analysis (NMA) [1,2]. In ENM the protein structure is modeled as a set of atoms and each contacting pair of atoms are connected by a harmonic spring. The equilibrium length of such a spring is set to the distance between the corresponding atom pairs in the native structure. The experimentally obtained structure is guaranteed to be at the global energy minimum. Because of this favorable property, ENM has been used extensively [5,6,7,8,9,10,11]
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