Proteins with many transitional conformations when changing from one conformation to another usually involve relative motions of domains. A good understanding of these movements will help the study of protein functions such as catalysis and regulations. In these papers, a theoretical method for studying collective motions in proteins, normal mode analysis (NMA) is used. With this tool, conformational changes can be expressed in term of superposition of collective variables, ie normal mode coordinates.

Normal Mode Theory:

The displacements of atomic coordinate i, r_i(t) with near by stationary point of the potential energy surface can be calculated using Goldstein equation (1950). Within this approach, a simplified potential energy function proposed by Tirion (1996) is used. This simplified potential energy function is designed such that any configuration of any system is a minimum of the function. With this method, NMA no longer require energy minimization step and thus, cut off CPU time. Another two techniques of the NMA in this study are all the normal mode calculation used a cutoff of 8 Å which has been used by Bahar et al (1997) and only C_α atoms were taken into account. This model allowed the study of backbone motions, which characterizing low frequency normal modes of large proteins, to be achieved with small amount of CPU time and lower computational expense. The simple potentials and models have been used in previous studies, and the results strongly suggested that simple potentials yielded low frequency normal mode as accurate as those with standard NMA.

In order to compare with the experimental method, the authors looked at two qualities, the overlap I_j and the correlation coefficient C_j where I_j is the overlap between delta_vector_r = {Δr₁, ..., Δr_i, ..., Δr_3N}, the conformation change in crystal structures and the jth normal mode of the protein; C_j is the similarity of the patterns of atomic displacements in the conformational change and in mode j. Equations for quantitatively calculations of C_j and I_j are given in the paper (p2-3). Note that delta_vector_r is calculated for pairs of crystallographic conformations of “open” and “closed” form after both conformations were superposed. The overlap and correlation are considered as functions of degree of collectivity (к) of the conformational change where degree of collectivity is a measurement of how collective a motion of the protein is (Bruschweiler, 1995). Overlap of the most involved modes in conformational changes calculated using simplified model are found to be almost equivalent as those obtained using standard NMA and to have smaller RMSD 1.2 – 1.9 Å comparing to 2-3 Å obtained in standard approach. The results also suggested that NMA performed better in the open form than closed (refer to table III), better with highly collective motions (refer to table IV) and better with more localized motions (refer to the case of tryglyceride lipase in table IV and V). In conclusion, a single normal mode can carry a lot of information about conformational transitions of proteins. The single mode with best correlation and best overlap is more likely not the lowest frequency mode but often one of the three lowest frequency modes.

Carrying on the NMA to study conformational change of protein, the work in the second paper performed NMA calculations to investigate the extend to which thermal motions of proteins could provide the general nature of conformational change upon protein-protein docking.

A set of 20 proteins with flexibility which have been observed to have large conformational change under forming complexation by Tama et al, is used in this study. Their result showed high agreement with the experiment in term of average collectivity, 0.40 for observed and 0.38 for predicted. They also stated that the RMSD of binding sites are found to be 1.2 times larger than those over the entire protein, which suggested that upon complexation, the protein conformational change has highly flexible regions around binding site. Further investigation of mobilities over the binding site for both observed and predicted using NMA were performed. Splitting the binding site into the core and the periphery residues, they found that the observed motion of the peripheral residues is more than twice large than that of the core residues. This confirm the hypothesis that binding site has regions of highly flexibility along with rigid regions upon docking (refer to figure3). There were no obvious trend for the overlap. They were observed to be different for different frequency modes. However, their results are in agreement with previous study that large conformational change of proteins usually have low frequency modes but not the lowest frequency mode. The protein size are also examined in this paper. They proposed that the larger the protein size the more collective motions it has and thus might also be used to predict conformational change. However the size is less reliable than the normal mode frequency.

Overall, this particular study showed that almost all proteins undergo large conformational change has thermal motions in isolation and required some intrinsic flexibility. In their prediction using NMA, only one third of the proteins have the direction and location of motion among the lowest modes is similar to the observed conformational transition. They suggested this because of the bound condition which might altered structural changes. In my opinion, this is one of the limitations of this work, along with unclear trends for overlap. In conclusion, the significant contribution of this study is that it suggested a model to study the conformational change during molecular recognition will be desirable in future work.

References:

Tama and Sanejouand, Protein Eng., 2001

Dobbins, Lesk, and Sternberg, PNAS, 2008