Normal mode analysis of human lysozyme : study of the relative motion of the two domains and characterization of the harmonic motion

A normal mode analysis of human lysozyme has been carried out at room temperature. Human lysozyme is an enzyme constituted of two domains separated by an active site cleft, the motion of which is thought to be relevant for biological function. This motion has been described as a hinge bending motion. McCammon et al. have determined the characteristics of the hinge bending motion but they assumed a prior knowledge of the hinge axis. In this work we propose a method which is free from this assumption and determines the hinge axis and root mean square (rms) rotation angle which give the best agreement with the pattern of changes in all the distances between nonhydrogen atoms in the two domains, obtained by the normal mode analysis. The hinge axis we found is notably different from the one previously determined and goes, roughly, through the C alpha 55 and C alpha 76, i.e., it is located at the base of the beta-sheet of the second domain. The rms value for the rotation angle is also twice as large as the previous one: 3.37 degrees. It is shown that this hinge bending motion provides a fairly good approximation of the dynamics of human lysozyme and that the normal mode with the lowest frequency has a dominating contribution to this hinge bending motion. A study of the accessible surface area of the residues within the cleft reveals that the motion does not result in a better exposure to the solvent of these residues. A characterization of the thermally excited state (under the hypothesis of the harmonicity of the potential energy surface) has been done using the concept of topology of atom packing. Under this hypothesis the thermal fluctuations result only in a small change of the topology of atom packing, leading therefore to nearly elastic deformations of the protein.