In this article we present a quantitative evaluation of the convergence of the conformational coordinates of proteins, obtained by the Essential Dynamics method. Using a detailed analysis of long molecular dynamics trajectories in combination with a statistical assessment of the significance of the measured convergence, we obtained that simulations of a few hundreds of picoseconds are in general sufficient to provide a stable and statistically reliable definition of the essential and near constraints subspaces, at least within the nanoseconds time range. Proteins 1999;36:419-424.

In this article we present a quantitative evaluation of the convergence of the conformational coordinates of proteins, obtained by the Essential Dynamics method. Using a detailed analysis of long molecular dynamics trajectories in combination with a statistical assessment of the significance of the measured convergence, we obtained that simulations of a few hundreds of picoseconds are in general sufficient to provide a stable and statistically reliable definition of the essential and near constraints subspaces, at least within the nanoseconds time range. Proteins 1999;36:419-424.

From a specific definition of the roto-translational ͑external͒ and intramolecular ͑internal͒ coordinates, a constrained dynamics algorithm is derived for removing the roto-translational motions during molecular dynamics simulations, within the leap-frog integration scheme. In the paper the theoretical basis of this new method and its statistical mechanical consistency are reported, together with two applications.

The understanding of protein dynamics is one of the major goals of structural biology. A direct link between protein dynamics and function has been provided by x-ray studies performed on ribonuclease A (RNase A) (B. F. Rasmussen et al., Nature, 1992, Vol. 357, pp. 423-424; L. Vitagliano et al., Proteins: Structure, Function, and Genetics, 2002, Vol. 46, pp. 97-104). Here we report a 3 ns molecular dynamics simulation of RNase A in water aimed at characterizing the dynamical behavior of the enzyme. The analysis of local and global motions provides interesting insight on the dynamics/function relationship of RNase A. In agreement with previous crystallographic reports, the present study confirms that the RNase A active site is constituted by rigid (His12, Asn44, Thr45) and flexible (Lys41, Asp83, His119, Asp121) residues. The analysis of the global motions, performed using essential dynamics, shows that the two beta-sheet regions of RNase A move coherently in opposite directions, thus modifying solvent accessibility of the active site, and that the mixed alpha/3(10)-helix (residues 50-60) behaves as a mechanical hinge during the breathing motion of the protein. These data demonstrate that this motion, essential for RNase A substrate binding and release, is an intrinsic dynamical property of the ligand-free enzyme.

The analysis of the dynamic behavior of enzymes is fundamental to structural biology. A direct relationship between protein flexibility and biological function has been shown for bovine pancreatic ribonuclease (RNase A) (Rasmussen et al., Nature 1992;357:423-424). More recently, crystallographic studies have shown that functional motions in RNase A involve the enzyme beta-sheet regions that move concertedly on substrate binding and release (Vitagliano et al., Proteins 2002;46:97-104). These motions have been shown to correspond to intrinsic dynamic properties of the native enzyme by molecular dynamics (MD) simulations. To unveil the occurrence of these collective motions in other members of pancreatic-like superfamily, we carried out MD simulations on human angiogenin (Ang). Essential dynamics (ED) analyses performed on the trajectories reveal that Ang exhibits collective motions similar to RNase A, despite the limited sequence identity (33%) of the two proteins. Furthermore, we show that these collective motions are also present in ensembles of experimentally determined structures of both Ang and RNase A. Finally, these subtle concerted beta-sheet motions were also observed for other two members of the pancreatic-like superfamily by comparing the ligand-bound and ligand-free structures of these enzymes. Taken together, these findings suggest that pancreatic-like ribonucleases share an evolutionary conserved dynamic behavior consisting of subtle beta-sheet motions, which are essential for substrate binding and release.