MD simulations of bacteriophage T4-lysozyme (T4L), an enzyme which is six times smaller than Cselp, impressively illustrate this sampling problem for relatively long MD trajectories. T4L has been extensively studied with X-ray crystallography (Faber and Matthews 1990; Kuroki et al. 1993) and, since it has been crystallized in many different conformations, represents one of the rare cases where information about functionally relevant modes can be directly obtained at atomic resolution from experimental data (Zhang et al. 1995; de Groot et al. 1998). The domain character of this enzyme is very pronounced (Matthews and Remington 1974) and from the differences between crystallographic structures of various mutants of T4L it has been suggested that a hinge-bending mode of T4L (Fig. 12.3) is an intrinsic property of the molecule (Dixon et al. 1992). Moreover, the domain fluctuations are predicted to be essential for the function of the enzyme, allowing the substrate to enter and the products to leave the active site in the open configuration, with the closed state presumably required for catalysis.
Fig. 12.3 Hinge-bending motion in bacteriophage T4-lysozyme. Domain fluctuations (domains are coloured differently) are essential for enzyme function, allowing the substrate to enter and the products to leave the active site
The wealth of experimental data also provides the opportunity to assess the reliability and sampling performance of simulation methods. Two MD simulations have been carried out using a closed (simulation 1) and an open conformation (simulation 2) as starting points, respectively. In order to assess the sampling efficiency a principal components analysis (PCA, see Sect. 12.2 below) has been carried out on the ensemble of experimentally determined structures and the X-ray ensemble and the two MD trajectories have been projected onto the first two eigenvectors. The first eigenvector represents the hinge-bending motion, whereas the second eigenvector represents a twist of the two domains of T4L. The projections are shown in Fig. 12.4. The X-ray ensemble is represented by dots, each dot representing a single conformation. Movement along the first eigenvector (x-axis) describes a collective motion from the closed to the open state. It can be seen that neither of the individual the MD trajectories, represented by lines, fully samples the entire conformational space covered by the X-ray ensemble, although the simulation times (184 ns for simulation 1 and 117 ns for simulation 2) are one order of magnitude larger than in the previously discussed Cse1p simulation. From the phase space density one can assume that an energy barrier exists between the closed and the open state and neither simulation achieves a full transition, from the closed to the open state, or vice versa.
Fig. 12.4 Principal components analysis of bacteriophage T4-lysozyme. The X-ray ensemble is represented by dots, MD trajectories by lines. A movement along the first eigenvector (x-axis) represents a collective motion from the open to the closed state. Neither simulation 1 started from a closed conformation—, nor simulation 2 started from an open conformation—show a full transition due to an energy barrier that separates the conformational states