computer modeling in molecular biology.pdf

8 Path Energy Minimization 219A further set of methods is based on adapting a MD simulation from one stateso that the molecule is forced to move towards the state of interest. At least threetechniques have independently been proposed. The Contra MD method [33, 341takes a short free MD run from one state. If the run moves “toward” the desiredtarget conformation it is “accepted” but if this is not case the run is restarted withanother set of initial atomic velocities. This process is repeated until the target conformationis reached. The measure of distance between two conformations used isbased on the same coordinates used for the adiabatic mapping study undertaken inthe work [33]. Ech-Cherif El-Kettani and Durup [42] working on a much larger problemtake a more direct approach in that the MD run is started with the initalvelocities set so that the system moves toward the desired state. The r. m. s. atomicdisplacement of the molecule with respect to the target conformation is monitoredduring dynamics and the run is halted when this quantity starts to rise. Velocities arethen reset toward the target conformations and the run is restarted. Once again theprocedure is repeated until the desired conformation is reached. In contrast, Schlitteret al. [43] use a MD simulation from one conformation with the constraint that thedistance to the target should decrease slowly with time. All these methods make theassumption that the best path between two states is reasonably direct which may notbe true (e. g., consider a change where the best route for a molecule to undergo asimple transition of a single dihedral angle from 0 to 90 degrees is to go through atransition state at 180 degrees). Furthermore the transition state configuration is notidentified and at best only a “ball park estimate” as to the energy barrier involvedis obtained. These methods may prove to be useful to provide initial routes to whichfurther optimization can be applied.The most effective method developed to date for reaction path generation in largesystems is the Self Penalty Walk (SPW) procedure due to Elber and co-workers[44, 451. A chain of positions is considered between the fixed end points. These aresimultaneously energy minimized with the restraint that the distance between adjacentpoints should be equal. Further restraints are added to avoid problems causedby rigid body translations and rotations, and to avoid the route folding back onitself. The method presented here, Path Energy Minimization (PEM), is also basedon an optimization of a series of conformations lying between the fixed end pointsbut has a number of novel features. The method is discussed at length in the nextsection.