computer modeling in molecular biology.pdf

8 Path Energy Minimization 217of a simulation high temperatures are often used. Karplus [ll] examined the motionof a loop which closes over the active site of triose phosphate isomerase (TIM) usingdynamics at room temperature, 500 K and 1000 K. Another example where this approachmay be useful is in the simulation of protein unfolding [12], as there is nodetailed model available for the unfolded state of a protein. However, simulationsat unrealistically high temperatures may favor pathways which are different fromthose at low temperatures. An alternative approach, also used to examine loop motionsin TIM, is to simplify the model used for the protein and perform browniandynamics which allows simulations of up to 100 ns to be performed [13].Other simulation methods do not initially include dynamical effects but concentrateon finding a “reaction coordinate” for the change, passing through a transitionstate. The reaction coordinate is a variable or function of variables which smoothlychanges between the end point conformations of interest. The transition state is thepeak energy position on the reaction coordinate. Transition state theory [14- 161states that the most favorable route for the change is the one with the lowest transitionstate potential energy. Once a suitable reaction coordinate has been identifiedit is possible to run dynamical simulations to obtain the potential of mean force forthe change (free energy profile along the reaction coordinate) and such variables asthe transmission coefficient [17-201. In this context, Elber [19] has shown that aseries of continguous positions for the molecule which link the end points can beused to effectively define a reaction coordinate for complex transitions.Most methods for identifying reaction coordinates have been developed by quantumchemists interested in chemical reactions of small molecules. Although this problemmay appear very similar to identifying a reaction coordinate for a conformationaltransition there are some important differences. The quantum chemist ingeneral deals with problems with a relatively small number of variables and thus afairly simple energy hypersurface. Evaluating the energy of a position of a moleculeis often computationally very expensive (though accurate). In contrast, macromolecularpotential energy functions are approximate but cheap. However, the energyhypersurface is invariably horrendously complicated with large numbers of energyminima thermally accessible to each other [21]. This makes the requirements ofroutines to find reaction coordinates very different in the two cases. The quantumchemist requires a technique to be as efficient as possible but the method need notbe completely robust. In contrast methods for obtaining reaction coordinates forlarge molecules must be robust even at the expense of computational efficiency.A number of methods developed in quantum chemistry concentrate on locatingtransition state configurations [22-271. The multitude of minima on the energyhypersurface of a large molecule leads one to expect that there would be at least asmany transition states. It is unlikely that a routine which attempts to locate a transitionstate would find the one of interest. In addition most of these routines requirethat the matrix of the second derivatives of the potential energy function (the Hessian)be calculated and manipulated. This also precludes their use for problems in-