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Abstract

There are several tools to improve initial structural estimates of a molecule under study. The methods described in this section weight the structural models according to the approximate internal energy as a function of the atomic coordinates provided by a force field. The method of conjugated gradients is a powerful tool to find the way downhill toward a local minimum. Surmounting barriers and escaping local minima require nonlocal optimization procedures. Of the various possible choices the Bremermann method has been described in greatest detail. The central idea for the implementation of this method is its application to a small number of relevant degrees of freedom, allowing the remaining ones to relax to a local energetic minimum.

Monte Carlo methods may be used to obtain statistical averaged quantities. Again the convergence of this method may be considerably increased if the randomly chosen directions mainly concentrate on the relevant directions. Molecular dynamics calculations not only provide averaged quantities but also give information about time-dependent processes.

Model building studies may be used to supplement structurally low resolution experimental data with detailed three-dimensional hypothetical atomic models. Because of the strong relation between structure and function in biological molecules such models may give a consistent, integral view of a wealth of experimental data. In most cases such models will predict the outcome of certain experiments. The outcome of these experiments will often either confirm the model may be used for further refinement or even demand a major revision of the model. Coordinates obtained from X-ray fiber diffraction data or in special cases single-crystal data may provide the elements for DNA or RNA model building. Local and nonlocal optimization may be used to refine these structures and to evaluate their statistical significance as estimated by a chosen force field. Appreciable progress using nonlocal optimization procedures can only be expected if the dimensionality of the problem can be reduced sufficiently to the relevant degrees of freedom. Taking advantage of structural symmetries may critically improve the convergence while refining the target molecule or its building blocks. Monte Carlo and molecular dynamics methods allow one to calculate averaged quantities. In addition, molecular dynamics provides time evolutions of certain averages. During the simulation of certain physical properties of molecules a huge amount of data will be generated. They will provide many answers, but these answers may not always apply to the original question. So what type of questions will be reliably answered by a force field? Relatively safe answers concern the local geometry of the molecules. If a conformation leads to strong distortions of bond distances or angles or to close van der Waals contacts, this conformation can safely be rejected. Optimizing such unfavorable structures energetically may lead to structures showing how to avoid such distortions. More difficult are energetical questions: which of two conformers is more stable, or what is the free energy of the substrate in the active site? One cannot always be sure that the force field provides the correct answer. Therefore, one should pose only those questions which can be checked experimentally. Because of the many possible answers, the experiment may benefit by starting with a choice proposed by the simulation. The application of this procedure to curved DNA and the DNA four-way junction was successful.