MOLECULAR DYNAMICS IN CRYSTALLOGRAPHY
Piet Gros
Dept. of Crystal and Structural Chemistry, Bijvoet Center for Biomolecular Research, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands. (E-mail: p.gros@chem.uu.nl)
Molecular Dynamics has become an important computational tool in crystallography and particularly in macromolecular (e.g. protein, DNA and RNA) crystallography. This overview will focus on three aspects of the use of Molecular Dynamics in (protein) crystallography: (a) Molecular Dynamics as an optimization tool in structure refinement, (b) generation of ensembles of structures describing the structural variations, and (c) the possible use of Molecular Dynamics in deriving ab initio phase information.
The most common application of Molecular Dynamics is in structure refinement, pioneered by A.T. Brünger in 1987 (see e.g. [1,2]). In Molecular Dynamics the equations of motion are evaluated, based on both the (pseudo-) potential and kinetic energy. Effectively, this allows for an enhanced convergence radius in optimization because energy barriers in potential energy may be overcome due to the kinetic energy. The enhanced convergence radius reduces the amount of model building (human intervention) in the refinement process and in general reduces the total amount of time needed to obtain the refined structure. Recently, this powerful optimization method has been combined with torsion-angle dynamics [3] and maximum-likelihood optimization [4,5]. In torsion-angle dynamics the number of degrees of freedom is significantly reduced by constraining the bond lengths and bond angles. In the maximum likelihood formulation the standard least-squares type of target function minimizing the differences between observed and calculated structure factor amplitudes is improved. Results from structure refinements using these combined methods will be presented. Furthermore the new program "Crystallography and NMR System" [6] used for the calculations will be presented. This program integrates various techniques in protein crystallography (phasing, molecular replacement and refinement).
The final result from a structure refinement typically is a model described by its coordinates and isotropic or anisotropic displacement (or 'temperature') factors. Multiple conformations (present in a crystal) are typically modelled in an ad hoc fashion. An attempt to model structural variations more rigorously is achieved by using a few separate models (i.e. multiple-model approaches). On the other hand, in Molecular Dynamics an ensemble of structures may be generated that describes all possible dynamical or structural variations of a molecule. The ensemble represents a Boltzmann-weighted distribution of models. The idea of 'time-averaging' [7,8] combines structure refinement with generating an ensemble of structures. In this overview, the background and developments will be presented.
The convergence radius in structure optimization has increased drastically over the last ten years. However, it is still impossible to 'refine' a random starting structure. To facilitate possible optimization starting from a completely random model, we have reformulated the topological constraints into restraints that may be applied to otherwise 'loose' atoms [9]. Progress in this area will be discussed.