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Alternatively, a starting configuration of points can be specified in three dimensions which is then refined, through incremental steps, towards an optimal resolution of the distance constraints. This approach is a standard minimization problem and can be tackled using a very wide variety of algorithms and will be refelred to here as the refizenzent approach (Briinger and Nilges 1993). 2 Projection versus refinement The two approaches introduced here have differing advantages and disadvantages which has often resulted in their application to qualitatively different problems.

The simplest rcpresc~itationis to connect a central atom in each residue (and for this the a-carbon is the obvious choice) resulting in a trace that shows the overall fold of the protein clearly and in which secondary structure (if present) can also be seen (figure 2. I(h)). Additio~iallevels of inl'ormation can be represented along the backbone trace and this can be done either with or without explicit delinition of the secondary structures. The orientation of the (flat) peptide plane (> N C: <) can be used to guide the surface of a ribbon rcpl-escntation (Carson 199 1) (figure 2.

Furthcrmorc. in this matrix, any distance values that were not rcfined in real-space can bc reset to their desired values (so maintaining a 'soft' bias towards the desired packing). Generally this is best done with a degree of strictness reflecting the importance of the effect. This process can then be repeated and the di~nensionalityof the projection reduced in cach subsccluent cycle until thrce dirncnsional space was reached (Asr6di and Taylor 1994a). This introduction of intermediate cycles of projection allowcd weighting to be introduccd but it does not.

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