Global shape complexity

In principle the global structure of an RNA junction could be determined when it is complexed with bound protein. This has not been accomplished to date in RNA, but it has proven itself for DNA junctions. For example, the structure of DNA junctions bound by the junctionresolving enzymes T4 endonuclease VII (Pohler et al., 1996) and T7 endonuclease I (Declais et al., 2003) have both been determined by comparative gel electrophoresis. It was found that both proteins substantially alter the global shape of the DNA junction in different ways. These structures were both recendy confirmed by X-ray crystallography (Biertiimpfel et al., 2007 Hadden et al., 2007), showing that comparative gel electrophoresis functions reliably for protein complexes. There is no reason to expect that the method would not work equally well for RNA junction complexes. The binding of the ribosomal protein SI 5 to a three-way RNA junction has been studied by an electrophoretic approach that is related to comparative gel electrophoresis (Batey and Williamson, 1998). 

The global and local shape codes can be used for measuring global and local shape compexity, respectively. Let w(s(a,b,M)) and w(lli)(a,b,M)) denote the number of different entries of the n-dimensional global shape matrix s(a,b,M) and a k-dimensional local shape matrix lb(a,b,M), respectively. Simple global and local shape complexity measures of molecule M are defined as the following ratios ... 

Table 14-1. Description of the protein-protein complexes used in the parameterization and test sets, in terms of the numbers of atoms and PKs, interface area, and global shape... 

Analysis of the shape of error surfaces. To conclude this section, we consider a more quantitative approach to error estimation. The first step is to estimate the accuracy of the individual data points this can either be done by analysis of the variability of replicate measurements, or from the variation of the fitted result. From that, one can assess the shape of the error surface in the region of the minimum. The procedure is straightforward the square root of the error, defined as the SSD, is taken as a measure of the quality of the fit. A maximum allowed error is defined which depends on the reliability of the individual points, for example, 30% more than with the best fit, if the points are scattered by about 30%. Then each variable (not the SSD as before) is minimised and also maximised. A further condition is imposed that the sum of errors squared (SSD) should not increase by more than the fraction defined above. This method allows good estimates to be made of the different accuracy of the component variables, and also enables accuracy to be estimated reliably even in complex analyses. Finally, it reveals whether parameters are correlated. This is an important matter since it happens often, and in some extreme cases where parameters are tightly correlated it leads to situations where individual constants are effectively not defined at all, merely their products or quotients. Correlations can also occur between global and local parameters. 

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