Distribution of Loop Lengths

Huppert and Balasubramanian then considered the length of the loops separating the G-tracts. It had been shown previously that the length of the loops linking the runs of oligo-G sequences play a significant role in determining the stability of the resultant quadruplexes  

More detailed analysis of the behaviour of the loops required analysis of the co-variance between the loops. All the PQS identified above were examined, and represented as a three-dimensional coordinate set ij,k , where i is the length of the first loop, j the second and k the third. 

The best method of modelling this behaviour is using a model called diagonal quasi-independence, and corresponds to a probability mixture model in which with probability a, the loops lengths are constrained to be the same, and with probability (1-a), they are independent. This method gives the relationship shown below, where Nik is the predicted count with first loop length i and third loop length k, (3 - and (3y are the two independent distributions. 

Most common loop lengths Least common loop lengths  

Loop 1 Loop 2 Loop 3 Number Loop 1 Loop 2 Loop 3 Number 

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For each set of loops, all examples were extracted from the Brookhaven Data Bank [7] and characterized according to loop length, 0, y/ conformation, sequence and structural superposition. The distribution of loop lengths (Figure 15.4) shows that nearly 70% have five or less residues. The loops that form structural families are indicated by shading in Figure 15.4 and summarized in Table 15.2. As expected, the families occur in the very short loops, where the number of possible conformations is small. These families are described in detail by Thornton and coworkers [22], and here we present just one family from each supersecondary group, as an example of the sorts of pattern observed. 

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