Gapless threading

Two sets of protein structures and sequences are used for the training of parameters in the present study. Hinds and Levitt developed the first set [43] that we call the HL set. It consists of 246 protein stractures and sequences. Gapless threading of all sequences into all structures generated the 4,003,727 constraints [i.e., the inequalities of Eq. (8)]. The gapless constraints were used to determine the potential parameters for the 20 amino acids. Because the number of parameters does not exceed a few hundred, the number of inequalities is larger than the number of unknowns by many orders of magnitude. 

The parameter-free models are insufficient to solve exactly even the HL set. By exact we mean that each of the sequences picks the native fold as the lowest in energy using a gapless threading procedure. Hence, all the inequalities in Eq. (12), for all sequences S and structures Xj, are satisfied and the LP problem of Eq. (12) is feasible. This section addresses the question What is the minimal number of parameters that is required to obtain an exact solution for the HL and for the TE sets The feasibility of the corresponding sets of inequalities [Eq. (12)] is correlated with the number of model parameters, as listed in Table III. 

Comparison of Performance of THOM2 and Knowledge-Based Pairwise Potentials Using Gapless Threading"... 

The HL set was partially learned (using gapless threading). The first test verifies that the additional flexibility of gaps and deletion maintain good prediction... 

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