2° structure dependency

In roder to introduce into the algorithm the 2° structure dependency we add to the calculation a topology factor and use Dssp (Kabsch W., 1983) to assign the residues of the aligned proteins with a secondary structure (alpha Helix, beta sheet or a loop). we regard the alpha Helix and beta sheet residues as Structure and loop residues as Loop.

The table above illustrates the criteria that influence the topology factor: the 2° structure assignment (red cells), and the spatial relation matrix (green cells). For example, cell i, j is an alignment of two loop assigned residues and is regarded as a match due to the spatial neighboring of Ca atoms i and j according to the spatial relation matrix. The figure at the bottom illustrates a graphic representation of the table. It shows the indices (black), the 2° structure assignment (red), the match between j and e Ca atoms and the mismatch between the e and k Ca atoms.

Once we have the secondary structure assignment and the SNRM of the alignemd proteins we can calculate every movement during the alignment as follows:

1. we check the movement type: (continue a mismatch region, continue a match region, open a mismatch region, open a match region, close a match region, close a mismatch region) in the figure above we can see the illustrated movment type of opening a mismatch region.
2. Check the secondary structure alignment ( in the figure above the alignment for aligning residues k,e together and after i,j gives a secondary structure alignment of L/L (i,j) and then L/S (k,e).
3. Calculate the payoff for a movement as the average value of performing the movment in the given secondary structure alignment. For example, the value for the movment in the figure above would be calculated as the avarage value of opening a mismatch in a L/L alignment (OM L/L) and opening a mismatch in a L/S alignment (OML/S). i.e. Payoff for the movement = 0.5 x (OML/S + OML/L).

 

The addition of the secondary structure dependency into the affine gap and affine mismatch alignment addes more gap types according to the secondary structure the cell the gap starts from aligns. Therefore, we have 6 gap types for every dirction up and left that we need to remeber their value, as depicited in the figure below:

movments weights

These payoffs are the weights that determine the alignment. The ratio between the payoffs endows upon the alignment its affine mismatch secondary structure-dependent nature. The ratio payoff has the following criteria:
(1) The payoff for opening a mismatch in a loop-to-loop is higher than that in a structure-to-structure alignment. Similarly, the payoff for continuing a mismatch in a loop-to-loop is higher than that in a structure-to-structure alignment. These ratios guarantee that the best alignment will favor few long mismatches over many short regions and favor mismatches in loops over mismatches in a-helix and ß-sheets.
(2) The payoff for a match in a structure-to-structure is higher than a match in a loop-to-loop alignment. This reflects the tendency for matches in structure-assigned residues.
(3) The payoff for opening a mismatch is always smaller than continuing an already opened mismatch. This favors few long mismatch regions over many short ones.
(4) We expect loop-to-structure alignment to appear more often in the margins of the assigned secondary structure, where the assignment might be imprecise. To ensure some flexibility in the alignment, the payoffs of loop-to-structure are the average of the loop-to-loop and structure-to-structure alignment payoffs.