Consider the problem of nding an optimum local multiple alignment of the three sequences X = X₁ X₂ ......X_n1

Y = Y₁ Y₂ ......Y_n2

Z = Z₁ Z₂ ......Z_n3.

You are given a linear scoring schemes (,,) where ,, {A,C,G,T,}. In other words,the match scores and gap penalties are built into a 555 array, and the contribution to the total score if in sequence X aligns with in sequence Y and in sequence Z is s(,,). You may further assume that s(,,) < 0 whenever any of , or is a gap. Write out, in pseudo-code, the algorithm for the generalisation of the SmithWaterman algorithm to this situation. Your pseudo-code should be under three headings:

Initialisation with the formula for initialising the array F(i,j,k) on the boundary i, j or k = 0 of the cubic array;

Iteration with the formula for iterating the array F(i,j,k);

Traceback indicating how to determine the optimum score from the array and where to trace the alignment back to.