Sequence Alignment with Affine Gaps Practice Problems CMSC 423 Check that you understand how the values in the matrices are computed. Check that an optimal alignment that you find by hand has the same score as the reported optimal. Draw the arrows on the matrices (requires recomputing the "max" part of the recurrence for each entry). Check that the path defined by the arrows matches your hand computed optimal alignment. ------------------------------------------------------------------------ (1) x = cart & y = cat Scoring: match = 10; mismatch = -2; gap_start = -15; gap_extend = -7 M matrix = * c a r t * 0 -inf -inf -inf -inf c -inf 10 -24 -31 -38 a -inf -24 20 -14 -21 t -inf -31 -14 18 8 X matrix = * c a r t * 0 -inf -inf -inf -inf c -22 -44 -51 -58 -65 a -29 -12 -34 -41 -48 t -36 -19 -2 -24 -31 Y matrix = * c a r t * 0 -22 -29 -36 -43 c -inf -44 -12 -19 -26 a -inf -51 -34 -2 -9 t -inf -58 -41 -24 -4 Optimal = 8 ------------------------------------------------------------------------ (2) x = carts & y = cat Scoring: match = 10; mismatch = -2; gap_start = -15; gap_extend = -7 M matrix = * c a r t s * 0 -inf -inf -inf -inf -inf c -inf 10 -24 -31 -38 -45 a -inf -24 20 -14 -21 -28 t -inf -31 -14 18 8 -11 X matrix = * c a r t s * 0 -inf -inf -inf -inf -inf c -22 -44 -51 -58 -65 -72 a -29 -12 -34 -41 -48 -55 t -36 -19 -2 -24 -31 -38 Y matrix = * c a r t s * 0 -22 -29 -36 -43 -50 c -inf -44 -12 -19 -26 -33 a -inf -51 -34 -2 -9 -16 t -inf -58 -41 -24 -4 -11 Optimal = -11 ------------------------------------------------------------------------ (3) x = aaa & y = abbbaa Scoring: match = 10; mismatch = -1; gap_start = -5; gap_extend = -5 M matrix = * a a a * 0 -inf -inf -inf a -inf 10 0 -5 b -inf -11 9 -1 b -inf -16 -1 8 b -inf -21 -6 -2 a -inf -15 0 4 a -inf -20 -5 10 X matrix = * a a a * 0 -inf -inf -inf a -10 -20 -25 -30 b -15 0 -10 -15 b -20 -5 -1 -11 b -25 -10 -6 -2 a -30 -15 -11 -7 a -35 -20 -10 -6 Y matrix = * a a a * 0 -10 -15 -20 a -inf -20 0 -5 b -inf -25 -10 -1 b -inf -30 -15 -11 b -inf -35 -20 -16 a -inf -40 -25 -10 a -inf -45 -30 -15 Optimal = 10 ------------------------------------------------------------------------ (4) x = aaa & y = abbbabbbaa Scoring: match = 10; mismatch = -1; gap_start = -5; gap_extend = -5 M matrix = * a a a * 0 -inf -inf -inf a -inf 10 0 -5 b -inf -11 9 -1 b -inf -16 -1 8 b -inf -21 -6 -2 a -inf -15 0 4 b -inf -31 -16 -1 b -inf -36 -21 -11 b -inf -41 -26 -16 a -inf -35 -20 -10 a -inf -40 -25 -10 X matrix = * a a a * 0 -inf -inf -inf a -10 -20 -25 -30 b -15 0 -10 -15 b -20 -5 -1 -11 b -25 -10 -6 -2 a -30 -15 -11 -7 b -35 -20 -10 -6 b -40 -25 -15 -11 b -45 -30 -20 -16 a -50 -35 -25 -21 a -55 -40 -30 -20 Y matrix = * a a a * 0 -10 -15 -20 a -inf -20 0 -5 b -inf -25 -10 -1 b -inf -30 -15 -11 b -inf -35 -20 -16 a -inf -40 -25 -10 b -inf -45 -30 -20 b -inf -50 -35 -25 b -inf -55 -40 -30 a -inf -60 -45 -30 a -inf -65 -50 -35 Optimal = -10 ------------------------------------------------------------------------ (5) x = tacgggtat & y = ggacgtacg Scoring: match = 1; mismatch = -1; gap_start = -20; gap_extend = -1 M matrix = * t a c g g g t a t * 0 -inf -inf -inf -inf -inf -inf -inf -inf -inf g -inf -1 -22 -23 -22 -23 -24 -27 -28 -29 g -inf -22 -2 -23 -22 -21 -22 -25 -28 -29 a -inf -23 -21 -3 -24 -23 -22 -23 -24 -29 c -inf -24 -24 -20 -4 -25 -24 -23 -24 -25 g -inf -25 -25 -25 -19 -3 -24 -25 -24 -25 t -inf -24 -26 -26 -26 -20 -4 -23 -26 -23 a -inf -27 -23 -27 -27 -27 -21 -5 -22 -27 c -inf -28 -28 -22 -28 -28 -26 -22 -6 -23 g -inf -29 -29 -29 -21 -27 -25 -27 -23 -7 X matrix = * t a c g g g t a t * 0 -inf -inf -inf -inf -inf -inf -inf -inf -inf g -21 -42 -43 -44 -45 -46 -47 -48 -49 -50 g -22 -22 -43 -44 -43 -44 -45 -48 -49 -50 a -23 -23 -23 -44 -43 -42 -43 -46 -49 -50 c -24 -24 -24 -24 -44 -43 -43 -44 -45 -50 g -25 -25 -25 -25 -25 -44 -44 -44 -45 -46 t -26 -26 -26 -26 -26 -24 -45 -45 -45 -46 a -27 -27 -27 -27 -27 -25 -25 -44 -46 -44 c -28 -28 -28 -28 -28 -26 -26 -26 -43 -45 g -29 -29 -29 -29 -29 -27 -27 -27 -27 -44 Y matrix = * t a c g g g t a t * 0 -21 -22 -23 -24 -25 -26 -27 -28 -29 g -inf -42 -22 -23 -24 -25 -26 -27 -28 -29 g -inf -43 -43 -23 -24 -25 -26 -27 -28 -29 a -inf -44 -44 -42 -24 -25 -26 -27 -28 -29 c -inf -45 -45 -45 -41 -25 -26 -27 -28 -29 g -inf -46 -46 -46 -46 -40 -24 -25 -26 -27 t -inf -47 -45 -46 -47 -47 -41 -25 -26 -27 a -inf -48 -48 -44 -45 -46 -46 -42 -26 -27 c -inf -49 -49 -49 -43 -44 -45 -46 -43 -27 g -inf -50 -50 -50 -50 -42 -43 -44 -45 -44 Optimal = -7 ------------------------------------------------------------------------ (6) x = aaa & y = bbbbbaaabbbb Scoring: match = 1; mismatch = -1; gap_start = -5; gap_extend = -5 M matrix = * a a a * 0 -inf -inf -inf b -inf -1 -11 -16 b -inf -11 -2 -12 b -inf -16 -12 -3 b -inf -21 -17 -13 b -inf -26 -22 -18 a -inf -29 -25 -21 a -inf -34 -28 -24 a -inf -39 -33 -27 b -inf -46 -40 -34 b -inf -51 -47 -41 b -inf -56 -52 -48 b -inf -61 -57 -53 X matrix = * a a a * 0 -inf -inf -inf b -10 -20 -25 -30 b -15 -11 -21 -26 b -20 -16 -12 -22 b -25 -21 -17 -13 b -30 -26 -22 -18 a -35 -31 -27 -23 a -40 -36 -32 -28 a -45 -41 -37 -33 b -50 -46 -42 -37 b -55 -51 -47 -42 b -60 -56 -52 -47 b -65 -61 -57 -52 Y matrix = * a a a * 0 -10 -15 -20 b -inf -20 -11 -16 b -inf -25 -21 -12 b -inf -30 -26 -22 b -inf -35 -31 -27 b -inf -40 -36 -32 a -inf -45 -39 -35 a -inf -50 -44 -38 a -inf -55 -49 -43 b -inf -60 -56 -50 b -inf -65 -61 -57 b -inf -70 -66 -62 b -inf -75 -71 -67 Optimal = -52