Homework Assignment

Homework Assignment • Check out PDB Data Bank at www.rcsb.org. Download the structure file for Protein 1HMV. • Download RasMol from www.umass.edu/microbio/rasmol. Use RasMol to display 1HMV. • Class Question: Can you prove that the problem of folding a closed chain is NP-hard?

Homework Assignment • Use Matlab to find the DME and RMSD between the side-chains TS1 and TS2 as given in the lecture. • For a given set of atoms, find a simple algorithm for the determination of the coordinates of the atoms, given all their distances. • Class question: Let X, Y, Q be as given in the lecture. Prove Q solves the optimization problem, minQ {||X – YQ||F : QQT = I}.

21.993 62.291 198.878 20.895 63.281 198.700 20.992 64.646 198.784 19.502 62.990 198.504 19.747 65.217 198.667 18.812 64.227 198.493 18.768 61.798 198.344 17.417 64.312 198.324 17.379 61.882 198.175 16.721 63.133 198.169 TS1 X = 10 × 3 15.541 91.776 216.531 15.585 93.269 216.262 16.415 94.169 216.856 14.735 94.039 215.381 16.139 95.441 216.425 15.112 95.394 215.513 13.693 93.714 214.495 14.482 96.441 214.787 13.062 94.764 213.767 13.465 96.105 213.923 TS2 Y = 10 × 3

Calculation of DME for TS1 and TS2 >> >> for i = 1 : 10 for j = 1 : 10 DX (i,j) = sum ((X (i,:) – X (j,:)) .^ 2); DX (i,j) = sqrt (DX (i,j)); end end >> >> for i = 1 : 10 for j = 1 : 10 DY (i,j) = sum ((Y (i,:) – Y (j,:)) .^ 2); DY (i,j) = sqrt (DY (i,j)); end end >> >> dme = sqrt (sum (sum ((DX – DY) .^ 2))) / 10 >> calculate distances for X calculate distances for Y

Calculation of RMSD for TS1 and TS2 >> >> xc = sum (X) / 10; yc = sum (Y) / 10; >> >> XX (:,1) = X (:,1) - xc (1); >> XX (:,2) = X (:,2) - xc (2); >> XX (:,3) = X (:,3) - xc (3); >> >> YY (:,1) = Y (:,1) - yc (1); >> YY (:,2) = Y (:,2) - yc (2); >> YY (:,3) = Y (:,3) - yc (3); >> >> C = YY’ * XX; >> [U, S, V] = svd ( C ); >> Q = U * V’; >> >> rmsd = sqrt (sum (sum ((XX – YY * Q) .^ 2)) / 10) >>

Homework Assignment