Protein Folding in the Hydrophobic-Hydrophilic (HP) Model is NP ...
Protein Folding in the Hydrophobic-Hydrophilic (HP) Model is NP ...
Protein Folding in the Hydrophobic-Hydrophilic (HP) Model is NP ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>the</strong> parity problem of <strong>the</strong> cubic lattice. Although our<br />
methods do not rely on parity arguments, <strong>the</strong>y fail because<br />
we cannot utilize as easily <strong>the</strong> different number of<br />
m<strong>is</strong>s<strong>in</strong>g neighbors between edge and face nodes <strong>in</strong> <strong>the</strong><br />
m<strong>in</strong>imum configuration arrangement.<br />
5 Acknowledgements<br />
Many thanks to Serafim Batzoglou, Sor<strong>in</strong> Istrail, Es<strong>the</strong>r<br />
Jesurum, and Lior Pachter for helpful comments, and to<br />
Sor<strong>in</strong> Istrail for po,&ng th<strong>is</strong> problem to us. Thanks are<br />
also due to anonymous referees for <strong>the</strong>ir helpful comments.<br />
B.B. <strong>is</strong> partially supported by an NSF Career<br />
Award B.B. and T-L. are partially supported by ARPA<br />
contract N0001495-1-1246 and AR0 grant DAAH04<br />
95-l-0607.<br />
References<br />
[l] R Agarwala, S. Batzoglou, V. Dam%, S. De<br />
catur, M. Farach, S. Hannenhahi, S. Skiena, and<br />
S. Muthukr<strong>is</strong>hnan. Local rules for prote<strong>in</strong> fold<strong>in</strong>g<br />
on a triangular lattice and generalized hydropho<br />
bicity <strong>in</strong> <strong>the</strong> <strong>HP</strong> model J. Computational BioL,<br />
4(3):2?5-296, Fall 1997.<br />
[2] T. Akutsu and S. Miyano. On <strong>the</strong> approximation<br />
of prote<strong>in</strong> thread<strong>in</strong>g. In Proc. First Annual<br />
Irk Conf. on Computational Molecular Biol. (RE<br />
COMB), pages 3-8, Santa Fe, NM, jan 1997. ACM.<br />
[3] B. Berger and T. Leighton. <strong>Prote<strong>in</strong></strong> fold<strong>in</strong>g <strong>in</strong><br />
<strong>the</strong> hydrophobic-hydrophilic (<strong>HP</strong>) model <strong>is</strong> <strong>NP</strong>complete.<br />
J. Computational BioL, Spr<strong>in</strong>g 1998. In<br />
press.<br />
143 J. D. Bryngelson, J. N- Onuchic, N. D. Socci,<br />
and P. G. T%701ynes. Funnels, pathways, and <strong>the</strong><br />
energy landscape of prote<strong>in</strong> fold<strong>in</strong>g: a syn<strong>the</strong>s<strong>is</strong>.<br />
PROTEINS: Structure, Function, and Genetics,<br />
21:167-195, 1995.<br />
[5] P. Crescenzi. D. Goldman. C. Paoadimitriou.<br />
A. Piccolbom, and M. Y&akak<strong>is</strong>. Cn <strong>the</strong> corn:<br />
plexity of prote<strong>in</strong> fold<strong>in</strong>g. In Proc. 2nd Annual<br />
Int. Conf. on Computational hfolecular Biology<br />
(RECOhfB), New York City, NY, March 1998.<br />
ACM. To appear-<br />
If51<br />
171 K- Dill, S. Bromberg, K. Yue, K. Fiebig, D. Yee,<br />
P. Thomas, and H. Ghan. Pr<strong>in</strong>ciples of prote<strong>in</strong><br />
fold&p A perspective from simple exact models.<br />
<strong>Prote<strong>in</strong></strong> Science, 4561-602, 1995.<br />
181<br />
PI<br />
K. DilL Theory for <strong>the</strong> fold<strong>in</strong>g and stability of glob<br />
nlar prote<strong>in</strong>s. Biochem<strong>is</strong>try, 24:1501-X09, 1985.<br />
A Fraenkel. Deexponentializ<strong>in</strong>g complex computational<br />
ma<strong>the</strong>matical problems us<strong>in</strong>g physical or biological<br />
systems. Technical Report CS90-30, Weizmann<br />
Inst. of Science, Dept. of Applied Math and<br />
Computer Science, 1990.<br />
A. Fraenkel. Complexity of prote<strong>in</strong> fold<strong>in</strong>g. Bull.<br />
hfath BioL, 55:1199-1210, 1993.<br />
PO1<br />
ml<br />
P21<br />
P31<br />
P41<br />
[I51<br />
[161<br />
1171 T. Leighton. Introduction to Parallel Algorithms<br />
and Architechtures: Arrays . Trees - Hypercubes,<br />
chapter Arrays and Trees, page 190. Morgan Kaufmann,<br />
San Mateo, CA, 1992.<br />
P31<br />
P91<br />
PO1<br />
Pll<br />
A. S. Fraenkel. <strong>Prote<strong>in</strong></strong> fold<strong>in</strong>g, sp<strong>in</strong> glass and computational<br />
complexity. In Third Annual DIMACS<br />
Workshop on DNA Based Computers, Philadelphia,<br />
PA, June 1997. To appear <strong>in</strong> proceed<strong>in</strong>gs<br />
as an <strong>in</strong>vited paper.<br />
M. Garey and D. Johnson. Computers and Intractability.<br />
Freeman, New York, 1979.<br />
W. Hart and S. Istrail. Fast prote<strong>in</strong> fold<strong>in</strong>g<br />
<strong>in</strong> <strong>the</strong> hydrophobic-hydrophilic model with<strong>in</strong><br />
three-eighths of optimal. J. Computational Biol.,<br />
3(1):53-96, Spr<strong>in</strong>g 1996.<br />
W. Hart and S. Istrail. Robust proofs of <strong>NP</strong>hardness<br />
for prote<strong>in</strong> fold<strong>in</strong>g: General lattices and<br />
energy potentials. J. Computationa Biol., 4(1):1-<br />
22, spr<strong>in</strong>g 1997.<br />
W. E. Hart. On <strong>the</strong> computational complexity<br />
of sequence design problems. In Proc. First Annual<br />
Int. Conf. on Computational Molecular Biology<br />
(RECOMB), pages 128-136, Santa Fe, NM, jan<br />
1997. ACM.<br />
W. E. Hart and S. Istrail. Lattice and off-lattice<br />
side cha<strong>in</strong> models of prote<strong>in</strong> fold<strong>in</strong>g: L<strong>in</strong>ear time<br />
structure prediction better than In Proc. First Annual<br />
Int. Conf. on Computational Molecular Biology<br />
(RECOMB), pages 137-146, Santa Fe, NM, jan<br />
1997. ACM.<br />
R. H. Lathrop. The prote<strong>in</strong> thread<strong>in</strong>g problem with<br />
sequence am<strong>in</strong>o acid <strong>in</strong>teraction preferences <strong>is</strong> npcomplete.<br />
<strong>Prote<strong>in</strong></strong> Eng<strong>in</strong>eer<strong>in</strong>g, 7:1059-1068, 1994.<br />
T. Leighton and A. Rosenberg. Three-dimensional<br />
circuit layouts. SIAM J. Comput<strong>in</strong>g, 15(3):793-<br />
813, 1986.<br />
A. Nayak, A. S<strong>in</strong>clair, and U. Zwick. Spatial codes<br />
and <strong>the</strong> hardness of str<strong>in</strong>g fold<strong>in</strong>g problems. In Proceed<strong>in</strong>gs<br />
of <strong>the</strong> N<strong>in</strong>th Annual ACM-SIAM Symposium<br />
on D<strong>is</strong>crete Alg orithms, Philadelphia, January<br />
1998. ACM/SIAM. To appear.<br />
J. Ngo and J. Marks. Computat<strong>in</strong>al complexity of a<br />
problem <strong>in</strong> molecular structure prediction. <strong>Prote<strong>in</strong></strong><br />
Eng<strong>in</strong>eer<strong>in</strong>g, 5:313-321, 1992.<br />
J. Ngo, J. Marks, and M. Karplus. The <strong>Prote<strong>in</strong></strong><br />
<strong>Fold<strong>in</strong>g</strong> Problem and Tertiary Structure Prediction,<br />
chapter Computational complexity, prote<strong>in</strong><br />
structure prediction, and <strong>the</strong> Lev<strong>in</strong>thal paradox.<br />
Birkhauser, Basel, 1994. Edited by K.M. Merz<br />
and S.M. LeGrand.<br />
[22] M. Paterson and T. Przytycka. On <strong>the</strong> complexity<br />
of str<strong>in</strong>g fold<strong>in</strong>g. D<strong>is</strong>crete Applied Ma<strong>the</strong>matics,<br />
71:217-230, 1996.<br />
[23] R Unger and J. Moult. F<strong>in</strong>d<strong>in</strong>g <strong>the</strong> lowest free<br />
energy conformato<strong>in</strong> of a prote<strong>in</strong> <strong>is</strong> an np-hard<br />
prblem:proof and implications. Bull. Math. Biol.,<br />
55:1183-1198, 1993.<br />
39