References

1

Y. Ueda, H. Taketomi, and N. Go, Biopolymers 17, 1531 (1978).

2

N. Go, J. Stat. Phys. 30, 413 (1983).

3

J. Skolnick and A. Kolinski, J. Mol. Biol. 212, 787 (1990).

4

A. Sikorski and J. Skolnick, J. Mol. Biol. 212, 819 (1990).

5

J. Skolnick and A. Kolinski, J. Mol. Biol. 221, 499 (1991).

6

A. Kolinski, M. Milik, and J. Skolnick, J. Chem. Phys. 94, 3978 (1991).

7

A. Kolinski and J. Skolnick, J. Chem. Phys. 97, 9412 (1992).

8

H. S. Chan and K. A. Dill, Annu. Rev. Biophys. Biophys. Chem. 20, 447 (1991).

9

R. Miller, C. A. Danko, M. J. Fasolka, A. C. Balazs, H. S. Chan, and K. A. Dill, J. Chem. Phys. 96, 768 (1992).

10

H. S. Chan and K. A. Dill, J. Chem. Phys. 99, 2116 (1993).

11

H. S. Chan and K. A. Dill, J. Chem. Phys. 100, (1994).

12

K. M. Fiebig and K. A. Dill, J. Chem. Phys. 98, 3475 (1993).

13

E. I. Shakhnovich and A. M. Gutin, Nature 346, 773 (1990).

14

E. Shakhnovich, G. Farztdinov, A. M. Gutin, and M. Karplus, Phys. Rev. Lett. 67, 1665 (1991).

15

E. I. Shakhnovich and A. M. Gutin, Proc. Natl. Acad. Sci. USA 90, 7195 (1993).

16

C. J. Camacho and D. Thirumalai, Proc. Natl. Acad. Sci. USA 90, 6369 (1993).

17

J. D. Bryngelson and P. G. Wolynes, Proc. Natl. Acad. Sci. USA 84, 7524 (1987).

18

J. D. Bryngelson and P. G. Wolynes, J. Phys. C 93, 6902 (1989).

19

M. Sasai and P. Wolynes, Phys. Rev. Lett. 65, 2740 (1990).

20

R. A. Goldstein, Z. A. Luthey-Schulten, and P. G. Wolynes, Proc. Natl. Acad. Sci. USA 89, 4918 (1992).

21

When we say a protein has a single native state we are ignoring the different conformations real proteins may have. Our model is too coarse to represent the slight differences between conformations of proteins.

22

K. A. Dill, Biochemistry 29, 7133 (1990).

23

P. H. Verdier and W. H. Stockmayer, J. Chem. Phys. 36, 227 (1962).

24

H. J. Hilhorst and J. M. Deutch, J. Chem. Phys. 63, 5153 (1975).

25

K. Kremer and K. Binder, Comp. Phys. Rept. 7, 259 (1988).

26

M. T. Gurler, C. C. Crabb, D. M. Dahlin, and J. Kovac, Macromolecules 16, 398 (1983).

27

N. Madras and A. D. Sokal, J. Stat. Phys. 47, 573 (1987).

28

G. E. Schulz and R. H. Schirmer, Principles of Protein Structure (Springer-Verlag, New York, 1979).

29

We are using the word knot here in a descriptive sense meaning what is commonly meant when one puts a knot in a string. Whether proteins have knots in them in the mathematical sense is rather subtle since proteins are open loops and mathematical knots are defined on closed loops.

30

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. N. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).

31

O. B. Ptitsyn, in Protein Folding, edited by T. E. Creighton (W. H. Freeman and Company, New York, 1992), Chap. 6, pp. 243-300.

32

B. Derrida, Phys. Rev. B 24, 2613 (1981).

33

P. E. Leopold, M. Montal, and J. N. Onuchic, Proc. Natl. Acad. Sci. USA 89, 8721 (1992).

34

K. Kuwajima, Proteins 6, 87 (1989).

35

K. Kuwajima, Current Opinions in Biotechnology 3, 462 (1992).

36

R. L. Baldwin, Current Opinions in Structural Biology 3, 84 (1993).

37

A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 61, 2635 (1988).