We investigate the relation between backbone and side-chain ordering in a small protein. For this purpose, we have performed multicanonical simulations of the villin headpiece subdomain HP-36, an often used toy model in protein studies. Concepts of circular statistics are introduced to analyze side-chain fluctuations. In contrast to earlier studies on homopolypeptides [Wei et al, J. Phys. Chem. B111, 4244 (2007)], we do not find collective effects leading to a separate transition. Rather, side-chain ordering is spread over a wide temperature range. Our results indicate a thermal hierarchy of ordering events, with side-chain ordering appearing at temperatures below the helix-coil transition but above the folding transition. We conjecture that this thermal hierarchy reflects an underlying temporal order, and that side-chain ordering facilitates the search for the correct backbone topology.

1.
A.
Ghosh
,
R.
Elber
, and
H.
Scheraga
,
Proc. Natl. Acad. Sci. U.S.A.
99
,
10394
(
2002
).
2.
S.
Kmiecik
and
A.
Kolinski
,
Proc. Natl. Acad. Sci. U.S.A.
104
,
12330
(
2007
).
3.
G.
Favrin
,
A.
Irbäck
, and
S.
Wallin
,
Proteins: Struct., Funct., Genet.
47
,
99
(
2002
).
4.
H.
Li
,
M.
Fajer
, and
W.
Yang
,
J. Chem. Phys.
126
,
24106
(
2007
).
5.
A.
Jagielska
and
J.
Skolnick
,
J. Comput. Chem.
28
,
1648
(
2007
).
6.
T.
Herges
and
W.
Wenzel
,
Biophys. J.
87
,
3100
(
2004
).
7.
U. H. E.
Hansmann
and
Y.
Okamoto
,
Annual Reviews in Computational Physics
edited by
D.
Stauffer
(
World Scientific
,
Singapore
,
1999
), Vol.
6
, pp.
129
157
.
8.
C. J.
Geyer
and
A.
Thompson
,
J. Am. Stat. Assoc.
90
,
909
(
1995
).
9.
K.
Hukushima
and
K.
Nemoto
,
J. Phys. Soc. Jpn.
65
,
1604
(
1996
).
10.
U. H. E.
Hansmann
,
Chem. Phys. Lett.
281
,
140
(
1997
).
11.
B. A.
Berg
and
T.
Neuhaus
,
Phys. Lett. B
267
,
249
(
1991
).
12.
B. A.
Berg
and
T.
Celik
,
Phys. Rev. Lett.
69
,
2292
(
1992
).
13.
U. H. E.
Hansmann
and
Y.
Okamoto
,
J. Comput. Chem.
14
,
1333
(
1993
).
14.
W.
Kwak
and
U. H. E.
Hansmann
,
Phys. Rev. Lett.
95
,
138102
(
2005
).
15.
Y.
Wei
,
W.
Nadler
, and
U. H. E.
Hansmann
,
J. Chem. Phys.
125
,
164902
(
2006
).
16.
Y.
Wei
,
W.
Nadler
, and
U. H. E.
Hansmann
,
J. Phys. Chem. B
111
,
4244
(
2007
).
17.
U. H. E.
Hansmann
and
L.
Wille
,
Phys. Rev. Lett.
88
,
068105
(
2002
).
18.
C. Y.
Lin
,
C. K.
Hu
, and
U. H. E.
Hansmann
,
Proteins: Struct., Funct., Genet.
52
,
436
(
2003
).
19.
S.
Trebst
,
M.
Troyer
, and
U. H. E.
Hansmann
,
J. Chem. Phys.
124
,
174903
(
2006
).
20.
M. Y.
Shen
and
K. F.
Freed
,
Proteins
49
,
439
(
2002
).
21.
D. R.
Ripoli
,
J. A.
Vila
, and
H. A.
Scheraga
,
J. Mol. Biol.
339
,
915
(
2004
).
22.
C. J.
McKnight
,
P. T.
Matsudaira
, and
P. S.
Kim
,
Nat. Struct. Biol.
4
,
180
(
1997
).
23.
Y.
Duan
and
P. A.
Kollman
,
Science
282
,
740
(
1998
).
26.
J.
Shimada
,
E.
Kussell
, and
E. I.
Shakhnovich
,
J. Mol. Biol.
308
,
79
(
2001
).
27.
E.
Kussell
and
E. I.
Shakhnovich
,
Phys. Rev. Lett.
89
,
168101
(
2002
).
28.
M. J.
Sippl
,
G.
Némethy
, and
H. A.
Scheraga
,
J. Phys. Chem.
88
,
6231
(
1984
) and references therein.
29.
F.
Eisenmenger
,
U. H. E.
Hansmann
,
Sh.
Hayryan
, and
C.-K.
Hu
,
Comput. Phys. Commun.
138
,
192
(
2001
).
30.
F.
Eisenmenger
,
U. H. E.
Hansmann
,
Sh.
Hayryan
,
C.-K.
Hu
,
Comput. Phys. Commun.
174
,
422
(
2006
).
31.
T.
Ooi
,
M.
Obatake
,
G.
Nemethy
, and
H. A.
Scheraga
,
Proc. Natl. Acad. Sci. U.S.A.
8
,
3086
(
1987
).
32.
U. H. E.
Hansmann
,
J. Chem. Phys.
120
,
417
(
2004
).
33.
A. M.
Ferrenberg
and
R. H.
Swendsen
,
Phys. Rev. Lett.
61
,
2635
(
1988
);
[PubMed]
A. M.
Ferrenberg
and
R. H.
Swendsen
,
Phys. Rev. Lett.
63
,
1658
(E) (
1989
), and references given in the erratum.
34.
S.
Trebst
,
D. A.
Huse
, and
M.
Troyer
,
Phys. Rev. E
70
,
046701
(
2004
).
35.
W.
Nadler
and
U. H. E.
Hansmann
,
Phys. Rev. E
75
,
036702
(
2007
).
36.
Y.
Okamoto
and
U. H. E.
Hansmann
,
J. Phys. Chem.
99
,
11276
(
1995
).
37.

The threshold of 6Å to characterize nativelike structures follows remarks by H. A. Scheraga at CBSB06, Jülich, Germany, 2006.

38.
H.
Lei
,
C.
Wei
,
H.
Liu
, and
Y.
Duan
,
Proc. Natl. Acad. Sci. U.S.A.
104
,
4930
(
2007
).
39.
G. M. S.
De Mori
,
G.
Colombo
, and
M.
Micheletti
,
Proteins: Struct., Funct., Bioinf.
58
,
459
(
2005
).
40.
G.
Jayachandran
,
V.
Vishal
, and
V. S.
Pande
,
J. Chem. Phys.
124
,
164902
(
2006
).
41.
J.
Kubelka
,
W. A.
Eaton
, and
J.
Hofrichter
,
J. Mol. Biol.
329
,
625
(
2003
).
42.
J.
Kubelka
,
T. K.
Chiu
,
D. R.
Davies
,
W. A.
Eaton
, and
J.
Hofrichter
,
J. Mol. Biol.
359
,
546
(
2006
).
43.
N. I.
Fisher
,
Statistical Analysis of Circular Data
(
Cambridge University Press
,
Cambridge
,
1995
).
44.
K. V.
Mardia
and
P. E.
Jupp
,
Directional Statistics
(
Wiley
,
New York
,
1999
).
45.
S.
Rao Jammalamadaka
and
A.
SenGupta
,
Topics in Circular Statistics
(
World Scientific
,
Singapore
,
2001
).
46.
L. P.
Kadanoff
,
Statistical Physics: Statics, Dynamics and Renormalization
(
World Scientific
,
Singapore
,
2000
).
47.

For example, for angles α distributed equally in the interval [β,β], the resulting variance is Vsin(α)=[2βsin(2β)]4β. Clearly, larger fluctuations give rise to oscillations in Vsin(α). Consequently, only the range 0Vsin(α)<12 describes fluctuations somewhat reliably, the latter value holding for an equidistribution of angles.

You do not currently have access to this content.