We study the influence of structural obstacles in a disordered environment on the size and shape characteristics of long flexible polymer macromolecules. We use the model of self-avoiding random walks on diluted regular lattices at the percolation threshold in space dimensions d=2 and d=3. Applying the pruned-enriched Rosenbluth method, we numerically estimate rotationally invariant universal quantities such as the averaged asphericity Ad and prolateness S of polymer chain configurations. Our results quantitatively reveal the extent of anisotropy of macromolecules due to the presence of structural defects.

1.
K. W.
Plaxco
,
K. T.
Simons
, and
D.
Baker
,
J. Mol. Biol.
277
,
985
(
1998
);
[PubMed]
Z.
Ouyang
and
J.
Liang
,
Protein Sci.
17
,
1256
(
2008
).
[PubMed]
2.
H.
Neurath
,
G. R.
Cooper
, and
J. O.
Erickson
,
J. Biol. Chem.
138
,
411
(
1941
);
J.
García de la Torre
,
O.
Llorca
,
J. L.
Carrascosa
, and
J. M.
Valpuesta
,
Eur. Biophys. J.
30
,
457
(
2001
).
[PubMed]
3.
H. P.
Erickson
,
Biol. Proced. Online
11
,
32
(
2009
).
R. O.
Herzog
,
R.
Illig
, and
H.
Kudar
,
Z. Phys. Chem. Abt. A
167
,
329
(
1934
);
5.
C.
Domb
and
F. T.
Hioe
,
J. Chem. Phys.
51
,
1915
(
1969
).
6.
T. A.
Witten
and
L.
Schäfer
,
J. Phys. A
11
,
1843
(
1978
);
J.
des Cloizeaux
,
J. Phys.
42
,
635
(
1981
).
7.
K.
Šolc
and
W. H.
Stockmayer
,
J. Chem. Phys.
54
,
2756
(
1971
);
K.
Šolc
,
J. Chem. Phys.
55
,
335
(
1971
).
8.
D. E.
Kranbuehl
and
P. H.
Verdier
,
J. Chem. Phys.
67
,
361
(
1977
).
9.
M.
Benhamou
and
G.
Mahoux
,
J. Phys. (France) Lett.
46
,
689
(
1985
).
10.
J. A.
Aronovitz
and
D. R.
Nelson
,
J. Phys. (Paris)
47
,
1445
(
1986
).
11.
J.
Rudnick
and
G.
Gaspari
,
J. Phys. A
19
,
L191
(
1986
);
G.
Gaspari
,
J.
Rudnick
, and
A.
Beldjenna
,
J. Phys. A
20
,
3393
(
1987
).
12.
M.
Bishop
and
C. J.
Saltiel
,
J. Chem. Phys.
88
,
6594
(
1988
).
13.
J. D.
Honeycutt
and
D.
Thirumalai
,
J. Chem. Phys.
90
,
4542
(
1989
).
14.
J. L.
Cardy
and
H.
Saleur
,
J. Phys. A
22
,
L601
(
1989
).
15.
J. W.
Cannon
,
J. A.
Aronovitz
, and
P.
Goldbart
,
J. Phys. I
1
,
629
(
1991
).
16.
O.
Jagodzinski
,
E.
Eisenriegler
, and
K.
Kremer
,
J. Phys. I
2
,
2243
(
1992
).
17.
R. I.
Dima
and
D.
Thirumalai
,
J. Phys. Chem. B
108
,
6564
(
2004
);
C.
Hyeon
,
R. I.
Dima
, and
D.
Thirumalai
,
J. Chem. Phys.
125
,
194905
(
2006
).
[PubMed]
18.
N.
Rawat
and
P.
Biswas
,
J. Chem. Phys.
131
,
165104
(
2009
).
19.
A. L.
Dullen
,
Porous Media: Fluid Transport and Pore Structure
(
Academic
,
New York
,
1979
).
20.
P. N.
Pusey
and
W.
van Megen
,
Nature (London)
320
,
340
(
1986
).
21.
D. S.
Cannell
and
F.
Rondelez
,
Macromolecules
13
,
1599
(
1980
).
22.
S.
Kumar
and
M. S.
Li
,
Phys. Rep.
486
,
1
(
2010
).
23.
M. T.
Record
,
E. S.
Courtenay
,
S.
Cayley
, and
H. J.
Guttman
,
Trends Biochem. Sci.
23
,
190
(
1998
);
[PubMed]
A. P.
Minton
,
J. Biol. Chem.
276
,
10577
(
2001
);
[PubMed]
R. J.
Ellis
and
A. P.
Minton
,
Nature (London)
425
,
27
(
2003
).
24.
A.
Horwich
,
Nature (London)
431
,
520
(
2004
).
25.
D. J.
Winzor
and
P. R.
Wills
,
Biophys. Chem.
119
,
186
(
2006
);
[PubMed]
H. -X.
Zhou
,
G.
Rivas
, and
A. P.
Minton
,
Annu. Rev. Biophys.
37
,
375
(
2008
).
[PubMed]
26.
S.
Kumar
,
I.
Jensen
,
J. L.
Jacobsen
, and
A. J.
Guttmann
,
Phys. Rev. Lett.
98
,
128101
(
2007
);
[PubMed]
A. R.
Singh
,
D.
Giri
, and
S.
Kumar
,
Phys. Rev. E
79
,
051801
(
2009
).
27.
C.
Echeverria
and
R.
Kaprai
,
J. Chem. Phys.
132
,
104902
(
2010
).
28.
A.
Samiotakis
,
P.
Wittung-Stafshede
, and
M. S.
Cheung
,
Int. J. Mol. Sci.
10
,
572
(
2009
).
S.
Zimmerman
and
A. P.
Minton
,
Annu. Rev. Biophys. Biomol. Struct.
22
,
27
(
1993
).
[PubMed]
30.
M. S.
Cheung
,
D.
Klimov
, and
D.
Thirumalai
,
Proc. Natl. Acad. Sci. U.S.A.
102
,
4753
(
2005
);
[PubMed]
D.
Klimov
,
D.
Newfield
, and
D.
Thirumalai
,
Proc. Natl. Acad. Sci. U.S.A.
99
,
8019
(
2002
).
[PubMed]
31.
D.
Homouz
,
M.
Perham
,
A.
Semiotakis
,
M. S.
Cheung
, and
P.
Wittung-Stafshede
,
Proc. Natl. Acad. Sci. U.S.A.
105
,
11754
(
2008
).
32.
33.
34.
D.
Stauffer
and
A.
Aharony
,
Introduction to Percolation Theory
(
Taylor & Francis
,
London
,
1992
).
35.
K. Y.
Woo
and
S. B.
Lee
,
Phys. Rev. A
44
,
999
(
1991
);
[PubMed]
S. B.
Lee
,
J. Korean Phys. Soc.
29
,
1
(
1996
);
H.
Nakanishi
and
S. B.
Lee
,
J. Phys. A
24
,
1355
(
1991
);
S. B.
Lee
and
H.
Nakanishi
,
Phys. Rev. Lett.
61
,
2022
(
1988
).
[PubMed]
36.
P.
Grassberger
,
J. Phys. A
26
,
1023
(
1993
).
37.
A.
Ordemann
,
M.
Porto
, and
H. E.
Roman
,
Phys. Rev. E
65
,
021107
(
2002
);
A.
Ordemann
,
M.
Porto
, and
H. E.
Roman
,
J. Phys. A
35
,
8029
(
2002
).
38.
M. D.
Rintoul
,
J.
Moon
, and
H.
Nakanishi
,
Phys. Rev. E
49
,
2790
(
1994
).
39.
H. -K.
Janssen
and
O.
Stenull
,
Phys. Rev. E
75
,
020801
(R) (
2007
).
40.
V.
Blavatska
and
W.
Janke
,
Europhys. Lett.
82
,
66006
(
2008
);
V.
Blavatska
and
W.
Janke
,
Phys. Rev. Lett.
101
,
125701
(
2008
);
[PubMed]
V.
Blavatska
and
W.
Janke
,
J. Phys. A
42
,
015001
(
2009
).
41.
J.
Hoshen
and
R.
Kopelman
,
Phys. Rev. E
14
,
3438
(
1976
).
42.
M.
Porto
,
A.
Bunde
,
S.
Havlin
, and
H. E.
Roman
,
Phys. Rev. E
56
,
1667
(
1997
).
43.
P.
Grassberger
,
Phys. Rev. E
56
,
3682
(
1997
).
44.
M. N.
Rosenbluth
and
A. W.
Rosenbluth
,
J. Chem. Phys.
23
,
356
(
1955
).
45.
F. T.
Wall
and
J. J.
Erpenbeck
,
J. Chem. Phys.
30
,
634
(
1959
).
46.
H. P.
Hsu
,
V.
Mehra
,
W.
Nadler
, and
P.
Grassberger
,
J. Chem. Phys.
118
,
444
(
2003
).
47.
M.
Bachmann
and
W.
Janke
,
Phys. Rev. Lett.
91
,
208105
(
2003
);
[PubMed]
M.
Bachmann
and
W.
Janke
,
J. Chem. Phys.
120
,
6779
(
2004
).
[PubMed]
48.
S.
Caracciolo
,
A. J.
Guttmann
,
I.
Jensen
,
A.
Pelissetto
,
A. N.
Rogers
, and
A.
Sokal
,
J. Stat. Phys.
120
,
1037
(
2005
).
49.
50.
V.
Blavatska
,
C.
von Ferber
, and
Yu.
Holovatch
,
Phys. Lett. A
374
,
2861
(
2010
).
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