The phenomenon of thermal fluctuations of biopolymers has been of active interest for some time with a view toward understanding the effect of filament confinement, migration, and bonding. In this study, we focus our attention on planar fluctuations of a single filament between parallel confining surfaces. Filament slopes, with respect to the centerline of the channel, commonly exceed 0.1 in magnitude and therefore fall outside the range of small amplitude fluctuations. Consequently, large amplitudes are anticipated from the outset. Determination of the partition function leads to the quantitative dependence of free energy and other thermodynamic parameters on the degree of confinement.

References

1.
Odijk
,
T.
,
1983
, “
On the Statistics and Dynamics of Confined or Entangled Stiff Polymers
,”
Macromolecules
,
16
(
8
), pp.
1340
1344
.10.1021/ma00242a015
2.
Gittes
,
F.
,
Mickey
,
B.
,
Nettleton
,
J.
, and
Howard
,
J.
,
1993
, “
Flexural Rigidity of Microtubules and Actin-Filaments Measured From Thermal Fluctuations in Shape
,”
J. Cell Biol.
,
120
(
4
), pp.
923
934
.10.1083/jcb.120.4.923
3.
Howard
,
J.
,
2001
,
Mechanics of Motor Proteins and the Cytoskeleton
,
Sinauer Associates
,
Sunderland, MA
.
4.
Köster
,
S.
,
Stark
,
H.
,
Pfohl
,
T.
, and
Kierfeld
,
J.
,
2007
, “
Fluctuations of Single Confined Actin Filaments
,”
Biophys. Rev. and Lett.
,
2
(
2
), pp.
155
166
.10.1142/S1793048007000374
5.
Nöding
,
B.
, and
Köster
,
S.
,
2012
, “
Intermediate Filaments in Small Configuration Spaces
,”
Phys. Rev. Lett.
,
108
(
8
), p.
088101
.10.1103/PhysRevLett.108.088101
6.
Choi
,
M. C.
,
Santangelo
,
C. D.
,
Pelletier
,
O.
,
Kim
,
J. H.
,
Kwon
,
S. Y.
,
Wen
,
Z.
,
Li
,
Y.
,
Pincus
,
P. A.
,
Safinya
,
C. R.
, and
Kim
,
M. W.
,
2005
, “
Direct Observation of Biaxial Confinement of a Semiflexible Filament in a Channel
,”
Macromolecules
,
38
(
23
), pp.
9882
9884
.10.1021/ma051348n
7.
Dai
,
L.
, and
Doyle
,
P. S.
,
2013
, “
Comparison of a Polymer in Confinement Versus Applied Force
,”
Macromolecules
,
46
(
15
), pp.
6336
6344
.10.1021/ma400674q
8.
Wang
,
Y.
,
Tree
,
D. R.
, and
Dorfman
,
K. D.
,
2011
, “
Simulation of DNA Extension in Nanochannels
,”
Marcromolecules
,
44
(
16
), pp.
6594
6604
.10.1021/ma201277e
9.
de Gennes
,
P. G.
,
1971
, “
Reptation of a Polymer Chain in the Presence of Fixed Obstacles
,”
J. Chem. Phys.
,
55
(
2
), pp.
572
579
.10.1063/1.1675789
10.
Wang
,
B.
,
Guan
,
J.
,
Anthony
,
S. M.
,
Bae
,
S. C.
,
Schweizer
,
K. S.
, and
Granick
,
S.
,
2010
, “
Confining Potential When a Biopolymer Filament Reptates
,”
Phys. Rev. Lett.
,
104
(
11
), p.
118301
.10.1103/PhysRevLett.104.118301
11.
Dijkstra
,
M.
,
Frenkel
,
D.
, and
Lekkerkerker
,
H. N.
,
1993
, “
Confinement Free Energy of Semiflexible Polymers
,”
Physica A
,
193
(
3–4
), pp.
374
393
.10.1016/0378-4371(93)90482-J
12.
Press
,
W. H.
,
Teukolsky
,
S. A.
,
Vetterling
,
W. T.
, and
Flannery
,
B. P.
,
1996
,
Numerical Recipes in Fortran 77: The Art of Scientific Computing
, 2nd ed.,
Cambridge University Press, Cambridge, UK
.
You do not currently have access to this content.