The ejection of a single polymer chain out of confinement is a ubiquitous phenomenon in various engineering and biological processes. A virus, for example, ejects a DNA from its viral capsid to a host cell in order to infect the host. The ejection of a polymer chain is often relatively fast such that the polymer hardly relaxes its conformation and stays in nonequilibrium states during the ejection. However, the effects of the nonequilibrium conformation on the ejection process still remain unanswered, especially when a complicated conformation such as a knot exists. In this study, we employ a generic coarse-grained model and perform extensive molecular simulations to investigate how the knot and its conformational relaxation would affect the kinetics of the ejection process. We find that the ejection becomes slower by a factor of nine or more when the polymer chain forms a knot conformation inside the confinement. The knot conformation makes the polymer chain highly tensed, thus hindering the polymer from being pulled from the capsid. In order to investigate the effect of the knot and its conformational relaxation systematically, we tune the molecular parameters of the polymer chain and control the degree of relaxation of the knot conformation. The relaxation of the knot conformation facilitates the ejection process significantly.

1.
U.
Sae-Ueng
,
D.
Li
,
X.
Zuo
,
J. B.
Huffman
,
F. L.
Homa
,
D.
Rau
, and
A.
Evilevitch
, “
Solid-to-fluid DNA transition inside HSV-1 capsid close to the temperature of infection
,”
Nat. Chem. Biol.
10
,
861
867
(
2014
).
2.
D.
Wu
,
D.
Van Valen
,
Q.
Hu
, and
R.
Phillips
, “
Ion-dependent dynamics of DNA ejections for bacteriophage λ
,”
Biophys. J.
99
,
1101
1109
(
2010
).
3.
I.
Ali
,
D.
Marenduzzo
, and
J. M.
Yeomans
, “
Ejection dynamics of polymeric chains from viral capsids: Effect of solvent quality
,”
Biophys. J.
94
,
4159
4164
(
2008
).
4.
A.
Evilevitch
,
L. T.
Fang
,
A. M.
Yoffe
,
M.
Castelnovo
,
D. C.
Rau
,
V. A.
Parsegian
,
W. M.
Gelbart
, and
C. M.
Knobler
, “
Effects of salt concentrations and bending energy on the extent of ejection of phage genomes
,”
Biophys. J.
94
,
1110
1120
(
2008
).
5.
P.
Grayson
,
L.
Han
,
T.
Winther
, and
R.
Phillips
, “
Real-time observations of single bacteriophage DNA ejections in vitro
,”
Proc. Natl. Acad. Sci. U. S. A.
104
,
14652
14657
(
2007
).
6.
A.
Evilevitch
, “
Effects of condensing agent and nuclease on the extent of ejection from phage λ †
,”
J. Phys. Chem. B
110
,
22261
22265
(
2006
).
7.
A.
Evilevitch
,
L.
Lavelle
,
C. M.
Knobler
,
E.
Raspaud
, and
W. M.
Gelbart
, “
Osmotic pressure inhibition of DNA ejection from phage
,”
Proc. Natl. Acad. Sci. U. S. A.
100
,
9292
9295
(
2003
).
8.
D.
Van Valen
,
D.
Wu
,
Y.-J.
Chen
,
H.
Tuson
,
P.
Wiggins
, and
R.
Phillips
, “
A single-molecule Hershey-Chase experiment
,”
Curr. Biol.
22
,
1339
1343
(
2012
).
9.
S.
Mangenot
,
M.
Hochrein
,
J.
Rädler
, and
L.
Letellier
, “
Real-time imaging of DNA ejection from single phage particles
,”
Curr. Biol.
15
,
430
435
(
2005
).
10.
N.
Keller
,
S.
Grimes
,
P. J.
Jardine
, and
D. E.
Smith
, “
Single DNA molecule jamming and history-dependent dynamics during motor-driven viral packaging
,”
Nat. Phys.
12
,
757
761
(
2016
).
11.
Y. R.
Chemla
and
T.
Ha
, “
Ultraslow relaxation of confined DNA
,”
Science
345
,
380
381
(
2014
).
12.
Z. T.
Berndsen
,
N.
Keller
,
S.
Grimes
,
P. J.
Jardine
, and
D. E.
Smith
, “
Nonequilibrium dynamics and ultraslow relaxation of confined DNA during viral packaging
,”
Proc. Natl. Acad. Sci. U. S. A.
111
,
8345
8350
(
2014
).
13.
D.
delToro
and
D. E.
Smith
, “
Accurate measurement of force and displacement with optical tweezers using DNA molecules as metrology standards
,”
Appl. Phys. Lett.
104
,
143701
143704
(
2014
).
14.
V. I.
Kottadiel
,
V. B.
Rao
, and
Y. R.
Chemla
, “
The dynamic pause-unpackaging state, an off-translocation recovery state of a DNA packaging motor from bacteriophage T4
,”
Proc. Natl. Acad. Sci. U. S. A.
109
,
20000
20005
(
2012
).
15.
A. S.
Petrov
and
S. C.
Harvey
, “
Packaging double-helical DNA into viral capsids: Structures, forces, and energetics
,”
Biophys. J.
95
,
497
502
(
2008
).
16.
J. P.
Rickgauer
,
D. N.
Fuller
,
S.
Grimes
,
P. J.
Jardine
,
D. L.
Anderson
, and
D. E.
Smith
, “
Portal motor velocity and internal force resisting viral DNA packaging in bacteriophage ϕ29
,”
Biophys. J.
94
,
159
167
(
2008
).
17.
T.
Sakaue
, “
Semiflexible polymer confined in closed spaces
,”
Macromolecules
40
,
5206
5211
(
2007
).
18.
J. P.
Rickgauer
,
D. N.
Fuller
, and
D. E.
Smith
, “
DNA as a metrology standard for length and force measurements with optical tweezers
,”
Biophys. J.
91
,
4253
4257
(
2006
).
19.
P. K.
Purohit
,
J.
Kondev
, and
R.
Phillips
, “
Mechanics of DNA packaging in viruses
,”
Proc. Natl. Acad. Sci. U. S. A.
100
,
3173
3178
(
2003
).
20.
S.
Tzlil
,
J. T.
Kindt
,
W. M.
Gelbart
, and
A.
Ben-Shaul
, “
Forces and pressures in DNA packaging and release from viral capsids
,”
Biophys. J.
84
,
1616
1627
(
2003
).
21.
J. T.
Kindt
,
S.
Tzlil
,
A.
Ben-Shaul
, and
W. M.
Gelbart
, “
DNA packaging and ejection forces in bacteriophage
,”
Proc. Natl. Acad. Sci. U. S. A.
98
,
13671
13674
(
2001
).
22.
D. E.
Smith
,
S. J.
Tans
,
S. B.
Smith
,
S.
Grimes
,
D. L.
Anderson
, and
C.
Bustamante
, “
The bacteriophage φ29 portal motor can package DNA against a large internal force
,”
Nature
413
,
748
752
(
2001
).
23.
J.
Arsuaga
,
M.
Vasquez
,
P.
McGuirk
,
S.
Trigueros
,
D. W.
Sumners
, and
J.
Roca
, “
DNA knots reveal a chiral organization of DNA in phage capsids
,”
Proc. Natl. Acad. Sci. U. S. A.
102
,
9165
9169
(
2005
).
24.
L. F.
Liu
,
L.
Perkocha
,
R.
Calendar
, and
J. C.
Wang
, “
Knotted DNA from bacteriophage capsids
,”
Proc. Natl. Acad. Sci. U. S. A.
78
,
5498
5502
(
1981
).
25.
C.
Micheletti
and
E.
Orlandini
, “
Knotting and unknotting dynamics of DNA strands in nanochannels
,”
ACS Macro Lett.
3
,
876
880
(
2014
).
26.
J.
Arsuaga
,
M.
Vazquez
,
S.
Trigueros
,
D. W.
Sumners
, and
J.
Roca
, “
Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids
,”
Proc. Natl. Acad. Sci. U. S. A.
99
,
5373
5377
(
2002
).
27.
D.
Li
,
T.
Liu
,
X.
Zuo
,
T.
Li
,
X.
Qiu
, and
A.
Evilevitch
, “
Ionic switch controls the DNA state in phage λ
,”
Nucleic Acids Res.
43
,
6348
6358
(
2015
).
28.
G. C.
Lander
,
J. E.
Johnson
,
D. C.
Rau
,
C. S.
Potter
,
B.
Carragher
, and
A.
Evilevitch
, “
DNA bending-induced phase transition of encapsidated genome in phage
,”
Nucleic Acids Res.
41
,
4518
4524
(
2013
).
29.
A. S.
Petrov
,
C. R.
Locker
, and
S. C.
Harvey
, “
Characterization of DNA conformation inside bacterial viruses
,”
Phys. Rev. E
80
,
021914
021919
(
2009
).
30.
L. R.
Comolli
,
A. J.
Spakowitz
,
C. E.
Siegerist
,
P. J.
Jardine
,
S.
Grimes
,
D. L.
Anderson
,
C.
Bustamante
, and
K. H.
Downing
, “
Three-dimensional architecture of the bacteriophage φ29 packaged genome and elucidation of its packaging process
,”
Virology
371
,
267
277
(
2008
).
31.
P. K.
Purohit
,
M. M.
Inamdar
,
P. D.
Grayson
,
T. M.
Squires
,
J.
Kondev
, and
R.
Phillips
, “
Forces during bacteriophage DNA packaging and ejection
,”
Biophys. J.
88
,
851
866
(
2005
).
32.
J.
Arsuaga
,
R. K.-Z.
Tan
,
M.
Vasquez
,
D. W.
Sumners
, and
S. C.
Harvey
, “
Investigation of viral DNA packaging using molecular mechanics models
,”
Biophys. Chem.
101-102
,
475
484
(
2002
).
33.
N. H.
Olson
,
M.
Gingery
,
F. A.
Eiserling
, and
T. S.
Baker
, “
The structure of isometric capsids of bacteriophage T4
,”
Virology
279
,
385
391
(
2001
).
34.
S.
Grimes
and
D.
Anderson
, “
The bacteriophage φ29 packaging proteins supercoil the DNA ends
,”
J. Mol. Biol.
266
,
901
914
(
1997
).
35.
T.
Saito
and
T.
Sakaue
, “
Dynamical diagram and scaling in polymer driven translocation
,”
Eur. Phys. J. E
34
,
135
(
2011
).
36.
T.
Sakaue
, “
Nonequilibrium dynamics of polymer translocation and straightening
,”
Phys. Rev. E
76
,
021803
021807
(
2007
).
37.
S.
Kwon
and
B. J.
Sung
, “
Effects of solvent quality and non-equilibrium conformations on polymer translocation
,”
J. Chem. Phys.
149
,
244907
244911
(
2018
).
38.
G.
Nir
,
M.
Lindner
,
H. R. C.
Dietrich
,
O.
Girshevitz
,
C. E.
Vorgias
, and
Y.
Garini
, “
HU protein induces incoherent DNA persistence length
,”
Biophys. J.
100
,
784
790
(
2011
).
39.
G. S.
Manning
, “
The persistence length of DNA is reached from the persistence length of its null isomer through an internal electrostatic stretching force
,”
Biophys. J.
91
,
3607
3616
(
2006
).
40.
K.
Kremer
and
G. S.
Grest
, “
Dynamics of entangled linear polymer melts: A molecular-dynamics simulation
,”
J. Chem. Phys.
92
,
5057
5086
(
1990
).
41.
M.
Yamanoi
,
O.
Pozo
, and
J. M.
Maia
, “
Linear and non-linear dynamics of entangled linear polymer melts by modified tunable coarse-grained level dissipative particle dynamics
,”
J. Chem. Phys.
135
,
044904
044910
(
2011
).
42.
F.
Goujon
,
P.
Malfreyt
, and
D. J.
Tildesley
, “
Mesoscopic simulation of entanglements using dissipative particle dynamics: Application to polymer brushes
,”
J. Chem. Phys.
129
,
034902
034910
(
2008
).
43.
T. W.
Sirk
,
Y. R.
Slizoberg
,
J. K.
Brennan
,
M.
Lisal
, and
J. W.
Andzelm
, “
An enhanced entangled polymer model for dissipative particle dynamics
,”
J. Chem. Phys.
136
,
134903
134911
(
2012
).
44.
L.
Dai
and
P. S.
Doyle
, “
Universal knot spectra for confined polymers
,”
Macromolecules
51
,
6327
6333
(
2018
).
45.
S.
Plipmtom
, “
Fast parallel algorithms for short-range molecular dynamics
,”
J. Comput. Phys.
117
,
1
19
(
1995
).
46.
T.
Sakaue
and
N.
Yoshinaga
, “
Dynamics of polymer decompression: Expansion, unfolding, and ejection
,”
Phys. Rev. Lett.
102
,
148302
148304
(
2009
).
47.
R.
Matthews
,
A. A.
Louis
, and
J. M.
Yeomans
, “
Knot-controlled ejection of a polymer from a virus capsid
,”
Phys. Rev. Lett.
102
,
088101
088104
(
2009
).
48.
A.
Suma
and
C.
Micheletti
, “
Pore translocation of knotted DNA rings
,”
Proc. Natl. Acad. Sci. U. S. A.
114
,
E2991
E2997
(
2017
).
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