The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the assembly dynamics. However, Brownian Dynamics of rotating anisotropic particles gives rise to a number of complications not encountered in translational Brownian Dynamics. We thoroughly test the Rotational Brownian Dynamics scheme proposed by Naess and Elsgaeter [Macromol. Theory Simul. 13, 419 (2004); Naess and Elsgaeter Macromol. Theory Simul. 14, 300 (2005)], confirming its validity. We then apply the algorithm to simulate a patchy particle model of clathrin, a three-legged protein involved in vesicle production from lipid membranes during endocytosis. Using this algorithm we recover time scales for cage assembly comparable to those from experiments. We also briefly discuss the undulatory dynamics of the polyhedral cage.
REFERENCES
1.
S. C.
Glotzer
and M. J.
Solomon
, Nat. Mater.
6
, 557
(2007
).2.
S.
Mann
, Nat. Mater.
8
, 781
(2009
).3.
G.
Yi
, D. J.
Pine
, and S.
Sacanna
, J. Phys.: Condens. Matter
25
, 193101
(2013
).4.
Z.
Zhang
, A. S.
Keys
, T.
Chen
, and S.
Glotzer
, Langmuir
21
, 11547
(2005
).5.
E.
Bianchi
, G.
Doppelbauer
, L.
Filion
, and M.
Dijkstra
, J. Chem. Phys.
136
, 214102
(2012
).6.
R.
Vacha
and D.
Frenkel
, Biophys. J.
101
, 1432
(2011
).7.
A. W.
Wilber
, J. P. K.
Doye
, A. A.
Louis
, E. G.
Noya
, M. A.
Miller
, and P.
Wong
, J. Chem. Phys.
127
, 085106
(2007
).8.
M. F.
Hagan
and D.
Chandler
, Biophys. J.
91
, 42
(2006
).9.
W. K.
den Otter
, M. R.
Renes
, and W. J.
Briels
, Biophys. J.
99
, 1231
(2010
).10.
W. K.
den Otter
and W. J.
Briels
, Traffic
12
, 1407
(2011
).11.
R.
Matthews
and C. N.
Likos
, Soft Matter
9
, 5794
(2013
).12.
D.
Frenkel
and B.
Smit
, Understanding Molecular Simulation
, 2nd ed. (Academic Press, Inc.
, Orlando, FL, USA
, 2001
).13.
D.
Landau
and K.
Binder
, A Guide to Monte Carlo Simulations in Statistical Physics
(Cambridge University Press
, New York, NY, USA
, 2005
).14.
C. D.
Michele
, T.
Bellini
, and F.
Sciortino
, Macromolecules
45
, 1090
(2012
).15.
P.
Strating
, Phys. Rev. E
59
, 2175
(1999
).16.
17.
X.
Sun
, T.
Lin
, and J. D.
Gezelter
, J. Chem. Phys.
128
, 234107
(2008
).18.
D. L.
Ermak
and J. A.
McCammon
, J. Chem. Phys.
69
, 1352
(1978
).19.
H.
Löwen
, Phys. Rev. E
50
, 1232
(1994
).20.
A.
Patti
and A.
Cuetos
, Phys. Rev. E
86
, 011403
(2012
).21.
Y.-G.
Tao
, W. K.
den Otter
, and W. J.
Briels
, Phys. Rev. Lett.
95
, 237802
(2005
).22.
H.
Goldstein
, Classical Mechanics
, 2nd ed. (Addison-Wesley Publishing Company
, Reading, MA
, 1980
).23.
M. P.
Allen
and D. J.
Tildesley
, Computer Simulation of Liquids
(Oxford University Press
, USA
, 1989
).24.
S. N.
Naess
and A.
Elgsaeter
, Macromol. Theory Simul.
13
, 419
(2004
).25.
T. R.
Evensen
, S. N.
Naess
, and A.
Elgsaeter
, Macromol. Theory Simul.
17
, 121
(2008
).26.
T. R.
Evensen
, S. N.
Naess
, and A.
Elgsaeter
, Macromol. Theory Simul.
17
, 403
(2008
).27.
T. R.
Evensen
, S. N.
Naess
, and A.
Elgsaeter
, Macromol. Theory Simul.
18
, 50
(2009
).28.
J.
Schluttig
, D.
Alamanova
, V.
Helms
, and U. S.
Schwarz
, J. Chem. Phys.
129
, 155106
(2008
).29.
G.
Huber
and S.
Kim
, Biophys. J.
70
, 97
(1996
).30.
M.
Cui
, J.
Shen
, J. M.
Briggs
, X.
Luo
, X.
Tan
, H.
Jiang
, K.
Chen
, and R.
Ji
, Biophys. J.
80
, 1659
(2001
).31.
J. H.
Sanchez
and C.
Rinaldi
, J. Magn. Magn. Mater
321
, 2985
(2009
).32.
P.
Nambi
, A.
Wierzbicki
, and S. A.
Allison
, J. Phys. Chem.
95
, 9595
(1991
).33.
H. C.
Öttinger
, Stochastic Processes in Polymeric Fluids. Tools and Examples for Developing Simulation Algorithms
(Springer
, Berlin
, 1996
).34.
S. N.
Naess
, H. M.
Adland
, A.
Mikkelsen
, and A.
Elgsaeter
, Physica A
294
, 323
(2001
).35.
S. N.
Naess
and A.
Elgsaeter
, Macromol. Theory Simul.
14
, 300
(2005
).36.
T. R.
Evensen
, A.
Elgsaeter
, and S. N.
Naess
, Colloids Surf., B
56
, 80
(2007
).37.
G.
Marsaglia
and W. W.
Tsang
, Stat. Probab. Lett.
66
, 183
(2004
).38.
D. J.
Griffiths
, Introduction to Electrodynamics
, 3rd ed. (Prentice Hall Inc.
, Upper Saddle River, NJ
, 1999
).39.
L. D.
Favro
, Phys. Rev.
119
, 53
(1960
).40.
J.
Garcia de la Torre
, S. E.
Harding
, and B.
Carrasco
, Eur. Biophys. J.
28
, 119
(1999
).41.
J.
Garcia de la Torre
and V. A.
Bloomfeld
, Q. Rev. Biophys.
14
, 81
(1981
).42.
Y. P.
Kalmykov
, J. Chem. Phys.
130
, 134105
(2009
).43.
R. A.
Crowther
and B. M. F.
Pearse
, J. Cell Biol.
91
, 790
(1981
).44.
F. M.
Brodsky
, Annu. Rev. Cell Dev. Biol
28
, 309
(2012
).45.
T.
Kirchhausen
, Annu. Rev. Biochem.
69
, 699
(2000
).46.
S. J.
Royle
, Cell. Mol. Life Sci.
63
, 1823
(2006
).47.
A.
Young
, Semin. Cell Dev. Biol.
18
, 448
(2007
).48.
A.
Fotin
, Y.
Cheng
, P.
Sliz
, N.
Grigorieff
, S. C.
Harrison
, T.
Kirchhausen
, and T.
Walz
, Nature
432
, 573
(2004
).49.
J. G.
de la Torre
, G.
del Rio
, and A.
Ortega
, J. Phys. Chem. B
111
, 955
(2007
).50.
J. G.
de la Torre
, S.
Navarro
, M. L.
Martinez
, F.
Diaz
, and J. L.
Cascales
, Biophys. J.
67
, 530
(1994
).51.
M. L.
Ferguson
, K.
Prasad
, D. L.
Sackett
, H.
Boukari
, E. M.
Lafer
, and R.
Nossal
, Biochemistry
45
, 5916
(2006
).52.
T.
Yoshimura
, K.
Kameyama
, S.
Maezawa
, and T.
Takagio
, Biochemistry
30
, 4528
(1991
).53.
W. M.
Gerlbart
, A.
Ben-Shaul
, and D.
Roux
, Micelles, Membranes, Microemulsions, and Monolayers
(Springer-Verlag
, New York
, 1994
).54.
M.
Muthukumar
and R.
Nossal
, J. Chem. Phys.
139
, 121928
(2013
).55.
M.
Saleem
, S.
Morlot
, A.
Hohendahl
, J.
Manzi
, M.
Lenz
, and A.
Roux
, “A balance between membrane elasticity and polymerization energy sets the shape of clathrin coats
,” Nat. Cell Biol. (submitted).56.
W.
Humphrey
, A.
Dalke
, and K.
Schulten
, J. Mol. Graphics
14
, 33
(1996
).57.
P. P. V.
Jaarsveld
, P. K.
Nandi
, R. E.
Lippoldt
, H.
Saroff
, and H.
Edelhoch
, Biochemistry
20
, 4129
(1981
).58.
H. T.
Pretorius
, R. R.
Lippoldt
, M. L.
Johnson
, J. H.
Keen
, I.
Pastan
, and H.
Edelhoch
, Biochemistry
20
, 2777
(1981
).59.
P. K.
Nandi
, P. P. V.
Jaarsveld
, R. E.
Lippoldt
, and H.
Edelhoch
, Biochemistry
20
, 6706
(1981
).60.
W. K.
den Otter
, M. R.
Renes
, and W. J.
Briels
, J. Phys.: Condens. Matter
22
, 104103
(2010
).61.
A. P.
Schoen
, N.
Cordella
, S.
Mehraeen
, M. A.
Arunagirinathan
, A. J.
Spakowitz
, and S. C.
Heilshorn
, Soft Matter
9
, 9137
(2013
).62.
See supplementary material at http://dx.doi.org/10.1063/1.4891306 for the expanded plot of the normalised undulatory auto-correlation function for the 36 triskelion hexagonal barrel.
63.
W. H.
Press
, S. A.
Teukolsky
, W. T.
Vetterling
, and B. P.
Flannery
, Numerical Recipes in FORTRAN; The Art of Scientific Computing
, 2nd ed. (Cambridge University Press
, New York, NY, USA
, 1993
).64.
In the simulated system, this bending rigidity of the cage results from the interaction potential between the rigid particles; in experiments, the internal flexibility of clathrin will also contribute to the cage's bending rigidity.
65.
U.
Seifert
and S. A.
Langer
, Europhys. Lett.
23
, 71
(1993
).66.
S. A.
Shkulipa
, W. K.
den Otter
, and W. J.
Briels
, Phys. Rev. Lett.
96
, 178302
(2006
).© 2014 AIP Publishing LLC.
2014
AIP Publishing LLC
You do not currently have access to this content.
