Electrostatic effects in nanosystems are understood via a physical picture built on their multiscale character and the distinct behavior of mobile ions versus charge groups fixed to the nanostructure. The Poisson–Boltzmann equation is nondimensionalized to introduce a factor that measures the density of mobile ion charge versus that due to fixed charges; the diffusive smearing and volume exclusion effects of the former tend to diminish its value relative to that from the fixed charges. We introduce the ratio of the average nearest-neighbor atom distance to the characteristic size of the features of the nanostructure of interest (e.g., a viral capsomer). We show that a unified treatment (i.e., ) and a perturbation expansion around yields, through analytic continuation, an approximation to the electrostatic potential of high accuracy and computational efficiency. The approach was analyzed via Padé approximants and demonstrated on viral system electrostatics; it can be generalized to accommodate extended Poisson-Boltzmann models, and has wider applicability to nonequilibrium electrodiffusion and many-particle quantum systems.
REFERENCES
1.
A. T.
Fenley
, J. C.
Gordon
, and A.
Onufriev
, J. Chem. Phys.
129
, 075101
(2008
).2.
B. Z.
Lu
, Y. C.
Zhou
, M. J.
Holst
, and J. A.
McCammon
, Comm. Comp. Phys.
3
, 973
(2008
).3.
L.
David
and M. J.
Field
, J. Comput. Chem.
18
, 343
(1997
).4.
Y.
Vorobjev
and H. J.
Scheraga
, J. Comput. Chem.
18
, 569
(1997
).5.
A. J.
Bordner
and G. A.
Huber
, J. Comput. Chem.
24
, 353
(2003
).6.
A.
Nicholls
and B. J.
Honig
, J. Comput. Chem.
12
, 435
(1991
).7.
R. E.
Bruccoleri
, J.
Novotony
, M. E.
Davis
, and K. A.
Sharp
, J. Comput. Chem.
18
, 268
(1997
).8.
J. A.
Grant
, B.
Pickup
, and A.
Nicholls
, J. Comput. Chem.
22
, 608
(2001
).9.
G. T.
Balls
and P.
Colella
, J. Comput. Phys.
180
, 25
(2002
).10.
A. H.
Boschitsch
and M. O.
Fenley
, J. Comput. Chem.
25
, 935
(2004
).11.
A.
Sayyed-Ahmad
, K.
Tuncay
, and P.
Ortoleva
, J. Comput. Chem.
25
, 1068
(2004
).12.
N. A.
Baker
, D.
Sept
, S.
Joseph
, M. J.
Holst
, and J. A.
McCammon
, Proc. Natl. Acad. Sci. U.S.A.
98
, 10037
(2001
).13.
M.
Holst
and F.
Saied
, J. Comput. Chem.
14
, 105
(1993
).14.
S.
Chandrasekhar
, Astrophys. J.
97
, 255
(1943
).15.
S.
Bose
and P.
Ortoleva
, J. Chem. Phys.
70
, 3041
(1979
).16.
S.
Bose
and P.
Ortoleva
, Phys. Lett. A
69
, 367
(1979
).17.
S.
Bose
and P.
Ortoleva
, J. Chem. Phys.
72
, 4258
(1980
).18.
S.
Bose
, M.
Medina-Noyola
, and P.
Ortoleva
, J. Chem. Phys.
75
, 1762
(1981
).19.
J. M.
Deutch
and I.
Oppenheim
, Faraday Discuss. Chem. Soc.
83
, 1
(1987
).20.
21.
J. E.
Shea
and I.
Oppenheim
, J. Phys. Chem.
100
, 19035
(1996
).22.
J. E.
Shea
and I.
Oppenheim
, Physica A
247
, 417
(1997
).23.
M. H.
Peters
, J. Chem. Phys.
110
, 528
(1999
).24.
M. H.
Peters
, J. Stat. Phys.
94
, 557
(1999
).25.
W. T.
Coffey
, Y. P.
Kalmykov
, and J. T.
Waldron
, The Langevin Equation with Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering
(World Scientific
, River Edge
, 2004
).26.
P. Y.
Ayala
, G. E.
Scuseria
, and A.
Savin
, Chem. Phys. Lett.
307
, 227
(1999
).27.
J.
Almlof
, Chem. Phys. Lett.
181
, 319
(1991
).28.
C. J.
Cramer
, Essentials of Computational Chemistry: Theories and Models
, 2nd ed. (Wiley
, New York
, 2004
).29.
V.
Gogonea
, L. M.
Westerhoff
, and K. M.
Merz
, Jr., J. Chem. Phys.
113
, 5604
(2000
).30.
H.
Lin
and D.
Truhlar
, Theor. Chem. Acc.
117
, 185
(2007
).31.
H.
Araki
, J.
Ehlers
, K.
Hepp
, R.
Kippenhahn
, A. H.
Weidenmuller
, J.
Weiss
, and J.
Zittartz
, Homogenization Techniques for Composite Media
(Springer-Verlag
, Berlin
, 1987
).32.
A.
Bensoussan
, J. L.
Lyons
, and G.
Papanicolnon
, Asymptotic Analysis for Periodic Structures
(North-Holland
, Amsterdam
, 1978
).33.
34.
U.
Hornung
, Composite Media and Homogenization Theory: An International Center for Theoretical Physics Workshop
, Trieste, Italy, January 1990
(Birkhauser
, Boston
, 1991
).35.
J.
Keller
, Statistical Mechanics and Statistical Method in Theory and Application
(Plenum
, New York
, 1977
).36.
37.
K.
Tuncay
and P.
Ortoleva
, Probability Functionals, Homogenization and Comprehensive Reservoir Simulators. Resource Recovery, Confinement, and Remediation of Environmental Hazards, Institute of Mathematics and its Application
(Springer-Verlag
, New York
, 2002
).38.
P.
Ortoleva
, J. Phys. Chem. B
109
, 21258
(2005
).39.
Y.
Miao
and P.
Ortoleva
, J. Chem. Phys.
125
, 044901
(2006
).40.
Y.
Miao
and P.
Ortoleva
, J. Chem. Phys.
125
, 214901
(2006
).41.
S.
Pankavich
, Y.
Miao
, J.
Ortoleva
, Z.
Shrif
, and P.
Ortoleva
, J. Chem. Phys.
128
, 234908
(2008
).42.
R.
Burridge
and J. B.
Keller
, J. Acoust. Soc. Am.
70
, 1140
(1981
).43.
M.
Holst
, N.
Baker
, and F.
Wang
, J. Comput. Chem.
21
, 1319
(2000
).44.
45.
Y.
Zhou
, M.
Karplus
, K. D.
Ball
, and R. E.
Berry
, J. Chem. Phys.
116
, 2323
(2002
).46.
T. M.
Truskett
, S.
Torquato
, S.
Sastry
P. G.
Debenedetti
, and F. H.
Stillinger
, Phys. Rev. E
58
, 3083
(1998
).47.
A. C.
Eaton
, G.
Goodyear
, and A. D. J.
Haymet
, Phys. Chem. Chem. Phys.
3
, 3778
(2001
).48.
S.
Biggin
and J. E.
Enderby
, J. Phys. C
15
, L305
(1982
).49.
Z.
Tan
and S.
Chen
, J. Chem. Phys.
122
, 044903
(2005
).50.
F.
Fogolari
, P.
Zuccato
, G.
Esposito
, and P.
Viglino
, Biophys. J.
76
, 1
(1999
).51.
D.
Chapot
, B.
Lydéric
, and T.
Emmanuel
, J. Colloid Interface Sci.
285
, 609
(2005
).52.
J.
Adams
, Appl. Math. Comput.
34
, 113
(1989
).53.
J. C.
Blackburn
and P. K.
Kilpatrick
, Ind. Eng. Chem. Res.
35
, 2823
(1996
).54.
55.
R.
Konecny
, J.
Trylska
, F.
Tama
, D.
Zhang
, N. A.
Baker
, C. L.
Brooks
III, and J. A.
McCammon
, Biopolymers
82
, 106
(2006
).56.
57.
R. P.
Ojha
and R. K.
Tiwari
, Nucleic Acids Res.
31
, 6373
(2003
).58.
M.
Gruziel
, P.
Grochowski
, and J.
Trylska
, J. Comput. Chem.
29
, 1970
(2008
).59.
G. A.
Baker
and P. G.
Morris
, Padé Approximants (Encyclopedia of Mathematics and its Applications)
(Cambridge University Press
, Cambridge
, 1996
).60.
P.
Ortoleva
, J. Chem. Phys.
69
, 300
(1978
).61.
P.
Li
, A.
Naknanishi
, M. A.
Tran
, K. I.
Ishizu
, M.
Phillips
, H.
Hiroshi
, R. C.
Liddington
and H.
Kasamatsu
, J. Virol.
77
, 7527
(2003
).62.
V. B.
Chu
, Y.
Bai
, L.
Jan
, D.
Herschlag
, and S.
Doniach
, Biophys. J.
93
, 3202
(2007
).63.
M. J.
Holst
and F.
Saied
, J. Comput. Chem.
16
, 337
(1995
).64.
I.
Rouzina
and A.
Bloomfield
, Biophys. J.
74
, 3152
(1998
).65.
© 2010 American Institute of Physics.
2010
American Institute of Physics
You do not currently have access to this content.
