Evaluating the transferability of coarse-grained, densitydependent implicit solvent models to mixtures and chains
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Citation
Allen, Erik C., and Gregory C. Rutledge. “Evaluating the
transferability of coarse-grained, density-dependent implicit
solvent models to mixtures and chains.” The Journal of Chemical
Physics 130.3 (2009): 034904.
As Published
http://dx.doi.org/10.1063/1.3055594
Publisher
American Institute of Physics
Version
Author's final manuscript
Accessed
Thu May 26 23:41:35 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/68988
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Detailed Terms
http://creativecommons.org/licenses/by-nc-sa/3.0/
Evaluating the Transferability of Coarse-Grained, Density
Dependent Implicit Solvent Models to Mixtures and Chains
Erik C. Allen, Gregory C. Rutledge*
Department of Chemical Engineering, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139 USA
*Corresponding author: rutledge@mit.edu
Keywords: Coarse-graining, implicit solvent, density dependence, mixing rule
Abstract:
Previously, we described a coarse-graining method for creating local density-dependent
implicit solvent (DDIS) potentials that reproduces the radial distribution function (RDF)
and solute excess chemical potential across a range of particle concentrations [E.C. Allen
and G.C. Rutledge, J. Chem. Phys. 128, 154115 (2008)]. In this work, we test the
transferability of these potentials, derived from simulations of monomeric solute in
monomeric solvent, to mixtures of solutes and to solute chains in the same monomeric
solvent. For this purpose, “transferability” refers to the predictive capability of the
potentials without additional optimization. We find that RDF transferability to mixtures
is very good, while RDF errors in systems of chains increase linearly with chain length.
Excess chemical potential transferability is good for mixtures at low solute concentration,
chains, and chains of mixed composition; at higher solute concentrations in mixtures,
chemical potential transferability fails due to the unique nature of the DDIS potentials.
With these results, we demonstrate that DDIS potentials derived for pure solutes can be
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transferability across a range of solute concentrations. This paper examines their
performance in other situations. Specifically, we create DDIS potentials generated from
simulations of pure monomeric solute particles in monomeric solvent, and then examine
the transferability of these potentials to two other cases – mixtures involving more than
one type of solute particle and solutes comprising chains particles – in the same implicit
solvent. These cases are of particular relevance for the study of surfactants, because
transferability would imply that one need parameterize CG potentials only for the head
and tail solute particles individually, thereby greatly extending their utility. Therefore,
we examine here the limits of transferability of density dependent potentials for these
cases.
II. Theory
!"#$i&'(N*&+&i*#(,*#-"#&i*#$(
In this work, !S refers to the &*&+/ density of solute particles, where the subscript “S”
stands for solute, and may include contributions from different solute types. !0,(!1, and
!,, respectively, are the densities of A, B, and C-type solute particles only. Finally, !
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5
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L
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! S,i
We also proposed a method to fit such potentials, such that the solute-solute RDF and
solute excess chemical potential, µAex, are reproduced across all solution compositions.
We present here only a brief sketch of the solution algorithm. For further details, the
reader is referred to Paper 1.38
The algorithm first involves generating pairwise potentials as a function of the global
solute density by performing RDF-inversion22 for a number of solute compositions.
Assuming that the distribution of local densities is centered about the global density in
these first simulations, the RDF-inversion potential obtained for a given global solute
density can then be taken as representative of the potential to be applied for a particle that
experiences a comparable local solute density, regardless of the actual global density of
the system in which the particle is found. Once the pairwise potentials are determined, an
iterative procedure is used to determine the self-interaction as a function of local solute
density such that the solute excess chemical potential is reproduced across all
compositions. The method does not guarantee fit to an arbitrary accuracy.
The measure of error in the RDF is given by the solute-solute energy, defined as:
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1#!
remaining system were switched off and a final state in which the test particle
interactions were fully enabled. Switching was applied to nonbonded interactions only,
with soft core interactions to avoid singularities and using a soft core interaction
parameter !=0.51. A total of 31 ! values were used (! = B0.00 0.03 0.0C 0.10 D. 0.E3
0.EC 1.00F).
Hmplicit solvent Ionte Jarlo simulations were carried out in the same manner as the
monomeric density dependent, implicit solvent simulations. Kearest bonded neighbor
particles were included in the calculation of local density. Hn addition to the chain
translation moves used for monomeric simulations, simulations of dimers included rigid
body rotation moves as well, in the proportion L0M translation:20M rotation. Por
tetramers, we also included rotation moves about individual bonds, in the proportion 50M
translation:20M rigid body rotation:30M bond rotation. Simulations of monomeric
solutes were equilibrated for 10# cycles, followed by sampling for 3 " 10# cycles.
Sampling of dimers was performed for twice as many cycles, or 6 " 10#, and chains of
length four were sampled for 1.2 " 105 IJ cycles. Pree energy was calculated using the
Bennett Acceptance Tation method##. Two ! values were used (! = B0.00,1.00F) with an
initial state comprising a non-interacting test particle and a final state having a fully
interacting test particle. Sampling was performed every two IJ cycles, which was
sufficient to generate statistically independent samples, as determined by the
autocorrelation function of the measured energy difference. TWP sampling was
performed every 100 IJ cycles.
1#
!"# %&'()*' +,- D/'0(''/1,
!
"#r%&'()!*+,)-!.-)/!&0!%1&-!23r4!
In the all-atom simulations described in this work, particles interact via the truncated and
shifted ;ennard-<ones potential, where the potential between particles & and 5 is described
by:
%%
'%! )* ! & !! "" " # !"#)* ! '+ ""# !!"# "" "# " ##&"# $ '+ ""#
!"#$% ! &"# !!"# "" "# "'(""# " # &% "# "# "# "#
'%
(%$###################################################&"# $ '+ ""#
("@)
with
*$#$ &$12 #$ &$& -$
" "#
" "# /$
! ! &"# !!"# ," "# " # 4!"# ,$%$
) %$
($
($
%$
($
%$
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'$ /$
.$
+$
$%
"#
("#)
where !&5 and "&5 are the ;ennard-<ones parameters for &5 interactions. Cquations ("@) and
("#) allow for the possibility of different cut-off radii (678&5) for interaction between
different particle types. ! and " values of unlike particles are governed by ;orentFGerthelot mixing rules.
In Iaper ", we examined the behavior of a single solute type (hereafter referred to as
JKL) in solvent (JML) at reduced temperature and density *9N".O# and #9NP.##. Gecause
the K-type particles were identical to the solvent M, the behavior of K-M mixtures was
identical for all compositions of K. Qor the work presented here, we find it useful to
"#
intro)*+e t-o a))itiona/ so/*te types3 -hi+h )isp/ay 5so/6ent7phi/i+8 an) 5so/6ent7
pho9i+8 9eha6ior3 respe+ti6e/y:
A so/*te<s re/ati6e pre=eren+e =or the so/6ent +an 9e meas*re) 9y the =ree energy o=
trans=er3 !!"@#""A3 )e=ine) as the =ree energy +hange asso+iate) -ith trans=erring a
sing/e so/*te parti+/e =rom a 9ath o= so/6ent parti+/es B to a 9ath o= so/*te parti+/es C:
Dhe =ree energy o= trans=er +an 9e +a/+*/ate) =rom the ex+ess +hemi+a/ potentia/ o= so/*te
parti+/esF
$%#
'%
$%#
'%
!!S ! # " S " # $Sex &% S # !)%* $Sex &% S # ")%
(%
%% #
(%
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@"#A
By 6arying parti+/e #$$<s an) %&,$(<s3 -e +reate) a 5so/6ent7phi/i+8 parti+/e @type BA an) a
5so/6ent7pho9i+8 parti+/e @type HA3 -ith intera+tion parameters gi6en in Da9/e ": Co/*te
type B is )isting*ishe) 9y its re)*+e) #) o= I:J3 +ompare) to ## o= ":I: Co/*te type H
intera+ts -ith the so/6ent B 6ia a re)*+e) +*to== ra)i*s o= ":KL$#3 -ith H7H an) B7B
intera+tions maintaining the *s*a/ J:I$# +*to==:
Da9/e " sho-s the so/*te enhan+ement ratio =or a// three types o= so/*te parti+/es at
%"M%NI:J: Dhe spe+i=i+ #$$<s an) %&,$(<s *se) -ere se/e+te) s*+h that B7type an) H7type
so/*te enhan+ement ratios -ere +/ose to ":I =or a// +ompositions: Dhis in)i+ates that 9oth
so/*te types3 -hi/e expressing re/ati6e pre=eren+e =or /iOe or *n/iOe intera+tions3 are
+omp/ete/y mis+i9/e in so/6ent at a// +ompositions3 an) 6a/i)ates the *se o= PQ*ations @#A7
@KA:
"#
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0/&'!&%(0*8.'-!('&+(0'1!*6!$%&'(!"=!%61!I+02!%('!-,&'(*+(!0+!02%0!+I0%*6'1!7+(!02'!C90/&'!
&+0'60*%.-?!!J2'!-0%61%(1!'((+(!*6!!(.!7+(!B90/&'!&%(0*8.'-!>%-!K?KL!/=!)'(-,-!K?""!/!7+(!C9
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(A2)
A similar equation can be written for the µ!’s. If values of µex$, µex!, !F1,$, and !F1,! can
be measured or estimated across as range of densities (!$,!!)? then the resulting system of
18 unknowns can then be optimiEed without the use of additional molecular simulations.
Fe elected to use a cubic correction instead of the simpler quadratic because
optimiEation over Equations (6)-(8) indicated a slightly superior fit with the cubic
correction. However, quadratic correction would likely provide adequate results in many
cases.
Fe examined the performance of this new algorithm in A/B/Z mixtures, and compared
the results to the original mixing rule. A subset of the results is shown in Figure A1. It
indicates that the two-dimensional density dependence improves transferability
substantially. The standard error with respect to µex is 0.18"( for the 13 points studied,
compared to 0.47"( for the original mixing rule.
Re#e$en&e'
1! S. IEvekov and U. A. Voth, W. Chem. Phys. ()*, 134105 (2005).
2! [. Shi, S. IEvekov, and U. A. Voth, W. Phys. Chem. B ((+, 15045 (2006).
3! S. IEvekov and U. A. Voth W. Chem. Phys. (),, 151101 (2006)
4! U. S. Ayton, F. U. \oid, and U. A. Voth, ]rs Bull. *), ^2^ (2007).
5! P. _iu, S. IEvekov, and U. A. Voth, W. Phys. Chem. B (((, 11566 (2007).
26
3
$
W. G. Noid, -. W. Chu, G. S. Ayton, and G. A. Voth, -. Phys. Chem. B !!!, 411$
(200#).
#
-. Bhou, I. F. Thorpe, S. IzveJov, and G. A. Voth, Biophys. -. "#, 4289 (200#).
8
-.D. McCoy and -.G. Curro, Macromolecules $!, 9Q$2 (1998).
9
R. Rremer and F. Muller-Plathe, Mol. Simulat. #%, #29 (2002).
10 N. B. Wilding, -. Chem. Phys. !!", 121$Q (200Q).
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12 M. Bathe, G. C. Rutledge, A. -. GrodzinsJy, and B. Tidor, Biophys. -. %%, Q8#0
(2005).
1Q G. C. Rutledge, Phys. Rev. W '$ 021111 (2000).
14 S. O. Nielsen, C. F. Yopez, G. Srinivas, and M. Y. Rlein, -. of Chem. Phys. !!",
#04Q (200Q).
15 W. Shinoda, R. Devane, and M. Y. Rlein, Mol. Simulat. $$, 2# (200#).
1$ R. Faller, H. Schmitz, O. Biermann, and F. Muller-Plathe, -. Comput. Chem. #(,
1009 (1999).
1# H. Meyer, O. Biermann, R. Faller, D. Reith, and F. Muller-Plathe, -. Chem. Phys.
!!$, $2$4 (2000).
18 D. Reith, H. Meyer, and F. Muller-Plathe, Macromolecules $&, 2QQ5 (2001).
19 D. Reith, M. Putz, and F. Muller-Plathe, -. Comput. Chem. #&, 1$24 (200Q).
20 G. Milano, S. Goudeau, and F. Muller-Plathe, -. Polym. Sci. Pol. Phys. &$ (8),
8#1 (2005).
21 G. Milano and F. Muller-Plathe, -. Phys. Chem. B !(", 18$09 (2005).
22 W. Schommers, Phys. Yett. A &$, 15# (19#Q).
2#
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Fig$re () $omparison of free energy changes upon particle insertion in the (a) allparticle and (b) density-dependent, implicit solvent cases. The density-dependent
potential introduces a secondary free energy change due to the change in energy models
associated with a change in global average solute density of the system.
Fig$re *) $omparison of excess chemical potential in all-atom (solid line) and coarsegrained (circles) simulations. LeftB C-type particles in solvent D. RightB $-type particles
in solvent D. The dashed lines demarcate errors of 0.06!!, and are provided as a guide to
compare the relative errors between the two coarse-grained potentials.
Fig$re +) $omparison of worst-fit solute RDF in all-atom (solid line) and coarse-grained
(circles) simulations. LeftB C-type particles in solvent D. RightB $-type particles in
solvent D.
Fig$re ,) $oarse-grained two-body term for local solute density ! S" /"=0.K (!A,-C,"""$)
Fig$re -) $oarse-grained one-body term as a function of local solute density ($irclesB Atype particles, SquaresB C-type particles, $rossesB $-type particles)
Fig$re .) Oorst case RDF reproduction for mixtures. Left SideB A/C/D mixture, Right
SiPeB A/$/D mixture (Solid Line Q all-atom resultsR $ircles QDDIS results).
30
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