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Solvation of the Guanidinium Ion in Pure Aqueous Environments. A Theoretical Study from an "Ab Initio"-based Polarizable Force Field Céline Houriez, Michael Mautner, and Michel Masella J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b07874 • Publication Date (Web): 28 Nov 2017 Downloaded from http://pubs.acs.org on December 6, 2017
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The Journal of Physical Chemistry
Solvation of the Guanidinium Ion in Pure Aqueous Environments. A Theoretical Study from an “Ab Initio”-Based Polarizable Force Field. C´eline Houriez,† Michael Meot-Ner (Mautner),‡ and Michel Masella∗,¶ †MINES ParisTech, PSL Research University, CTP - Centre Thermodynamique des Proc´ed´es, 35 rue Saint-Honor´e, 77300 Fontainebleau, France ‡Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23284-2006, United States, and Department of Chemistry, University of Canterbury, Christchurch, New Zealand 8001 ¶Laboratoire de Biologie Structurale et Radiobiologie, Service de Bio´energ´etique, Biologie Structurale et M´ecanismes, Institut de Biologie et de Technologies de Saclay, CEA Saclay, F-91191 Gif sur Yvette Cedex, France E-mail:
[email protected] 1
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Abstract
1
2
We report simulation results regarding the hydration process of the guanidinium
3
cation in water droplets and in bulk liquid water, at a low concentration of 0.03 M,
4
performed using a polarizable approach to model both water/water and ion/water
5
interactions. In line with earlier theoretical studies, our simulations show a preferential
6
orientation of guanidinium at water/vacuum interfaces, i.e. a parallel orientation of the
7
guanidinium plane to the aqueous surface. In an apparent contradiction with earlier
8
simulation studies, we show also that guanidinium has a stronger propensity for the
9
cores of aqueous systems than the ammonium cation. However our bulk simulation
10
conditions correspond to weaker cation concentrations than in earlier studies, by two
11
orders of magnitude, and that the same simulations performed using a standard non-
12
polarizable force field leads to the same conclusion. From droplet data, we extrapolate
13
the guanidinium single hydration enthalpy value to be -82.9 ± 2.2 kcal mol−1 . That
14
is about half as large as the sole experimental estimate reported to date, about -
15
144 kcal mol−1 . Our result yields a guanidinium absolute bulk hydration free energy
16
at ambiant conditions to be -78.4 ± 2.6 kcal mol−1 , a value smaller by 3 kcal mol−1
17
compared to ammonium. The relatively large magnitude of our guanidinium hydration
18
free energy estimate suggests the Gdm+ protein denaturing properties to result from a
19
competition between the cation hydration effects and the cation/protein interactions, a
20
competition that can be modulated by weak differences in the protein or in the cation
21
chemical environment.
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The Journal of Physical Chemistry
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1
Introduction
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+ The guanidinium ion C(NH2 )+ 3 , denoted by Gdm , is an overall large, symmetric and planar
24
organic cation that plays a key role in biochemistry, in particular because it is the main
25
constituent of the arginine amino acid side chain. Gdm+ salts are also well known protein
26
denaturing agents, 1 even if we may note the conflicting observation that Gdm+ can be found
27
both at the head and at the tail of the cation Hofmeister series, 2,3 i.e. a series where ions are
28
ordered based on their ability in stabilizing/destabilizing folded protein structures. Other
29
striking properties of Gdm+ are (1) its ability to form charge-like pairs in aqueous environ-
30
ments, 3–5 even when belonging to arginine side chains, 6,7 and (2) its ability to preferentially
31
interact with aromatics than with aliphatics in aqueous phase. 8 The original properties of
32
Gdm+ are inferred to arise from asymmetric hydration properties tied to its planar structure.
33
For instance, the three Gmd+ NH2 moieties defining the cation symmetry plane are shown
34
from neutron scattering experiments to form NH − O hydrogen bonds with water molecules
35
in the Gdm+ first hydration shell, whereas the region above the Gdm+ symmetry plane is
36
considered as hydrophobic. 4
37
Despite noticeable efforts devoted to understand the original properties of Gdm+ , the
38
role of Gdm+ /water interactions on these properties is still largely debated, in particular
39
because of the lack of reliable experimental evidence and data regarding the Gdm+ hydration
40
process. For instance, the sole available experimental-based estimate of the Gdm+ single ion
41
hydration enthalpy ∆Hhyd (Gdm+ ) is 144 kcal mol−1 as reported recently by Y. Marcus. 9
42
However that value is considered as “puzzling” by the latter author 9 as it is even larger
43
by 10 kcal mol−1 than all the reported hydration enthalpy estimates of the smallest alkali
44
cation Li+ and also because that largely conflicts with the well accepted property of Gdm+ ,
45
i.e. it interacts weakly with water. 10–12 We may also note here that the latter experimental
46
∆Hhyd (Gdm+ ) value is conflicting with theoretical hydration free energy estimates ∆Ghyd
47
for Gdm+ that are about 60 kcal mol−1 from quantum computations where the solvent is
48
accounted for using a polarizable continuum approach. 13 Assuming the reliability of the 3
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latter experimental and theoretical thermodynamic values, they yield a hydration entropy
50
component −T∆Shyd for Gdm+ of 84 kcal mol−1 , a value which is one order of magnitude
51
larger than all the reported values for alkali and small organic cations 14 as well as the
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experimental-based value reported by Marcus 9 for Gdm+ (about 5 ± 1 kcal mol−1 ). Lastly
53
we may here also quote a recent experimental study of Heiles et al 15 dealing with the solvation
54
of Gdm+ in small water droplets (comprising at most 100 water molecules) that shows the
55
strength of the Gdm+ /water interactions to be modulated by the chemical surroundings.
56
In particular the latter authors concluded that Gdm+ interacts more strongly with water
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in chemical environments where water is partially excluded and that this feature is tied
58
to the effectiveness of Gdm+ as protein denaturant. Nevertheless these findings is a priori
59
contradictory with the large magnitude of the ∆Hhyd (Gdm+ ) value in bulk water.
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Theoretically, most of the studies devoted to investigating the Gdm+ hydration process
61
were performed using standard pairwise force fields, 4,5,7,16–19 whose accuracy is still debated
62
for such a cation. 17,18 More sophisticated theoretical approaches have been proposed, based
63
on a quantum ab initio scheme 20 or on polarizable force fields, 21–23 for instance. However,
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these approaches have still not been used to perform an in-depth analysis of the Gdm+
65
hydration process in various aqueous environments. Recently we proposed a rigid polarizable
66
force field for water, TCPE/2013, 24 whose parameters are mostly assigned from high level
67
quantum computations regarding small water clusters. In particular, this model is a priori
68
well suited to be used for investigating ion hydration processes in aqueous environments
69
(small clusters, large droplets, water/vacuum interfaces and bulk phase) not only because it
70
is able to accurately model a wide range of water systems under different physical conditions,
71
but also because we paid attention to assign its parameters to reproduce the magnitude of
72
the repulsive water/water interactions in cation first hydration shells. We have already
73
applied this water model to investigate the hydration process in water finite size systems or
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in bulk water of monoatomic heavy cations (Cm3+ and Th4+ ), 24 of methylated ammonium
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cations, 25,26 of monoatomic anions 27 and of alkylated carboxylates. 28 In these studies, we
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only assigned the force field parameters handling the ion/water interactions on the basis
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of high level quantum computational results. Even if there is still some room to improve
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our force-field approach, most of the results are in line with experiment. For instance,
79
by extrapolating ion/water interaction results from nanodrop simulations, we computed an
80
estimate of the proton hydration enthalpy ∆Hhyd (H+ ) in liquid water that ranges from 269
81
to 274 kcal mol−1 , depending on the ion considered, in good agreement with experimental
82
based estimates (ranging from 271 to 275 kcal mol−1 29–31 ). This demonstrates the capacity
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of the so-called ab initio-based force-fields to provide accurate data regarding the hydration
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process of any kind of ion, in particular those suffering from a lack of experimental evidence
85
in particular chemical environments.
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The aim of the present paper is to apply our ab initio-based force field methodology to
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the particular case of the Gdm+ ion to complement the available data regarding its hydration
88
process both in aqueous nanodrops and in bulk environments. At the difference of recent
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theoretical studies dealing with guanidinium/chloride salts, 17,18 here we simulate Gdm+ as
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solvated alone in water environnements in order to estimate its individual hydration prop-
91
erties. This is the first step to understand the hydration properties of aqueous Gdm+ /anion
92
salt solutions (in particular to discuss the existence and thus the possible consequences of
93
Gdm+ /anion/water cooperative effects).
94
As standard (i.e. non polarizable) force fields were shown to reproduce recent experi-
95
mental studies about the solvation of guanidinium/chloride salt solutions, 17,18 we performed
96
all our simulations twice by using also the standard force field proposed by Wernersson et
97
all 17 to cross check the reliability both of our polarizable approach and of standard force
98
fields to investigate the Gdm+ hydration properties. Lastly, as the ammonium cation is the
99
second kind of positively charged chemical groups present in amino acids, we will here also
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compare the hydration properties of Gdm+ to the NH+ 4 ones as computed from out polariz-
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able approach (here we consider the data reported in our recent studies 25,26 ) and also from
102
the standard additive force field used by Werner and coworkers 19 (however only in the liquid
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water-vacuum case).
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2
105
In the following, M is the total number of atoms considered, Mion is the total number of
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atoms in an ion, Mµ is the total number of polarizable atoms, N is the total number of water
107
molecules and Mw is the total number of atoms belonging to the water molecules.
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2.1
109
The interactions of Gdm+ with 1 to 3 water molecules are investigated using ab initio quan-
110
tum computations at the MP2 level (using the frozen core approximation) with the basis
111
sets aug-cc-pVXZ (X = D,T and Q). The Gdm+ /water binding energies, ∆U , are computed
112
from aggregate geometries optimized at the same level of theory for X=D and T, and from
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aug-cc-pVTZ ones for X=Q. All ab initio computations are performed with the package of
114
programs GAUSSIAN09 version C01. 32 Complete Basis Set (CBS) limit estimates of the
115
Gdm+ /water aggregate binding energies are extrapolated from our MP2/aug-c–pVXZ data
116
according to standard schemes. 33,34 We also computed at the MP2/CBS limit level of the-
117
ory two radial elongation profiles corresponding to the interaction of Gdm+ with a single
118
water molecule. These profiles correspond to (1) a water molecule interacting with two NH2
119
moieties in the Gdm+ plane (see the cation/water hetero dimer structure shown in Figure
120
1), and (2) a water molecule set orthogonally to the Gdm+ plane (see Figure 2). These
121
two profiles are computed for oxygen-carbon distances ranging from 2 to 8 ˚ A and regularly
122
spaced. We also performed single energy point calculations at the coupled cluster level of
123
theory, including single, double and triple excitations, CCSD(T), using the above basis sets
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for a few hydrated Gdm+ aggregates. The CCSD(T) results agree with the MP2 ones within
125
less than 0.1 kcal mol−1 .
Theoretical details
Quantum Computations
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2.2
Molecular Force Fields
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Our polarizable force field is based on a decomposition of the total potential energy U of
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Gdm+ /water systems into three main energy terms, namely the ion internal energy U rel ,
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and the ion/water U iw and water/water U ww interaction energies. For U ww , we consider
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the rigid and polarizable water model TCPE/2013 24 that was shown to provide an accurate
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description of both isolated water clusters in vacuum and bulk water systems for a wide range
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of temperature and pressure conditions. Besides a specific anisotropic many body energy
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term U lh introduced to accurately model water hydrogen bond (HB) networks, TCPE/2013
134
also considers a repulsive U rep term, a Coulombic U qq term, and a polarization U pol term
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based on an induced dipole moment approach that includes damping effects: 24
0
U rep =
X
aij exp (−bij rij ) ,
(1)
1 X qi qj , 4π0 i,j rij
(2)
i,j 136 0
U qq = 137
N
U pol
N
N
N∗
µ µ µ µ X p2i X 1X 1X pi Tij pj . = − pi · Eqi − 2 i=1 αi i=1 2 i=1 j=1
(3)
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Here, the sums run on pairs of atoms i and j belonging to different molecules. rij is the
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distance between the atoms i and j. The {qi } are the static charges located on atomic centers.
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aij and bij are adjustable parameters. αi is the isotropic polarizability of a polarizable atomic
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centre i (all the atoms except the hydrogens), Tij is the dipolar interaction tensor and Eqi
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is the electric field generated on the polarizable center i by the surrounding static charges
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qj . Tij and Eqi include both a short range damping component. These energy terms were
144
already detailed in our former studies dealing with ammonium and carboxylate ions. 25,28 To
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model the Gdm+ /water interactions, we consider also the three above intermolecular terms
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to which we add a standard additive dispersion term U disp
U
disp
=−
X i,j
ij
∗ rij rij
!6
.
(4)
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∗ are two adjustable parameters. The Gdm+ /water interaction potential U iw Here, ij and rij
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is thus the same sum of four terms that we considered to investigate the hydration process
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of methylated ammonium cations 0
U iw = U rep + U qq + U pol + U disp .
(5)
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The Gdm+ intramolecular degrees of freedom are handled by a dedicated relaxation en-
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ergy term U rel , which includes standard stretching, bending and torsional terms and an
152
improper torsional term U imp =
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gles centered on the cation carbon and nitrogen atoms. As in our former studies, we still
154
consider for the stretching and bending intramolecular term the parameters of the force
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field CHARMM v2.7. 35 As we systematically constrain the X − H bonds and the H − X − H
156
angles along our simulations and as we simulate Gdm+ in pure water environments (that
157
prevents the force-field artifacts mentioned in Ref. 17 and originating from Gdm+ /chloride
158
interactions), the choice of the stretching and bending parameters has an overall negligible
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effect on our gas phase cluster results. Concerning the standard dihedral 6 N − C − N − H
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torsional term, we assign its parameters to reproduce the ab initio energy profile correspond-
161
ing to that degree of freedom from MP2/aug-cc-pVTZ data (see Supporting Information).
1 k ψ2, 2 imp
where ψ stands for the improper dihedral an-
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To assign the U iw parameters, we consider as reference data the ab initio results con-
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cerning three small guanidium/(H2 O)n clusters (n=1-3) in their geometries optimized at the
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MP2/aug-cc-pVTZ level and the two radial elongation profiles mentioned in the above sec-
165
tion. All the energy data correspond to extrapolated MP2/CBS limit values from MP2(FC)/aug-
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cc-pVXZ computations (X=D,T and Q). As in our former studies, 25,28 the static electrostatic
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charges of the Gdm+ atoms were assigned from the quantum Natural Population Analysis 8
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results concerning the isolated ion at the MP2/aug-cc-pVTZ level. The Gdm+ atomic po-
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larizabilities were assigned to reproduce the experimental ion molecular polarizability (4.4
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˚ ˚3 ), A3 , 9 a value that agrees with the one computed at the MP2/aug-cc-pVTZ level, 4.0 A
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˚3 , respectively. Here we by setting the carbon and nitrogen polarizabilities to 0.8 and 1.2 A
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only consider the three Gdm+ nitrogens as dispersion centers. The parameter set is able to
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reproduce the Gdm+ /water interaction energies within less than 0.5 kcal mol−1 on average
174
and the Gdm+ distances N · · · O within about 0.01 ˚ A (see Figure 1 and more details are
175
provided as Supporting Information).
176
For comparison purposes, we performed all our computations twice using a standard non
177
polarizable force field (for which the inter molecular interactions are decomposed into two
178
additive energy terms, the Lennard-Jones and the Coulombic ones) used in conjunction with
179
a parameter set that was shown to successfully reproduce experimental results regarding the
180
behavior of Gdm+ /Cl− salts at the liquid water-vacuum interface. 17,19 Regarding the stepwise
181
binding energies of the micro hydrated Gdm+ clusters shown Figure 1, the standard force
182
field provides fairly accurate results compared to quantum MP2/CBS data, within about 1
183
kcal mol−1 on average (see Figure 1). However it overestimates the Gdm+ nitrogen/water
184
oxygen distance in the latter clusters compared to quantum computations, by about 0.15 ˚ A
185
on average. Regarding the case of a water molecule interacting orthogonally to the Gdm+
186
plane, the standard force field predicts the carbon/oxygen distance corresponding to the
187
A. Gdm+ /water interaction energy minimum to be greater than the quantum one by 0.5 ˚
188
Note also that force field systematically overestimates the Gdm+ /water binding energy by
189
1 kcal mol−1 for carbon/oxygen distances greater than 3.5 ˚ A. Lastly, we investigated also
190
the behavior of the ammonium cation NH+ 4 at the liquid water/vacuum interface using the
191
standard additive force field used by the above authors. 17,36
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2.3
Simulation details
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We detail here briefly the theoretical protocol that we used to perform the simulations when
194
using both our polarizable force field and the standard one. More details are provided as
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Supporting Information. All the molecular modeling computations were performed with
196
our in-house code POLARIS(MD). All the molecular dynamics, MD, simulations of ions
197
solvated either in nanodrops or at the liquid water-vacuum interface are performed in the
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NVT ensemble, while bulk simulations are done in the NPT ensemble. The simulations
199
are all performed at the 10 ns scale according to the same theoretical protocol as in our
200
former studies. 25,26,28 In particular, bulk and liquid water-vacuum interface simulations are
201
performed using the SPME approach detailed in Ref. 37 The trajectories are sampled each 1
202
ps to generate the ensemble used to compute the statistical averages.
203
To minimize the effects of water evaporation phenomena in nanodrop simulations, we
204
consider the droplets confined in a spherical cavity, whose radius corresponds to the largest
205
distance droplet center of mass (COM)/water oxygen to which 12 ˚ A is added. As a water
206
molecule crosses the cavity boundary, it undergoes a smooth repulsive potential favoring
207
it returns to the main droplet region as we proposed recently. 26 Note that this repulsive
208
potential has no effect on the droplet dynamics, as it is zero for any atom/droplet COM
209
distance smaller than the cavity radius.
210
The potentials of mean force (PMF) corresponding to the interaction of Gdm+ with
211
a water system (droplet or liquid water) are computed according to a standard umbrella
212
sampling protocol. The degree of freedom harmonically constrained during the simulations
213
is the distance r between the Gdm+ carbon and the droplet COM or the projection z of the
214
distance between that carbon and the simulation cell center (SCC) on the axis orthogonal
215
to the liquid water-vacuum interface. We denote rc and zc the target values of the latter
216
parameters along the umbrella sampling simulations. The PMF are computed from the
217
constrained simulations at the 10 ns scale using the Umbrella Integration scheme. 38
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3
Results and discussion
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In the following, if not mentioned the results correspond to our polarizable force field. We
220
note l⊥ the axis orthogonal to the Gdm+ symmetry plane (computed as the cross product
221
of two of the three carbon-nitrogen vectors).
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3.1
223
The Gdm+ carbon-water oxygen and Gdm+ nitrogen-water oxygen radial distribution func-
224
tions gC (r) and gN (r) in liquid water at ambient conditions (and the results of their inte-
225
gration) computed along our bulk MD simulations are shown in Figure 3. We also plot on
226
that figure the functions gX (r, φ0 ) corresponding to atom pairs for which the angle φ between
227
the axe connecting them and the vector l⊥ obeys |φ| ≥ φ0 , as well as the complementary
228
functions gX∗ (r, φ0 ) = gX (r) − gX (r, φ0 ). We set the angle φ0 to the values 30 and 60◦ for the
229
carbon and the nitrogen-centered functions, respectively. All these functions are scaled by
230
the mean water bulk density ρwater at ambiant conditions (0.0331 molecules per ˚ A3 ), and the
231
nitrogen ones are averaged over the three nitrogen data. The functions gC (r) and gN (r) con-
232
verge thus towards ρ˜water = 1 for large r values, and the functions gX∗ (r, φ0 ) converge towards
233
ρ˜φ0 = ρ˜water cos(φ0 ) (for φ0 = 30◦ and 60◦ we get then ρ˜φ0 = 0.87 and 0.50, respectively).
Guanidinium structural properties in bulk water
234
The function gC (r) is characterized by a first peak located at about 3.8 ˚ A that ends at
235
about 5.4 ˚ A. That peak corresponds to the first hydration shell of the Gdm+ central carbon,
236
which comprises about n ¯ C = 20.5 ± 0.5 water molecules. That value equals the number
237
of water molecules in the first hydration shell of the methane molecule. 39 The second peak
238
of gC (r) (located at about 6.3 ˚ A) is particularly flat. Lastly, gC (r) may be considered as
239
converged to ρ˜water as soon as 7 ˚ A. From the plots of the functions gC (r, 30◦ ) and gC∗ (r, 30◦ ),
240
it appears that the water molecules can be closer by about 0.2 ˚ A to the Gdm+ carbon atom
241
when located in the apical direction of the Gdm+ plane than when they are in the plane.
242
The function gN (r) is characterized by two sharp peaks located around 2.9 and 4.9 ˚ A.
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However, their heights are only 1.60 and 1.25, respectively. Between these peaks, we note
244
a much flatter peak at about 3.7 ˚ A (its height is about 1.10). By comparing the profiles of
245
A of the function gN (r) the functions gN (r, 60◦ ) and gN∗ (r, 60◦ ), the two peaks at 2.9 and 4.9 ˚
246
correspond to water molecules interacting with the three Gdm+ NH2 moieties mainly in the
247
cation symmetry plane, while the gN (r) peak at 3.7 ˚ A arises mainly from water molecules
248
located above this plane. The weak heights of the gN (r) first peaks agree with all the
249
former experimental and theoretical conclusions regarding Gdm+ , i.e. the weakness of its
250
hydration structure, which is usually inferred to be at the origin of its protein denaturing
251
agent nature. 10
252
The main features of our radial distribution functions are in line with those computed
253
from the standard force field simulations (see Supporting Information). The main difference
254
between these two kinds of functions is the location of their first peaks. The standard force
255
field ones are shifted to larger distances compared to our polarizable model, by about 0.2
256
(nitrogen) and 0.5 (carbon) ˚ A for gX (r) and gX (r, φ0 ) functions. That was expected from
257
the comparison of quantum and standard force field structures of the dimer Gdm+ /H2 O (see
258
∗ Section 2.1). Regarding the complementary functions gX,φ , the polarizable and standard 0
259
force field ones remarkably agree, even if the first peak location of standard force field
260
functions is also shifted to larger Gdm+ /water distances.
261
In line with Warren and Patel, 40 we assume the sum of the water and Gdm+ molecular
262
radii Rwater +RGdm+ to correspond to the most probable carbon/water oxygen distance in the
263
Gdm+ first hydration shell. Our data yields then Rwater + RGdm+ = 3.8 ˚ A. From pure liquid
264
water simulations, the TCPE/2013 water model yields Rwater = 1.4 ˚ A. Hence RGdm+ = 2.4
265
˚ A, a value which is in line with that reported by Marcus, 2.1 ± 0.2 ˚ A. 9 The standard force
266
field leads to a slightly larger value for RGdm+ , about 2.6 ˚ A. Lastly, the data of our former
267
study focusing on methylated ammonium ions yields RNH+4 = 1.4 ˚ A.
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268
3.2
269
3.2.1
270
The Gdm+ PMF profiles at droplet or at liquid water-vacuum interfaces and computed
271
from our polarizable approach are plotted as a function of the distance r or z in Figure 4,
272
+ together with the profiles of NH+ 4 and of K (only in the liquid water/vacuum case for the
273
latter cation). For the latter two ions their liquid water-vacuum profiles are taken from our
274
earlier study dealing with methylated ammonium cations. 25 The Gdm+ droplet PMF profiles
275
computed from the standard force field are provided as Supporting Information, and in the
276
liquid water/vacuum case, the PMF is also plotted in Figure 4(b) (together with the NH+ 4
277
one as computed also from a standard force field 36 ). The PMF profiles are set to zero at the
278
droplet centers and at the water slab cores.
279
280
Guanidinium properties at the water-vacuum interface Guanidinium propensity for water-vacuum interfaces
From the PMF functions, we define in the present study the ion propensity for the water/vacuum interface, PI, in the droplet case as ! Z r+ PMF(r) 1 Z r+ exp − P (r)dr = × 4πr2 dr, PI = Z r− kB T r−
(6)
281
here, P (r) is the ion location probability density, Z is the normalization factor, and r− and
282
r+ are the distances for which the water density drops from 95% to 5% of its value within
283
the droplet core (typically r+ − r− = 4 ˚ A). PI is thus the probability for an ion to be at the
284
droplet surface. In the liquid water/vacuum case, we define PI as
PI =
Z
z+
z−
h
!
i PMF(z) exp − − 1 dz, kB T
(7)
285
here, z − and z + are defined as above. In the slab case, the PI definition is reminiscent of
286
the function usually considered to estimate the surface excess/deficiency of a species. 41 The
287
PI numerical values are summarized in Figure 4.
288
In the droplet case, the PI value decreases as the droplet size increases regardless of
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289
the ion and the force field. Our polarizable approach predicts the Gdm+ PI values to be
290
+ from 3 to 5 times smaller than the NH+ 4 ones, and the standard force field Gdm values are
291
in between the latter ones. In line with the standard force field, our polarizable approach
292
predicts thus Gdm+ to have a weaker propensity for the droplet surface than NH+ 4 . The plots
293
of Figure 4(b) also show that Gdm+ is predicted by both our our polarizable approach and
294
the standard force field to have a weaker propensity for the liquid water/vacuum interface
295
+ than both NH+ 4 and K .
296
Regarding our polarizable approach, the weakest propensity of Gdm+ for aqueous inter-
297
+ faces compared to NH+ 4 and K may be explained not only from both its large size and its
298
structure (that are inferred to be responsible for its hydration asymmetric properties 12,19 ),
299
but also because ion/water dispersion plays a stronger role for the Gdm+ hydration than for
300
+ the hydration of the two smaller cations NH+ 4 and K . From the plots of the mean ion/water
301
interaction energy values within the droplets (see Supporting Information), it appears that
302
the Gdm+ /water U¯ iw profile is very flat within the droplets, and that the ion/water energy
303
iw iw components U¯rep and U¯pol are centrifugal whereas the energy term U¯ ww and the ion/water
304
iw iw are centripetal. All these results are in line with our earlier and U¯qq energy components U¯disp
305
ones regarding both methylated ammonium and alkylated carboxylate ions. 25,28 They sug-
306
gest thus the hydration energetics of monovalent ions to obey a common pattern (within the
307
framework of our polarizable force field). However, the magnitude of the latter energy terms
308
iw values and components depends on the ion nature. In particular, the difference in the U¯disp
309
between the droplet core and the droplet surface is about twice as large for Gdm+ than for
310
25 + NH+ 4 (see Ref. ). Moreover, in the Gdm case, the latter difference is larger in magnitude
311
than the one corresponding to the sum of the electrostatic and polarization energy com-
312
ponents. As dispersion is an isotropic energy term favoring hydration within aqueous core
313
environment, that explains (at least partially) the weaker propensity of Gdm+ compared to
314
NH+ 4 for the droplet surface.
315
Another striking feature of the Gdm+ droplet PMF profiles computed from our polariz-
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316
able approach is their very close properties among them and also as compared to the liquid
317
water-vacuum profile. That suggests the interfacial behavior of Gdm+ to be independent
318
from aqueous environments comprising at least 200 water molecules. That seems to be in
319
line with a recent infrared dissociation (IRPD) spectroscopy study of Heiles et al 15 of Gdm+
320
hydrated in small water environments (comprising from 5 to 100 water molecules) and show-
321
ing the profile of the IPRD spectra corresponding to NH bonded groups to be converged as
322
soon as Gdm+ hydrated aggregates comprising 50 water molecules.
323
However the weakest surface propensity of Gdm+ compared to NH+ 4 predicted by both
324
our polarizable approach and the standard force field contrasts with recent simulation find-
325
ings of Werner et all 19 agreeing with PhotoElectron spectroscopy experiments, i.e. Gdm+
326
− has a higher relative surface propensity than NH+ 4 in pure cation/Cl 2 M salt solutions.
327
Interestingly, the standard force field that we considered in the present study is the one used
328
by the latter authors. However we discuss in the present study the properties at the liquid
329
water-vacuum interface of hydrated cations in absence of explicit counter ions and at a much
330
smaller concentration (0.03 M) than in the latter studies. We may note also that simula-
331
tions based on the standard force field showed a dependence of the Gdm+ relative surface
332
propensity on the GdmCl salt concentration (in particular the Gdm+ surface propensity is
333
shown to increase with the salt concentration 18,19 ). Our results considered together with the
334
earlier ones seem thus to show the aqueous interfacial behavior of Gdm+ to depend strongly
335
on its concentration. However, as mentioned above, we don’t explicitly account for counter
336
ions in our interface simulations and halide ions like Cl− and Br− are considered to have a
337
strong propensity for water/vacuum interfaces. 42 Hence one may reasonably propose that
338
these anions can ”drive” cations to the surface. We are presently studying the interactions
339
of the latter halide ions with ammonium and guanidinium in water using our polarizable ap-
340
proach to investigate the role played by counter ions on the modulation of the guanidinium
341
propensity for the liquid water/vacuum interface.
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342
3.2.2
Guanidinium orientational properties at water-vacuum interfaces
343
Recent theoretical studies 17,18 concluded that a parallel orientation relative to the interface
344
of the Gdm+ symmetry plane is strongly favored close to the liquid water surface. Following
345
the ideas of Ou et al, 18 we investigate the Gdm+ orientation behavior by computing the mean
346
value of the second order Legendre polynomial along our droplet and liquid water-vacuum
347
simulations L2 (θ) =
1 3 cos2 θ − 1 , 2
(8)
348
where θ is the angle between the vector l⊥ and the vector connecting the droplet COM to the
349
Gdm+ carbon atom or between l⊥ and the axe orthogonal the liquid water-vacuum interface.
350
¯ 2 (dc ) computed along the umbrella sampling simulations The corresponding mean values L
351
based on our polarizable model are plotted as a function of the target distances dc in Figure
352
¯ 2 ≈ 0) from the droplet or 5. From that plot, the Gdm+ plane orientation is random (i.e. L
353
the water slab core up to about 3 ˚ A before the interface, whereas a parallel orientation is
354
¯ 2 ≥ 0.7), regardless of the water system (droplet or bulk). favored close to the interface (L
355
The transition in the Gdm+ orientation is particularly abrupt (it is achieved 1 ˚ A before the
356
interface).
357
Regarding the liquid water-vacuum interface, our result agrees with simulations generated
358
using either a standard pairwise force field 17 and a fluctuating charge polarizable approach. 18
359
Hence a parallel orientation of Gdm+ to the liquid water-vacuum interface is predicted by
360
all the MD simulations reported to date, regardless of the force field sophistication and the
361
parameterization protocol used to assign their parameters. That result clearly contrasts with
362
a recent heterodyne-detected vibrational sum frequency generation study of Strazdaite et al 43
363
who concluded a near-parallel orientation to the liquid water-air surface to be observed for
364
only a minor fraction of the methyl guanidinium ions.
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365
3.3
Guanidinium bulk hydration enthalpy
366
As in our recent studies, 25,26,28 we extrapolated single ion bulk hydration enthalpies by
367
adjusting the parameters of the following power law function of the droplet size N
iw f (N ) = U∞ +
a N 1/3
(9)
368
to reproduce the mean ion/water potential energy in droplets U¯ iw (N ) computed from the
369
umbrella sampling simulations according to
U¯ iw (N ) =
X
U¯ iw (rci ) × P (rci ).
(10)
i
370
Here the sum runs on the umbrella sampling simulations whose target distances are rci .
371
ww Denoting by ∆Ubulk the bulk solvent destabilization energy induced by the ion presence, we
372
iw ww assumed in our former studies that the sum U∞ +∆Ubulk yields the ion hydration microscopic
373
iw + energy in bulk water and thus the ion bulk hydration enthalpy according to ∆Hhyd = U∞
374
ww − RT . Below, if not discussed, the error estimates corresponding to mean energy ∆Ubulk
375
values are computed from the root mean square deviations of the data extracted along
376
the last 9 ns segment of the MD simulations and by considering these data as temporally
377
uncorrelated (along each simulations, 9 000 regularly spaced data are extracted).
378
As several authors, 15,44–46 we thus extrapolate bulk data from isolated finite size system
379
results. A priori, the reliability of such an extrapolation process is physically founded if the
380
finite size systems are simulated by accounting for bulk environment effects on them. 47,48
381
However we may note that from our own TCPE/2013 computations the interfacial potential
382
at the water-vacuum boundary in droplets whose size is ≥ 100 is already converged to the
383
bulk value (this will be discussed elsewhere). That suggests that the water HB network struc-
384
ture at the water-vacuum interface in intermediate size droplets is predicted by the model
385
TCPE/2013 to be close to the bulk one and, thus, that justifies a priori our extrapolation
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386
protocol.
387
ww is computed by comparing the total water interaction energy from a Gdm+ 10 ∆Ubulk
388
ns bulk simulation to that of a pure water one (and comprising the same number of water
389
ww molecules as for Gdm+ ). For our polarizable model, ∆Ubulk = +29.7 ± 0.8 kcal mol−1 , a
390
25 value which is smaller by about 6 kcal mol−1 than for NH+ Hence, even if Gdm+ is a 4.
391
˚ larger ion than NH+ 4 (their molecular radii are 2.4 and 1.4 A, respectively), it destabilizes
392
less the bulk water HB network than NH+ 4 . That can be a consequence of the more diluted
393
+ ion charge in Gdm+ than in NH+ 4 and of the absence of hydrophobic faces/moieties in NH4 .
394
ww value for Gdm+ is 40.1 ± 1.1 kcal Computed accordingly, the standard force field ∆Ubulk
395
mol−1 , a value larger by 25 % than the polarizable model estimate.
396
In Figure 6, we plot the values U¯ iw (N ) as a function of N −1/3 for both Gdm+ and NH+ 4
397
solvated in the four water droplets considered in the present study, as well as the results of
398
the linear regression process to adjust the f (N ) parameters (in that figure, we also reported
399
iw the data for Gdm+ computed from the standard force field). For Gdm+ , the parameter U∞
400
computed from our polarizable approach is -112.6 kcal mol−1 , a value 10 kcal mol−1 smaller
401
+ −1 iw than for NH+ 4 (-122.4 kcal mol ). Note that if we extrapolate the value U∞ for NH4 by
402
considering all together our earlier droplet data 25,26 and the present new ones (that leads to
403
a data set including the results of droplets whose size ranges from 50 up to 10 000 molecules),
404
we get then again the same value than the latter one, within 0.1 kcal mol−1 .
405
As discussed in Section 3.2.1, the U¯ iw (rci ) profiles are very flat, regardless of the ion loca-
406
tion within the droplet. As already discussed for both methylated ammonium and alkylated
407
carboxylate ions, 26 the values U¯ iw (N) depend thus marginally on the features of the ion
408
location probability density P (r). As for the latter two kinds of ions, we estimate here also
409
that the uncertainty affecting the values U¯ iw (N ) and arising from possible P (r) drawbacks
410
iw to be 1 kcal mol−1 . As the uncertainty regarding the parameters U∞ and originating from
411
the linear fitting process is 0.3 kcal mol−1 and the uncertainty affecting the values U¯ iw (N)
412
arising from the finite size of the data extracted along the MD simulations is 0.1 kcal mol−1 ,
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413
The Journal of Physical Chemistry
iw the total uncertainty affecting the parameters U∞ is 1.4 kcal mol−1 .
414
iw ww computed from our polarizable approach and U∞ The above results regarding ∆Ubulk
415
are in line with the common assumption that the Gdm+ /water interactions are weaker than
416
+ the NH+ 4 ones. They lead to a Gdm bulk hydration enthalpy ∆Hhyd of -82.9 ± 2.2 kcal
417
mol−1 , which is about 4 kcal mol−1 weaker than the NH+ 4 one computed using the same
418
theoretical protocol (-87.1 ± 2.2 kcal mol−1 ). Our Gdm+ estimate is almost half as large
419
as the experimental-based one reported recently by Marcus, 9 about -143.8 ± 1.9 kcal mol−1
420
(however, that value is considered as puzzling by the latter author). Assuming the reliability
421
of the hydration entropy component −T∆Shyd computed from the data reported by Mar-
422
cus 9 for Gdm+ , 4.5±0.5 kcal mol−1 at 300 K, that yields 78.4±2.6 kcal mol−1 for the single
423
hydration free energy of Gdm+ , ∆Ghyd (Gdm+ ). Regarding NH+ 4 , by considering the hydra-
424
tion entropy component −T∆Shyd value of 6.6 kcal mol−1 reported in Ref., 14 our theoretical
425
−1 protocol yields thus ∆Ghyd (NH+ 4 )= −80.5 ± 2.2 kcal mol , in very good agreement with
426
the experimental-based estimate, about -81 kcal mol−1 . 14 We computed also the absolute
427
bulk hydration free energies ∆Ghyd for Gdm+ and NH+ 4 using our polarizable approach and a
428
standard Thermodynamical Integration scheme (by considering 40 intermediate steps and by
429
accounting for all the corrections arising from periodic condition drawbacks, like the absence
430
of explicit water/vacuum interface). For the two ions, we get then ∆Ghyd values very close
431
to that above ones, i.e. -76 and -78 kcal mol−1 for Gdm+ and NH+ 4 , respectively, however
432
with a large uncertainty for Gdm+ , about ±5 kcal mol−1 a value three times larger than
433
+ for NH+ 4 (this arises from the very large intra molecular electrostatic energy within Gdm
434
for our polarizable approach, about 250 kcal mol−1 , and because our TI decoupling scheme
435
scales all the atomic static charges and not only the Gdm+ /water electrostatic interactions).
436
iw Computed accordingly, the standard force field U∞ value is -130.6 ± 1.4 kcal mol−1 ,
437
larger by 18 kcal mol−1 than the one computed by our polarizable approach. Accounting for
438
ww ∆Ubulk , the standard force field yields a ∆Hhyd value of -90.5 ± 1.9 kcal mol−1 and a ∆Ghyd
439
value of -86.0 kcal mol−1 for Gdm+ . Both the latter value are 10 kcal mol−1 larger than our
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440
polarizable model estimates. However the standard force field ∆Hhyd (Gdm+ ) value is also
441
largely weaker than the experimental estimate reported by Marcus, by about 54 kcal mol−1 .
442
The ∆Ghyd (Gdm+ ) value computed by our polarizable approach is by 18 kcal mol−1
443
larger in magnitude than the ones computed from quantum computations coupled with a
444
polarizable continuous solvent approach (QM/PCM), 13 about 58 kcal mol−1 . However, the
445
results of this kind of coupled theoretical approach are highly sensitive to a set of empir-
446
ical parameters, the atomic radii, whose quality is assessed by comparing to experiment
447
the QM/PCM estimates regarding the experimental bulk hydration free energies of a set of
448
training molecules and ions, 49,50 and as far as we know, no reliable experimental thermody-
449
namical data is available for Gdm+ . It is thus not obvious to comment here the difference
450
between our ∆Ghyd (Gdm+ ) estimate and the quantum ones. Nevertheless, we may note
451
that the QM/PCM ∆Ghyd value for Gdm+ is also largely underestimated compared to that
452
of the methyl-guanidinium ion and computed using the popular macroscopic solvent model
453
FDPB/γ developed by Honig and co-workers, 51 -66.1 kcal mol−1 .
454
Considering our polarizable approach results, the bulk hydration enthalpy and free energy
455
values for Gdm+ are only a few kcal mol−1 smaller than the NH+ 4 ones. This arises from
456
ww iw discussed above and ∆Ubulk two phenomena with opposite energetic trends as the values U∞
457
suggest. First, the Gdm+ /water interactions are weaker than NH+ 4 ones, which in turn leads
458
to a weaker perturbation of the bulk water HB network in presence of Gdm+ as compared
459
+ to NH+ 4 . In all, this is in line with the well accepted property of Gdm , i.e. it interacts
460
“weakly” with water.
461
4
462
We report a theoretical analysis of the hydration process of the Gdm+ in finite and infinite
463
aqueous environments from microscopic simulations performed using a polarizable force field
464
approach. Our results show Gdm+ to have a strong propensity for the core of aqueous
Conclusions
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465
environment and a weak propensity for water/vacuum interfaces. In particular, the Gdm+
466
propensity for water-vacuum interface is predicted by our approach to be weaker than the
467
+ NH+ 4 and K ones. This a priori conflicts with earlier simulations based on standard pairwise
468
force field approaches. 17,18 However, besides theoretical methodology differences, it has to
469
be noted here that we simulate the hydration process of Gdm+ in bulk water at an ion
470
concentration that is about two order of magnitude smaller than in the latter theoretical
471
studies (0.03 and 2 to 5 M, respectively). Nevertheless, as already theoretically shown, 17,18
472
our approach predicts a preferential parallel orientation of the Gdm+ symmetry plane to
473
the water surface near water-vacuum interfaces, which is in contradiction with a recent
474
experimental study. 43
475
For both the cations Gdm+ and NH+ 4 , we estimate their absolute bulk hydration en-
476
thalpy ∆Hhyd and free energy ∆Ghyd values by extrapolating droplet data computed from
477
our polarizable model and by considering available hydration entropy values. Our NH+ 4
478
thermodynamic values match the experimental-based ones, within the uncertainty bars. In
479
−1 + particular, we get ∆Ghyd (NH+ 4 ) = -80.1 ± 2.2 kcal mol . Regarding Gdm , both our ∆Hhyd
480
and ∆Ghyd values are a few kcal mol−1 smaller in magnitude than their NH+ 4 counterparts,
481
i.e. ∆Hhyd (Gdm+ ) = -82.9 ± 2.2 kcal mol−1 and ∆Ghyd (Gdm+ )= -78.4 ± 2.6 kcal mol−1 .
482
Compared to monoatomic alkali cations, the latter difference between the Gdm+ and NH+ 4
483
∆Ghyd estimates is close to that existing between Rb+ and K+ . 52
484
Our ∆Hhyd (Gdm+ ) value is about half as large as the experimental based one reported by
485
Marcus 9 that is clearly puzzling as it is even larger in magnitude than all the available ∆Hhyd
486
estimates for the smallest alkali cation Li+ by at least 10 kcal mol−1 . On the other hand,
487
our ∆Ghyd (Gdm+ ) value is by about 18 kcal mol−1 larger in magnitude than theoretical
488
quantum based estimates, 13 which can be considered as surprisingly low when compared
489
to the target hydration free energy value of the methyl guanidinium cation considered in
490
popular theoretical methods like the FDPB/γ one developed by Honig and co-workers 51
491
(-58 and -66 kcal mol−1 , respectively). Within our polarizable theoretical framework, the
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492
overall large hydration energy value of Gdm+ arises mainly from the weak perturbation of
493
the water bulk HB network due to the Gdm+ presence, that compensates weak Gdm+ /water
494
interactions (at least weaker than for NH+ 4 ).
495
For comparison purposes, we also computed the Gdm+ single ion hydration thermody-
496
namic data from the same theoretical protocol, however, by considering the standard (i.e.
497
non polarizable) force field that was shown by Wernesson et al to provide accurate results
498
regarding the Gdm+ salts behavior at the liquid water interface. If most of our polarizable
499
model predictions agree qualitatively with the standard force field ones, we may note that
500
the standard force field leads to overestimate both the Gdm+ single ion hydration enthalpy
501
and free energy values compared to our polarizable approach, by about 10 kcal mol−1 . In
502
all, a standard force field approach may be thus considered as providing an accurate enough
503
picture of the hydration process of complex organic ions like Gdm+ .
504
The relatively large magnitude of our hydration energy values for Gdm+ suggests a
505
relatively high affinity of that cation for aqueous environment. Hence the Gdm+ original
506
protein denaturing properties have to result from a competition between Gdm+ hydration
507
effects and Gdm+ /solute interactions that can be modulated by weak differences in the
508
protein chemical environment or by the nature of the counter ion with which it is paired. 53
509
That suggests in particular the pivotal role played by the Gdm+ hydrophobic faces to explain
510
the original properties of that cation rather than a weak propensity for aqueous environments.
511
Supporting Information Available
512
This material is available free of charge via the Internet at http://pubs.acs.org. It pro-
513
vides more detailed discussions about the polarizable force field accuracy to model gas
514
phase hydrated Gdm+ clusters, the force field parameters, the quantum VDZ/VTZ/VQZ
515
Gdm+ /water binding energies and a comparison with the data of both the standard and
516
the polarizable force field, the radial elongation energy profiles of a single water molecule
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The Journal of Physical Chemistry
517
interacting with Gdm+ within its symmetry plane or orthogonally to it, the stepwise binding
518
energies for the Gdm+ micro hydrated structures where a water molecule is in the cation sec-
519
ond hydration shell, the angular distribution function corresponding to the angle CN − Owater
520
in bulk water, a comparison of the radial Gdm+ /water distribution functions computed from
521
standard and polarizable force field bulk simulations, the Gdm+ location probability densi-
522
ties within the droplets and the Gdm+ /water interaction energy decomposition in droplets
523
(from the polarizable model).
524
Acknowledgments
525
This work was granted access to the HPC resources of [CCRT/CINES/IDRIS] under the
526
allocation 2016-[6100] by GENCI (Grand Equipement National de Calcul Intensif).
527
References
528
(1) Greene, R. F.; Pace, C. N. Urea and Guanidine Hydrochloride Denaturation of Ribonu-
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(2) Okur, H. I.; Hladlkov, J.; Rembert, K. B.; Cho, Y.; Heyda, J.; Dzubiella, J.; Cre-
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(3) Shih, O.; England, A. H.; Dallinger, G. C.; Smith, J. W.; Duffey, K. C.; Cohen, R. C.;
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Prendergast, D.; Saykally, R. J. Cation-Cation Contact Pairing in Water: Guanidinium.
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The Journal of Chemical Physics 2013, 139, 035104.
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(4) Mason, P. E.; Neilson, G. W.; Enderby, J. E.; Saboungi, M.-L.; Dempsey, C. E.; MacK-
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erell, A. D.; Brady, J. W. The Structure of Aqueous Guanidinium Chloride Solutions.
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Journal of the American Chemical Society 2004, 126, 11462–11470.
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Figure 1: Most stable Gdm+ /(H2 O)n aggregate structures for n = 1 − 3 from MP2 quantum computations, from our polarizable and a standard force field. 19 The energies provided correspond to the stepwise binding energies ∆Un−1,n . The quantum data are provided in brackets and the standard force field ones in parentheses.
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Figure 2: A water molecule interacting orthogonally to the Gdm+ plane.
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Figure 3: Radial distribution functions centered at the Gdm+ nitrogen (a) and carbon (b) atoms from our polarizable force field. Black line: full functions, green lines : functions gX (r, φ0 ), blue line : complementary functions gX∗ (r, φ0 ). The nitrogen functions are averaged over the data of the three Gdm+ nitrogen atoms.
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Figure 4: Ion/water PMFs at the water-vacuum interfaces. (a) Droplet profiles, in bold and dashed lines, PMF profiles for Gdm+ and NH+ 4 , respectively, the results for 200, 400, 600 and 800 water droplets are shown in black, blue, green and orange, respectively. (b) + 25 liquid water-vacuum profiles, black: Gdm+ , blue: NH+ 4 , red: K profile (from Ref. ) (bold 19 lines, our polarizable model, and dashed lines, the standard force field ). The vertical dashed lines show the water-vacuum boundaries. The numerical values correspond to the ion interface propensities PI. For droplets, and they are expressed in % (in parentheses, the ˚ NH+ 4 ones); and for the liquid water-vacuum interface, they are expressed in A (in parentheses the standard force field values).
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Figure 5: Gdm+ orientation at water-vacuum interfaces. (a) droplet and (b) liquid watervacuum case from our polarizable force field. θ is the angle between the vector l⊥ and the vector connecting the droplet COM to the Gdm+ carbon atom (a) or between l⊥ and the vector orthogonal to the liquid water-vacuum interface (b). The results for 200, 400, 600 and 800 water molecule droplets are shown in black, blue, green and orange, respectively.
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Figure 6: Gdm+ (black: our polarizable force-field approach, grey: standard force field −1/3 ¯ iw approach 19 ) and NH+ , 4 (blue) - water mean interaction energy U (N ) as a function of N where N is the water droplet size. Full symbols correspond to the droplets considered in the 25,26 present study. For NH+ regarding 4 , the empty symbols correspond to our earlier data droplets whose size varies from N = 50 up to 10 000. Dashed lines: results of the linear regression (the regression coefficients are greater than 0.99, regardless of the ions and the force field used).
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