Urea parametrization for molecular dynamics simulations

Urea parametrization for molecular dynamics simulations

Ana Caballero-Herrera, Lennart Nilsson *

Karolinska Institutet, Department of Biosciences at NOVUM, SE-141 57 Huddinge, Sweden

Received 15 June 2005; received in revised form 14 October 2005; accepted 15 October 2005

Available online 27 December 2005

Abstract

Although the idea of urea as water structure breaker is widely spread, urea dimer formation is also thought to be an important factor influencing

the behavior of urea–water solutions. We use this last idea to obtain a potential for urea to use in molecular dynamic simulations of protein

unfolding processes and we compare this with the potentials obtained from density functional theory (DFT). Three potentials for urea are

generated. One based on a parametrization for proteins to reproduce substantial dimer formation; and the other two from DFT quantum

calculations. Simulations of 2 M and 8 M urea aqueous solutions with the three set of charges were performed. Cyclic dimers with very favorable

interactions appear in the simulation with the non-DFT urea potential. Head-to-tail dimer formation occurs too, as found in crystals. This set of

charges maintains a good balance between the urea-urea and urea-water interactions, with urea flexibility being important. In the simulations using

the quantum derived charge sets dimers are rarely found and with very low interaction energies. Thus, the parametrization obtained from the DFT

ab initio calculations is inadequate for molecular dynamics simulations of urea-aqueous solutions. However, the DFT calculations indicate that the

urea molecule in water solution may have a planar structure as in the crystal.

q 2006 Elsevier B.V. All rights reserved.

Keywords: Density functional theory; Dimer; Radial function distribution

1. Introduction

Several different diseases are caused by protein misfolding

or aggregation [1], and it is therefore essential to characterize

protein unfolding pathways and intermediate states. In order

to map the unfolding pathways it is necessary to denature the

protein, which is often done experimentally using urea as

denaturing agent. The solubility of most protein side chains

and backbone increases with denaturant concentration [2]

and the denatured state is stabilized upon a higher exposition

to the solvent compared to the native state. Urea mixes very

well with water and high concentrations of denaturant,

typically around 6–8 M, are required to observe denaturation

[3]. However, the molecular mechanism by which urea

denatures proteins is not well understood. Since simulations

have the advantage to give an atomic description of the

unfolding process, different molecular dynamics (MD)

simulations have tried to shed light on this process [4–10].

Nevertheless, complete unfolding has not been observed and

0166-1280/$ - see front matter q 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.theochem.2005.10.018

* Corresponding author. Tel.: C46 8 608 9228; fax: C46 8 608 9290.

E-mail address: [email protected] (L. Nilsson).

relatively high temperatures are used by the most successful

simulations.

Two models have been proposed to describe the properties

of aqueous urea solutions. The first model [11–13], suggests

that urea aqueous properties arise from the formation of urea

dimers and oligomers while the water structure remains

unperturbed. In the second model [14], urea as an indirect

water structure breaker. Both models explain thermodynamic

data, and experiments have been unable to ascertain, which of

these models best describes the effect of urea in aqueous

solutions [15]. A fundamental hindrance is the inability to

measure the hydrogen bonds directly; therefore, to interpret the

data about hydrogen bond formation a theoretical model is

always needed. Computer simulations did not close the

controversy (see [15] for review), emphasizing the importance

of a correct parametrization for urea, consistent with the type of

force field used for the simulation and with a balance in the

strengths of the urea–urea, urea–water, and urea–protein

interactions. Several published studies using different empiri-

cal force fields and water models clearly differ in this respect,

for example urea dimer formation is reported in some

simulations [16–19], whereas others did not find or outline

any substantial aggregation of urea molecules [7,20–23].

An accurate description of the urea dimer formation is

fundamental to the characterization of urea aqueous solutions.

In this work, we present a new set of urea parameters, which

Journal of Molecular Structure: THEOCHEM 758 (2006) 139–148

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A. Caballero-Herrera, L. Nilsson / Journal of Molecular Structure: THEOCHEM 758 (2006) 139–148140

takes into account urea dimer formation while being consistent

with the protein parameters [24] used with the CHARMM [25]

program and the TIP3P [26] water model. We determine a set

of simple charges that fit the urea–urea and urea–water

potentials obtained from ab initio calculations [27] with the

NEMO [28] potential. This set of charges is compared with

other sets of quantum-chemical effective atomic charges of the

urea molecule that we calculate with density functional (DFT)

methods.

2. Methods

2.1. MD simulation protocol

The CHARMM [25] program with the all-atom parameter

set [24] was used in the energy minimizations and molecular

dynamics simulations. An atom-based force-shift method for

the long-range electrostatic interactions with the relative

dielectric constant equal to 1.0 was used to truncate the non

bonded interactions. This method is known to produce accurate

and stable simulations [29]. An atom-based shifting function

for the van der Waals interactions was used to truncate the non

bonded interactions. The truncation cutoff was set to 12 A, and

the non-bonded list was generated to 14 A, with updates as

soon as any atom had moved more than 1 A. Bonds to

hydrogens were constrained using the SHAKE algorithm [30].

The leap-frog algorithm was used in all simulations with a 2 fs

integration time step and the coordinates were saved every

0.2 ps for analysis. Periodic boundary conditions were used in

the energy minimization and the molecular dynamics

simulations of the urea aqueous solution. The model of water

used was the TIP3P model [26].

The cyclic and linear urea dimers used for the calculation of

the interaction energy as function of the distance between the

two C atoms were constructed from planar urea molecules as

perfect symmetric dimers (Fig. 1). The orientation between the

two urea molecules of the cyclic dimer corresponds to the

configuration of global energy minimum reported by Astrand

et al. [19] whereas the linear complex is the type of complex

found in crystals [19]. The initial configuration for the urea–

water complex was also constructed from a planar urea

molecule and a water molecule placed between the urea

Fig. 1. Urea dimer in the (a) cyclic and (b) linear configuration.

oxygen and one of the cis hydrogen atoms, in such a way that

the water molecule could potentially form hydrogen bonds to

the urea oxygen and Hcis simultaneously. This kind of structure

is known to be the structure of the urea–water complex in the

energy minimum of the NEMO potential [27]. Thereafter, the

urea–water complex was minimized 2000 steps of steepest-

descent minimization and 23,000 of adopted basis Newton–

Raphson minimization.

The potential energy as a function of distance between the

urea carbon atoms (or urea carbon and water oxygen) was

obtained by translating one molecule along the Curea–Curea (or

Curea–Owater) axis, without any further minimization.

The 2 M (8 M) urea aqueous solution box was prepared by

first randomly distributing 5 urea molecules (20 for 8 M) in a

cubic box with 20.9 A side length. For each of these urea

molecules a new urea molecule was constructed forming a

cyclic dimer in the minimum energy conformation of the

CHARMM potential obtained in the previous step. The 5 (20

for 8M) urea cyclic dimers were then immersed in an

equilibrated (20.9 A)3 box of water molecules. All water

molecules overlapping with the urea molecules were removed.

The final system contained 10 (40 for 8 M) urea molecules and

277 (183 for 8 M) water molecules, for comparison with the

system of Astrand et al. [19]. The systems were minimized

1000 steps of steepest-descent minimization followed by 1000

steps of adopted basis Newton–Raphson minimization. The

systems were gradually heated from 50 to 300 K in a 10 ps

period. An equilibration period of 35 ps followed, and

molecular dynamics simulations of 465 ps at 300 K were

performed.

Hydrogen bonds and their life-times were calculated along

the simulations using the criterion r(H-Acceptor) !2.4 A.

Diffusion coefficients were computed over the last 265 ps of

the simulation time using the Einstein relation.

First order dipole rotational correlation times, t, were

computed for water and urea molecules by fitting a single-

exponential function to the correlation functions obtained from

the MD simulations.

2.2. Density functional calculations

Calculations were performed using the program GAUS-

SIAN 03 [31]. The hybrid B3LYP [32] DFT method was used

for geometry optimizations and frequency calculations. This

method consists in Becke’s exchange [33] 3-parameter [34]

hybrid functionals and the non-local correlation provided by

the LYP correlation functional [35]. The 6-31G(d,p) basis sets

was employed.

Zero-point vibrational energies (ZPVE) were obtained

within the harmonic approximation in order to include

vibrational corrections at zero absolute temperature. The

molar internal energy at zero absolute temperature (E0) is the

sum of the total electronic energy (Etot) and the ZPVE.

The Onsager method was used as continuum solvation

model. This method replaces the water solution by a continuum

dielectric medium, homogeneous and isotropic characterized

by the dielectric constant (3watZ78.39). The solute is then

Fig. 2. The urea–urea (squares, cyclic dimer; circles, linear dimer) and urea–

A. Caballero-Herrera, L. Nilsson / Journal of Molecular Structure: THEOCHEM 758 (2006) 139–148 141

placed in a spherical cavity within the solvation self-consistent

reaction field (SCRF). The response of the solvent to the

dielectric field generated by the polar solvent located in the

cavity is assumed to be linear. The dipole of the solute changes

as a response to the reaction field generated by the dielectric

medium [36]. The cavity radii applied herein were those related

with the molecular volume as obtained from the GAUSSIAN

program. Single urea molecules and urea–water complexes

were further optimized inside the cavities at the DFT level with

the 6-31G(d,p) basis set.

Partial atomic charges were derived from the electrostatic-

potential using the CHelpG scheme [37–39], which is

convenient for calculating intermolecular coulombic inter-

actions in semiempirical force fields such as CHARMM, since

the definition of the effective atomic charges takes into account

that the atoms are symmetrical and nuclear centered [40].
water (triangles) interaction energy as a function of the distance between the C
atoms, in the case of urea–urea interaction, or between Curea and Owater atoms,

in the case of the urea–water interaction. The relative orientation between the

molecules was constant.
3. Results and discussion
3.1. Empirical energy parameters for urea

Parameters for urea were transferred from the CHARMM22

parameters [24] for the Asn side chain, which closely

resembles the urea molecule. The structural model of urea

was constructed using the bond length and angle values from

this parameter set, and the missing NCN bond angle value was

chosen equal to 1178 as in the crystal structure [41]. Cyclic and

linear urea dimers were formed by two planar molecules (see

Section 2) The urea molecule of the urea–water complex

remained planar after the initial minimization.

Different symmetric (the charges are the same on the two

NH2 groups) sets of atomic charges were tested to reproduce

the urea dimer and urea–water complex interaction energies

reported by Astrand et al. [27]. The initial set of charges tested

was the set of charges of the OPLS parameters for urea [21] and

then a total of 10 new sets were generated from these,

modifying them iteratively, until a good agreement between

our calculated urea–urea and urea–water energies and those

from the literature [27] was obtained (Table 1, and Fig. 2). This

set of charges (Table 2) will be referred to as the MD set of

charges. Minor differences are seen between the urea–urea and

Table 1

The urea–urea dimer and urea–water complex at the minimum energy

configurations obtained with the MD set of charges

R (A) Emin (kcal/mol)

Cyclic dimmer a 4.0b K20.0c 4.1d K21.9

Linear dimmer a 4.7b K10.4c 4.9d K10.3

Urea–water

complex

a 2.0e K13.4

c 1.9e K11.2

a With our MD set of charges.b Distance Cu

1–Cu2.

c From Ref. [27].d Distance between the mass centers of the two urea molecules.e Distance Hu

cis–Ow.

urea–water complex interaction energies obtained with our MD

set of charges and those from the literature [27]. In our case the

interaction energy between the urea molecules in the cyclic

dimer was closer to the interaction energy between urea and

water, consistent with the suggestion that these interactions

should be more balanced in order to yield good structural and

dynamic properties of urea solutions [20].

3.2. Urea described by density functional methods

In order to calculate the effective atomic partial charges of

the urea molecule, we first performed geometry optimizations

of the urea molecule in vacuum. Since our interest was the

behavior of urea in an aqueous solution, we also performed

calculations for the urea monomer in a dielectric medium using

the Onsager method (see Section 2), as well as for the urea

molecule in complex with three water molecules, both in

vacuum and in a dielectric medium.

3.3. Energetics and dipole moment of the urea monomer

The most energetically favorable structure of the urea

monomer in vacuum is a non-planar anti-conformation of C2

symmetry with the amine hydrogens pyramidalized at opposite

sides of the molecule. However, the urea molecule is slightly

more stable in a C2v planar conformation at 298 K [42]. Our

results for the urea monomer in vacuum agreed with these

results (Table 3). As also found by Masunov et al [42], the

dipole moment of the C2 conformation was closer to the

experimental value of urea in the gas phase, i.e., 3.83 D [43],

whereas the dipole moment of the C2v configuration was more

Table 2

MD charges for urea

N Hcis Htrans C O

K0.569 0.416 0.333 0.142 K0.502

Table 3

Total electronic energy and dipole moment of urea monomer

m (Debye) Dm (Debye) E0 (a. u.) DE0 (kcal/mol)

C2v C2 C2v C2

B3LYP 6-31(d,p) vacuum 4.2480 3.5366 0.7114 K225.27119 K225.27379 1.63152

SCRF 5.2266 4.3019 0.9247 K225.27999 K225.27769 K1.44327

Table 4

Total electronic energy and zero-point corrected total energy of urea-three water complex

Etot (a.u.) DEtot (kcal/mol) E0 (a.u.) DE0(kcal/mol)

Vacuum Asymmetric u–w

complex

K454.5938734 0.00 K454.453256 0.00

Symmetric u–w

complex

K454.5901784 2.32 K454.451141 1.33

SCRF Asymmetric u–w

complex SCRF

K454.5976572 3.49

Symmetric u–w

complex SCRF

K454.6032114 0.00

EtotZtotal electronic energy (a.u.); (EtotZrelative total electronic energy (kcal/mol); E0ZEtotCZPVEZinternal energy at 0 K (a.u.). (E0Zrelative internal energy

at 0 K (kcal/mol).


similar to the solution experimental value,, i.e., 4.2 D [44].

However, in the SCRF, the C2v planar structure was slightly

more stable (by 1.4 kcal/mol) than the non-planar C2

conformation. Moreover, the dipole moment (4.3 D) was in

perfect agreement with the experimental value in solution.

3.4. Energetics of urea in complex with three water molecules

Four different starting configurations for the complex were

tested with planar and non-planar urea structures and the three

water molecules at different positions for the geometry

optimizations. Normal mode calculations revealed that those

complexes in, which the urea conformation was planar were

saddle points on the potential energy surface, and hence, they

were neglected for further analysis. Two minima were found

for the urea–water complex with the urea molecule in a non-

planar conformation in vacuum (Table 4, Fig. 3(a) and (b)).

The conformation shown in Fig. 3(a) was predicted to have the

lowest total electronic energy and zero-point corrected total

energy by (1.33 and 2.32 kcal/mol, respectively). In this case,

the urea structure lost its symmetry because of the inter-

molecular urea–water hydrogen bonding pattern. This con-

figuration will be referred to as the asymmetric complex. The

second minimum (Fig. 3(b)) corresponds to a structure in,

which the urea molecule structure remains symmetric, and we

refer to this configuration as the symmetric complex. When the

SCRF was added to these two configurations, the energetic

behavior was reversed, i.e., the complex with the lowest energy

(by w3.5 kcal/mol) was the symmetric complex (Fig. 3(b 0)).

Fig. 3. Urea–water complexes. (a) and (a 0) have asymmetric urea molecule

structures, whereas in (b) and (b0) the urea molecule display symmetric

structure and is nearly planar, specially in the SCRF (b 0).

3.5. Structural parameters of urea

The optimized geometries are summarized in Tables 5, 6

and 7. The C–O bond length of the non planar C2 conformation

was shorter than in the planar conformation C2v and those in

the urea–water complexes, both in vacuum and in the SCRF. In

addition, this length was even shorter in vacuum than in the

SCRF. The opposite is noticed for the C–N bond. The

calculated bond lengths of the symmetric urea–water complex

in the SCRF (Table 5 and Fig. 3(b 0)) were in very good

agreement with values from neutron diffraction data [41], in

particular when the experimental data are corrected for

harmonic thermal motion [41]. Regarding bond angles, the

largest differences were obtained from the bonds involving the

hydrogen atoms. The bond angles of the symmetric urea–water

complex in vacuum and in the SCRF (Table 6, Fig. 3(b) and

Table 5

Bond Lengths (A)

C–O C–N N–Htrans N–Hcis

C2 vacuum 1.221 1.390 1.011 1.010

C2 SCRF 1.227 1.382 1.010 1.008

C2v vacuum 1.224 1.377 1.006 1.005

C2v SCRF 1.235 1.370 1.008 1.004

Asymmetric u–w

complex

1.238 1.406 1.018 1.012

1.352 1.015 1.017

Asymmetric u–w

complex SCRF

1.241 1.361 1.019 1.007

1.391 1.018 1.019

Symmetric u–w

complex

1.257 1.361 1.011 1.017

1.361 1.011 1.017

Symmetric u–w

complex SCRF

1.266 1.353 1.015 1.011

1.352 1.015 1.011

X-ray diffractiona 1.2565 1.3384 1.0020 1.005

Neutron diffractionb

(correction for har-

monic motion and

anharmonic bond

streching)

1.264 1.350 0.997 1.005



monic thermal

motion. Average)

1.264 1.350 1.013 1.019


(uncorrected

values)

1.260 1.343 1.008 1.003

Neutron diffractionc


monic thermal

motion)

1.260 1.352 1.003 0.998

a From Ref. [54].b From Ref. [41].c From Ref. [55].


(b 0)) were very close to the values for the planar conformation

C2v. In fact, the values of the dihedral angles (Table 7) showed

that in this complex the urea molecule becomes practically

planar, although the symmetry of the molecule is a syn-

conformation Cs. In this conformation all the four hydrogen

atoms of the molecule point out to the same side of the plane

defined by the heavy atoms. It is known from ab initio

calculations that the syn-conformation Cs of the urea monomer

in vacuum is also a stable conformation that can be reached

from the C2 anti-conformation by inversion or rotation [42]. In

the asymmetrical urea–water complex in vacuum one of the

Table 6

Bond angles (degrees)

HcisNHtrans CNHtrans

C2 vacuum 114.1 117.4

C2 SCRF 115.1 119.3

C2v vacuum 119.1 124.3

C2v SCRF 118.5 124.0

Asymmetric u–w

complex

114.5 115.1

123.1 121.0

Asymmetric u–w

complex SCRF

119.8 119.7

116.6 115.7

Symmetric u–w

complex

120.9 119.4

120.9 119.4

Symmetric u–w

complex SCRF

122.0 120.5

122.0 120.5

NH2 groups remained nearly in the same plane as the heavy

atoms, and in the SCRF, this complex also adopted a syn-

conformation Cs. For the urea non-planar monomer C2v, the

Htrans atoms were further outside the urea molecular plane than

the Hcis (w30 and 158, respectively). The SCRF promoted

more planar structures.

3.6. Effective atomic charges in urea

The calculated effective atomic charges of the urea

monomer (Table 8) did not change substantially between the

C2 and C2v conformations, although the planar C2v confor-

mation had w5% higher absolute charges. Since the dipole

moment of the planar C2v urea conformation was 20% higher

than the non-planar C2 conformation (Table 9), the change in

dipole moment between both conformations has to be

attributed mainly to the change in geometry. Addition of the

SCRF did not produce very appreciable changes in the effective

atomic charges.

The CHelpG charges obtained for urea in the urea–water

complexes gave a net charge of ca. 0.01 on the urea

molecules, and they were therefore slightly adjusted to give

neutral urea molecules (Table 8) before being used for

further calculations. The effective atomic charges differed

by up to 35% for the urea atoms of the two urea–water

complexes, i.e., symmetric and asymmetric, and by up to

44% in the presence of the SCRF. There is a clear

similarity between the effective atomic charges of the urea

atoms of the symmetric urea–water complex and the

effective atomic charges of the urea monomer with the

SCRF. In particular, the charges from the symmetric

complex in vacuum and from the SCRF calculations are

approximately the same as those of the urea monomer in

the SCRF planar C2v conformation and non-planar C2

conformation, respectively (the largest standard deviation

(SD) is is 0.04 at the atomic charge of the N and C atoms

whereas for the rest the SD is 0.02). The urea molecule of

the asymmetric urea–water complex also exhibited asym-

metry in the atomic charges both in vacuum and in the

presence of the SCRF. For instance, the N atom that formed

a hydrogen bond with one water molecule had a higher

effective charge than the other N atom. Since this

CNHcis NCN OCN

112.4 113.8 112.4

113.8 114.2 122.9

116.6 114.9 122.5

117.5 114.9 122.6

111.2 115.2 120.4

115.9 124.4

116.3 115.0 122.8

112.0 122.0

115.4 117.2 121.4

115.4 121.4

117.1 117.2 121.4

117.1 121.4

Table 7

Dihedral and Improper angles (degrees)

OCNHtrans OCNHcis NCNHtrans NCNHcis ONCN Planarity

C2 vacuum 148.8 13.5 K31.2 K166.5 K180.0 C2a

C2 SCRF 155.4 14.1 K24.6 K165.9 K180.0 C2

Asymmetric u–w

complex

153.4 21.1 2.6 K176.7 177.1 C1b

179.6 0.3 K29.5 K161.7

Asymmetric u–w

complex SCRF

169.4 12.2 30.3 167.3 175.6 Csc

K154.1 K17.1 K15.0 K172.2

Symmetric u–w

complex

167.9 11.1 14.8 171.5 177.4 Cs

K167.9 K11.1 K14.7 K171.5

Symmetric u–w

complex SCRF

K174.9 K2.1 K5.8 K178.6 K179.3 Cs

174.9 2.1 5.8 178.6

a C2 denotes a planar molecule.b C1 denotes that the molecule is planar on one side whereas on the other side the hydrogen atoms of the NH2 group point out of the plane of the plane defined by

the O, C, N atoms. At this side water is not hydrogen bonded to the N atom.c Cs denotes a syn-conformation with the hydrogen atoms of both NH2 groups pyramidalized on the same side.

Table 8

Calculated atomic charges with the CHelpG scheme and DFT

Urea–water complex Urea monomer

N Htrans Hcis C O N Htrans Hcis C O

Asymmetric u–w

complex

K0.73 0.34 0.32 0.81 K0.61 C2v K0.99 0.41 0.40 0.97 K0.61

K0.89 0.39 0.38

Symmetric u–w

complex

K0.99 0.46 0.37 1.01 K0.67 C2v SCRF K0.99 0.44 0.40 0.98 K0.68

K0.99 0.46 0.37

Asymmetric u–w

complex SCRF

K0.86 0.38 0.39 0.75 K0.59 C2 K0.94 0.39 0.38 0.92 K0.59

K0.64 0.32 0.27

Symmetric u–w

complex SCRF

K0.91 0.46 0.36 0.91 K0.63 C2 SCRF K0.93 0.40 0.38 0.91 K0.62

K0.91 0.46 0.36


asymmetry arose from the way water molecules are bonded,

and since our complex contained three water molecules

only, we believe that even the lowest energy complex is not

a realistic model for the urea molecule solvated by waters.

The dipole moment of the urea molecule in the urea–

water complexes ranged between 4.3–4.5 Debye (Table 9).

These relatively high dipole moments, which agree with the

urea dipole moment enhancement upon hydrogen bonding

[45], are mainly due to the planarity of the molecule in

these cases.

Table 9

Dipole moments (Debye) calculated with the different ChelpG charge sets from Ta

Geometry

Asyma AsymSCRF b Symc S

Charge Asym 4.37 4.57 4.52 4

AsymSCRF 4.41 4.54 4.50 4

Sym 4.20 4.44 4.34 4

SymSCRF 4.17 4.40 4.30 4

C2v 4.24 4.47 4.38 4

CSCRF2v

4.62 4.85 4.77 4

C2 4.09 4.31 4.23 4

CSCRF2

4.33 4.55 4.48 4

a AsymZasymmetric urea–water complex.b AsymSCRFZasymmetric urea–water complex SCRF.c SymZsymmetric urea–water complex.d SymSCRFZsymmetric urea–water complex SCRF.

3.7. Urea dimer and urea–water complex interaction energies

with the ab initio set of charges

The effective charges from the previous ab initio calcu-

lations of the urea monomer in the SCRF planar C2v

conformation and non-planar C2 conformation (Table 8) were

used to investigate the interaction energies of the urea dimer

and of the urea–water complex. These sets of charges will be

called QMPl and QMN–Pl, respectively. We constructed, as for

the MD set of charges, a cyclic and linear urea dimer as well as

ble 8, in the various minimum geometries given in Tables 3 and 4

ymSCRF d C2v CSCRF2v

C2 CSCRF2

.51 4.36 4.45 3.86 4.10

.50 4.37 4.45 3.90 4.13

.29 4.12 4.22 3.54 3.82

.25 4.10 4.20 3.54 3.81

.34 4.16 4.26 3.56 3.84

.74 4.57 4.67 3.97 4.25

.19 4.03 4.12 3.46 3.73

.44 4.28 4.37 3.71 3.98

Fig. 4. Histogram of the number of favorable interactions between any pair of

urea molecules as function of the interaction energy. Red: simulation with the

MD charges for urea; yellow: QMPl urea charges and blue: QMNPl charges for

urea molecules (For interpretation of the references to colour in this figure

legend, the reader is referred to the web version of this article.).

Table 10

The urea dimers and urea–water complex at the minimum energy

configurations obtained with the QM charge sets

Configuration Charge set R (A) Emin (kcal/mol)

Cyclic dimmer QMPl 4.1a K14.9

QMNPL 4.1a K12.9

Linear dimmer QMPl 4.6a K13.4

QMNPl 4.7a K10.9

Urea–water

complex

QMPl 3.2b K11.1

QMNPl 3.0b K9.9

a Carbon–carbon distance.b Urea carbon–water oxygen distance.


a urea–water complex (Fig. 1), this last complex was subject to

minimization as outlined in Section 2. The urea–urea and urea–

water interaction energies were calculated as a function of

distance along the urea carbon–carbon or urea carbon–water

oxygen axis (Table 10). In this case the optimal urea–urea

interaction energy was much less favorable than in the case of

the MD set of charges, and the energies of the linear dimer

were practically the same as those of the cyclic dimer. In

addition, the urea–urea and urea–water interaction energies

were very similar. This finding does not agree with the work of

the Astrand et al.[27] in which the formation of linear

complexes is less favorable than the interaction urea–water.

In the case of the QMN–Pl charges the energies were higher than

those with the QMPl set of charges.

Fig. 5. Cyclic dimer structure at the minimum interaction energy in the

simulation of the 2 M urea aqueous solution with the MD set of charges.

3.8. MD simulation of 2 M urea aqueous solution

Three simulations of 2 M urea aqueous solution were

performed using the three sets of charges (MD, QMPl and

QMN–Pl). The interaction energies between any pair of urea

molecules in the boxes at 0.2 ps intervals were monitored. For

the box with the MD charges there was significant formation of

dimers with interaction energies close and even lower than

K20 kcal/mol, and there was a distinct peak around

K12 kcal/mol in the distribution of urea dimer interaction

energies (Fig. 4). The minimum interaction energy between

any pair of urea molecules was K24.7 kcal/mol, which is

lower than the interaction energy minimum of the planar cyclic

dimer calculated before (K20.0 kcal/mol). The reason for this

stability enhancement could be explained when looking at the

structure of the dimer in the minimum energy conformation

obtained in the simulation (Fig. 5). The dimer formed was

cyclic but both urea molecules were slightly bent (the molecule

was flexible) allowing closer contacts than in the planar cyclic

dimer (by w0.1 A only). A similar dimer is found by ab initio

calculations to have the lowest energy among the dimers under

study and as in hexagonal crystals [46]. On the other hand in

the simulations with the QMPl and QMN–Pl sets of charges

formation of urea dimers with significant energy of interaction

was rare (Fig. 4). The interaction energy minimum was

K13.6 kcal/mol for the QMPl box and K13.0 kcal/mol for the

QMN–Pl box, comparable to the interaction energy minimum of

the respective cyclic planar dimers (K14.9 and K12.9 kcal/

mol, respectively). Therefore, in these cases no stability gain is

obtained by allowing flexibility.

Hydrogen bond analysis is summarized in Table 11. In the

simulation with the MD charge set the urea molecules were

forming Ou–Hu hydrogen bonds 15% of the simulation time.

The hydrogen bonds were formed with Hcis but also with the

Htrans. However, formation of hydrogen bonds with the Hcis

urea atoms was slightly more frequent. Their mean lifetimes

were approximately twice longer than mean those fomed with

the Htrans. Furthermore the most long-lived Ou–Hcisu hydrogen

bond had a duration of 21.4 ps, twice as long as for Ou–Htransu

hydrogen bonds. The probability that once a hydrogen bond of

the type Ou–Hcisu had been established between any two urea

molecules, these two molecules will form a cyclic dimer was

0.34, and the probability of forming a head-to-tail dimer

(perturbed linear dimer) given that a Ou–Htransu hydrogen bond

had been formed was only 0.17 (half of the probability of cyclic

dimer formation).

In contrast, with the QM charges urea molecules formed

fewer hydrogen bonds, which had shorter duration than in the

Table 11

Hydrogen bond occupancy, mean lifetimes and probability (P) of dimer formation in the2 M urea MD simulations. P is the conditional probability that a cyclic (tail-

to-headZperturbed linear) dimer is formed once a OuHcisu ðOu–Htrans

u Þhydrogen bond is formed

Charge set Occupancy Ou–

Htransu

!LifetimeOOu–

Htransu (ps)

P tail-to-head dimer Occupancy Ou–Hcisu hLifetimei Ou–Hcis

u

(ps)

P Cyclic dimer

MD 0.073 0.86 0.17 0.077 1.58 0.34

QMPl 0.059 0.94 0.23 0.037 0.97 0.21

QMNPl 0.029 0.61 0.18 0.035 0.74 0.17


simulation with the MD charges, particularly with the QMN–Pl

set of charges. This was also observed in the interaction energy

histograms. With the QMPl charges, the probability of head-to-

tail dimer formation was significantly higher than that in the

MD box and the probability of cyclic dimer formation. In

general we can say that in the QMN–Pl box the probability of

urea–urea interaction was very small.

The type of interaction established between urea molecules

during dynamics can be characterized by the radial distribution

functions (RDF) gðOuHcisu Þ and gðOuHtrans

u Þ (Fig. 6). The first

peak of gðOuHcisu Þ corresponds to cyclic dimer formation

while the second corresponds to head-to-tail dimer formation.

In gðOuHtransu Þ the trend is the opposite, the first peak

corresponds to head-to-tail dimers whereas the second to

cyclic dimers. A main difference is observed with respect to the

RDF reported by Astrand et al.[19]: The second peak of

gðOuHcisu Þ, at w3.4 A, and the first peak of gðOuHtrans

u Þ, at

w1.9 A, which arise from head-to-tail dimer formation in our

Fig. 6. Atomic radial distribution functions. (a) Ourea–Hcisurea with the MD set of charg

and (b 0), and QMNPl, (c) and (c 0), charge sets.

simulations were not observed by Astrand et al.[19]. The third

peak is due to the presence of the Hcisu =Htrans

u on the other side of

the urea molecule. The RDF also evidenced lower cyclic dimer

formation for both QM boxes than for the MD box, and

relatively high head-to-tail dimer formation for the planar set

of charges although poor formation for the non-planar set of

charges, this also was reflected in the interaction energy

histogram (Fig. 4).

The diffusion coefficients of water and urea were 5.1!10K9

and 2.6!10K9 m2/s, respectively. These values are about

twice larger than the experimental values, i.e., 2.6!10K9 m2/s

for water [47] and 1.245!10K9 m2/s for 2 M urea [48].

However it is known that the TIP3P water model has too fast

dynamics and too little structure [49]. The diffusion coefficient

of simulations of the TIP3P water at 298 K is around 5.0!10K

9 m2/s [50]. Thus, there is a consistence between the faster

dynamics of the water model used here and the faster dynamics

of the urea molecule.

es. (a 0) Ourea–Htransurea with the MD set of charges. Analogously for the QMPl, (b)

Fig. 7. Atomic radial distribution functions at 8 M urea (black) and 2 M urea

(red). (Solid) Curea–Curea, (Dashed) Curea–Owater, (Dotted) Owater–Owater (For

interpretation of the references to colour in


3.9. MD simulation of 8 M urea aqueous solution

MD simulations of an 8 M urea solution were performed in

order to obtain an estimate of the concentration dependence of

our model. Kirkwood–Buff theory provides an elegant way of

characterizing liquids [51]. When applied to urea solutions it

shows urea hydration and urea self-solvation to be nearly

equal, and concentration independent, thus making urea

solutions nearly ideal [52]. Recently a urea model has also

been devised based on Kirkwood–Buff theory [53]. We have

however chosen to restrict our analysis to radial distribution

functions and diffusion parameters since the Kirkwood–Buff

integrals become very sensitive to noise in the tail of the radial

distribution functions, which are quite structureless for the

TIP3P water model; with our (20.9 A)3 box it is also not

meaningful to extend the radial distrubution functions out to

13.5 A, as deemed necessary to obtain good estimates for the

Kirkwood–Buff integrals [53].

The analysis of the trajectories of the simulation of the 8 M

urea box indicated that the radial distribution functions of urea

are indeed independent of the urea concentration (Fig. 7), in

agreement with the known ideal behavior of the urea osmolyte

[52,53]. On the other hand the diffusion coefficient of water and

urea in the 8 M urea box decreased significantly, to 3.5!10K9

and 1.5!10K9 m2/s, for water and urea, respectively. Another

indication of the decreased water and urea mobility at higher

urea concentrations was the increased rotation relaxation times

in 8 M urea, 4.0 and 22.8 ps for water and urea, respectively,

compared to 2.5 and 9.2 ps in 2 M urea. These trends agree

with the expected behavior [48,53].

4. Conclusions

Considerable urea dimer formation was observed in the 2 M

urea aqueous box with the simple set of charges (MD charges)

calculated here to approximately fit previously reported

interaction energies [27]. In contrast to that study, our urea–

urea and urea–water interaction energies are less different, as

suggested by Tsai et al. [20], and in addition to cyclic dimers,

seen by Astrand et al. [27], we also observed head-to-tail

dimers. These results are consistent with the fact that this kind

of dimers are also observed in urea crystals [54]. The flexibility

of the urea molecule was important in order to achieve more

stable urea–urea interactions.

Our set of charges thus gives a good balance between urea–

urea and urea–water interaction, using the TIP3P water model

[26], and the nearly ideal urea behavior in urea–water mixtures

[52,53] is achieved since urea hydration and self-solvation are

practically independent of urea concentration. The water model

used in the simulations of urea–aqueous solutions is of crucial

importance for water and urea diffusion, as well as for the

solution average structure. For example, although a good

agreement of the urea diffusion coefficient with experimental

data can be obtained with one set of urea charges [20], the

diffusion coefficient obtained with the same set of charges but

different water model was lower than those reported by the first

group [23].

The charge sets obtained from ab initio calculations are

inadequate. Very poor and unstable dimer formation was

observed in the simulations with these charges, and when urea–

urea interactions were formed, head-to-tail dimers were

preferred over cyclic dimers. The non-planar QM set of

charges gave the smallest number of hydrogen bonds between

urea molecules, and they were also the most short-lived

hydrogen bonds. On the other hand our ab initio calculations

indicate that the urea molecule in water solution also may have

a planar structure as seen in crystals [19].

Although a priori this urea parametrization should

support the SKKS model [11–13] of urea properties in

aqueous solution, since it is set to promote urea

dimerization, additional studies have to be performed to

ascertain whether the water structure is disturbed, to which

extent urea molecules form polymers, and the influence of

these factors in the denaturation process. Our MD

simulations of the C peptide in 8 M urea solution suggest

that the dynamics of water is slightly reduced on the protein

surface in presence of urea and that both the indirect and

direct model induce peptide denaturation [10].

Acknowledgements

We thank Dr. Jorge Llano for critical comments and helpful

discussions and Dr. Kersti Hermansson for initial support.

Financial support was provided by the Swedish Research

Council and the National Graduate School for Scientific

Computing.

References

[1] A.R. Dinner, et al., Trends Biochem. Sci. 25 (2000) 331–339.

[2] Y. Nozaki, C. Tanford, J. Biol. Chem. 238 (1963) 4074–4081.

[3] A. Wallqvist, D.G. Covell, D. Thirumalai, J. Am. Chem. Soc. 120 (1998)

427–428.

[4] J. Tirado-Rives, M. Orozco, W.L. Jorgensen, Biochemistry 36 (1997)

7313–7329.


[5] B.J. Bennion, V. Daggett, Proc. Natl Acad. Sci. USA 100 (2003) 5142–

5147.

[6] B.J. Bennion, V. Daggett, Proc. Natl Acad. Sci. USA 101 (2004) 6433–

6438.

[7] A. Caflisch, M. Karplus, Struct. Fold. Des. 7 (1999) 477–488.

[8] Z. Zhang, Y. Zhu, Y. Shi, Biophys. Chem. 89 (2001) 145–162.

[9] L.J. Smith, R.M. Jones, W.F. Van Gunsteren, Proteins 58 (2005) 439–449.

[10] A. Caballero-Herrera, et al., Biophys. J. 89 (2005) 842–857.

[11] J.A. Schellman, C.R. Trav. Lab. Carlsberg Ser. Chim. 29 (1955) 223.

[12] G.C. Kresheck, H.A. Scheraga, J. Phys. Chem. 69 (1965) 1704.

[13] R.H. Stokes, Aust. J. Chem. 20 (1967) 2087.

[14] H.S. Frank, F. Franks, J. Chem. Phys. 48 (1968) 4746.

[15] A. Idrissi, Spectrochim. Acta, Part A Mol. Biomol. Spectrosc. 61 (2005)

1–17.

[16] H. Tanaka, K. Nakanishi, H. Touhara, J. Chem. Phys. 82 (1985) 5184–

5191.

[17] J. Hernandez-Cobos, et al., J. Chem. Phys. 99 (1993) 9122–9134.

[18] R. Chitra, P.E. Smith, J. Phys. Chem. B 106 (2002) 1491–1500.

[19] P.O. Astrand, A. Wallqvist, G. Karlstrom, J. Phys. Chem. 98 (1994)

8224–8233.

[20] J. Tsai, M. Gerstein, M. Levitt, J. Chem. Phys. 104 (1996) 9417–9430.

[21] E.M. Duffy, P.J. Kowalczyk, W.L. Jorgensen, J. Am. Chem. Soc. 115

(1993) 9271–9275.

[22] L.J. Smith, H.J.C. Berendsen, W.F. Van Gunsteren, J. Phys. Chem. B 108

(2004) 1065–1071.

[23] F. Sokolic, A. Idrissi, A. Perera, J. Mol. Liq. 101 (2002) 81–87.

[24] A.D. MacKerell, et al., J. Phys. Chem. B 102 (1998) 3586–3616.

[25] B.R. Brooks, et al., J. Comput. Chem. 4 (1983) 187–217.

[26] W.L. Jorgensen, et al., J. Chem. Phys. 79 (1983) 926–935.

[27] P.O. Astrand, A. Wallqvist, G. Karlstrom, J. Chem. Phys. 100 (1994)

1262–1273.

[28] A. Wallqvist, G. Karlstrom, Chem. Scr. 29A (1989) 131–137.

[29] J. Norberg, L. Nilsson, Biophys. J. 79 (2000) 1537–1553.

[30] J.P. Ryckaert, G. Ciccotti, H.J.C. Berendsen, J. Comput. Phys. 23 (1977)

327–341.

[31] M.J. Frisch, et al., GAUSSIAN 03, Revision B04, Gaussian Inc., Pittsburgh,

PA, 2003.

[32] P.J. Stephens, et al., J. Phys. Chem. 98 (1994) 11623–11627.

[33] A.D. Becke, Phys. Rev. A 38 (1988) 3098–3100.

[34] A.D. Becke, J. Chem. Phys. 98 (1993) 5648–5652.

[35] C.T. Lee, W.T. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785–789.

[36] C.J. Cramer, D.G. Truhlar, Chem. Rev. 99 (1999) 2161–2200.

[37] D.E. Williams, J. Comput. Chem. 9 (1988) 745–763.

[38] F.A. Momany, J. Phys. Chem. 82 (1978) 592–601.

[39] C.M. Breneman, K.B. Wiberg, J. Comput. Chem. 11 (1990) 361–373.

[40] K.B. Wiberg, P.R. Rablen, J. Comput. Chem. 14 (1993) 1504–1518.

[41] S. Swaminathan, B.M. Craven, R.K. McMullan, Acta Crystallogr. B40

(1984) 300–306.

[42] A. Masunov, J.J. Dannenberg, J. Phys. Chem. A 103 (1999) 178–184.

[43] R.D. Brown, P.D. Godfrey, J. Storey, J. Mol. Spectrosc. 58 (1975) 445–

450.

[44] W.R. Gilkerson, K.K. Srivastava, J. Phys. Chem. 64 (1960) 1485–1487.

[45] M.A. Spackman, et al., Acta Crystallogr., Sect. A 55 (1999) 30–47.

[46] R.V. Belosludov, Z.-Q. Li, Y. Kawazoe, Mol. Eng. 8 (1999) 105–119.

[47] K. Krynicki, C.D. Green, D.W. Sawyer, Faraday Discuss. (1978) 199–

208.

[48] L.J. Gosting, D.F. Akeley, J. Am. Chem. Soc. 74 (1952) 2058–2060.

[49] P. Mark, L. Nilsson, J. Phys. Chem. B 105 (2001) 9954–9960.

[50] P. Mark, L. Nilsson, J. Comput. Chem. 23 (2002) 1211–1219.

[51] J.G. Kirkwood, F.P. Buff, J. Chem. Phys. 19 (1951) 774–777.

[52] J. Rosgen, M. Pettitt, D.W. Bolen, Biophys. J. (2005) (101529/bio-

physj.105.067330).

[53] S. Weerasinghe, P.E. Smith, J. Phys. Chem. B 109 (2005) 15080–15086.

[54] H. Birkedal, et al., Acta Crystallogr., Sect. A 60 (2004) 371–381.

[55] A.W. Pryor, P.L. Sanger, Acta Crystallogr. A26 (1970) 543–558.

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Urea parametrization for molecular dynamics simulations