CHINESE JOURNAL OF PHYSICS
VOL. 45, NO. 6-I
DECEMBER 2007
Solvation Model Effects on Two Specific Peptides of Milk Protein
Fatih Yaşar1, ∗ and Kadir Demir2
1
Department of Physics Engineering, Hacettepe University, 06532, Ankara, Turkey
2
Department of Physics, Zonguldak Karaelmas University, Zonguldak, Turkey.
(Received January 3, 2007)
The equilibrium thermodynamic properties of two bioactive peptide sequences which have
great effects on blood pressure were studied by three-dimensional molecular modeling in
an aqueous solution. Our first peptide, Tyrosine-Glycine-Leucine-Phenylalanine (YGLF, in
a one letter code), is found in the primary structure of bovine milk whey protein α-LA
(residue 50-53). The other peptide, Lysine-Valine-Leusine-Proline-Valine-Proline-Glutamine
(KVLPVPQ) takes in the β-casein (β-CN) (residue 169-175) part of milk. All the threedimensional conformations of each peptide sequences were obtained by multicanonical simulations with the use of an ECEPP/2 force field, and the solvation contributions are included
by a term that is proportional to the solvent accessible surface area of the peptide. Each
simulation was started from a completely random initial conformation. No a-priori information about the ground-state was used in the simulations. In the present study, in order to
determine the solvation model dependency of the thermodynamic properties, we calculated
the average values of the total energy, specific heat, fourth-order cumulant, and end-to-end
distance for these peptide sequences of milk protein as a function of temperature in two solvation models. We observed that the specific heat of each peptide shows a different behavior
in the solvation models, which have one or two peaks as a function of temperature. That
is why we have also investigated the structural properties to gain insight into the relation
of these peaks with the structural transitions. Our results indicate that the calculated thermodynamic and structural properties of each peptide really depend on the chosen solvent
model.
PACS numbers: 75.40.Mg, 87.15.-v
I. INTRODUCTION
The structure of proteins is highly flexible, and as a results, there is an extremely large
number of possible conformations for any given protein. Since globular proteins are usually
in aqueous solution, there are important solvent effects on these conformations. Hence the
behavior of a peptide conformation in a solvent may be quite different from that in vacuum.
Peptides tend to take conformations whose conformational energies are as low as possible.
The solvent, on the other hand, tries to force the peptide to take conformations with the
lowest possible solvation free energies. The conformation of the peptide in the solvent is
determined by the competition of these factors.
Since ab initio computations starting from the quantum mechanical many-body problem are not feasible, one has to use phenomenological potentials/force fields. Several such
force fields have been employed to study the protein folding problem by simulation. Most
http://PSROC.phys.ntu.edu.tw/cjp
622
c 2007 THE PHYSICAL SOCIETY
OF THE REPUBLIC OF CHINA
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realistic simulations use potential energy functions (or force fields) that are based on all
atom models of proteins molecules. Well-known potential energy functions are AMBER [1],
CHARMM [2], GROMOS [3] and ECEPP [4]. These functions have been parameterized
to fit the experimental data of small molecules and, for some terms, quantum chemistry
calculations. According to these functions, the energy of a protein in a solvent is given by
the sum of two terms: the conformational energy Ep for the protein model itself and the
solvation energy Esolv for the interaction of protein with the surrounding solvent. If the
bond lengths and bond angles are kept fixed (as in ECEPP), Ep contains an electrostatic
term EC , a 12-6 Lenard-Jones term ELJ , and a hydrogen-bond term EHB for all pairs of
atoms in the peptide, together with a torsion term Etor for all torsion angles:
Ep = EC + ELJ + EHB + Etor ,
EC =
X 332qi qj
i<j
ELJ =
(2)
!
Bij
Aij
− 6
12
rij
rij
X
Cij
Dij
12 − r 10
rij
ij
i<j
Etor =
,
X
i<j
EHB =
rij
X
(1)
,
!
(3)
,
Ul [1 ± cos(nl αl )] ,
(4)
(5)
l
where rij is the distance between the atoms i and j, qi and qj are the partial charges on the
atoms i and j, is the electric permittivity of the environment, Aij , Bij , Cij , and Dij are
the parameters that define the well depth and width for a given Lenard-Jones or Hydrogen
bond interaction, and αl is the lth torsion angle. The factor 332 in Eq. (2) is used to express
the energy in kcal/mol.
Like other biomolecules, proteins exist in the environment of solvents. Modeling
the solvent explicitly, however, is extremely computationally expensive, due to the large
number of degrees of freedom. Moreover, when using Monte Carlo (MC) methods [5] to
search configuration space, the presence of water molecules leads to very small acceptance
ratios, so one has to have recourse to much slower molecular dynamics (MD) methods [6].
Therefore the explicit modeling of water can be impractical when deriving many physical
properties. Hence, a number of approximations of solvent effects have been developed. The
main idea in these approximations is to develop an optimal method to represent the effect
SOLVATION MODEL EFFECTS . . .
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of a solvent without including solvation in the calculation. One commonly used model
representing solvent contributions is by terms proportional to the solvent accessible surface
areas (SASA) of protein molecules. In this model, one assumes that the protein-solvent
interaction can be described as the sum of contributions such that the contribution of each
atomic species is proportional to its surface area exposed to the solvent. This model is
quite popular because of its simplicity and ease of application. The solvation energy Esolv
in this approximation is given by
Esolv =
X
σi Ai ,
(6)
i
where Ai is the SASA of atoms of type i, and σi is a proportionality constant which
depends on the type of atom and includes all the contributions from the solvent. The
choice of a set of σi parameters (ASPs) defines a model of solvation, and there are several
sets of ASPs in the literature. Some of these sets were derived by a least-squares fitting to
experimentally observed changes in the free energies of simple model compounds when the
solvent was changed from an organic liquid to water, others were calculated by the transfer
free energies of model compounds from vacuum or octanol to water by MD simulations with
existing force fields [7–13]. These sets were studied by Juffer et al. [14], and it has been
found that they give rather distinct contributions to the free energy of proteins. Recently,
Berg et al. [15] also studied these sets by biased Metropolis MC methods [16] and parallel
tempering [17, 18].
Together with a number of techniques that have been used to resolve the conformational structures of peptides, computational molecular modeling of peptides from their
primary amino acid sequences can contribute to a better understanding of the interplay
between the protein and the surrounding solvent, as well as their three-dimensional structures. On the other hand, determination of the three-dimensional structure of a peptide
only from its primary structure is extremely difficult. The major difficulty in conventional
protein simulations such as the Metropolis MC method or MD lies in the fact that simulations get trapped for a long simulation time in one of a huge number of energy local minima.
This problem of the MC and MD methods can, to a large extent, be alleviated by various
non-traditional MC simulation techniques such as the multicanonical (Muca) [19], parallel
tempering [17, 18], and the Wang-Landau algorithm [20, 21]. Although these methods are
numerically different from each other, they can allow one to cross-check obtained results
in protein simulations. Basically, the Muca method (for a recent review, see Ref. [22]) is
characterized by the equiprobability of all energy states, so one can easily jump from a
state to another. This method has been applied firstly to a peptide model by Hansmann et
al. [23], and others [24, 25]. Recently, the detailed translation of the Muca method was also
applied to the simulation of the pentapeptide Leu-enkephalin in our previous work [26].
In the present study, we have applied the Muca method to two special peptide sequences of milk protein in order to investigate their thermodynamic and structural properties in a solvent. For this two implicit solvent models were chosen. Hence, it is possible to study the effect of the solvation model dependency on these peptide sequences.
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Many peptides of Milk protein are bioactive and directly influence numerous biological
process evoking behavioral, gastrointestinal, hormonal, immunological, neurological, and
nutritional responses. In addition, some bioactive peptides may effect the treatment of infection or the prevention of disease [27]. Essentially, milk is rich in protein which is divided
into two broad classes, caseins and whey proteins. Both caseins and whey proteins are rich
sources of angiotensin-converting enzyme (ACE) inhibitory peptides. Briefly, ACE plays
an important role in the regulation of blood pressure in mammals. This enzyme converts
angiotensin I to angiotensin II, while angiotensin I is an inactive hormone, angiotensin
II is a molecule that directly constricts vascular smooth muscle thereby increasing blood
pressure [28]. Several studies in spontaneously hypertensive rats (SHR) show that these
caseins (or casokinins) and whey proteins (or lactokinins) can significantly reduce blood
pressure [29–31]. Clinical trials on hypertension also show that these can bring about a
significant reduction in hypertension [32, 33].
In order to achieve our aim, we have chosen two peptides of this protein. One of them,
YGLF (peptide I), is a synthetic tetrapeptide called α-lactorphin; it is found in the primary
structure of bovine milk whey protein α-LA (residue 50-53). It is an ACE inhibitor. The
other peptide, KVLPVPQ, (peptide II) is an antihypertensive peptide; it takes part in βcasein (β-CN)(residue 169-175). Although the X-ray assignments of the secondary structure
of α-LA have been shown by Acharya et al. [34], β-casein cannot be crystallized and a direct
observation of its secondary structure by X-ray crystallography is not possible. According
to the X-ray results, peptide I indicates the turn structures. On the other hand, the amount
of various secondary structures of β-casein has been estimated from measurements using
various spectral techniques (Raman, Fourier-transform infrared, and circular dichroism)
and using algorithms to predict a secondary structure from its primary structure [35]. The
spectroscopic techniques indicate the presence of a significant amount of α-helices (up to
29 % of the residues), β-sheets (up to 34 % of the residues) and turns (up to 35 % of
the residues) [36–40]. A model for the secondary structure of β-casein was then suggested
by Kumosinski et al. [41] that predicted the possible secondary structural assignments
for β-casein using a molecular dynamic simulation, modifying the secondary structural
algorithms of Garnier et al. [42] and the Raman spectroscopy results. According to this
work, turns were also predicted for the peptide II. From this point of view, our work is also
intended to compare the predictions by the other molecular modelings and spectroscopic
investigations. Also, as these peptides give rather more contribution to a decrease in the
blood pressure than the other milk peptides, we have also compared with the results of
these peptides, which show similar behavior or not according to the thermodynamic and
structural properties in the solvent model. Thus, modeling of these peptides can provide
important insight into the study of bioactive peptides which are chemically synthesized to
confirm the biological properties with a specific amino acid sequence.
SOLVATION MODEL EFFECTS . . .
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100000
Histogram
10000
1000
100
WE92
OONS
10
−10
−20
−30
−40
−50
−60
E(kcal/mol)
FIG. 1: The multicanonical energy histograms for peptide II in WE92 and OONS.
II. SIMULATION MODEL
For all these sequences, NH2 and COOH were chosen as the N- and C- terminal
groups, respectively. All molecules are modeled by the potential energy function ECEPP/2
(Empirical Conformational Energy Program for Peptides), which assumes rigid geometry
and is based on electrostatic, 12-6 Lenard-Jones, and hydrogen-bond terms for all pairs of
atoms in the peptide, together with torsion terms for all torsion angles [4, 43]. For the
present sequences, the peptide bond angles ω were kept fixed at 180◦ , which leaves the
dihedral angles φ, ψ in the backbone and χ in the side chain as the independent degrees
of freedom. Therefore the conformation is defined by these variables. The solvation free
energy that we used is a sum of terms that are proportional to the SASA of the atomic
groups of the solute. For this, two solvent models (or ASP sets) which are named here
as WE92 [12] and OONS [8] were used, due to the fact that these solvation models were
classified as in the fast class according to their integrated autocorrelations times by Berg et
al. [15]. The potential energy function ECEPP/2 and these solvent models are implemented
in the package FANTOM [44], which is used for the present simulations.
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FATIH YAŞAR AND KADIR DEMIR
0
627
−25
−30
−5
<E>
<E>
−35
−10
−15
−40
−45
−50
−55
−20
(a)
WE92
OONS
100
200
300
400
500
(b)
−60
−25
600
WE92
OONS
−65
100
200
300
T[K]
400
500
600
T[K]
FIG. 2: The Boltzmann average energy of the multicanonical simulation in WE92 and OONS for
(a) peptide I and (b) peptide II.
6
4.5
WE92
OONS
5.5
WE92
OONS
4
5
C(T)
4.5
4
3.5
3
3.5
3
2.5
(a)
2.5
(b)
2
100
200
300
400
500
2
600
100
200
T[K]
300
400
500
600
T[K]
FIG. 3: Specific heats of the multicanonical simulation as a function of temperature in WE92 and
OONS for (a) peptide I and (b) peptide II.
0.7
0.67
WE92
OONS
0.65
WE92
OONS
0.66
Binder Cumulant
0.6
0.55
0.5
0.45
0.65
0.64
0.63
0.4
0.62
(a)
0.35
0.3
100
200
300
400
500
(b)
0.61
600
100
200
T[K]
300
400
500
600
T[K]
FIG. 4: Binder cumulant of the multicanonical simulation as a function of temperature in WE92
and OONS for (a) peptide I and (b) peptide II.
17.5
WE92
OONS
12
WE92
OONS
17
< d(e−e) >
10
8
6
16.5
16
15.5
4
15
(a)
2
100
200
300
T[K]
400
500
600
(b)
14.5
100
200
300
400
500
600
T[K]
FIG. 5: The average end-to-end distance of the multicanonical simulation in WE92 and OONS for
(a) peptide I and (b) peptide II.
SOLVATION MODEL EFFECTS . . .
628
150
150
100
100
50
50
0
0
-50
-50
-100
-100
-150
VOL. 45
-150
-150
-100
-50
0
50
100
150
150
150
100
100
50
50
0
0
-50
-50
-100
-100
-150
-150
-100
-50
0
50
100
150
-150
-100
-50
0
50
100
150
-150
-100
-50
0
50
100
150
-150
-100
-50
0
50
100
150
-150
-150
-100
-50
0
50
100
150
150
150
100
100
50
50
0
0
-50
-50
-100
-100
-150
-150
-150
-100
-50
0
50
100
150
150
150
100
100
50
50
0
0
-50
-50
-100
-100
-150
-150
-150
-100
-50
0
50
100
150
FIG. 6: Ramachandran plots of each residue (from top to bottom) of peptide I. The abcissa is the
angle φ and the ordinate is ψ. The left column shows all the conformations below the temperature
210 K in WE92 and the right column shows all the conformations below the temperature 220 K in
OONS.
III. COMPUTATIONAL DETAILS
In the present work, at each Muca update step a trial conformation was obtained
by changing one dihedral angle at random within the range [−180◦ ; 180◦ ], followed by the
Metropolis test. The dihedral angles were always visited in a predefined order going from
the first to last residue; a cycle of N MC steps is called a sweep. Since the peptide bond
angles ω are kept fixed at 180◦ , the number degrees of freedom are 17 and 31 for peptide I
and II, respectively.
For the calculation of the Muca weight factors, they were built recursively during a
single long simulation, where the Muca parameters were re-calculated every 6000 and 7000
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FATIH YAŞAR AND KADIR DEMIR
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sweeps and 100 times for peptide I and II, respectively. These numbers depend on the
degrees of freedom of the peptide to get enough statistics. Several such simulations were
carried out, and the final Muca weights of the best simulation were used in the following
Muca production run of another 5x106 sweeps. In all cases, each Muca simulation was
started from a completely random initial conformation. No a-priori information about the
ground-state was used in the simulations.
All thermodynamics quantities were calculated from one Muca production run of
4x106 sweeps, which followed an additional 106 sweeps for equilibration. In order to reduce
bias problems, the jackknife estimators were employed. For this, we divided our time series
into four bins of 4x106 sweeps, and then the physical quantities were calculated separately
for each bin and their difference was taken as an estimate for the error, which we included
for certain temperatures in all figures.
IV. RESULTS AND DISCUSSION
Fig. 1 displays the energy histograms of the Muca simulation for this peptide, which
are obtained with the fixed Muca weight factors in WE92 and OONS. To obtain a quite
flat histogram in the recursive evaluation steps of the Muca weight factors, more sweeps
are needed when the degrees of freedom of the peptide increased.
The results from a single simulation run in the Muca ensemble can be used to calculate various thermodynamic quantities as a function of temperature for a wide range of
temperatures by applying the histogram re-weighting [45]:
< Q >=
R
−1 (E)e−βE
dEQ(E)P mu wmu
R
,
−1
dEP mu wmu
(E)e−βE
(7)
where Q is any physical quantity, wmu (E) is the Muca weight factor and P mu is the energy
distribution obtained by the final simulation. The first example of such calculations is the
average energy as a function of temperature. In Fig. 2, a and b, we plot the canonically reweighted energy E as a function of T for peptide I and II in WE92 and OONS, respectively.
As seen in these figures, although the average energy values with the parameter set WE92
are greater than the ones with OONS for peptide I, this case is completely reversed for
peptide II. In addition, the average energies of peptide II are lower than those of the
peptide I for each case. This can be explained, since these peptides have different amino
acid residues and also different peptide lengths in which the length of peptide II is longer
than peptide I. The second example is the specific heat, which is the fluctuation of the
energy. Here, the quantity is defined as
(< E 2 >T − < E >2T )
,
(8)
N
where N is the number of amino acid residues in the peptide. In Fig. 3, a and b, we show
the specific heats as a function of temperature for peptide I and II with the parameter sets
C(T ) = (kB T )2
SOLVATION MODEL EFFECTS . . .
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WE92 and OONS. The jackknife error bars for the Muca estimated specific heats are shown
at selected temperature values and are found to be considerably larger than those for the
energy. This is to be expected as the specific heat is a derivative of the energy. As seen in
Fig. 3 a, the specific heats have significant differences for peptide I. Even though the specific
heat has two peaks for OONS, one peak takes place in the neighborhood T ∼110 K and the
other takes place at T ∼ 220 K; it seems that it has one peak in the neighborhood T ∼ 210
K for WE92. On the other hand, for peptide II (Fig. 3 b), the specific heats have one sharp
peak around T ∼ 315 K, and it also seems that there are little peaks in the neighborhood
T ∼ 120 K for each of the ASP sets. At the low-temperature region, the observed peak with
WE92 is more evident than the one with OONS in this figure. To check whether all peaks
for both peptides have physical meaning or whether they are due to insufficient sampling,
we created more than two samples for each of the peptides by Muca simulations of equal
length. Each sample has behavior similar to that which we see in the specific heat figures.
This is the reason why we applied long production sweeps for each peptide with the two
sets of ASPs. As we know, this behavior in the specific heat has also been observed in our
previous studies [46, 47]. Besides, two and three peaks in the specific heat have also been
obtained in the other simulations of chain models [48–50].
As can be seen from the specific heat figures, our data showing the presence of two
peaks can also explain the presence of transitions of states. To investigate a transition
one can try to study a phase transition using a finite-size scaling (FSS) analysis. But, the
properties of the protein depend strongly on the number of amino acid and its compositions,
which may change completely by adding or subtracting an amino acid. Therefore, it is not
possible to study phase transitions using a FSS analysis except for homopolymers [51].
However, we have computed the Binder cumulant [52] as a function of temperature for
both peptides in the chosen solvent models. As is known, this quantity is a vehicle of the
FSS analysis, which is useful in clarifying the nature of the transition. In particular it
shows peculiar behavior only for a system exhibiting a first-order phase transition, and it
is not sensitive in the case of a second order one. Hence it can be possible to at least get
insight into the order of the phase transitions of systems. The temperature variation of the
fourth-order Binder cumulant U of the order parameter is defined by
U (T ) = 1 −
< E 4 >T
.
3 < E 2 >2T
(9)
This quantity is plotted in Fig. 4, a and b, and this shows that there is no significant
difference between the behavior of the peptide I and II for each solvent model. According
to the FSS arguments conjectured on lattices, when one computes the Binder cumulant
UL (T ), it can take a minimum value at the transition temperature. For a second-order
phase transition, it can be shown that the limL→∞ [2/3 − UL (T )] = 0, while at a firstorder phase transition the same limit measures the latent heat [53]. From the point of this
conjecture, the behavior of the Binder cumulants of each of our peptide sequences may be
consistent with a continuous phase transition in the chosen solvent models.
We also display the average end-to-end distances < de−e >T as a function of temper-
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FATIH YAŞAR AND KADIR DEMIR
631
TABLE I: Predicted probabilities of γ-turn for peptide I with the parameter sets OONS and WE92.
Amino acid residue
OONS ASPs
WE92 ASPs
in the i + 1 position
T ≤ 220 K
T > 220 K
T ≤ 210 K
T > 210 K
of γ-turn
Classical Inverse Classical Inverse Classical Inverse Classical Inverse
Y
0.11
0.06
0.23
0.03
0.09
0.17
G
14.61
6.31
1.07
2.72
0.37
0.44
0.39
1.35
L
1.81
0.01
2.06
2.20
2.06
F
0.09
0.76
0.84
1.44
ature for the two peptides with WE92 and OONS in Fig. 5, a and b. Here, de−e is defined
to be the distance between the nitrogen of the first and the oxygen of last residues, and is
a measure for the compactness of the conformation. It is clear that there are significant
differences between the WE92 and OONS. For instance, as the temperature decreases, de−e
also decreases for peptide I and II in OONS. On the other hand, it increases when the
temperature decreases for WE92. The conformations of each peptide in OONS are more
compact than the ones with WE92 at low-temperature regions.
Second, in order to determine the observed peaks in Fig. 3, a and b, whether they
are related with any structural differences, the distribution of backbone φ and ψ angles
were analyzed and the Ramachandran plots were prepared for each amino acid residue of
the conformations which were obtained in the course of the Muca simulation. Fig. 6 shows
these plots for peptide I of all the simulated conformations (4,000,000) below 210 K (the
left column) and 220 K (the right column) which represent their first maximum point of
specific heats for WE92 and OONS, respectively. These Ramachandran plots were analyzed
to estimate the occurrence probabilities of various secondary structures (β-turns, γ-turns,
and helical structures) in the simulated conformations. There are various experimental
methods used to investigate the conformational structures of proteins. These methods
give an idea mainly about the most common conformational structure of a protein. On the
other hand, computer molecular modeling techniques can be used to prepare Ramachandran
plots, which provide the distributions of the dihedral angles and distinguish different types of
conformations and estimate their occurrence probabilities. These are the major advantages
of the simulation method which we used in the present study.
To analyze the probability of the helix conformation first, the criterion adopted for
the helix state is the following: a residue is considered to be in the helix configuration
when the dihedral angles (φ, ψ) fall in the range (−70◦ ± 10◦ , −37◦ ± 10◦ ). The length
l of a helical segment is then defined by the number of successive residues which are in
the helix configuration. A conformation is considered as helical if it has a helical segment
with l ≥ 3 [54]. According to this criterion, no helical structures were detected for either
peptide with the parameter sets WE92 and OONS for all conformations. On this point,
our result is consistent with the results of spectroscopic techniques and other prediction
methods [34, 41]. Actually, this is also expected for the peptide II, due to the destabilizing
effect of proline on helical structures. Proline residues with their cyclic side chains are only
allowed a value for of −60◦ ± 20◦ , depending upon the extent to which the ring system can
632
SOLVATION MODEL EFFECTS . . .
VOL. 45
TABLE II: Predicted probabilities of γ-turn for peptide II with the parameter sets OONS and
WE92.
Amino acid residue
OONS ASPs
WE92 ASPs
in the i + 1 position
T ≤ 315 K
T > 315 K
T ≤ 315 K
T > 315 K
of γ-turn
Classical Inverse Classical Inverse Classical Inverse Classical Inverse
K
0.07
0.11
0.38
0.51
0.10
0.11
0.50
0.51
V
0.17
0.47
0.06
0.31
L
P
1.88
5.63
3.42
6.33
V
P
7.61
8.19
7.30
8.71
Q
1.46
2.17
6.55
3.21
be distorted [55]. Besides, our structural predictions of these peptides indicate that the
occurrence possibilities of β-turns were a very small ratio for OONS and WE92. For this
result, the range of the permitted φ and ψ angles for various β-turn structures are taken
from Creighton [55] with ±10◦ of tolerance.
The probabilities of inverse and classical γ-turns in the peptide I and II are presented in TABLE I and II. These numbers indicate the percent occurrence probabilities of
a considered structure in the total number of configurations in the temperature interval.
A γ-turn is defined by the existence of a H-bond between the C=O group of one residue
(i) and the N-H of the (i + 2)th residue. They occur as one of two possible isomers called
classical and inverse γ-turns. For OONS below the temperature 220 K, which represents
up to the first maximum peak of its specific heat, the probability of an inverse γ-turn was
the highest for G in the i + 2 position (6.31 %) and the probability of a classical γ-turn
was the highest for G placed in the i + 2 position of the turn (14.61%) in peptide I. On
the other hand, above this temperature, inverse and classical γ-turns were found for G in
the i + 2 position (2.72 %) and (1.07 %), respectively (TABLE I). In other words, above
this temperature, the probabilities of inverse and classical γ-turns sharply decreased for G
in the i + 2 position. For the other residues, there was no appreciable change. In the case
of WE92, we monitored that there is no remarkable differences in the γ-turns below and
above the temperature 210 K, which represents the maximum point of its specific heats.
The highest probabilities of inverse γ-turns were observed for L in the i + 3 position (2.20
% for T ≤ 210 K, 2.06 % for T > 210 K). Even though, for these solvent models, the
probability values for L in the i + 3 position were approximately equal to each other, and
both inverse and classical γ-turns values are significantly different for G in the i+ 2 position
for OONS.
For peptide II, the probabilities of an inverse γ-turn were quite high values for P in
the i + 4 and i + 6 position and for Q in the i + 7 position for each of the parameter sets
(TABLE II). The range of permitted angles for inverse γ-turns is −70◦ to −85◦ , which is
quite suitable for having P in the i+4 and i+6 positions [56]. This explains the higher
probability of inverse γ-turns in the considered sequence. Below the temperature 315 K,
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FATIH YAŞAR AND KADIR DEMIR
633
which represents the maximum point of its specific heat, the inverse γ-turn probabilities of
all residues except Q were lower than the probabilities of the ones above this temperature
for each of the solvent models. However, Q has greater values below 315 K for WE92. In
OONS, the inverse γ-turn probabilities for P in the i + 4 and for Q in the i + 7 positions
were significantly less than the ones with WE92.
V. CONCLUSIONS
We have studied the thermodynamic and structural properties of each peptide in two
different solvent models by Muca simulation. The three-dimensional conformations of the
given peptides are obtained from their primary sequence by this simulation technique by
using the ECEPP/2 force field. Although there is no exact agreement in the literature as
to which set of ASPs give better solvation contributions, we have chosen the WE92 and
OONS parameter sets of ASPs (or solvent models).
First, each peptide has shown a different thermodynamical behavior in the different
solvent models. In particular, in OONS, we observed a very sharp second peak around
T ∼ 110 K in the specific heat for peptide I. The second peak in WE92 model is hardly
visible at around T ∼ 100 K. For peptide II, it was observed that there are two small peaks
for each of the solvent models, but not only are these peaks not as sharp as those of peptide
I in OONS, but also the peak in WE92 is clearer than the ones with the OONS parameter
set. But these observed peaks of each peptide take place very close to each other for the
OONS and WE92 solvent model, respectively. For instance, the transition temperatures
of peptide II are the same as in OONS and WE92. Besides, the solvation contributions of
these sets of ASPs to the energies of each peptide are rather different. These rather distinct
contributions were also observed in the average end-to-end distance de−e as a function of
temperature in Fig. 5, a and b. As can be seen from these figures, the conformations of each
peptide in OONS is more compact than the ones with WE92 at low-temperature regions.
On the other hand, when peptide I and II were compared according to thermodynamical
quantities, we have just observed that the Binder cumulant of each peptide showed a similar
behavior to each other.
Second, to gain insight into the relation between the peaks observed in the specific
heats and secondary structural properties of the given peptide sequences, we calculated
the occurrence probabilities of secondary structures for these peptides. At this point, we
considered that these occurrence probabilities may give insight for explaining these peaks
or may be related to distinct behavior in the specific heat for the WE92 and OONS solvent
models. From the point of view of secondary structures, while these peptides of milk protein
do not indicate any helix structures, the other kind of structure β-turns have very low
probabilities. It was just observed that the probabilities of the classical and inverse γ-turns
were generally high for each solvent model. For peptide I in OONS, the total probabilities
of the γ-turn was remarkable different from the ones with WE92. This difference may be
the reason why we observed a sharp peak in the specific heat for peptide I with OONS.
When compared between OONS and WE92, the results indicated two peaks in the specific
634
SOLVATION MODEL EFFECTS . . .
VOL. 45
heats for peptide II; there are no appreciable differences between their structures from each
other except for Q. For the WE92 model, the total of the occurrence probabilities have a
higher value, and the second peak in the specific heat is more evident than the ones with
OONS. As seen, the occurrence probabilities of secondary structures for each peptide really
gave insight for explaining the peaks in the specific heat in the solvent model.
In conclusion, our results indicate that the calculated thermodynamical quantities of
each peptide depend on the solvent models and are consistent with the literature about the
solvent models dependency [14, 57]. Although these peptides show turn-structures, which
are also consistent with the literature, it was seen that the probabilities of the secondary
structures also depend on the solvent model. Therefore, it is not easy to decide which
one is a better implicit solvation model for our peptide sequences. Nevertheless, these
peptides show similar secondary structures such as γ-turns in each solvent model. At least
these similar structures may explain why these peptides give rather more contribution to
a decrease in the blood pressure than the other milk peptides according to experimental
studies.
VI. ACKNOWLEDGMENTS
We acknowledge the support of the Hacettepe University Scientific Research Fund
through the project 02.02.602.003.
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635
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