Letter pubs.acs.org/JPCL
Pressure-Induced Helical Structure of a Peptide Studied by Simulated Tempering Molecular Dynamics Simulations Yoshiharu Mori*,† and Hisashi Okumura‡,§ †
Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan Research Center for Computational Science, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan § Department of Structural Molecular Science, The Graduate University for Advanced Studies, Okazaki, Aichi 444-8585, Japan ‡
ABSTRACT: It is known experimentally that an AK16 peptide forms more α-helix structures with increasing pressure while proteins unfold in general. In order to understand this abnormality, molecular dynamics (MD) simulations with the simulated tempering method for the isobaric−isothermal ensemble were performed in a wide pressure range from 1.0 × 10−4 GPa to 1.4 GPa. From the results of the simulations, it is found that the fraction of the folded state decreases once and increases after that with increasing pressure. The partial molar volume change from the folded state to unfolded state increases monotonically from a negative value to a positive value with pressure. The behavior under high pressure conditions is consistent with the experimental results. The radius of gyration of highly helical structures decreases with increasing pressure, which indicates that the helix structure shrinks with pressure. This is the reason why the fraction of the folded state increases as pressure increases.
SECTION: Biophysical Chemistry and Biomolecules
T
he function of a protein is closely related to its structure. It is therefore important to determine structures of proteins. Many studies on the structure of proteins have been carried out over a long period of time. There are many experimental and theoretical studies on the structure of proteins. Recently, several studies on the pressure dependence of biomolecules were performed.1−12 Most of them reported so-called pressure-induced denaturation of proteins. Pressureinduced denaturation of proteins means that a protein changes to a state that does not have the regular structure under high pressure conditions. On the other hand, FT-IR spectroscopic studies revealed that the folded structures of some α-helix peptides such as an AK16 peptide increase with increasing pressure.3,4 We refer to the AK16 peptide as simply AK16 below. AK16 has 16 amino acid residues, and the amino acid sequence is YGAAKAAAAKAAAAKA. A coil structure and the folded one of AK16 are shown in Figure 1. Ala-rich peptides such as AK16 have been studied to understand the mechanism of helix formation.13 The tendency that AK16 is more folded under high pressure conditions seems to be opposite to that of usual proteins. We © XXXX American Chemical Society
Figure 1. Coil structure of an AK16 peptide (left) and the helically folded structure of the peptide (right). The fraction of the helical structure of the AK16 peptide is known to increase as pressure increases by experiments.3 The coil structure is a typical snapshot at P = 0.6 GPa and the helically folded structure is that at P = 1.4 GPa obtained from our MD simulations. These figures were rendered by the PyMOL program.
Received: April 11, 2013 Accepted: June 5, 2013
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Figure 2. Time series of (a) the pressure, (b) the potential energy, and (c) the volume in one of the ST MD simulations.
which amino acid residue formed a helical structure. We defined the helical structure of AK16 as α-helix, π-helix, and 310-helix structures. Using this criterion, we calculated the fraction f of folded amino acid residues with the MBAR method at several pressure values. The fractions of α-helix ( fα), π-helix ( fπ), and 310-helix ( f 310) structures at three pressure values are listed in Table 1. The total fraction of the helical structure f is expressed as f = fα + fπ + f 310. The fraction of α-helix fα principally contributes to the total fraction f.
therefore desire to understand the molecular mechanism of the pressure-induced folded structures of AK16 in detail. Molecular dynamics (MD) simulations are a useful tool to study molecular mechanism of structural changes of proteins and peptides. For applications to biomolecular systems, however, MD simulations often get trapped in the free-energy local-minimum states because of the complicated free energy surface and higher free energy barriers than typical thermal energy. Moreover, it is more difficult for atoms to move under high pressure conditions than at atmospheric pressure because the volume of a simulation system at a high pressure is smaller than that at a low pressure. To overcome such difficulties, we need to use some methods that enhance conformational sampling of MD simulations. Generalized-ensemble algorithms can be used for performing MD simulations more efficiently.14 There are some well-known generalized-ensemble algorithms, which are the replica-exchange method,15−17 the multicanonical algorithm,18−21 and the simulated tempering (ST) method.22,23 Generalized-ensemble algorithms have been extended to methods that can give correct physical quantities in the isobaric−isothermal ensemble.24−32 The algorithms have been applied to biomolecular simulations to study the pressure dependence of proteins and peptides.33−37 We used the modified version of the ST method for the isobaric−isothermal ensemble.32 We can calculate physical quantities from the results of ST simulations using several reweighting techniques such as the multiple histogram reweighting techniques,38 the weighted histogram analysis method (WHAM),39 and the multistate Bennett acceptance ratio method (MBAR).40 We performed MD simulations with the ST method for the system of AK16 to study pressure-induced structural changes of AK16 (see Computational Details). MD simulations with the ST method can realize random walks in temperature and pressure space. In this application, however, because we used only pressure as a parameter at a fixed temperature, a random walk was expected to be realized in pressure space. Time series of the pressure, the potential energy, and the volume are shown in Figure 2. Figure 2a shows that the pressure was fluctuated from the lowest pressure value (1.0 × 10−4 GPa) to the highest value (1.4 GPa). This fluctuation means that a random walk in pressure space was realized. The random walk of the pressure caused random walks of the potential energy and the volume (see Figure 2b,c). These large fluctuations of the potential energy and the volume enabled us to sample structures of AK16 efficiently. In order to study the pressure dependence of AK16 structures, we calculated the fraction of the folded amino-acid residues that formed helical structures in AK16 at several pressure values. We used the DSSP program41,42 to specify
Table 1. Fraction of Each Helix Structure pressure (GPa) 1.0 × 10 0.6 1.4
−4
fα
fπ
f 310
0.717 0.646 0.717
0.005 0.005 0.003
0.000 0.000 0.000
We then calculated the free energy difference ΔG defined as follows: ⎛1 − f ⎞ ΔG = Gunfold − Gfold = −RT ln⎜ ⎟ ⎝ f ⎠
(1)
where R is the gas constant and T is a temperature value. The subscripts “unfold” and “fold” mean the unfolded and folded states, respectively. Figure 3 shows ΔG. While ΔG decreases until pressure reaches around 0.6 GPa, ΔG increases at pressures higher than 0.6 GPa. This indicates that the fraction of the folded state decreases in the lower pressure range up to 0.6 GPa and increases in the higher pressure range.
Figure 3. Pressure dependence of the free energy difference ΔG. Each data in the figure was calculated by MBAR. The calculated data were represented by filled circles with error bars. The fitted curve is also shown in this figure. The curve was obtained by fitting the calculated free energies by a third-order polynomial. 2080
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We calculated the partial molar volume changes ΔV of AK16 at several pressure values. The partial molar volume change ΔV was calculated as follows from the obtained free energy difference: ΔV = Vunfold − Vfold =
⎛ ∂ΔG ⎞ ⎜ ⎟ ⎝ ∂P ⎠T
residues. The radius of gyration of the highly helical conformations decreases as pressure increases. On the other hand, that of the less helical conformations is almost constant except at pressures higher than 1.3 GPa. The pressure dependence of the highly helical conformations is reflected in that of the folded state, and the pressure dependence of the less helical conformations corresponds to that of the unfolded state. These results mean that the folded state shrinks as pressure increases, while the unfolded state does not change its volume as much as the folded state. Figure 4 shows that the partial molar volume of the folded state is less than the unfolded state at a room pressure. As pressure increases, the volume of the helix conformations decreases as indicated by Rg in Figure 5, and the volume of the folded state becomes equal to that of the unfolded state around P = 0.6 GPa. The volume of the helix conformations further decreases, and ΔV is then positive at pressures higher than 0.6 GPa. This is why the fraction of the folded structures decreases in the low pressure region and increases in the high pressure region. To give further proof that the folded state shrinks with pressure, the distribution of interatomic distance between the backbone oxygen of Ala7 and the backbone nitrogen of Ala11 is shown as an example in Figure 6. These atoms form a hydrogen
(2)
where P stands for pressure. We defined the partial molar volume change as a change from the folded state to the unfolded state. Figure 4 shows the partial molar volume change
Figure 4. Pressure dependence of the partial molar volume change ΔV of AK16. The curve was obtained by differentiating the fitted curve in Figure 3. The error bars of ΔV are also shown and were calculated by MBAR.
ΔV of AK16 in the range from 1.0 × 10−4 GPa to 1.4 GPa. While the partial molar volume change is negative at pressures less than 0.6 GPa, it becomes positive at pressures higher than 0.6 GPa. This means that the folded conformation has a smaller partial molar volume than the unfolded conformation under high pressure conditions. These results in the high pressure region are consistent with the experimental results,3 which showed that the partial molar volume change of AK16 had a positive value. In order to understand the conformational change of AK16 by pressure in Figure 3 and 4, we calculated the radius of gyration Rg of AK16 at several pressure values, as shown in Figure 5. Here, R g was calculated for two extreme conformations: One is highly helical conformations in which 12 or more out of 16 residues form helical structures. The other is less helical conformations which has six or less helical
Figure 6. Distribution of interatomic distance between the backbone oxygen of Ala7 and the backbone nitrogen of Ala11 at P = 0.1 MPa, 0.6 GPa, and 1.4 GPa calculated by MBAR.
bond when the α-helix is formed. The peak around 3 Å, which corresponds to the interatomic distance with a hydrogen bond, shifts toward left-hand side and becomes sharper with pressure. This result also means that the α-helix structure shrinks as pressure increases. While our MD simulation results show that ΔV is negative in the low pressure region (lower than 0.6 GPa), it is positive in the whole pressure region in the experiments. A possible reason of this inconsistency is the force field used in this study. To reproduce the experimental results more accurately, the partial molar volume of the folded state should be evaluated smaller than that of the unfolded state from the room pressure to high pressures with a given force field. However, there is not perfect force field at the moment.43 In this case, the partial molar volume of the folded state was calculated larger than that of the unfolded state at the room pressure. Thus, although the MD simulation successfully indicated that the folded state shrinks with pressure, ΔV was negative in the low pressure region. Paschek et al. performed replica-exchange MD simulations of an AK20 peptide.33 They reported that the fraction of the folded state only decreased with pressure. This feature is opposite from the experiments.3,4 Because their replicaexchange MD simulation covered the pressure ranges up to
Figure 5. Pressure dependence of the radius of gyration Rg of AK16. The red filled circles stand for the radius of gyration of the highly helical conformations of AK16, and the green filled circles stand for that of the less helical conformations. The radius of gyration of all conformations is also shown by the blue filled circles. The error bars were calculated by MBAR. 2081
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also higher temperature.4 We used 40 pressure values (1.01 × 10−4, 1.67 × 10−2, 3.41 × 10−2, 5.24 × 10−2, 7.16 × 10−2, 9.18 × 10−2, 1.13 × 10−1, 1.35 × 10−1, 1.58 × 10−1, 1.83 × 10−1, 2.08 × 10−1, 2.35 × 10−1, 2.63 × 10−1, 2.92 × 10−1, 3.22 × 10−1, 3.53 × 10−1, 3.85 × 10−1, 4.18 × 10−1, 4.52 × 10−1, 4.86 × 10−1, 5.22 × 10−1, 5.58 × 10−1, 5.96 × 10−1, 6.34 × 10−1, 6.73 × 10−1, 7.14 × 10−1, 7.55 × 10−1, 7.98 × 10−1, 8.42 × 10−1, 8.87 × 10−1, 9.34 × 10−1, 9.82 × 10−1, 1.03, 1.08, 1.13, 1.18, 1.24, 1.29, 1.34, 1.40 GPa) for the ST method, and these 40 values were determined so that the transition probabilities of the ST method can be uniform. The integration step time was set to 2.0 fs. We performed four independent ST MD simulations with different initial velocities. Transitions of pressure values were attempted every 1.0 ps during the ST MD simulations. Each of the simulations was carried out for 100 ns to equilibrate the system and for 500 ns to sample structural data of AK16. The total simulation time of the production runs was, as a result, 2.0 μs. In MD simulations with ST, the weight factors of ST have to be determined before a production run. In this study, we determined the weight factors as follows. First, we performed 46 constant temperature and pressure MD simulations. Each simulation was carried out for 10 ns in the same conditions as each other except for the pressure values. We used 46 different pressure values in the range from 1.0 × 10−4 GPa to 1.4 GPa. We then calculated the weight factors of ST using MBAR.
0.4 GPa at T = 300 K and up to 0.7 GPa at T = 406 K, probably they observed only the lower pressure side in Figure 3 and did not find the increase of the folded state with increasing pressure. In this Letter, we reported the pressure dependence of an AK16 peptide. We performed molecular dynamics simulations of AK16 to study the detail mechanism of the high pressure behavior. We used the simulated tempering method for the isobaric−isothermal ensemble to enhance conformation sampling of AK16 in the MD simulations. From the results of the MD simulations, we found that the fraction of helical structures of AK16 decreases first with increasing pressure, and then increases in the high pressure region. The partial molar volume change increases from a negative value to a positive value. We reproduced experimental features on the pressure dependence of AK16 structures in the high-pressure region. We calculated the radius of gyration and found that the volume of the folded state of AK16 decreases as pressure increases, which indicates that the folded structures of AK16 become smaller than the unfolded state at high pressures. This is why the fraction of the folded state increases with increasing pressure in the high pressure region. Our results show that MD simulations with a generalizedensemble algorithm can be used for studying structural changes of peptides and proteins induced by pressure. We, therefore, expect that MD simulations in a wide range of pressure enable us to understand the structure of proteins.
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AUTHOR INFORMATION
Corresponding Author
COMPUTATIONAL DETAILS We performed MD simulations with the ST method for the isobaric−isothermal ensemble to study the pressure dependence of AK16 structures. We prepared a simulation system, which consisted of AK16, 4414 water molecules, and three chloride ions. The total number of atoms in the system was 13 446. The N-terminus of AK16 was capped by an acetyl group and the C-terminus was amidated. The system was placed in a cubic simulation cell with periodic boundary conditions. The MD simulations were carried out by the NAMD program package (version 2.9).44 We implemented a tcl script that performs the ST method. We used the CHARMM22 force field45 with the CMAP corrections46 for AK16 and chloride ions and the TIP3P water model.45,47 The electrostatic interactions were calculated by using the particle mesh Ewald method (PME).48,49 The cutoff distance for the van der Waals interactions and the electrostatic interactions in the real space of PME was set to 13.0 Å. In the van der Waals interaction calculations, we used the switching function of which the switching distance was set to 11.0 Å. In the PME calculations, the interpolation order was set to 6, and the number of grid points was set to 54 × 54 × 54. The temperature and pressure control was carried out by the Nosé−Hoover Langevin piston pressure control method,44,50 which is based on the Nosé− Hoover thermostat51,52 and the Langevin piston method.53 The damping coefficient for the temperature control was set to 5 ps−1. The oscillation period and damping time scale for the pressure control were set to 200 and 100 fs, respectively. We set the temperature parameter to 400 K. This temperature value is far from physiological conditions. We considered, however, that it was valid and convenient in this study to use such a high temperature value for conformational search because a related research on the pressure dependence of an alanine-based peptide suggested that the helical structure of the peptide increases with high pressure at not only room temperature but
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Some of the computations were performed on the supercomputers at the Research Center for Computational Science, Institute for Molecular Science. This work was supported, in part, by Grants-in-Aid for JSPS Fellows.
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REFERENCES
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