Article Outline

Article Information

PubMed

Related Articles

  • …more

Copyright © 2000 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 78, Issue 6, 2752-2760, 1 June 2000

doi:10.1016/S0006-3495(00)76820-2

Biophysical Theory and Modeling

On the Temperature and Pressure Dependence of a Range of Properties of a Type of Water Model Commonly Used in High-Temperature Protein Unfolding Simulations

Regula Walser, Alan E. Mark1 and Wilfred F. van GunsterenGo To Corresponding Author,  

Laboratory of Physical Chemistry, Swiss Federal Institute of Technology Zürich, CH-8092 Zürich, Switzerland

Address reprint requests to Prof. Wilfred F. van Gunsteren, Laboratory of Physical Chemistry, ETH-Zürich, CH-8092 Zürich, Switzerland. Tel: +41-1-6325502; Fax: +41-1-6321039.

1 The present address of Prof. Mark is Laboratory of Biophysical Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands.

Abstract

Molecular dynamics simulations of protein folding and unfolding are often carried out at temperatures (400–600K) that are much higher than physiological or room temperature to speed up the (un)folding process. Use of such high temperatures changes both the protein and solvent properties considerably, compared to physiological or room temperature. Water models designed for use in conjunction with biomolecules, such as the simple point charge (SPC) model, have generally been calibrated at room temperature and pressure. To determine the distortive effect of high simulation temperatures on the behavior of such “room temperature” water models, the structural, dynamic, and thermodynamic properties of the much-used SPC water model are investigated in the temperature range from 300 to 500K. Both constant pressure and constant volume conditions, as used in protein simulations, were analyzed. We found that all properties analyzed change markedly with increasing temperature, but no phase transition in this temperature range was observed.

Introduction

Molecular dynamics simulations are widely used to gain insight into the equilibrium properties of proteins in solution. Increasingly, simulations are also being used to study time- and environment-dependent phenomena, such as the folding or unfolding of proteins. In particular, many simulations of the process of thermal denaturation have been performed. Currently accessible time scales of ∼10−9s are insufficient, however, to simulate folding and unfolding processes at experimentally relevant temperatures. To circumvent this problem most simulations of protein unfolding have used high simulation temperatures to shorten the time scale of the unfolding process. For example, the thermal unfolding of hen egg white (HEW) lysozyme in water was simulated at 500K (Mark and van Gunsteren, 1992). The destabilization of bovine pancreatic trypsin inhibitor (BPTI) and its reduced form in water was simulated at 423K and 498K (Daggett and Levitt, 1992,Daggett and Levitt, 1993). The denaturation of the C-terminal fragment (CTF) of the L7/L12 ribosomal protein was simulated at 498K (Daggett, 1993), that of the enzyme β-lactamase at 600K (Vijayakumar et al), and that of the protein barnase at 498K and 600K (Caflisch and Karplus, 1994,Caflisch and Karplus, 1995,Li and Daggett, 1998,Bond et al). Potato carboxypeptidase inhibitor was simulated at 600K (Martì-Renom et al), and cutinase was simulated at 393K (Creveld et al).

In each of these cases the proteins unfold. The question is, how relevant are the results from a simulation of a protein at 500K to the process of thermal denaturation close to physiological temperatures? At a more basic level one must also ask if the molecular models and simulation protocols developed for use at 300K are still appropriate at elevated temperatures.

The process of protein folding and unfolding is driven by the balance between protein-protein, protein-water, and water-water interactions. Each of these interactions involves some degree of enthalpy-entropy compensation and will depend on the temperature. At nonphysiological temperatures the unfolding pathways may also be quite different from that at 300K. For one, at high temperature the structural, dynamic, and thermodynamic properties of a solvent such as water will differ from those at 300K, which will in turn affect the process of protein unfolding.

In this paper we investigate the extent to which the structural, dynamic, and thermodynamic properties of a water model commonly used in biomolecular simulations, the simple point charge (SPC) model (Berendsen et al), change as a function of temperature between 300 and 500K.

Because protein unfolding simulations at high temperatures have been carried out at constant volume as well as at constant pressure, the properties of liquid water are investigated under both these conditions.

Other studies of the temperature dependence of the properties of water have been published. However, these studies have not covered the whole range of temperatures or properties relevant to protein destabilization and denaturation simulations. They have either focused on the range up to 373K (Jorgensen and Jenson, 1998), on the phase equilibrium (Boulougouris et al,de Pablo et al), or on the supercritical conditions (Jedlovszky et al,Jedlovszky and Richardi, 1999,Bursulaya and Kim, 1999a,Bursulaya and Kim, 1999b), or considered only a limited set of properties. When Levitt et al developed and tested their flexible water model F3C, they also examined some of its properties, i.e., energy, heat capacity, radial distribution function, and diffusion constant at higher temperatures. Brodholt and Wood, 1993 investigated the behavior of the energy, pressure, heat capacity, and radial distribution function of TIP4P (Jorgensen et al) as well as SPC/E (Berendsen et al) and a model by Watanabe and Klein, 1989 over a wide temperature range (up to 2600K). However, none of these studies looked at the free energy and dynamical properties of water, which also might affect protein (un)folding. Here we concentrate in particular on those properties of water that may influence the process of protein unfolding and lead to artifacts in unfolding simulations.


Method

Simulation

At five temperatures, 300, 350, 400, 450, and 500K, two simulations were performed, one at constant pressure and one at constant volume. The system consisted of a cubic periodic box containing 1000 SPC water molecules (Berendsen et al). Bond lengths and angles were constrained using the SHAKE algorithm (Ryckaert et al), with a relative tolerance of 10−4. The system was equilibrated for 50ps at each temperature and then simulated for 250ps for analysis. Configurations 0.05ps apart were saved. The temperature was kept constant by a Berendsen thermostat (Berendsen et al) (weak coupling) with a coupling time of 0.1ps. In the constant-pressure simulations the pressure was kept at 1atm by weak coupling to an external bath (Berendsen et al) with a relaxation time of 0.5ps and a compressibility of 7.5×10−4molnm3/kJ. In the constant-volume simulations the volume was fixed at 29.9151nm3 (box length of 3.1043nm), which corresponds to a density of 602.22u/nm3 (1.0g/cm3). All simulations were performed using the GROMOS96 simulation package (van Gunsteren et al,Scott et al) with a time step of 2 fs. The nonbonded interactions were calculated using a twin cutoff of 0.9 nm/1.4nm for the oxygen-oxygen distances. The interaction between water molecules with oxygen-oxygen distances between 0.9nm and 1.4nm were updated every 10 fs. No reaction-field correction to long-range electrostatic interactions was applied.

The excess free energy ΔAexs of the water model at each temperature was determined using the thermodynamic integration method. The volume was kept constant. All intermolecular interactions were scaled as a function of the coupling parameter λ (Daura et al). Simulations were performed at 29 λ points between λ=0 and λ=1. At each λ-point 20ps for equilibration and 50ps for analysis were calculated.

The hydration free enthalpy ΔGhyd was calculated in the same way, except that the pressure was kept constant and the intermolecular interactions of only one molecule were scaled as a function of the coupling parameter.


Analysis

The presence of a hydrogen bond was determined based on a geometric criterion. If the O&cjs0807;H distance was less then 0.25nm and the O-H&cjs0807;O angle greater than 135°, a hydrogen bond was considered to exist between the two water molecules. The diffusion constant was estimated from the Einstein formula,

(1)
where r(t) is the position vector of a molecule’s center of mass at time t. The thermal expansion coefficients α have always been calculated from two simulations at constant pressure with ΔT=50K via (Tironi and van Gunsteren, 1994)
(2)
in which ρ1 and ρ2 are the densities at temperatures T1 and T2.

The heat capacity Cp was calculated using (Postma, 1985)

(3)
where Eint is the (quantum) contribution of intramolecular vibrational modes to the specific heat. Eext is the difference between the quantum-mechanical and the classical intermolecular vibrational energy. Those corrections have been calculated as described by Postma, 1985. At 300K their combined value is −9.3Jmol−1K−1 (Postma, 1985). The rotational correlation times τl were calculated by fitting to the linear part in a logarithmic plot of the Legendre polynomial correlation function of rank l, 〈Pl(cos θ(t))〉, where cos(θ(t)) denotes the scalar product of the corresponding dipole vectors of unit length separated by a time t.



Results

Thermodynamic properties

Fig. 1 shows the total energy, the kinetic energy, the potential energy, the van der Waals energy, the electrostatic energy, and the heat of vaporization for the SPC model as a function of temperature. In the simulations with constant pressure the change in the total energy is larger than in the simulations with constant volume, as the computational box is unable to relax in the latter. The heat of vaporization ΔHvap is estimated from the simulations as

(4)
where pΔV can be approximated by RT, because ΔV is essentially equal to Vgas. Qint is the intramolecular (quantum) contribution for the difference in vibrational energy between the liquid state and the gas phase, and Qext is its intermolecular counterpart (Postma, 1985). At 300K, Qint+Qext=−0.23 kJ/mol (Postma, 1985).

Display large version of this figure
Figure 1
The total, kinetic, potential, van der Waals, and electrostatic energies (in kJ/mol) are shown as a function of temperature for the simulations with constant pressure (×, – – –, p=1 atm=0.061kJ/mol/nm3) and with constant volume (+, ——, ρ=1.0g/cm3=602u/nm3). All quantities are given per molecule. In f the heat of vaporization, calculated with Eq. (4), is compared to the experimental heat of vaporization (□, - - - -) (Marsh, 1987). The lines have been added to guide the eye.

Comparing the vaporization enthalpy calculated in this way to the experimental vaporization enthalpy (Marsh, 1987) along the liquid-vapor curve, there is good agreement, although the simulated values are higher than the experimental ones.

The pressures and densities are shown in Fig. 2. The decrease in density as a function of temperature in the constant-pressure simulations is greater than observed experimentally for water up to 373K. Beyond 373K, where water is a gas at 1atm, the simulations clearly overestimate the density. No sudden decrease in density with temperature, which would indicate vaporization, was observed.

Display large version of this figure
Figure 2
Pressure (p), density (ρ), and free energies (ΔGhyd and ΔAexs) are shown as a function of temperature. In a the pressure is compared to the experimental pressure of water with density 1.00g/cm3 (■, - - - -). The values were taken from Haar et al. The experimental values for the density were taken from Kell, 1967; those above 373K refer to the metastable liquid. The excess free energy ΔAexs (+, ——) is compared with the experimental values (■, - - - -) calculated as described in the text. ΔGhyd (×, – – –) is the hydration free enthalpy. For further explanation see caption of Fig. 1.

The calculated free energies are shown and compared to the experimental values in Figure 2c. The experimental values of the excess free energy ΔAexs are calculated from the vapor pressure by

(5)
where pvap is the vapor pressure at temperature T and v is the molar volume of water. The values for pvap and v are taken from Schmidt, 1989. The calculated excess free energy agrees well with the experimental one over the whole temperature range from 300 to 500K.

In Figure 3a the results for the thermal expansion coefficient α are shown. The values are too high compared to the experimental values (Kell, 1967), as can also be seen in Figure 2b, where the density decreases faster than the experimental density. Although the thermal expansion coefficient is too large, its behavior with increasing temperature is correct, because the slope is about the same as for the experimental values. The heat capacity CP, shown in Figure 3b, agrees very well with the experimental values (Weast, 1976) up to 373K. Above 373K, the results are noncomparable, as in the simulation the water does not evaporate. Jorgensen and Jenson, 1998 calculated CP and α for SPC at 298K from the fluctuations of the energy and volume. They obtained values that are slightly higher than the values calculated here, 1.06×10−3K−1 (Jorgensen and Jenson, 1998) for α compared to 0.97×10−3K−1 and 84.5Jmol−1K−1 (Jorgensen and Jenson, 1998) for CP compared to 76.4Jmol−1K−1.

Display large version of this figure
Figure 3
Thermal expansion coefficient α and heat capacity CP were calculated from the simulations at constant pressure with Eqs. (2). The experimental values for α were taken from Kell, 1967. The values above 373K refer to the metastable liquid at 1atm. The experimental values for CP were taken from Weast, 1976. The average number of hydrogen bonds per molecule (〈nHB〉) is shown as a function of temperature. The hydrogen bond criterion is given in the text. The experimental values obtained by Raman spectroscopy were estimated from the graph in Walrafen, 1966; those obtained by energetic considerations were taken from Haggis et al. For further explanation see caption of Fig. 1.

Structural properties

The number of hydrogen bonds per molecule shown in Figure 3c decreases almost linearly in the constant-volume simulations. The value of 3.46 hydrogen bonds per molecule under ambient conditions corresponds well to the results of Jorgensen et al, who found 3.54 hydrogen bonds per molecule, although they used an energetic definition of a hydrogen bond. The results also agree well with the experimental results of Haggis et al, who determined the percentage of broken hydrogen bonds by energetic considerations. However, they are completely different from the experimental results of Walrafen, 1966, who determined the fraction of hydrogen bonds by Raman spectroscopy. In the constant-pressure simulations the number levels off above 450K. This could indicate clustering of molecules, but no clustering was observed from visual inspection of specific configurations. The computational box did not expand further after ∼20ps (see Fig. 4), and we found no indication that the liquid would evaporate on a 100-ps time scale.

Display large version of this figure
Figure 4
Box volume of the simulation at 500K with constant pressure (1 atm=0.061kJ/mol/nm3) as a function of time.

Figure 5 and Figure 6 show radial distribution functions g(r) between the oxygen atoms of different molecules at the different temperatures. With constant pressure and with constant volume, the peak height decreases with increasing temperature and the first minimum shifts toward longer distances. The second peak that is visible at 300K disappears at higher temperatures, but there seems to be a second peak reappearing at 500K. This agrees somewhat with the results of Brodholt and Wood, 1993 for the TIP4P water model, who saw the second peak disappearing at 340K and reappearing at 771K.

Display large version of this figure
Figure 5
Oxygen-oxygen radial distribution function g(r) of the simulations with constant volume (ρ=1.0g/cm3=602u/nm3) for different temperatures. The different curves are vertically shifted by one unit for better visibility.
Display large version of this figure
Figure 6
Oxygen-oxygen radial distribution function g(r) of the simulations with constant pressure (p=1 atm=0.061kJ/mol/nm3) for different temperatures. The different curves are vertically shifted by one unit for better visibility.

Dynamic properties

The results for the dynamic properties are shown in Fig. 7. The simulated diffusion coefficient is larger than the experimental one (Becke, 1974,Krynicki et al) up to ∼400K, but it changes less with increasing temperature than in the experiment. The increase with temperature is stronger for constant-pressure simulations, especially for temperatures above 400K. The dipolar rotational correlation times τl decrease with increasing temperature. There is no significant difference between the constant-pressure and the constant-volume simulations. τ1 is compared to the experimentally measurable decay time τD of the macroscopic polarization (Collie et al). It should be between ½τD and τD (Powles, 1953,Nee and Zwanzig, 1970). Although the values at 300K lie in this range, it looks like τ1 is not decaying fast enough with temperature compared to experiment. The ratio between τ1 and τ2 is for most temperatures between 2.5 and 3, except for constant pressure at 450K and for constant volume at 500K, where it is 1.8 and 3.5, respectively. These deviations probably result from the way τl is calculated. At high temperatures the exponential part in the decay function is short. Thus few points for fitting are available.

Display large version of this figure
Figure 7
The translational diffusion constant (D) and the dipolar rotational correlation times (τl) are shown as a function of temperature. The experimental values for D at atmospheric pressure (□) were taken from Becke, 1974, those at the pressure corresponding (according to Haar et al) to a density ρ of 1.0g/cm3 (■) were taken from Krynicki et al. The experimental values for τ1 correspond to τD and ½τD as described in the text. Values for τD were taken from Collie et al. For further explanation see caption of Fig. 1.


Conclusions

In an attempt to investigate the behavior of the solvent in simulations at higher temperatures, simulations of SPC water have been performed at temperatures up to 500K. From the present work, the conclusion is that the structure of the solvent changes with increasing temperature. Although there is no vaporization of the water even at temperatures up to 500K, the number of hydrogen bonds per molecule decreases. The excess free energy and hydration free enthalpy per water molecule change by ∼10 kJ/mol over this temperature range. Both of these factors would be expected to affect the folding of a protein. In addition, the dynamics of the water molecules changes quite dramatically. Of course, all dynamic properties indicate that the molecules move much faster; the diffusion increases by four- (NVT) to sevenfold (NPT) when the temperature is raised from 300K to 500K.

In general the properties of the NVT and NPT systems, which are effectively equivalent at 300K, 1atm, and a density of 1g/cm3, deviate widely with increasing temperature. The choice of ensemble in simulations of proteins at high temperature is thus a critical issue.

Overall, in comparison with the available experimental data, it is apparent that the SPC water model performs well over a wide range of temperature. This said, it is also clear that at elevated temperatures not only does the model begin to deviate from experiment, but the properties of water as a solvent are also very different from those under which thermal denaturation is studied experimentally. The use of temperatures beyond 400K in simulations of proteins in water is very likely to significantly affect the (un)folding thermodynamics, pathways, and kinetics. Its results should therefore be very cautiously interpreted.


Acknowledgments

Financial support was obtained from the Schweizerischer Nationalfonds, project number 21-50929.97, which is gratefully acknowledged.

References

Becke, 1974 In Gmelin Handbuch der anorganischen Chemie. Becke, M., ed. 8th Ed., (Berlin: Springer-Verlag). PubMed

Berendsen et al., 1987 Berendsen, H.J.C., Grigera, J.R., and Straatsma, T.P. (1987). The missing term in effective pair potentials. J. Phys. Chem. 91, 6269–6271. CrossRef | PubMed

Berendsen et al., 1984 Berendsen, H.J.C., Postma, J.P.M., van Gunsteren, W.F., DiNola, A., and Haak, J.R. (1984). Molecular dynamics with coupling to an external bath. J. Chem. Phys. 81, 3684–3690. CrossRef | PubMed

Berendsen et al., 1981 Berendsen, H.J.C., Postma, J.P.M., van Gunsteren, W.F., and Hermans, J. (1981). Interaction models for water in relation to protein hydration. In Intermolecular Forces. Pullman, B., ed. (Dordrecht, the Netherlands: Reidel), pp. 331–342. PubMed

Bond et al., 1997 Bond, C.J., Wong, K.-B., Clarke, J., Fersht, A.R., and Daggett, V. (1997). Characterization of residual structure in the thermally denatured state of barnase by simulation and experiment: description of the folding pathway. Proc. Natl. Acad. Sci. USA 94, 13409–13413. CrossRef | PubMed

Boulougouris et al., 1998 Boulougouris, G.C., Economou, I.G., and Theodorou, D.N. (1998). Engineering a molecular model for water phase equilibrium over a wide temperature range. J. Phys. Chem. B. 102, 1029–1035. PubMed

Brodholt and Wood, 1993 Brodholt, J., and Wood, B. (1993). Simulation of the structure and thermodynamic properties of water at high pressures and temperatures. J. Geophys. Res. 98, 519–536. PubMed

Bursulaya and Kim, 1999a Bursulaya, B.D., and Kim, H.J. (1999). Molecular dynamics simulation study of water near critical conditions. I. Structure and solvation free energetics. J. Chem. Phys. 110, 9646–9655. CrossRef | PubMed

Bursulaya and Kim, 1999b Bursulaya, B.D., and Kim, H.J. (1999). Molecular dynamics simulation study of water near critical conditions. II. Dynamics and spectroscopy. J. Chem. Phys. 110, 9656–9665. CrossRef | PubMed

Caflisch and Karplus, 1994 Caflisch, A., and Karplus, M. (1994). Molecular dynamics simulation of protein denaturation: solvation of the hydrophobic cores and secondary structure of barnase. Proc. Natl. Acad. Sci. USA 91, 1746–1750. CrossRef | PubMed

Caflisch and Karplus, 1995 Caflisch, A., and Karplus, M. (1995). Acid and thermal denaturation of barnase investigated by molecular dynamics simulations. J. Mol. Biol. 252, 672–708. CrossRef | PubMed

Collie et al., 1948 Collie, C.H., Hasted, J.B., and Ritson, D.M. (1948). The dielectric properties of water and heavy water. Proc. Phys. Soc. 60, 145–160. PubMed

Creveld et al., 1998 Creveld, L.D., Amadei, A., van Schaik, R.C., Pepermans, H.A.M., de Vlieg, J., and Berendsen, H.J.C. (1998). Identification of functional and unfolding motions of cutinase as obtained from molecular dynamics computer simulations. Proteins 33, 253–264. CrossRef | PubMed

Daggett, 1993 Daggett, V. (1993). A model for the molten globule state of (CTF) generated using molecular dynamics. In Techniques in Protein Chemistry IV. Angeletti, R.H., ed. (San Diego: Academic Press), pp. 525–532. PubMed

Daggett and Levitt, 1992 Daggett, V., and Levitt, M. (1992). A model of the molten globule state from molecular dynamics simulations. Proc. Natl. Acad. Sci. USA 89, 5142–5146. CrossRef | PubMed

Daggett and Levitt, 1993 Daggett, V., and Levitt, M. (1993). Protein unfolding pathways explored through molecular dynamics simulations. J. Mol. Biol. 232, 600–619. CrossRef | PubMed

Daura et al., 1996 Daura, X., Hünenberger, P.H., Mark, A.E., Querol, E., Avilés, F.X., and van Gunsteren, W.F. (1996). Free energies of transfer of Trp analogs from chloroform to water: comparison of theory and experiment and the importance of adequate treatment of electrostatic and internal interactions. J. Am. Chem. Soc. 118, 6285–6294. CrossRef | PubMed

de Pablo et al., 1990 de Pablo, J.J., Prausnitz, J.M., Strauch, H.J., and Cummings, P.T. (1990). Molecular simulation of water along the liquid-vapor coexistence curve from 25°C to the critical point. J. Chem. Phys. 93, 7355–7359. CrossRef | PubMed

Haar et al., 1988 Haar, L., Gallagher, J.S., and Kell, G.S. (1988). NBS)/NRC Wasserdampftafeln. (Berlin: Springer-Verlag). PubMed

Haggis et al., 1952 Haggis, G.H., Hasted, J.B., and Buchanan, T.J. (1952). The dielectric properties of water in solutions. J. Chem. Phys. 20, 1453–1465. PubMed

Jedlovszky et al., 1998 Jedlovszky, P., Brodholt, J.P., Bruni, F., Ricci, M.A., Soper, A.K., and Vallauri, R. (1998). Analysis of the hydrogen-bonded structure of water from ambient to supercritical conditions. J. Chem. Phys. 108, 8528–8540. CrossRef | PubMed

Jedlovszky and Richardi, 1999 Jedlovszky, P., and Richardi, J. (1999). Comparison of different water models from ambient to supercritical conditions: a Monte Carlo simulation and molecular Ornstein-Zernike study. J. Chem. Phys. 110, 8019–8031. CrossRef | PubMed

Jorgensen et al., 1983 Jorgensen, W.L., Chandrasekhar, J., Madura, J.D., Impey, R.W., and Klein, M.L. (1983). Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 79, 926–935. CrossRef | PubMed

Jorgensen and Jenson, 1998 Jorgensen, W.L., and Jenson, C. (1998). Temperature dependence of TIP3P, SPC, and TIP4P water from NPT Monte Carlo simulations: seeking temperatures of maximum density. J. Comp. Chem. 19, 1179–1186. PubMed

Kell, 1967 Kell, G.S. (1967). Precise representation of volume properties of water at one atmosphere. J. Chem. Eng. Data 12, 66–69. PubMed

Krynicki et al., 1978 Krynicki, K., Green, C.D., and Sawyer, D.W. (1978). Pressure and temperature dependence of self-diffusion in water. Faraday Discuss. Chem. Soc. 66, 199–208. PubMed

Levitt et al., 1997 Levitt, M., Hirshberg, M., Sharon, R., Laidig, K.E., and Daggett, V. (1997). Calibration and testing of a water model for simulation of the molecular dynamics of proteins and nucleic acids in solution. J. Phys. Chem. B. 101, 5051–5061. PubMed

Li and Daggett, 1998 Li, A., and Daggett, V. (1998). Molecular dynamics simulation of the unfolding of barnase: characterization of the major intermediate. J. Mol. Biol. 275, 677–694. CrossRef | PubMed

Mark and van Gunsteren, 1992 Mark, A.E., and van Gunsteren, W.F. (1992). Simulation of the thermal denaturation of hen egg white lysozyme: trapping the molten globule state. Biochemistry 31, 7745–7748. PubMed

Marsh, 1987 Marsh, K.N. (1987). Recommended Reference Materials for the Realization of Physicochemical Properties. (Oxford: Blackwell Scientific Publications). PubMed

Martì-Renom et al., 1998 Martì-Renom, M.A., Stote, R.H., Querol, E., Avilés, F.X., and Karplus, M. (1998). Refolding of potato carboxypeptidase inhibitor by molecular dynamics simulation with disulfide bond constraints. J. Mol. Biol. 284, 145–172. CrossRef | PubMed

Nee and Zwanzig, 1970 Nee, T.-W., and Zwanzig, R. (1970). Theory of dielectric relaxation in polar liquids. J. Chem. Phys. 52, 6353–6363. CrossRef | PubMed

Postma, 1985 Postma, J. P. M. 1985. MD of H2O. Ph.D. thesis. Rijksuniversiteit, Groningen, the Netherlands..

Powles, 1953 Powles, J.G. (1953). Dielectric relaxation and the internal field. J. Chem. Phys. 21, 633–637. CrossRef | PubMed

Ryckaert et al., 1977 Ryckaert, J.-P., Ciccotti, G., and Berendsen, H.J.C. (1977). Numerical integration of the Cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes. J. Comp. Chem. 23, 327–341. PubMed

Schmidt, 1989 Schmidt, E. (1989). Zustandsgrössen von Wasser und Wasserdampf in SI-Einheiten (Properties of Water and Steam in SI-Units). 4th Ed., (Berlin: Springer-Verlag). PubMed

Scott et al., 1999 Scott, W.R.P., Hünenberger, P.H., Tironi, I.G., Mark, A.E., Billeter, S.R., Fennen, J., Torda, A., Huber, T., Krüger, P., and van Gunsteren, W.F. (1999). The GROMOS biomolecular simulation program package. J. Phys. Chem. 103, 3596–3607. PubMed

Tironi and van Gunsteren, 1994 Tironi, I.G., and van Gunsteren, W.F. (1994). A molecular dynamics simulation study of chloroform. Mol. Phys. 83, 381–403. PubMed

van Gunsteren et al., 1996 van Gunsteren, W.F., Billeter, S.R., Eising, A.A., Hünenberger, P.H., Krüger, P., Mark, A.E., Scott, W.R.P., and Tironi, I.G. (1996). Biomolecular Simulation: The GROMOS96 Manual and User Guide. (ETH Zürich, Switzerland: vdf Hochschulverlag). PubMed

Vijayakumar et al., 1993 Vijayakumar, S., Vishveshwara, S., Ravishanker, G., and Beveridge, D.L. (1993). Differential stability of β-sheets and α-helices in β-lactamase: a high temperature molecular dynamics study of unfolding intermediates. Biophys. J. 65, 2304–2312. Abstract | | CrossRef | PubMed

Walrafen, 1966 Walrafen, G.E. (1966). Raman spectral studies of the effects of temperature on water and electrolyte solutions. J. Chem. Phys. 44, 1546–1558. CrossRef | PubMed

Watanabe and Klein, 1989 Watanabe, K., and Klein, M.L. (1989). Effective pair potentials and the properties of water. Chem. Phys. 131, 157–167. PubMed

Weast, 1976 In Handbook of Chemistry and Physics. Weast, R.C., ed. 56th Ed., (Boca Raton, FL: CRC Press). PubMed

Publication Information


Received: November 15, 1999
Accepted: March 13, 2000