Departament de Quimica Analítica, Universitat de Barcelona, Martí i Franqués, 1-11, 08028, Barcelona and 1 Institut de Biologia Fonamental and Departament de Bioquímica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
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Abstract |
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Keywords: electrostatics/molecular dynamics/procarboxypeptidase B/reaction field/salt effects
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Introduction |
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While experimental knowledge is essential for the understanding of the effects of counterions on the structure and dynamic properties of proteins in solution, theoretical studies and computer simulations, such as molecular dynamics (MD), complement the experimental data. One of the most demanding systems for such studies is the highly charged globular proteins lacking disulfide bridges. A previous study examined the influence of the counterions and volume on the simulated dynamics of the activation domain of procarboxypeptidase B (ADBp), a highly charged globular protein (Martí-Renom et al., 1998). The enlargement of the water box stabilizes the system and a similar trend was also observed when counterions were included in the MD simulation. However, the overall structure of ADBp was not maintained during the simulations owing to unsatisfactory treatment of electrostatic forces, and all the secondary structures of ADP were distorted.
The most important factor in the calculation of forces in MD simulations is that of the electrostatic interactions. Besides, the calculation of the electrostatic forces takes most of the CPU time. In systems with a large number of atoms, the computational load can be reduced by the use of rapid but approximate methods. Two areas in which accuracy is exchanged for speed are long-range interactions and electronic polarizability (Gilson, 1995). Electrostatic interactions are long-range forces and truncation, i.e. the use of cut-offs significantly affects results (Schreiber and Steinhauer, 1992). Moreover, long MD simulations of proteins without electrostatic cut-offs yield trajectories that resemble known crystallographic structures more than similar simulations with cut-offs.
Improvements in MD studies of highly charged systems that reduce CPU time have been proposed (Berendsen, 1993; Luty et al., 1994
; Saito, 1994
; Cheatham et al., 1995
). Some of them separate the force of each charge into short- and long-range parts, and use special methods for dealing with the latter. Among them, the inclusion in the calculation of electrostatic forces of a reaction field (RF) term based on the PoisonBoltzman approach has been used in the study of polar and ionic systems (Tironi et al., 1995
). Here we report the effect of the inclusion of an RF term in the treatment of the electrostatic contribution for the study of ADBp dynamics in solution.
We used as a model the activation domain of porcine procarboxypeptidase B, which corresponds to the 75 residue N-terminal globular part of the pro-segment. The domain is attached to the carboxypeptidase B moiety by a 15 residue-connecting segment. It consists of a four-stranded antiparallel ß-sheet with two -helices and one 310-helix packed over its external face in an antiparallel
/antiparallel ß topology (Figure 1
). The structure has two internal salt bridges (4Glu49Arg, 49Arg30Asp) and there are no disulfide bridges in this domain. The activation domain has charged residues and its stability in solution depends on the ionic composition of the medium (Conejo-Lara et al., 1991
).
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Materials and methods |
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In simulation 1, which is representative of a non-counterbalanced protein charged system, the minimized solvated structure was the starting point for an MD simulation run under periodic boundary conditions at constant temperature and pressure and neutral pH.
For simulation 2 the charges of ADBp were neutralized by seven Cl ions and 18 Na+ ions. Therefore, the water molecules closest to the charges in the minimized solvated structure were replaced by the counterions and the system was again energetically minimized using 100 steps of steepest descent. This minimized structure (protein, solvent and ions) was the starting point for the MD simulation in the same conditions of temperature, pressure and pH. The time step was 0.002 ps.
The Coulomb force acting on a charge qi, at the center of the cut-off sphere of radius Rrf, due to a charge qj, for solute and solvent sites, including the PB generalized reaction field contribution is
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The first and second terms in eqn 1 refer to the short- and long-range forces, respectively. The last term is constant and has been added to make the interaction zero at the reaction-field cut-off distance Rrf. A charge group pairlist was built in the first step of the simulation and updated every 5 steps. A cut-off radius of 8 Å was chosen to select nearest-neighbor charge groups and a cut-off radius of 12 Å for the long range electrostatics. The continuum RF term was calculated for the region beyond 12 Å (Rrf).
Four physical properties of the system were analyzed throughout the simulations (root mean square deviation, temperature B-factors, radius of gyration and hydrogen bonding net). The root mean square deviation (r.m.s.d.) was analyzed in order to characterize the conformational changes of the protein. MD B-factors derived from the matrix of the atomic fluctuations were calculated using the equation B-factor = 82(r.m.s.d.)2/3. The analysis of the changes in the radius of gyration provided an additional measure of the global changes in the protein structure. Finally, the hydrogen bonding net was used to characterize the stability and distortions of the secondary structure.
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Results |
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Figure 2 shows a time series of r.m.s.d. values for the whole protein,
-helices and ß-sheet C
atoms for simulations 1 and 2 (in the absence and presence of counterions, respectively). R.m.s.d. results for the whole protein (Figure 2a
) show that both simulations reached structural equilibrium. Simulation 1 shows r.m.s.d. values near 3 Å from 600 to 2000 ps. The whole of simulation 2 between 400 and 2000 ps showed the best agreement with respect to X-ray experimental structure, with r.m.s.d. values near 2 Å. Figure 2b and c
show the r.m.s.d. values for the
-helix 1 and
-helix 2. For both simulations, the values are lower than 1 Å. Finally, Figure 2d
shows the r.m.s.d. values for the ß-sheet. As in the case of the whole protein, the whole of simulation 2 shows the lowest r.m.s.d. series from 400 to 2000 ps. R.m.s.d. values for simulation 1 were near 1.3 Å and near 1 Å for simulation 2.
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Table III shows the backbone hydrogen bonds found in the X-ray structure and the frequency of their occurrence in the simulations (>40%). In general, most of the hydrogen bonds present initially in the X-ray structure were maintained throughout the simulations. Hence, hydrogen bonds in ß-sheet 1, ß-sheet 3 and ß-sheet 4 structures were maintained in both simulations and the same happened with hydrogen bonds in
-helix 1 and
-helix 2. In contrast, ß-strand 2 lost most of its original hydrogen bonds in both simulations, as was the case for the 310-helix.
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Discussion |
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From the results obtained when the RF term was not included in the calculation of electrostatic forces, it was concluded that the whole structure of ADBp was not well maintained for all simulations (Martí-Renom et al., 1998). This was probably due to the fact that ADBp is a highly charged protein with a clear excess of negative charges, so a large number of counterions and an appropriate treatment of the electrostatics was considered necessary in a later stage to compensate the system. The present work has been carried out in similar conditions to those described in the previous study but including the RF term in order to assess the importance of this correction on the final results.
In the present work, the structure of ADBp was maintained for the simulations carried out with and without counterions in the system. R.m.s.d. values for both simulations show that the protein reached an equilibrium in a short time. Moreover, r.m.s.d. values for both simulations in the equilibrium were acceptable, particularly in simulation 2 (r.m.s.d. near 2 Å). A similar pattern was also observed for the individual secondary structures. On the whole, -helices are the most stable part of the entire protein, particularly in the presence of counterions. This is probably due to the fact that
-helix 1 is the most charged secondary structure of ADBp and the presence of counterions is needed to equilibrate the electrostatic forces. This trend was also observed when this system was studied without the inclusion of the RF term into the calculation of electrostatic forces (Martí-Renom et al., 1998
). ß-Sheets were also maintained in the simulations showing r.m.s.d. values under 2 Å. As in the case for
-helices, the inclusion of counterions also improved the stability of their structure. Surprisingly, this was not observed for the 310-helix, where the largest fluctuations were observed when counterions were added.
A partial unfolding of ADBp during simulations without the RF term is observed when water molecules interact with the protein core (Martí-Renom et al., 1998), competing with the original proteinprotein hydrogen bonds. In the present study, water penetration into the protein core was not observed, a fact which is reflected in the radius of gyration, which was equilibrated along the simulations around 11 Å.
Figure 5 shows the averaged structures calculated for simulation 1 (in the time range from 600 to 2000 ps) and for simulation 2 (from 400 to 2000 ps). The averaged structures are similar to the initial X-ray structure shown in Figure 1a
and they do not show serious unfolding. Only the structure obtained in simulation 1 is slightly different from the X-ray structure; the main difference is the small displacement of the
-helices from a parallel arrangement in the X-ray structure to a slightly crossed arrangement in the average structure from simulation 1. This small displacement is reflected in the loss of the hydrogen bond in the X-ray structure between 66Glu and 19Glu (
-helix 1) in simulation 1. A new hydrogen bond appeared between 26Thr (
-helix 1) and 65Asn, which was not present in the X-ray structure. On the other hand, simulation 2 shows a similar spatial arrangement of
-helices and hydrogen bond pattern to that observed in the X-ray structure. Hence, the hydrogen bond between 66Glu and 19Glu was maintained in the simulation when counterions were present. This is probably due to the fact that the charges on both Glu were screened by ions.
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Ionic interactions are the main focus of a study of highly charged biomolecules. In proteins, ionic interactions are extremely complex because they can exist on the fully exposed surface of the protein, fully buried in the interior of the protein or in a partially buried environment with varying degrees of hydrophobicity of the surrounding residues. In addition, buffer conditions (salts and pH) can have dramatic effects on the contribution of ion pairs to protein stability (Goto et al., 1990; Kohn et al., 1997
).
The stability of the ADBp conformation in simulation 1, carried out without counterions, can be related to the presence of hydrophobic residues (Leu23, Ile29, Val58, Leu62 and Leu67) that form a hydrophobic face on the -helices of the protein. Theoretical calculations (Hendsch and Tidor, 1994
; Sindelar et al., 1998
) and experimental studies (Wimley et al., 1996
) suggested that hydrophobic interactions are more stabilizing than salt bridges in protein folding. That is, salt bridges in proteins are generally destabilizing relative to replacement with hydrophobic groups of the same size and shape. Kohn and co-workers also studied the role of surface-accessible ion pairs in protein stability by determining the effect of added salt on the stability of two-stranded
-helical coiled-coils (Zhou et al., 1992
; Kohn et al., 1997
). Moreover, there are also charged residues in
-helices, which have been predicted to be involved in interhelical ion pairs and thereby to contribute to coiled-coil stability (Talbot and Hodges, 1982
).
In addition to the hydrophobic interactions, the higher stability of ADBp in simulation 2 is due to the presence of counterions. Here, it has been shown that the presence of counterions stabilizes ADBp, reaching structural equilibrium in the protein 200 ps before that in simulation 1. The higher stability of simulation 2 is also reflected in the stabilization of the internal hydrogen bonds. This stabilization is correlated with the decrease in fluctuation of the charged side chain when a counterion neutralizes the residue charge, as shown in the B-factor analyses. Table II shows that the higher r.m.s.d. values obtained in simulation 1 are those related to charged groups, the acidic groups being the most affected. The results of this study illustrate the influence of salt concentration on the stability of proteins. In addition to the ionic strength effect of general charge screening, specific counterion-binding to charged residues on the protein as well as effects of the salt on the solvent structure and properties influence protein stability (Goto et al., 1990
).
MD simulations of the ADBp system yield a globally stable system with small yet significant internal readjustments. The results confirmed the quality of the standard GROMOS96 force field and the validity of including the RF term in the calculation of electrostatics forces for highly charged biomolecules. The present study complements the work of Roxström et al. (1998) on MD simulations of the DNAprotein complex. Those results show that the GROMOS87 force field can provide reliable results in the study of such highly-charged systems with some corrections for the appropriate representation of coion (ion atmosphere) effects on the counterions, and corrections for hydrophobicity default in the water to solute parameter.
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Acknowledgments |
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Notes |
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References |
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Received July 28, 1999; revised November 10, 1999; accepted November 16, 1999.