Molecular dynamics model structures for the molten globule state of {alpha}-lactalbumin: aromatic residue clusters I and II

Minoru Saito1

Faculty of Science and Technology, Hirosaki University, 3 Bunkyo-cho, Hirosaki, Aomori 036-8561, Japan


    Abstract
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 Abstract
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 Materials and methods
 Results and discussion
 References
 
To model the molten globule structure of {alpha}-lactalbumin, molecular dynamics (MD) simulations were carried out for the protein in explicit water at high temperature. In these simulations, long-range Coulomb interactions were evaluated explicitly with an original method (particle–particle and particle–cell: PPPC) to avoid artifacts caused by the cut-off. The MD simulations were started from two initial conditions to verify that similar results would be obtained. From the last 150 ps trajectories of the two MD simulations, two partially unfolded average structures were obtained. These structures had the following common structural features which are characteristic of the molten globule state. The radii of gyration for these conformations were 7.4 and 9.6% larger than that of the native state. These values were almost the same as the experimental value (9.6%) observed recently by small-angle X-ray scattering (Kataoka,M., Kuwajima,K., Tokunaga,F. and Goto,Y., 1997, Protein Sci., 6, 422–430). Furthermore, aromatic residues of clusters I and II in these structures were far apart from each other except for Try103–Trp104. This result is in good agreement with NMR experimental results for the acid-denatured molten globule state (Alexandrescu et al., 1992Go, 1993Go); that is, NOE signals between the aromatic residues were not observed, except for that of Try103–Trp104 in the molten globule state. Other structural features of these models for the molten globule state are discussed with reference to native state structures.

Keywords: {alpha}-lactalbumin/aromatic residue cluster/gyration radius/molecular dynamics/molten globule


    Introduction
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 Abstract
 Introduction
 Materials and methods
 Results and discussion
 References
 
Molten globule states of proteins attract considerable attention as equilibrium intermediate states on their folding/unfolding transitions. Their physicochemical properties were extensively investigated to reveal the folding mechanisms for a few typical proteins e.g. {alpha}-lactalbumin, ß-lactamase and carbonic anhydrase B (Kuwajima, 1989Go; Christensen and Pain, 1991Go; Haynie and Freire, 1993Go).

For {alpha}-lactalbumin, a few partially unfolded equilibrium intermediates were stabilized under a variety of denaturing conditions (e.g. high temperature, extremes of pH and removal of Ca2+). For these equilibrium intermediates, structural features and physicochemical properties were investigated using various experimental techniques, e.g. small-angle X-ray scattering, quasielastic light scattering, intrinsic viscosity measurements, circular dichroism spectroscopy, etc. (Dolgikh et al., 1985Go; Kuwajima et al., 1985Go; Gast et al., 1986Go; Yutani et al., 1992Go; Kataoka et al., 1997Go). These experimental studies showed that those equilibrium intermediates have common structural features which are characteristic of the molten globule state and also have physicochemical properties similar to a kinetic intermediate on the folding pathway (Ikeguchi et al., 1986Go).

The experimental studies based on the above techniques provided rather a global picture of the molten globule state but not the tertiary structure at atomic resolution. The precise tertiary structure at atomic resolution has not been clarified yet for the molten globule state, because its large flexibility prevents experimental approaches based on X-ray crystallography and NMR distance geometry.

In recent years, Dobson and co-workers have successfully observed NOE signals between aromatic protons in aromatic residue clusters I and II of {alpha}-lactalbumin for both the native state and the acid-denatured molten globule state (i.e. A-state) (Alexandrescu et al., 1992Go, 1993Go). They found that NOE patters were significantly different between the native state and A-state. That is, the NOE signals of the native state disappeared, maintained or appeared associating with the transition to the A-state. Their observations provided fragmental but valuable information at atomic resolution about the tertiary structural change associating with the transition from the native state to the A-state.

In this study, I present a possible tertiary model structure at atomic resolution of the molten globule state of {alpha}-lactalbumin by simulating an early stage of the unfolding process from the native structure to a partially unfolded structure. The simulation of the unfolding process is carried out at the atomic level by molecular dynamics (MD) simulations at high temperature. High-temperature MD simulations have an advantage in accelerating unfolding processes and thus have already been applied to study early stages of unfolding processes for a few proteins (Mark and van Gunsteren, 1992Go; Daggett and Levitt, 1993Go; Tirado-Rives and Jorgensen, 1993Go; Caflisch and Karplus, 1994Go; Boczko and Brooks III, 1995Go; Alonso and Daggett, 1998Go; de Bakker et al., 1999Go).

Recently, Murphy et al. (1998) performed MD simulations for {alpha}-lactalbumin at room temperature and low pH to study the molten globule state. They found a decrease of 43% in the total number of interdomain hydrogen bonds but did not describe the radius of gyration for the molten globule state. Smith et al. (1999b) also performed low pH simulations for {alpha}-lactalbumin at room temperature and calculated the radius of gyration. They showed that the gyration radius decreased by lowering pH, contrary to the experimental result of Kataoka et al. (1997). Furthermore, they performed low pH MD simulations at room temperature by largely changing {chi}1 torsion angles of an initial structure instead of elevating temperature (Smith et al., 1999aGo). They obtained non-native structures with large root mean square deviation (r.m.s.d.) from the initial structure. However, their gyration radii were almost the same as that of the neutral pH structure within a difference of ±3% (Smith et al., 1999aGo). This result is not in agreement with the experimental result (9.7% increase; Kataoka et al., 1997). At the present time, it is not straightforward for room temperature simulations to trace the unfolding process of {alpha}-lactalbumin.

In the present study, MD simulations of {alpha}-lactalbumin were carried out over 1 ns in solution at high temperature and neutral pH. The long-range Coulomb interactions were explicitly calculated by an original efficient method (particle–particle and particle–cell: PPPC) to avoid artificial structural instabilities caused by the cut-off method. The superiority of my methodology over the conventional cut-off approximation can be demonstrated by calculating NMR order parameter, abnormal pKa shift and relative melting temperature (Saito, 1992Go, 1994Go, 1995Go; Saito and Tanimura, 1995Go; Yamasaki et al., 1995Go; Tanimura and Saito, 1996Go; Kono et al., 1999). First, an equilibrium solution structure of {alpha}-lactalbumin at room temperature is obtained from the MD simulations. I ensure that distances between the aromatic residues are kept within the typical NOE distances. Next, the temperature at two different moments (370 ps and 460 ps) of the room temperature simulations is increased, and then two early stage structures of unfolding are obtained, which are adopted as two model structures of the molten globule state of {alpha}-lactalbumin. These models are checked to see if they have common structural features which are characteristic of the molten globule state, i.e. whether the radii of gyration of these models are close to the experimental values obtained by Kataoka et al. (1997) from their small-angle X-ray scattering study and whether relative positions of the aromatic residues in the model structures are consistent with the experimental results for NOE effects reported by Dobson and co-workers (Alexandrescu et al., 1992Go, 1993Go). Last, other structural features of the two models of the molten globule state are discussed.


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{alpha}-Lactalbumin was simulated in water in this study. Initially, this system ({alpha}-lactalbumin in water) was prepared by immersing Baboon {alpha}-lactalbumin and surrounding crystal waters (PDB code, 1ALC; Acharya et al., 1989) into a 34 Å water sphere with a density of 1.0 g/cm3. In this process, water molecules colliding with the protein atoms and the crystal waters were removed from the sphere; the total number of water molecules in this system was 4742. The force fields used in this study were AMBER/OPLS for the protein atoms (Weiner et al., 1984Go; Jorgensen and Tirado-Rives, 1988Go; Seibel et al., 1989Go) and SPC for water molecules (Berendsen et al., 1981Go). In the AMBER/OPLS force field, carbon atoms with hydrogen atoms were treated as united carbon atoms. S–S bonds were treated as ordinary chemical bonds with harmonic force constants and kept during high temperature simulations. The charge states of the Glu, Asp and His residues were assigned to be consistent with those at neutral pH. The present system consisted of 15 428 atoms.

In general, a large system like this includes a large number of Coulombic interaction pairs to be calculated (about 108). For this reason, conventional MD simulations, which are based on the direct summation method, were performed for this large system by truncating Coulomb interactions at finite distances of 8–12 Å. Several years ago, I developed an original method, particle–particle and particle–cell (PPPC), to calculate efficiently Coulomb interactions (Saito, 1992Go). In this method, Coulomb forces from a large number of distant charges were efficiently calculated by grouping those charges into cubic cells and representing the charges in each cell by a net charge and point dipole. Further, the Coulomb forces from the net charges and point dipoles were less frequently updated during MD simulations. These procedures are reasonable approximations, because the Coulomb forces from distant charges are insensitive in both time development and precise position of those charges. Actually, MD simulations/free energy calculations based on the PPPC method determined successfully relative melting temperatures of RNase HI mutant proteins and the pKa shift of human lysozyme (Saito, 1995Go; Saito and Tanimura, 1995Go; Tanimura and Saito, 1996Go) Since all simulations in this study were performed on the basis of the PPPC method, the present simulation results did not suffer any artifacts caused by the truncations (Schreiber and Steinhauser, 1992Go; Saito, 1994Go).

First, to derive the equilibrium structure of {alpha}-lactalbumin in solution at 300 K, MD simulations were carried out at 300 K, initially for 10 ps with position restraints for heavy atoms of the protein and crystal waters and finally without such restraints for 240 ps (that is from 10 to 250 ps), as shown in Figure 1Go. From the last 150 ps trajectory, 150 native conformations were sampled every picosecond. Second, Ca2+ in {alpha}-lactalbumin was eliminated by gradually decreasing its atomic charge for the period from 250 to 340 ps and then setting its vdW parameters to zero at 340 ps. The Ca2+ ion has an important role to play in stabilizing {alpha}-lactalbumin in the native state. The absence of Ca2+ destabilizes the native state of {alpha}-lactalbumin. To accelerate the unfolding process of {alpha}-lactalbumin, the Ca2+ ion was eliminated. However, it is not straightforward for MD simulations at room temperature and neutral pH to trace the process of apo {alpha}-lactalbumin unfolding, because such MD simulations require impractically long computation times, even if super computers are used.



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Fig. 1. Procedure of MD simulations. Details are described in the Materials and methods section.

 
Last, to accelerate the unfolding process of the apo {alpha}-lactalbumin, the temperature of this system was increased from 300 to 500 K. The 500 K simulations were started from two different moments of the 300 K simulation, 370 and 460 ps, to obtain two different trajectories, A and B, respectively. Associated with the increase in temperature, the water sphere expanded slightly (from 34 to 36 Å) to relieve the increase in pressure. The high temperature MD simulations were carried out for 630 ps (from 370 to 1000 ps) and 690 ps (from 460 to 1150 ps). From the last 150 ps trajectory (850–1000 ps for trajectory A and 1000–1150 ps for trajectory B), 150 partially unfolded conformations were sampled every picosecond. Averaging over each set of 150 conformations, two model structures were obtained of the molten globule state.

All calculations of the present MD simulations were carried out using Fujitsu VP2600 (maximum speed of 5G flops). These MD simulations consumed CPU time of about a few weeks.


    Results and discussion
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Root-mean-square deviation and gyration radius

The overall structural changes are usually measured by r.m.s.d.'s of main-chain atoms from their initial X-ray positions in MD simulation studies and by the radius of gyration (Rg) in small-angle X-ray scattering studies. In the present study, both quantities, r.m.s.d. and Rg, were evaluated according to the MD simulation trajectories (Figure 2Go). R.m.s.d. value increased quickly at 10 ps, when the position restraints for the heavy atoms were released. Then, the r.m.s.d. value reached a plateau at about 100 ps and remained within 0.1 Å of 1.6 Å throughout the rest of the equilibrium process (100–250 ps). In contrast, Rg fluctuated around the initial X-ray Rg value during the whole equilibration process (0–250 ps). Therefore, the structural change characterized by the r.m.s.d. of 1.6 Å was not associated with a volume expansion of the protein.




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Fig. 2. (a) Root mean square deviation (r.m.s.d.) of main-chain atoms from their initial X-ray positions as a function of time. (b) Radius of gyration (Rg) as a function of time. The r.m.s.d. of main-chain atoms was evaluated from the MD simulation trajectories according to the following definition:

where n is the total number of main-chain atoms, ri denotes the position vector of a main-chain atom i, and ri0 denotes the position vector of the main-chain atom i of the initial X-ray structure. Rg is commonly used as a measure for specifying the molten globule state. The radius of gyration can be observed by the small-angle X-ray scattering method and easily evaluated from simulation trajectories by the following equation:

where mi denotes the mass of atom i and ri denotes the position vector of atom i from the center of mass.

 
The r.m.s.d. value of 1.6 Å is almost the same as those obtained in previous MD studies of human lysozyme and RNase HI in solution (1.8 and 1.6 Å, respectively) (Saito, 1994Go, 1995Go; Yamasaki et al., 1995Go). These r.m.s.d. values are due mainly to large structural changes of amino acids in the loop regions that contact with neighboring proteins in the crystal. Therefore, the deviations of the solution structures from the X-ray structures are considered to be due to the differences in the environmental conditions of the proteins in the X-ray crystal studies from those in the MD simulations (Saito, 1994Go, 1995Go).

The present r.m.s.d. and Rg results imply that {alpha}-lactalbumin, deviating quickly from the initial structure revealed by X-ray diffraction due to release of the position restraints, reached a new equilibrium solution structure that was characterized by an r.m.s.d. of 1.6±0.1 Å and almost the same size as the initial structure. An equilibrium solution structure at 300 K was obtained by averaging over the 150 conformations that were sampled every picosecond from 100 to 250 ps.

During the next Ca2+-elimination process (250–370 ps), the r.m.s.d. of main-chain atoms increased slightly but remained small (about 1.8 Å; Figure 2aGo). The Rg value also remained near the equilibrium value (Figure 2bGo). Therefore, the overall structure of {alpha}-lactalbumin remained close to the X-ray structure during the Ca2+-elimination process, although the side chains of three amino acids (82, 87 and 88) binding to the Ca2+ ion detached during this process. This result suggests that simulation times of a few hundred ps are too short to observe the structural transition of apo {alpha}-lactalbumin to the molten globule state at room temperature and neutral pH.

To accelerate the structural transition to a partially unfolded state, the temperature was increased from 300 to 500 K at 370 and 460 ps (see Figure 2Go trajectory A and B, respectively). Immediately after the temperature was increased, both r.m.s.d. and Rg began to increase for both trajectories A and B, as shown in Figure 2Go. The rate of r.m.s.d. increase slowed at about 850 ps for trajectory A (thick line) and at about 1000 ps for trajectory B (thin line). Associated with the saturation of r.m.s.d., the Rg value reached a plateau at 850 ps in trajectory A and at 1000 ps in trajectory B. These r.m.s.d. and Rg results mean that {alpha}-lactalbumin had partially unfolded and marginally stable structures for the periods, 850–1000 ps in trajectory A and 1000–1150 ps in trajectory B. The Rg values averaged over these marginally stable periods were 9.6 and 7.4% greater than that of the native state for the trajectories A and B, respectively.

Recently, Kataoka et al. (1997) precisely observed the radius of gyration of the native and molten globule states of {alpha}-lactalbumin; they found the radius of gyration of the molten globule state to be 9.6% larger than that for the native state. This increment of the gyration radius is close to the values I calculated, 9.6% for trajectory A and 7.4% for trajectory B. These calculated values are also consistent with the expansion of the hydrodynamic radius (about 12.4%; Gast et al., 1986). On the other hand, Smith et al. (1999b) performed MD simulations for {alpha}-lactalbumin at low pH and room temperature. They showed that the radius of gyration decreased by lowering pH. They also performed the similar simulations by largely changing {chi}1 torsion angles of the initial structure. They showed that the gyration radii of the non-native structures depended on initial values of the {chi}1 angles and had close values to that of the native state within a difference of ±3% (Smith et al., 1999aGo). These results are contrary to the experimental results of Kataoka et al. (1997).

The marginally stable structures obtained above are not absolutely stable because of the extremely high temperature. The above agreement between MD simulation and experimental studies suggests that the early stage of the unfolding path calculated pass through a near-molten globule state. Therefore, we adopt the two partially unfolded structures, that averaged over 850–1000 ps in trajectory A and that over 1000–1150 ps in trajectory B, as two realistic models of the molten globule state.

Distance distribution function P(r)

Distance distribution function P(r) was calculated for the two native state structures (X-ray and MD) and the two molten globule model structures A and B, as shown in Figure 3Go. The native state structure equilibrated by MD (thin dotted curve) gave almost the same P(r) as the X-ray structure (thick dotted curve). The two molten globule model structures A (thick curve) and B (thin curve) gave almost the same P(r). The molten globule P(r) was a unimodal shape, as that of the native structure, but its peak distance rmax and maximum chord dmax were shifted to the right compared with the native P(r). These features of P(r) were in agreement with the experimental P(r) of the molten globule state (Kataoka et al., 1997Go). Strictly, values of rmax and dmax for both states were equally smaller than their experimental values. These discrepancies may be attributed to solvent water molecules strongly hydrogen- bonding to the protein surface. Such water molecules were not taken into account in the present estimation of P(r).



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Fig. 3. Comparison of distance distribution function P(r) for the native and molten globule states of {alpha}-lactalbumin. Dotted curves denote the X-ray structure (thick) and MD structure equilibrated at 300 K (thin). Thick and thin curves denote the molten globule model structures A and B, respectively.

 
Aromatic residue clusters I and II

The native {alpha}-lactalbumin in crystal form has aromatic residue clusters I (Phe31, His32, Tyr36 and Trp118) and II (Phe53, Trp60, Tyr103 and Trp104) (Acharya et al., 1989Go). These clusters were conserved in the solution structure; NMR NOE signals were observed between residues 31–32, 31–36, 31–118 and 32–118 for cluster I and 53–104, 60–103 and 103–104 for cluster II (Alexandrescu et al., 1992Go). Most of these signals were found to disappear in the acid-denatured molten globule state (Alexandrescu et al., 1993Go), suggesting that the aromatic residue clusters would be broken in the molten globule state.

In order to compare the experimental NOE results of Alexandrescu et al. (1992, 1993) with those of the present simulation, I evaluated the minimum interatomic distances between the aromatic residues for the trajectory for the native state (100–250 ps) and for the trajectories for the models of the molten globule state (850–1000 ps for trajectory A and 1000–1150 ps for trajectory B). Average and standard-deviation values of the interatomic distances are listed in Table IGo.


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Table I. The minimum interatomic distancesa (A) between the aromatic residues in the cluster I (Phe31, His32, Tyr36 and Trp118) and II (Phe53, Trp60, Tyr103 and Trp104)
 
For the native state, all of the interatomic distances averaged were almost the same (to within 1.0 Å) as those in the X-ray derived crystal structure. Thermal fluctuations of the interatomic distances were quite small (0.3–0.7 Å). Therefore, clusters I and II of {alpha}-lactalbumin were conserved during the native state simulations at 300 K. In general, minimum proton–proton distances between the aromatic residues are shorter than minimum carbon–carbon distances between the same residues. The minimum interatomic distances in the native state (see Table IGo) were short enough for NOE signals to be observed, in agreement with the experimental observation of NOE signals between the residues of the native protein in solution (Alexandrescu et al., 1992Go).

In contrast, in the models of the molten globule state A and B, all the interatomic distances, except for Try103–Trp104 and Phe53–Trp104 of model B, were significantly larger than those of the native state and beyond the typical range of NOE (see Table IGo), in good agreement with the corresponding experimental results for the molten globule state (Alexandrescu et al., 1993Go); that is, NOE signals were not observed between the aromatic residues except for Try103–Trp104 in the molten globule state.

Residue Tyr103 and its neighbor Trp104 remained close together in both the native state (3.8±0.2 Å) and the calculated molten globule state (3.9±0.4 Å for model A and 4.8±1.3 Å for mode B). This result is in good agreement with the experimental result, i.e. the interatomic NOE between them was observed in both states. In contrast, the residue Phe31 and its neighbor His32 were close to each other in the native state (3.8±0.3 Å) but far apart in the calculated molten globule state (9.7±0.8 Å for model A and 8.5±1.1 Å for model B). In fact, the interatomic NOE between these residues disappeared in the molten globule state, although they are neighbors in the amino-acid sequence.

His107 was far from cluster II in the native state (8.8±0.6 Å). In the molten globule state, the distance between Tyr103 and His107 (7.1±1.1 Å for model A and 9.9±1.1 Å for mode B) was beyond the typical NOE distance, although an NOE signal was observed between those residues. This discrepancy may be due to the difference in the charge state of His107, which is positive in the NMR experiments but neutral in the present simulations. In fact, Alexandrescu et al. (1993) and Smith et al. (1994) demonstrated that the NOE between Tyr103 and His107 was observed only for the positively charged His107 but not for the neutral His107.

The two models of the molten globule state, A and B, gave almost identical results for Rg and aromatic clusters, although those models were obtained from independent MD simulations. The agreement between these calculation results and the experimental results supports strongly the validity of the models. These models differed in several details. First, the Rg increment of model B (7.4%) was smaller than that of model A (9.6%), which was the same as the experimental value (9.6%). Second, the residues Phe53 and Trp104 were clearly apart from each other in model A (7.5±1.2 Å) but rather near in model B (4.5±1.0 Å), which is inconsistent with the disappearance of NOE. Third, the residues Tyr103 and Trp104 were close to each other in model A (3.9±0.4 Å) but slightly farther apart in model B (4.8±1.3 Å), although the distance between the aromatic carbons, 4.8 Å, was still within the range of NOE. Therefore, model A was more reliable in detail as a microscopic model of the molten globule state than was model B.

Other structural features

Significant differences were found between the tertiary structures of the molten globule models and that of the native structure (Figures 4 and 5GoGo). The molten globule model structures (thick lines) were slightly expanded in comparison with the native structure (thin lines), as expected from the increase of the gyration radii. Two helices, 8–15 and 85–92, which form the hinge of the cleft were partly separated in the models of the molten globule state. Thus, the hinge was found to come out of joint in the molten globule structure. The positions of the residues at the opposite side of the hinge, residues 31–36 and 103–107 which form the bottom of the cleft, deviated largely from their positions in the native structures and extend to the solvent region, as shown in Figures 4 and 5GoGo. These results are consistent with the disappearance of the NOE signals for the clusters I and II, because those residues form parts of these clusters. As a results, the bottom of the cleft in the molten globule state is widely exposed to solvent molecules and the cleft geometry is altered, permitting solvent molecules to penetrate into the hinge.



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Fig. 4. Tertiary main-chain structures of the native state and two models of the molten globule state of {alpha}-lactalbumin. The thin lines denote the native structure averaged over 150 conformations from 100 to 250 ps. Numbers denote the residue numbers. The thick lines denote (a) model structure A obtained from trajectory A and (b) model structure B obtained from trajectory B. The model structures were superimposed on the native structure by the least-squares fitting method. These figures give a stereo view perspective through the hinge and the bottom of the cleft.

 


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Fig. 5. Connolly surfaces of two models of the molten globule state A (a) and B (b) and the native state (c). These figures give the same view as Figure 4Go. Yellow denotes hydrophobic residues.

 
{alpha}-Lactalbumin has a small antiparallel ß-sheet consisting of two ß-strands which are bound together by eight hydrogen bonds. These hydrogen bonds were maintained during the native state simulations; their bond distances were kept smaller than 3.5 Å. In contrast, about one half of the hydrogen bonds were broken in both models A and B; their bond distances were larger than 3.5 Å. Thus, the ß-sheet does not keep its X-ray structure in the molten globule state, as suggested by NMR experiments (Chyan et al., 1993Go; Alexandrescu et al., 1993Go).

Uchiyama et al. (1995) investigated the thermal stability of Thr29->Ile and Thr33->Ile mutants to clarify an environmental condition around them in the molten globule state. In the native structure, Thr29 and Thr33 are located between the two aromatic residue clusters I and II. Thr29 is buried in the protein but Thr33 is exposed to the solvent. They found that the Thr29 mutation stabilized significantly the native state but only slightly stabilized the molten globule state like the Thr33->Ile mutation. They supposed that Thr29 in the molten globule is exposed to the solvent like Thr33 in the native structure. I confirmed the position of Thr29 in models A and B to check the validity of their guess and my models and then found that Thr29 in model A is significantly exposed to the solvent but that in model B is not clearly exposed to the solvent (Figure 6Go). This agreement between model A and the experimental suggestion is reasonable, because model A was in much agreement with both the experimental value of {Delta}Rg/Rg and results of NOE than was model B.



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Fig. 6. Connolly surfaces of two models of the molten globule state A (a) and B (b) and the native state (c). Components of Thr29 and Thr33 are shown by red and blue.

 
Since the protein is completely unfolded at high temperature (>=380 K), the equilibrium state at 500 K is an unfolded state but not a molten globule state. However, we expect that the protein spends a short time in a molten globule state even at 500 K. As demonstrated in this study, the radius of gyration as a function of time reached a plateau (Figure 2bGo). However, the time spent in the molten globule state (a few hundred picoseconds) is too short to sample various conformations from the ensemble of the molten globule state. At least, we usually perform a few high temperature simulations from different initial conditions. In the present study, the 500 K trajectories A and B were started from the structures at 370 ps and 460 ps of the equilibrium 300 K trajectory. The difference in time (90 ps) between the initial structures was necessary to obtain statistically independent trajectories. The gyration radii, Rg of these trajectories showed a plateau as a function of time and had values close to the experimental value. Molten globule model structures A and B were sampled from the plateau regions. Model A was in good agreement with the experimental results of small-angle X-ray, NMR and mutant stability. This means that the model A is a sample that has common structural features of the molten globule state. In order to clarify a structural variety of the molten globule state, several additional simulations should be performed from different initial conditions.


    Notes
 
1 To whom correspondence should be addressed; email: msaito{at}si.hirosaki-u.ac.jp Back


    References
 Top
 Abstract
 Introduction
 Materials and methods
 Results and discussion
 References
 
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Received July 22, 1999; revised September 6, 1999; accepted September 21, 1999.