Laboratoire de Dynamique Moléculaire, Institut de Biologie StructuraleJean-Pierre Ebel, 41 Avenue des Martyrs, F-38027 Grenoble Cedex 01, France
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Abstract |
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Keywords: allosteric transition/aspartate transcarbamylase/mutant proteins/targeted molecular dynamics simulations/tertiary and quaternary structural changes
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Introduction |
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Several crystal structures of ATCase from Escherichia coli have been determined by Lipscomb and co-workers (Ke et al., 1988; Stevens et al., 1990
). Unligated structures exist for the two allosteric states and also for complexed structures with different effectors and/or substrate analogues (for a review, see Lipscomb, 1992
, 1994
). The holoenzyme is a dodecamer with C3 symmetry. There is a slight deviation from D3 symmetry which is due to the existence of low- and high-affinity CTP-binding sites (Kim et al., 1987
; Lipscomb, 1992
). The protein is organized into two catalytic trimers and three regulatory dimers. The trimers are composed of catalytic chains (C1C6) of 310 residues each and the dimers of regulatory chains (R1R6) of 153 residues each. The catalytic chains have two ligand-binding domains, the N-terminal carbamylphosphate domain (CP domain) and the C-terminal aspartate domain (ASP domain), which are linked by helices H5 and H12. The regulatory chains are also composed of two domains, namely the allosteric domain (ALLO domain), which binds the effectors, and the zinc domain (ZN domain), which contains a structural zinc atom. The structure of ATCase is shown in Figure 1
.
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The work described in this paper is part of an ongoing project to investigate the mechanism of the allosteric transition in ATCase using theoretical simulation techniques. In particular, we want to learn more about the type of quaternary and tertiary motions and the order in which they occur. In three recent publications we calculated the normal modes of each state to obtain an idea of the movements that could be important in the initial stages of the transition (Thomas et al., 1996a,b
, 1999
). In this work we attempted a more direct approach by generating pathways for the complete transition using a molecular dynamics simulation technique. It is not possible to study the transition with free molecular dynamics (MD) because the time-scale for the transition is of the order of 1 µs whereas the maximum times currently accessible by MD simulations are of the order of 1 ns (for a protein system in water). To circumvent this problem, we employ a targeted molecular dynamics (TMD) approach, in which a single constraint is used to direct the structure from one state (T or R) to the other (Schlitter et al., 1993
). This technique and others like it have been shown to provide useful insights into the mechanisms of conformational transitions in proteins (Elber and Karplus, 1987
; Lazaridis et al., 1990
; Ech-Cherif El-Kettani and Durup, 1992
; Guilbert et al., 1995
; Ma and Karplus, 1997
; Wroblowski et al., 1997
). Although some criticisms have been levelled at the TMD method, we feel that it can be a valid tool if properly employed (M.J.Field, unpublished data) and that the results we have obtained using it permit some interesting connections to be made with what is known about the ATCase transition pathways.
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Methods |
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In order to enable a valid comparison to be made with the results of our previous calculations, the starting structures and models were the same as those used in the work of Thomas et al. (1996a,b, 1999). As full details are given in the original papers, only a brief description will be given here.
The initial crystal structures were taken from the Brookhaven Protein Data Bank (Bernstein et al., 1977). The coordinates of the T state protein were those of the most recently refined structure of Kosman et al. (1993) obtained at a resolution of 2.5 Å. The coordinates of the R state protein correspond to the structure resolved at 2.8 Å by Gouaux et al. (1990). In both structures there are CTP molecules that bind to each allosteric site. There are no water molecules in the R structure, so the 81 water molecules present in the T state were omitted. There is also no substrate in the T state, so the N-(phosphonoacetyl)-L-aspartate (PALA) molecules present in the R state were removed. The removal of the PALA molecules is necessary because the TMD algorithm (like all other reaction path-finding algorithms) requires the same numbers of atoms for both the initial and reference structures. All polar hydrogen atoms were included explicitly in the calculations whereas the others were treated with a united atom model. In the R state crystal structure, the first seven residues of each regulatory chain are missing because they are disordered. These were left out of our calculations, giving 146 residues per regulatory chain only. Our final model protein had 2736 amino acids and 26 370 atoms.
All calculations were performed with version 23 of the CHARMM molecular modelling software and with the CHARMM 19 polar hydrogen force field (Brooks et al., 1983). The CTP parameters were obtained as a combination of ATP and cytosine parameters from version 21 of the QUANTA force field (Molecular Simulations, San Diego, CA). The programs VMD (Humphrey et al., 1996
) and Raster3D (Merritt and Murphy, 1994
) were used for graphical display.
An explicitly solvated ATCase molecule requires ~105 water molecules. These, together with the ~3 x 104 atoms of the protein, comprise a system which is too large for our current computational resources and so we employed an implicit model for the solvent, which, of course, is a strong approximation. The choice and justification of the model were fully discussed previously (Thomas et al., 1996a) but, to summarize what was said there, we approximated the effect of the solvent with a linear distance-dependent dielectric constant (Loncharich and Brooks, 1989
), a shifted electrostatic potential and a switched van der Waals potential (Steinbach and Brooks, 1994
). The cut-off for non-bonding interactions was taken to be 9 Å. The screening effect of the solvent was modelled by weighting the atomic charges of the ends of the charged amino acid side chains (Lys, Asp, Glu, Arg) by 0.3 (Mouawad and Perahia, 1996
). The charges of CTP were treated similarly. The histidine residues were taken as neutral and their enantiomeric states were the same as those assigned by Kosman et al. (1993). The coordinates of the polar hydrogens were determined using the HBUILD algorithm (Brünger and Karplus, 1988
).
Both the R and T state structures were minimized using the same model until their r.m.s. gradient norms were <0.0001 kcal/mol. The r.m.s. coordinate differences (r.m.s.c.d.s) of the minimized structures from the corresponding crystallographic structures were 2.65 and 3.40 Å, respectively. The minimized structures, which we denote as Rmin and Tmin, were used both as reference structures in the TMD simulations and as starting points for the generation of the dynamics structures described below.
The starting dynamics structures
To generate structures suitable for the TMD calculations, molecular dynamics simulations without constraints were performed on the minimized structures described earlier. For each structure, there was a 4 ps heating phase in which the temperature was increased from 0 to 300 K followed by a 96 ps equilibration phase. During the heating phase, a harmonic constraint was placed on all the atoms of each structure to prevent too strong a deviation from the minimized structure. The starting value of the constraint force constant was 400 kcal/mol.Å2 but this was reduced every 400 fs. The full protocol is detailed in Table I. The time step for all dynamics simulations was 1 fs. No constraints were put on the symmetry of the system so the structures were free to deviate from C3 symmetry. The two structures resulting from the simulations were used as both starting and reference structures for the TMD simulations and we call them R300 and T300.
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The TMD protocol that we use is similar to that developed by Schlitter et al. (1993) and employed in several studies (Jacoby et al., 1996; Díaz et al., 1997
; Ma and Karplus, 1997
; Wroblowski et al., 1997
). In the scheme, the r.m.s.c.d. between the structure undergoing the dynamics simulation (X) and a reference structure (Ref) is constrained to have a particular value. The (mass-weighted) r.m.s.c.d., d, between structures X and Ref is defined as
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The r.m.s.c.d. constraint, by itself, is not sufficient to prevent global rotations and translations of the structure X with respect to Ref. It is therefore necessary to impose an additional set of six linear constraints which for the rotations take the form
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The strategy for performing a TMD simulation with these constraints is as follows:
There are a number of ways to enforce the constraints, but we chose to use the SHAKE method developed by Ryckaert (1985). The implementation is straightforward and experience showed that the constraints could be satisfied to a high degree of precision (typically with a deviation of 1010) in a small number of iterations. The method described above was implemented as a module (TMD) into version 23 of the CHARMM program. The simulations were performed with the Verlet algorithm (Allen and Tildesley, 1987) with a time step of 1 fs at a temperature of 300 K.
Four trajectories were generated. Each consisted of 1 ps of equilibration in which the r.m.s.c.d.s between the dynamic and reference structures were held constant and then 200 ps of dynamics in which the r.m.s.c.d.s were reduced at each step. Two of the 200 ps simulations went from R T and two from T
R. As the r.m.s.c.d. between the R and T structures is of the order of 8 Å, the target distance for the constraint was reduced by about 4 x 105 Å per dynamics step. In each case the starting structure for the simulations was the appropriate dynamics structure, either R300 or T300, but different reference structures were used for the pair of TMD simulations in each direction. In one the reference structure was the minimized structure of the appropriate form (Rmin or Tmin) and in the other it was the dynamics structure (R300 or T300). This was done to test the effect of a different target on the calculated transition. Each simulation took about 1500 h (2 months) of CPU time on an HP 735 workstation. Subsequently we have performed a simulation of 500 ps with the TMD algorithm to see how the generated path changes with trajectory length. Our analysis shows that the results of the longer calculation are fully coherent with those of the 200 ps simulations.
Analysis of structural and energetic changes during the transitions
All four trajectories were analysed independently and then the results were compared. As no constraint was put on the symmetry of the system, the analysis was performed for all the chains (six catalytic chains and six regulatory chains) within the protein.
To indicate the extent to which the transition between the two forms has occurred, we define a reaction coordinate or `transition progress' parameter, f (t), of the form
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The simulations were analysed for the first 90% of each trajectory. For structures too close to the reference structure, there is a conflict between the constraint and the thermal fluctuations of the atoms that causes the potential energy of the system to rise considerably. In any case, at a progress parameter of 90%, the r.m.s.c.d.s between the dynamic and reference structures are <1 Å and the dynamic structures of all four trajectories have the correct characteristics of the reference structures.
The most important analyses that we performed were the examination of the global rotation and translation of the trimers and the dimers of each intermediate structure with respect to the reference structures and the determination of the relative movements of the domains and their axes of rotation. The tools that we used for these analyses were algorithms for the superposition of molecular structures using either the Kabsch algorithm or an algorithm based upon quaternions (Kneller, 1991). These functions were implemented in the program CHARMM and in the Molecular Modeling Tool Kit (Hinsen, 1997
), respectively.
The exact definitions of the quantities discussed in the Results section are as follows:
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Results and discussion |
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After the minimization, the r.m.s.c.d. between the T state crystallographic and minimized structures was equal to 3.40 Å if the analysis was performed for all atoms and 3.12 Å if the analysis was carried out for the heavy atoms of the backbone only (N, C, C). The corresponding values for the R state were 2.65 and 2.42 Å, respectively. These changes have been fully discussed in previous papers (Thomas et al., 1996a
,b
). Despite their large structural differences, the R and T minimized structures have total potential energies that differ by only 13 kcal/mol (mainly in the non-bonding interactions).
The 300 K initial structures
After the 100 ps dynamics simulation (both heating and equilibration), the r.m.s.c.d. between the structures, Tmin and T300, had stabilized at 4.28 Å for all the atoms of the protein and 3.82 Å for the backbone atoms. For the R state structures the differences were slightly larger at 5.46 Å (all atoms) and 5.11 Å (backbone atoms). In both cases the deformation was distributed over the whole protein. The r.m.s.c.d. for the backbone atoms was 1.91 and 1.56 Å on average for the catalytic chains of the T and R states, respectively, and 2.69 and 2.47 Å for the regulatory chains. The larger changes in the regulatory chains can be related to the higher mobility of the dimers which is observed in the crystallographic structures.
A more detailed analysis of the energetic and structural differences between the minimized and dynamic R and T state forms is contained in Tables II and III. Table II
lists the different energetic contributions for the structures and Table III
lists geometric parameters that highlight global, quaternary and tertiary structural differences between pairs of R and T state structures. The quantities listed in Table III
are fully defined in the Methods section.
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The transition pathways
The four transitions studied were T300 R300, T300
Rmin, R300
T300 and R300
Tmin. The only differences between the simulations were the initial and the reference structures as the same simulation protocol was used.
Figure 2 shows the r.m.s.c.d.s between the intermediate structures and both the initial and the reference structures for the T300
R300 and the R300
T300 pathways. That the TMD's r.m.s.c.d. constraint works as desired is clear from the linearity of the variation of the r.m.s.c.d.s between the intermediate and the reference structures along the paths. In contrast, the variation of the r.m.s.c.d.s between the intermediate and the starting structures is initially steeper, although approximately linear, but then slows as the transition progresses (at ~40 and ~60% of the transition for the R300
T300 and the T300
R300 pathways, respectively).
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Rotation and translation of the trimers.
The relative positions of the two trimers (C1C2C3, C4,C5,C6) of ATCase change substantially during the allosteric transition. For the T R pathway the intertrimer distance between the crystallographic structures increases by 12 Å whereas there is a 10° rotation around the threefold axis (and vice versa for the transition in the other direction).
The relative rotations of the trimers with respect to the reference structures during the four transition pathways are shown in Figure 3. There are differences, but the overall qualitative behaviour is similar. There is an initial increase in the rotation angle (i.e. a moving away from the reference structure) before the angle decreases monotonically to zero. The relative rotation of the trimers is finished at about 70% of the transition in all the transitions. There is a similar behaviour in Figure 4
which shows the relative rotation angle of the trimers during the transition with respect to the initial simulation structures. Also apparent from this figure is a brief period (~5%) at the beginning of the simulations during which there is no rotation.
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Figure 6 plots the relative intertrimer translations for each of the transition pathways. The main translation occurs along the threefold axis of symmetry. There is no significant translation along the other axes (data not shown). The overall qualitative behaviour of the changes is the same with the translations diminishing monotonically to zero. The detailed behaviours of the pathways in the two directions, however, are slightly different with the R
T translations decreasing more rapidly than those of the T
R pathways.
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As already remarked, the rotational and translational movements of the trimers appear to be complete after about 70% of the transition. It is pertinent to ask what happens in the remaining 30% of the transition. One way to investigate this is to calculate the r.m.s.c.d.s for the trimers between the intermediate structures of each pathway and the pathway's starting and reference structures. As the behaviour of these results for all the simulations is similar, only the results for the T300 R300 pathway are shown. The r.m.s.c.d.s for the trimers with respect to the reference structure, R300 (Figure 7a
), are roughly constant for the first 60% of the transition but decrease rapidly thereafter. The behaviour with respect to the initial structure, T300, is different (Figure 7b
). There is a rapid increase in the first steps of the simulation (this is a typical property of r.m.s.c.d.s for simulation structures) and, subsequently, a gradual increase. These results indicate that whereas there are movements within the trimer throughout the transition, it is the large amplitude quaternary motions that are primarily responsible for bringing the dynamics structures towards the reference structure and it is only at the end of the transition that the more localized tertiary rearrangements occur.
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In contrast to the case of the rotation angles of the catalytic trimers where there were large differences in quantitative behaviour, the behaviour of the dimer rotations is more uniform (Figure 8). The rotations all decrease in a relatively steady way, with a few oscillations, until the rotation in the reference state is reached at f (t)
75%. Four of the 12 curves show a slight increase in the rotation angle in the first ~10% of the transition, but these are proportionately much smaller than those observed for the trimers.
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Tertiary changes.
In addition to quaternary motions, changes in the tertiary structure are also important during the transition. The most notable of these are the variations in the relative positions of the domains within the catalytic and regulatory chains. Thus, for example, the CP and the ASP domains of the catalytic chains come together during the T R transition. There is also an opening of up to 15° between the ZN and ALLO domains of the regulatory chains (Lipscomb, 1994
), although in our simulations we can obtain larger values depending upon the pairs of structures that are being compared (see Table III
).
Other important tertiary structure changes are the rearrangements that occur at the interfaces of the subunits. These movements are not analysed in this paper but will be discussed in a future paper along with the results obtained with additional simulations of the transition pathways. There we will also compare our results with the normal mode data generated by Thomas et al. (1996a,b, 1999).
Catalytic domain closure. The domain closure associated with the binding of substrate and substrate analogues has been observed in the R state by Krause et al. (1985, 1987). We omitted the substrate in our simulations so we will not be able to see any substrate-induced changes. However, we should see some of the motions that are possible in these domains during the transition.
The variations in the angles between the domains of the catalytic and regulatory chains as a function of the transition progress parameter for the R300 Tmin pathway are shown in Figure 9
. The data for the other transitions are similar and are not shown. The concerted aspect of the transition, already noted above, is confirmed by these graphs, which indicate that the changes for the catalytic and regulatory chains occur in a synchronous fashion.
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We hypothesize that this difference in behaviour is consistent with the separation of the action of the allosteric effectors and of aspartate, which forms the basis of the `primarysecondary effects' (Thiry and Hervé, 1978; Hervé, 1989
) and the `effector modulated transition' (Xi et al., 1991
) mechanisms of regulation. The effectors cannot induce the transition but change the quaternary structure to make the transition easier (ATP increases the intertrimer distance by 0.4 Å) or more difficult (CTP decreases the intertrimer distance by 0.5 Å) whereas aspartate is necessary for the transition to the high activityhigh affinity state of the enzyme (Stevens et al., 1990
). Thus, in our model, the fact that the regulatory domain and the quaternary motions occur before the catalytic domain motions means that the former can modulate the latter. These results are also in agreement with those of Tanner et al. (1993), who performed a molecular dynamics simulation and a rigid-body analysis of the R state structure and observed that there is a decoupling of the allosteric domains from the rest of the enzyme and, hence, a separation of the catalytic and regulatory effects.
These observations could also give a structural explanation of the results obtained for ATCases with a Tyr77 Phe mutation in the hydrophobic pockets of the regulatory chains. This mutation converts ATP into an inhibitor of ATCase instead of an activator and reduces the activity of the enzyme (Van Vliet et al., 1991
). It is possible that this mutant inhibits, although does not entirely stop, the opening of the regulatory domains. This prevent the full transition from occurring and means that the mutant enzyme displays predominantly weak activityweak affinity T state characteristics (see position Y77F in Figure 11
).
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Conclusion |
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Figure 11 provides a summary of the order of the motions that take place in the transitions that we calculated but, as noted above, we cannot draw any conclusions about how fast each of these events occurs. The other main points that we would like to emphasize from our study are:
Clearly, there is a lot more work to do even to be able to scratch the surface of this complex problem. Currently we are completing the analysis of other transition pathways that we have calculated with a variety of alternative reaction path finding algorithms using the same molecular mechanical representation of the protein. These results will be presented in due course. In the near future we would like to improve the model that we use for the ATCase molecule and investigate more fully the effects that the binding of effector and substrate molecules have on the transition pathways that we obtain.
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Acknowledgments |
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Notes |
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References |
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Received July 23, 1998; revised December 11, 1998; accepted December 16, 1998.