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. 2001 Apr;10(4):798–808. doi: 10.1110/ps.40401

Extending the capabilities of targeted molecular dynamics: Simulation of a large conformational transition in plasminogen activator inhibitor 1

Peter Krüger 1, Stefan Verheyden 1, Paul J Declerck 2, Yves Engelborghs 1
PMCID: PMC2373958  PMID: 11274471

Abstract

Plasminogen activator inhibitor type 1 (PAI-1) is an inhibitor of plasminogen activators such as tissue-type plasminogen activator or urokinase-type plasminogen activator. For this molecule, different conformations are known. The inhibiting form that interacts with the proteinases is called the active form. The noninhibitory, noncleavable form is called the latent form. X-ray and modeling studies have revealed a large change in position of the reactive center loop (RCL), responsible for the interaction with the proteinases, that is inserted into a β-sheet (s4A) in the latent form. The mechanism underlying this spontaneous conformational change (half-life = 2 h at 37°C) is not known in detail. This investigation attempts to predict a transition path from the active to the latent structure at the atomic level, by using simulation techniques. Together with targeted molecular dynamics (TMD), a plausible assumption on a rigid body movement of the RCL was applied to define an initial guess for an intermediate. Different pathways were simulated, from the active to the intermediate, from the intermediate to the latent structure and vice versa under different conditions. Equilibrium simulations at different steps of the path also were performed. The results show that a continuous pathway from the active to the latent structure can be modeled. This study also shows that this approach may be applied in general to model large conformational changes in any kind of protein for which the initial and final three-dimensional structure is known.

Keywords: Targeted molecular dynamics, molecular dynamics simulation, conformational change, plasminogen activator inhibitor 1, serpin, pathway calculation

Plasminogen activator inhibitor 1 (PAI-1) is the most important physiological inhibitor of tissue-type and urokinase-type plasminogen activator. It is a 50-kD protein with 379 amino acids belonging to the serpin superfamily. The protein plays an important role in the equilibrium between blood clot formation and blood clot lysis (Juhan-Vague et al. 1995; Nilsson et al. 1985; Wiman 1999). PAI-1 is synthesized as an active molecule that spontaneously converts into a latent form that cannot inhibit the protease. A spontaneous conversion to this form is unique for PAI-1. Even though for two other serpins a latent form has been described (Carrell et al. 1994; Lomas et al. 1995; Chang and Lomas 1998), these could only be generated under denaturing conditions. The capability to change the conformation from active to latent has been preserved during evolution (Berkenpas et al. 1995). This emphasizes the importance of the conformational change for the function of the molecule.

X-ray structures of PAI-1 in the latent, the cleaved (mutant alanine to proline at position 335 (A335P), and, recently, the active conformation are known (Aertgeerts et al. 1995 [PDB id: 9PAI]; Mottonen et al. 1992 [PDB id: 1C5G]; Nar et al. 2000 [PDB id: 1DB2]; Sharp et al. 1999 [PDB id: 1B3K]). As for the other serpins, only part of the structure of the enzyme–inhibitor complex is known (Fa et al. 2000; Huntington et al. 2000). A model of the active structure is shown in Figure 1 ▶ (Aertgeerts et al. 1994). The molecule consists of three β-sheets (named sheet A, sheet B, sheet C) and nine α-helices (named hA to hI). The basic structural differences between the active and latent molecule can be deduced from Figure 2 ▶ and are mainly (1) the insertion of the N-terminal portion (P14-P4) of the reactive center loop (RCL, P14-P13′; notation used as in Schechter and Berger 1967) into β-sheet A, resulting in the formation of an additional strand (s4A, strand 4 of β-sheet A), and (2) concomitant movement of the C-terminal portion (P3-P13′) of the RCL resulting in the disruption of s1C (strand 1 of β-sheet C; see Fig. 1 ▶; Mottonen et al. 1992). The C-terminal portion of the RCL has to move through a gate formed between two loops, designated `loop 1' (residues 185–200) and `loop 2' (residues 242–246), respectively (Aertgeerts et al. 1995).

Fig. 1.

Fig. 1.

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The molecule PAI-1 in the modeled active conformation (with reactive center loop [RCL]) and the two loops 1 and 2 (drawing made with Molscript; Kraulis 1991). hF and hE are abbreviations for helices F and E.

Fig. 2.

Fig. 2.

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Representation of different steps of the conformational transition. The simulations CM and CJ were concatenated. (For a detailed description of the simulations see Table 1.) (A) CM start, (B) CM 80 ps, (C) CM 160 ps, (D) CM 320 ps, (E) CM 400 ps, (F) CM 480 ps, (G) CJ start, (H) CJ 320 ps, (I) CJ 480 ps close to the latent structure. (D–F) A situation close to the intermediate. (black arrows) RCL; (gray arrows) loop 1 (drawing made with Molscript; Kraulis 1991).

Not only the change to the latent structure but also the binding to the protease itself seems to be associated with a conformational change in the molecule. Former studies have suggested that the inhibitory activity of a serpin is associated with the insertion of the RCL into β-sheet A (s4A formation), that is, at least a partial insertion is a prerequisite for initial binding (Wilczynska et al. 1997; Huntington et al. 2000). Model studies proposed a sequence of events for the insertion starting at the N-terminal end of the RCL continuing with the residues P16, P14, etc. The X-ray structure of stable mutants of PAI-1 in the active state shows two different molecules in the crystal (Sharp et al. 1999; Nar et al. 2000). One molecule for which the position of the RCL could not be determined indicates the high flexibility of that loop. In the other molecule, part of the RCL forms a seventh β-strand of β-sheet A of the adjacent molecule.

The mutant A335P (at position P12) gives additional insight into the requirements for inhibition, because it behaves as a noninhibitory substrate for serine proteases. The X-ray structure of the cleaved (at P1-P1′) form reveals an insertion of the N-terminal part of the RCL in the s4A position. It was concluded that the insertion of the RCL to form the s4A is not an exclusive prerequisite for inhibitory activity.

The conversion from the active to the latent structure plays a key role in the modulation of the function of the protein. Whereas in plasma PAI-1 occurs mainly in the active conformation, platelet PAI-1 (even though representing 90% of total PAI-1 in blood) predominantly occurs in the latent conformation. Latent PAI-1 can be reactivated in vitro through a process of denaturation and renaturation (Hekman and Loskutoff 1985). It has also been suggested that latent PAI-1 might be reactivated in vivo (Vaughan et al. 1990). Therefore, the understanding of the details of the transition is of utmost importance. Several scenarios have been developed to describe this conformational change. They are based on the limiting X-ray structures (active, latent, or cleaved) of PAI-1 or other proteins of the serpin family, like α1-antitrypsin, antithrombin III, etc. and on various mutation experiments (Aertgeerts et al. 1995; Gils et al. 1997). These scenarios discuss the way of insertion into the β-sheet as well as the hindering or modulating influence of loops or residues on the pathway of insertion. In a recent article, the conformational change from the S → R structure of the related protein, α1-antitrypsin, was discussed (Whisstock et al. 2000) by comparing limiting X-ray structures and predicting a sequence of events based on translation or rotation of segments. Nevertheless, the trajectory of the atoms during the conformational transition could not be described, neither on an experimental basis nor with modeling or simulation methods. The aim of this study is to complement the scenarios mentioned above and to describe the mechanism of the transition in detail, by computer simulations.

The conformational change outlined here is very large and complex and therefore unlikely to happen in an ordinary molecular dynamics (MD) simulation. Targeted molecular dynamics (TMD) is a method based on MD simulation and in principle is able to simulate more elaborate conformational changes in proteins. It has been applied previously to investigate conformational transitions of insulin, ras–-p21, chymotrypsin, aspartate transcarbamylase, and other molecules (Engels et al. 1992; Schlitter et al. 1994; Jacoby et al. 1995; Wroblowski et al. 1997, Díaz et al. 1997; Ma and Karplus 1997; Roche and Field 1999). The TMD method establishes a distance constraint between two structures, such that the sum over the distances of all atoms between the initial and the target structure has to be reduced in every step of the simulation.

Previous investigations have shown that pathways can be modeled using TMD, if the two limiting structures are not exceedingly different. The conformational transition in PAI-1, however, is too large for an unmodified TMD procedure. Orienting simulations of PAI-1 based on the active structure as initial and the latent structure as target have not been successful (B. Wroblowski, pers. comm.). The reason for this failure can be seen if the loops 1 and 2 are taken into account: these hinder the movement of the RCL to its final position. Although TMD has already some intrinsic flexibility, it is not able to surround an obstacle of that size, for which a large deviation from the direct pathway is required.

To overcome the obstacle character of loop 1 and 2, we decided to make an assumption on an intermediate structure on the pathway. It originated from the idea to describe the motion of the RCL as a rigid body motion. The simulation pathway therefore was split into two parts: a TMD simulation from the active structure to the intermediate, and one from the intermediate to the latent structure. The intermediate was only used as a first guess, and TMD enables a refinement of the intermediate structures on the pathway. The applicability of this method to PAI-1 is tested and discussed with reference to experimental results obtained from mutant studies.

Because of the size of the conformational change, the first aim of this investigation was to show whether a continuous trajectory from the active to the latent structure can be modeled. The next step was to look for parameters that can influence the calculated pathway. Once one or several pathways are predicted, they can be used to give interpretation to experiments.

Results

Energies

For all simulations discussed, a stabilization of the total and potential energy can be seen after an initial phase of ∼50 pico seconds (ps) (not depicted). All simulations show a stable total and stable potential energy. Only the dihedral angle energies of the series D increase by ∼5% at the end of the simulation. Apart from this fact, no pronounced profile on the noisy energy spectrum of the TMD simulations (fluctuations Δ 150 kJ/mole, <0.05% of the absolute potential energy) could be seen. The noise of the unconstrained MD simulation is not significantly lower. This indicates that the features in the energy trajectories cannot be related easily to structural events.

Relative comparison of the pathways

An overview on the conformational change from the active to the latent form is given in Figure 2 ▶, which concatenates two trajectories. Figure 3 ▶ shows a comparison of the conformational space of the different simulations. The graph gives a two-dimensional representation of the multidimensional conformational space. The procedure used for the calculation is described by Diamond (1974) and Levitt (1983). It is based on a matrix of the averaged rms positional differences of all C-α atoms. The structures of all trajectories were superimposed to a reference structure (first structure of the first simulation). The projection of the distances between all structures into two-dimensional Cartesian coordinates can represent the relative differences between structures of all trajectories. Nevertheless, one has to be aware that certain structural difference can still be hidden given the simplified representation.

Fig. 3.

Fig. 3.

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Two-dimensional projection (best plane projections) of the conformational space of all simulations. The x- and y-axes are relative differences. (I) Intermediate; (A) active; (L) latent structure.

Figure 3 ▶ shows the pathways from the initial to the final structure via the intermediate. Comparing simulations CB and CC shows the influence of the temperature, with differences especially in the first part of the transition. The other simulations from active to intermediate (CE, CM) are different in the target they use. CE uses the relaxed intermediate (last structure of CB) and CM an even more relaxed intermediate, namely, the last structure of the equilibrium simulation of the intermediate (last structure CH). The pathways are not dramatically different; only in the last part of the trajectory the divergence emerges. This means that the nature of the intermediate does not influence the pathways very strongly in the beginning. The backward direction (simulation CG) shows larger deviations close to the intermediate. The simulation with full charges DC does not take a path that is significantly different from the simulations without charges. Only in the middle of the DC trajectory the differences are more pronounced. That means that the variation of the charge influences the pathways less than the direction taken. The variation of the target or the temperature has almost the same effect. It has been seen in other TMD simulations that the forward and backward direction can be quite different. For PAI-1, this does not seem to be so. There is overlap between the pathways in each direction. This conclusion can be drawn from the trajectories in Figure 3 ▶ and also has been confirmed by visual inspection of the structures. Obviously, there are no high energy barriers between the two directions. This can be due to the relative freedom that the RCL experiences during the conformational change.

The unconstrained MD simulations starting from the intermediate position (CH, CS) reflect clearly the flexibility of the RCL. The simulation CH at higher temperature covers even the conformational space of the simulation in which the CH structures have not been used as target or initial structures (e.g., CB, CC, CG). This again emphasizes that there is no high energy barrier between the different structures close to the intermediate. The low temperature simulation also has some overlap with that of 350K. The unconstrained equilibrium simulation at the active position drifts away from the direction taken by the constrained simulations. This indicates the flexibility of the RCL. The RCL has a lot of freedom to move in this position, with obviously no bias toward the intermediate structure. Although the presentation in Figure 3 ▶ cannot quantify the fluctuation, the movement of the unconstrained simulation of the latent structure seems to be more localized. This is because the RCL is inserted in the β-sheet and therefore more restricted in mobility. Deviation from the pathways also are not seen for this simulation.

The simulations toward the final structure (latent) can be performed taking different structures from the simulations toward the intermediate. In TMD simulation of the insulin T → R transition, it could be seen that for one molecule an unsuccessful pathway was taken (Jacoby et al. 1995). This was reflected by the increase of the potential energy. In the case of PAI-1, no indication for an unsuccessful pathway appeared. That means the whole trajectory can be simulated by concatenating the two pieces of the trajectories (active-intermediate, intermediate-latent). Nevertheless, the trajectories from the intermediate to the final structure are different, depending on the conditions used. Small differences are visible between CD and CI, which use different starting conditions. The outlier is simulation CL, but this is mainly due to the different starting condition. The backward simulation CR crosses all the other simulations but does not find a new pathway. The simulation with charges is again, as in the first part of the trajectory (active-intermediate) in the same conformational space.

Rms fluctuations

The rms fluctuation for the equilibrium simulation and for the simulations from active to intermediate and from intermediate to latent are shown in Figure 4A– C ▶. In case of the equilibrium simulations CH, CK, and CS, the highest rms fluctuations are visible in the region of the RCL (between 330 and 360). The RCL is largely solvent exposed in the active and intermediate position and therefore prone to a high flexibility even without applying any constraint to perform a conformational transition. In the latent form (simulation CP), the rms fluctuations of the RCL are comparable to those of other segments. The simulation CK also shows high fluctuation in the regions 100–110, 150–160, and 180–210. The loop 100–110 (ts2AhE) connects strand 2A with helix E, and the loop 150–160 (thFs3A) connects helix F with strand 3A. Both of these loops are solvent exposed. The region 180–210 includes loop 1 of the gate and is also largely solvent exposed. Interestingly, the two simulations at the intermediate CH and CS show a quite different pattern in fluctuation. This is also in accordance with the projection of the conformational space (see Fig. 3 ▶) and shows the possible alternatives at the intermediate position.

Fig. 4.

Fig. 4.

Fig. 4.

Fig. 4.

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Rms fluctuations of the Cα atoms of the different simulations shown per residue. (A) Equilibrium simulations: CH, CK, CP, and CS. (B) Simulations between active and intermediate: CB, CC, CE, CG, CM, and DC. (C) Simulations between intermediate and latent: CD, CI, CJ, CL, CR, and DF.

In the TMD simulations, the local fluctuations are overlayed by the movement resulting from the conformational transition. Therefore, one must speak about fluctuation in the sense of mobility. It is quite clear that the segment that moves most (here the RCL) shows the highest fluctuations. Figure 4B ▶ shows an amplitude for the RCL between 10 and 16 Å, which is approximately twice of that seen for the equilibrium simulation. Overall, smaller shifts in other segments than the RCL are seen for the simulations CE and CM. Both move to a more relaxed intermediate structure. The simulation including charges DC does not show significant differences compared with the simulation of the C series.

In the segment between the residues 180–200 (loop 1), an overall higher fluctuation can be seen, especially in simulation CC and CG. Loop 2 (242–246) is flexible, but not more than other parts of the molecule as, for instance, the region between 260–270 that is opposite to loop 1 or at the backside of the RCL (see Figs. 1,2 ▶ ▶). Taking this fact together with the finding that in the equilibrium simulation loop 2 does not show a pronounced flexibility indicates that the conformational transition is mainly affecting loop 1 and to a minor extent loop 2. This result also has been confirmed by visual inspection of the trajectory.

An even clearer picture emerges form the trajectories when going from the intermediate to the final structure: a large fluctuation for the RCL segment and a smaller but still significant one for loop 1 is seen. This means that just a few arrangements in the structure (i.e., in loop 1) are necessary to enable a pathway of the RCL. Only the simulation CL shows larger movements in the region between 200 and 300, which is probably a consequence of the conformation of the starting structure. Using the last structure of the relaxed simulation CH as the target in the simulation from the active form to the intermediate, we found reduced overall shifts or fluctuations, whereas the shifts are increased when going from the same starting structure to the latent form. This indicates that a relaxed structure can be a suitable target starting from the active but a less favorable one starting from the intermediate to reach the latent form. It also shows that the rms fluctuation can be used as a criterion for the likeliness of a pathway, which is assumed to be the one with smallest overall fluctuations, that is, lowest hindrance.

The deviation of the trajectory DC with charges is within the range of the deviations seen for the other simulations of this set.

Changes in secondary structure elements

The changes in secondary structure elements during the conformational transition were calculated. For this purpose, a simple criterion for the φ, ϕ dihedral angle was applied: for the sheet region, a range between −160 and −60 for the φ angle and 90 and 150 for the ϕ angle was used, and for the helical region, a range between −80 and −40 for the φ and ϕ angle was used. All the other φ, ϕ-dihedral angle combinations were defined as `extended' structure. The wide definition for the changes in secondary structure has been used to obtain the gross changes.

The unconstrained equilibrium simulations show a tendency to a more helical structure, respectively, a less extended structure. In addition to the unconstrained simulation, the simulations with ions (DC, DF) also show a larger tendency toward the helical situation. The simulations that show an increase in the helical dihedral angles also show a decrease in the extended structure. The simulations close to the latent structure do not show a significant tendency toward β-sheet formation. On the one hand, this can be due to the fact that the criterion used in this case is not very tight and, on the other hand, to the fact that the final insertion only happens at the very end of the transition.

A visual inspection of the graphically displayed structures makes clear that the stretched RCL loop from the initial structure moves down to the surface of the molecule and winds up, with some φ, ϕ pairs closer to helical dihedral angles. The formation of a helix as, for instance, present in an other related serpin, that is, the ovalbumin structure, could not be seen. This is in accordance with the X-ray analysis of the active structure for which a helix formation has not been found but a large flexibility for the free RCL, that is, in case it has no contact to a partner molecule (Sharp et al. 1999; Nar et al. 2000).

Distances between loop 1 and 2

The calculation of the distances between the two loops of the gateway (loop 1 and 2) can show whether an opening or a widening takes place during the conformational transition. To monitor this process, we used the distance between the geometric centers of the Cα atoms of loop 1 (185–200) and loop 2 (242–246). All simulations show large fluctuations with distances between 16 Å and 22 Å. The equilibrium simulations at the intermediate (CH, CS) do not show a very clear tendency toward opening or closing. In contrast with expectation, the simulation CM shows a reduced distance toward the end of the simulation, although the target structure is the intermediate. Using only the distance between the loops as a criterion for the opening of the gate can be misleading because the graphical inspection shows that the loop 1 can have a kink, which is not apparent in the loop distance.

The equilibrium simulation at the active structure does show similar fluctuation for the loop distances as seen in the transformation simulations. This shows that the two loops are quite flexible, as already indicated by the rms fluctuations. It is obviously not possible to consider this as a gate opening mechanism. Especially loop 1 is very flexible and prone to other movements than lateral shifts, such as, for instance, a kink. The simulations using full charges have similar properties as simulations without charges. An opening or closure of the gate influenced by the charges cannot be seen in the simulations.

Distances between RCL and the rest of the molecule

The distance between the RCL (N Glu 330 to C Asp 355) and the rest of the molecule is shown in Figure 5 ▶. It is obvious that only in the simulations from the intermediate to the latent structure the distances are significantly decreased. Simulation CR consequently shows an increase in distance. The equilibrium simulation at the latent structure (CP) stays close to its initial distance. The simulations from the active to the intermediate and the equilibrium simulations at the active or intermediate structure do not show a clear change in distance. This indicates that the pathway between the active and intermediate structure requires an open or stretched conformation, before it is inserted to the core of the molecule, that is, when passing from the intermediate to the latent structure. Because of steric reasons, it is not very likely that the RCL can surround the obstacle (loop 1) without having this stretched conformation. Only after the RCL has passed loop 1 the way is free for the final insertion into the β-sheet. The unconstrained equilibrium simulations at the intermediate (CH and CS) show only for CH a slight tendency to reduce the distance to the molecule's body. The limited computer time cannot give a full picture of the conformational space available at the intermediate. Nevertheless, up to now, there is no indication that the conformational change is possible with a significantly less stretched RCL than seen in these simulations. Loop 1 is flexible as it has been seen by the rms fluctuations or the distances between loop 1 and 2. It is unlikely that an enhanced flexibility or movement beyond the one already seen in the simulations will be able to reduce significantly the obstacle character of loop 1. Therefore, we concluded that it is necessary to have a wide and stretched structure of the RCL to surround loop 1.

Fig. 5.

Fig. 5.

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Distance between the geometrical center of the RCL and the geometrical center of the body of the molecule.

Contacts during conformational transition

Mutations in the loop 1 region have been used in the past to analyze the interaction between loop 1 and the RCL. For instance, a mutation in the residues R186E, R187E and H190E, K191E have shown an increased speed for the conformational transition (Gils et al. 1997). To find out which residues in the RCL and loop 1 approach closest, we calculated a contact map. In this contact map, the time series of the number of contacts was calculated (within a distance of 3–10 Å) of the Cα atoms of the residues 186 and 194. The number of contacts are given per residue. This was performed for the equilibrium simulations at the intermediate (CH and CS) and as a comparison for a simulation from the active to the intermediate (CB) and from the intermediate to the latent structure (CD). In Figure 6A–D ▶, the contacts around residue 186 are displayed. The main number of contacts are between the two opposite chains of loop 1 (around residue 186 and 200). Only a few contacts with the RCL (around residue 340) and with ts2Cs6A (around residue 277) can be seen. Exception is simulation CB in which several contacts appear toward the end of the simulation.

Fig. 6.

Fig. 6.

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Number of contacts in a sphere of 10 Å around Cα atom of residue 186 during the simulation time. (A) For simulation CB, (B) for simulation CS, (C) for simulation CD, (D) for simulation CH.

The same analysis with residue 194 is shown is Figure 7A–D ▶. The two equilibrium simulations at the intermediate show both contacts between the loop 1 and the RCL (around residue 350) and also contacts to the C terminus of the molecule within this radius. Simulation CB shows that only contacts with the residues behind the C-terminal end of the RCL are present (residue 355). This is a part that does not move significantly during the conformational transition. Further contacts are present in the region of residue 28 and the C terminus of the chain. In simulation CD, contacts are present between 345 and 355. A further set of contacts appears at residues 275 and 28.

Fig. 7.

Fig. 7.

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Number of contacts in a sphere of 10 Å around Cα atom of residue 194 during the simulation time. (A) For simulation CB, (B) for simulation CS, (C) for simulation CD, (D) for simulation CH.

A similar analysis has been conducted for the other simulations as well, showing a close interaction between the residues 194 and 350 (plus or minus five residues).

Discussion

The present investigation is an attempt to model the conformational transition of the PAI-1 molecule from the active to the latent structure with full atomic details by using simulation techniques. The complex conformational transition could be simulated using a combination of a rigid body movement together with the TMD method. This is to our knowledge the first time that a very complex conformational transition could be simulated with a combination of a rigid body movement and an all atom description. The basis for the rigid body rotation is the stretched RCL. This structure also has been assumed as starting geometry of the initial (active) structure. Our simulations and also the experimental structures (Sharp et al. 1999; Nar et al. 2000) indicate that the RCL is quite flexible. The choice of the RCL conformation was fortunate because it could deliver, after rotation around an axis through the hinge atoms, a reasonable intermediate for the simulation. Although this choice of the RCL conformation was arbitrary to some extent, the simulation has given some confidence that its position is within the conformational space accessible to the loop.

Different pathways are obtained under different simulation conditions such as temperature, initial velocities, direction (forward and backward), and nature of the target. None of these parameters has a superior influence. There are several pathways possible, but the energetic criteria are not sufficient to decide on the relative probability of a pathway. That we see a broad valley of different pathways of equal energy can be special for PAI-1, because the RCL has many degrees of freedom, indicated by its flexibility. Two different areas of the conformational space are scanned as seen when starting an equilibrium simulation from the intermediate. Nevertheless, there is always one region visible where loop 1 and the RCL come into close contact. Different intermediate structures will lead to different pathways. Close to the intermediate, the equilibrium simulations show the contacts between the RCL and loop 1 in the unconstrained situation. Equilibrium simulations in principle can be conducted at each stage of the pathway. We predict that the overlapping part of the conformational space of such a set of equilibrium simulations indicates the most probable conformations independent of the target.

The importance of these particular interactions has been hypothesized in previous studies (Aertgeerts et al. 1995). The relevance of the present observations and calculated pathway is further confirmed by biochemical experiments indicating that the reversal or removal of charged residues in this region (Arg 186–Arg 187, His 190–Lys 191 in loop 1 or Arg 356 in the RCL) results in an accelerated conversion from the active to the latent form (Gils et al. 1997; Vleugels et al. 2000).

The RCL has to stretch out to some extend to surround the loop 1. An indicator is the close contact between the RCL and loop 1. Loop 2 is much less affected, and it is less likely to influence the motion of the RCL. This finding also is confirmed by the observation that mutations in this region (i.e., replacement of Glu 242–Lys 243–Glu 244 by Ala 242–Ala 243–Ala 244) does not destabilize the active conformation (A.-P. Bijnens and P.J. Declerck, unpubl.). The distance between loop 1 and 2 varies with no clear trend. We must assume that loop 1 is quite flexible. The simulations indicate that the flexibility of loop 1 is more important than the actual distance between the gate residues derived from the X-ray structures. This is also in agreement with previous findings in which on comparison of various three-dimensional structures of PAI-1 in this gate region the position of loop 1 is different (Aertgeerts et al. 1995). Nevertheless, the flexibility of loop 1 is also limited, which makes a stretched conformation of the RCL necessary. The possibility to adopt this conformation is indicated by the RCL flexibility. The general flexibility of the RCL could be seen in the unconstrained simulation of the active structure and is in agreement with previous reports based on X-ray measurements (Sharp et al. 1999; Nar et al. 2000). This makes us confident that the stretched structure of the RCL is among the possible ones.

The changes in secondary structure have been analyzed with a very simple criterion, showing a tendency toward helical dihedral angles for the unconstrained simulations. Despite this tendency, a continuous helix formation cannot be seen. This is in agreement with the claimed flexibility for the RCL: if a rigid secondary structure is going to show up during the transformation, the transformation might be unlikely because loop 1 cannot be surrounded. This also may explain why other serpins do not convert spontaneously to a latent structure.

Computational procedure

To model the conformational transition of PAI-1, we combined several methods: TMD simulations to calculate the conformational change between two structures, standard MD simulations to relax the structures of the active, the intermediate and the latent molecule and the rigid body rotation of the RCL to obtain a first guess for the intermediate.

The TMD method

The TMD (Schlitter et al. 1993) method establishes a distance constraint between two structures. Two structures are necessary to perform a simulation, for example, an initial and a final structure. The pathway from the initial to the final structure describes the direction the simulation takes. In each step of the simulation, first an unconstrained step of a MD simulation is performed. After the free simulation step, the distance between the initial and target structure has to be reduced. This is realized by the distance constraints ρ that is defined as the sum of distances of all atom positions. ρ is a time-dependent constraint that reduces the distance in each step of the simulation.

Defining the intermediate

TMD using the active as initial structure and the latent as target structure could not deliver a successful pathway. Therefore, the pathway was split into two parts: from the initial structure to an intermediate and further from those intermediate to the latent structure. Here, the intermediate is not defined by one structure. The first intermediate is obtained from a rough guess, and afterward it is refined so that it is possible to speak of a `refined intermediate.' A first guess for the intermediate structure was obtained by a rigid body movement of the RCL. The active structure of PAI-1 was used as starting structure to derive the first guess for the RCL. In this first guess structure, the new position of the RCL loop was obtained by a rotation of the atoms in the loop, relative to the rest of the molecule, around an axis that intersects with the hinge atoms of the loop (Carrell et al. 1991). The position of the atoms of the RCL after rotation was not refined (e.g., by simulation), and therefore in this first guess structure several clashes with the remaining molecule were still present. This structure nevertheless could be used as an intermediate target in a TMD simulation, because the exact position of the target would not be reached at the end of the TMD. The last structure of the TMD simulation was further relaxed using standard MD simulation in a separate procedure in which no constraint was applied.

Defining the rotation axis

To obtain the first guess in which the RCL was rotated around an axis through the hinge atoms, we regarded the RCL loop as one entity. The procedure to find a rotation axis was inspired by the program DynDom (Hayward et al. 1997; Hayward and Berendsen 1998). A DynDom calculation using the active and latent structure delivered in this special case several rotation axes from which we had to select one. The first guess intermediate should have more or less the same bond length pattern as the intact molecule. Therefore, a DynDom axis was chosen that closely meets the hinge atoms. The axis for the rotation of the RCL was defined by the backbone atoms N of residue Glu 330 and C of residue Asp 355. This loop was rotated by 120°. The coordinates of the Cα atoms of the hinge residues were taken to define the axis. The segment rotation itself was performed with the program TARMOD (P. Krüger, unpubl.).

Structures used

At the time the project was started, the X-ray structure of the active molecule was not available. Therefore, a model structure for the active PAI-1 molecule was used. The modeling was performed as described in Aertgeerts et al. (1994). In this structure, a defined (stretched out) conformation of the RCL was assumed. Comparing this structure with the X-ray structure of a stable active mutant (Nar et al. 2000), which became only available during the course of this study, shows that the RCL conformation is different. Apart from uncertainties in the modeling, the position of the RCL in the crystal structure is strongly influenced by the molecule–molecule interaction. It therefore is reasonable to assume that the presently used model of the active form is still a representative structure as a starting point in the present calculations. The coordinates of the latent structure were taken from Mottonen et al. (1992).

Simulation

All simulations were performed with the simulation package GROMOS96 (Van Gunsteren et al. 1996) with an additional extension for the TMD algorithm (W. Swegat, pers. comm.). A time step to integrate the equation of motion of 0.002 ps was used. Bond length constraints using the method SHAKE (van Gunsteren and Berendsen 1977) were applied. Short- and long-range interaction were calculated with a cut-off of 0.8 nm and 1.0 nm. The water model SPC-E was used (Berendsen et al. 1987), and periodic boundary conditions were applied. The system was started with initial velocities of a given temperature (see below) having a Maxwell distribution. Different velocities were assigned to the atoms by setting different seeds for the random number generator.

Two simulation series were performed: series C with only partial charges and series D with full charges including the counter ions for the acid and basic groups (van Gunsteren et al. 1996). The series A and B performed under vacuum conditions are not presented here. The simulation series C and D made it possible to investigate the influence of charges on the pathways. Constant volume conditions were applied, and a rectangular periodic box was used with a length of x = 5.29 nm, y = 6.38 nm, and z = 9.18 nm. For series C, the system consists of 3829 protein atoms with 25,344 water atoms, for series D, 3831 protein atoms, 39 Na, 36 Cl, and 25,116 water atoms. Therefore, both systems comprised nearly 30,000 atoms. Table 1 compiles the simulations used in this investigation. One series of simulations was performed from the active to the intermediate (respectively, refined intermediate) and from the intermediate to the final structure. The simulations CG and CR are the simulations in the backward direction from the intermediate to the active and from the latent to the intermediate structure. Besides the change in charge, different targets, different initial velocities, and different temperatures were used to vary the simulation conditions. The temperatures were kept constant with a thermostat according to Berendsen et al. (1984) and the reference temperature given in Table 1. Simulations at elevated temperatures, that is, 350K, were performed to cross local low energy barriers. The TMD simulations were performed over a period of 500 ps. All atoms of the protein were used to define the target. Usually a TMD simulation stops before the final step is reached, either because the distance to the target is below the final distance criterion to the target structure (ρ = 0.8 nm) or because the potential energy increases. The equilibrium MD simulations starting from the active, intermediate, and latent structure were conducted without a distance constraint over a time span of 400 ps.

Table 1.

Simulations performed

Simulation Type Temp. Pathway Comments
CB TMD 293 Active → intermediate Target: rotated RCL
CC TMD 350 Active → intermediate Target: rotated RCL
CD TMD 293 Intermediate (CB) → latent Target: latent structure
CE TMD 293 Active → intermediate (CB) Target: final structure of CB
CG TMD 293 Intermediate (CB) → active Start: final structure CB
Target: active structure
CH EQU 350 Equilibrium at intermediate Start: last structure of CB as CD but different initial velocities
CI TMD 293 Intermediate (CB) → latent
CJ TMD 293 Intermediate (CE) → latent Start: final structure CE
Target: latent structure
CK EQU 350 Equilibrium at active Start: X-ray latent
CL TMD 293 Intermediate (CH) → latent Start: final structure CH,
Target: latent structure
CM TMD 293 Active → intermediate (CH) Target: final structure CH
CP EQU 293 Equilibrium at latent Start: last structure of CJ
CR TMD 293 Latent → intermediate Target: last structure CB
CS EQU 293 Equilibrium at intermediate Start: last structure CB as simulation CH but 293K
DC TMD 293 Active → intermediate Full charge and counterions
Target: last structure CH
DF TMD 293 Intermediate → latent Start: final structure DC
Target: latent structure
Open in a new tab

TMD: simulations using targeted molecular dynamics, the initial and final structure is indicated under `Pathway.'

EQU: equilibrium simulation without constraint, the starting structure is indicated under `Pathway.'

For the analysis of the trajectory, the program SIMLYS was used (Krüger et al. 1991; Krüger and Szameit 1992).

Acknowledgments

We thank Dr. Steven Hayward for providing us with the program DynDom and many helpful discussions. We acknowledge Dr. Phys. Wolfgang Swegat for providing us with the GROMOS96 version including TMD and Dr. Berthold Wroblowski for performing the first orienting simulations on PAI-1. We also thank Dr. K. Aertgeerts for discussions in an initial phase of the study and Dr. A. Gils for discussions during the course of these investigations. PK is a recipient of the fellowship F/97/115 and SV of an IWT fellowship. The research is supported by OT/97/19 and the IWT.

The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 USC section 1734 solely to indicate this fact.

Article and publication are at www.proteinscience.org/cgi/doi/10.1110/ps.40401.

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