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Medicinal Chemistry and Molecular Pharmacology Department, Markey Center for Structural Biology and Purdue Cancer Center, Purdue University, West Lafayette, Indiana 47907-2091, USA
(RECEIVED November 28, 2005; FINAL REVISION January 28, 2006; ACCEPTED January 31, 2006)
| Abstract |
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-helix (
C), which is located at the interface between the two lobes, into or away from the catalytic cleft. Conformational activation was investigated using biased molecular dynamics to explore the transition pathway between the active and the down-regulated conformation of CD for the Src-kinase family member Lyn kinase, and to gain insight into the interdependence of these changes. Lobe opening is observed to be a facile motion, whereas movement of the A-loop motion is more complex requiring secondary structure changes as well as communication with
C. A key result is that the conformational transition involves a switch in an electrostatic network of six polar residues between the active and the down-regulated conformations. The exchange between interactions links the three main motions of the CD. Kinetic experiments that would demonstrate the contribution of the switched electrostatic network to the enzyme mechanism are proposed. Possible implications for regulation conferred by interdomain interactions are also discussed. Keywords: enzyme activation; protein electrostatics; activated molecular dynamics; allosterism; phosphoproteins
| Introduction |
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Normal cellular function requires tight control of Src kinase activity and the equilibrium between active and down-regulated conformations. Src kinases comprise SH3, SH2, and catalytic domains, flanked by N- and C-terminal tails. The end states of Src conformational activation are known from the considerable structural information accumulated for protein kinases and the Src family. The CD is highly conserved among all protein kinases, and the first view of this structure was reported for protein kinase A (Knighton et al. 1991). The structure of the activated form was determined for an isolated CD fragment from the Src family member Lck (Yamaguchi and Hendrickson 1996), and the down-regulated forms were first reported for constructs lacking only the N-terminal unique region of the two family members Hck (Sicheri et al. 1997) and Src (Williams et al. 1997; Xu et al. 1997). These studies not only revealed the key conformational differences between active and down-regulated forms of Src family CD but also defined for the first time how SH2 and SH3 contacts with CD influence activation.
The kinase catalytic domain has an N-terminal lobe (N-lobe) (Fig. 1, cyan and blue) and a C-terminal lobe (C-lobe) (Fig. 1, gold and red) separated by a deep cleft where ATP and substrate bind. The activation loop (A-loop) (Fig. 1, red) forms part of this cleft. Autophosphorylation of Tyr416 (chicken c-Src numbering is used throughout this report) on the A-loop activates Src in the cell (Barker et al. 1995). Several features distinguish this active CD conformation (CDact) (Yamaguchi and Hendrickson 1996; Breitenlechner et al. 2005) from the down-regulated conformation (CDdown) (Sicheri et al. 1997; Williams et al. 1997; Xu et al. 1997, 1999; Schindler et al. 1999; Cowan-Jacob et al. 2005). The primary difference is the alternative conformations of the A-loop; in CDact (Fig. 1AC), the A-loop forms an extended structure that opens the cleft region to make the active site available for substrate binding. In contrast, the A-loop in CDdown (Fig. 1DF) is more compact and forms two short
-helices that fill the cleft and thus occlude substrate. In addition, lobelobe orientation and the internal position of the
-helix (
C) differ. The orientation of the N- and C-lobes is more open in CDact relative to that in CDdown so that the size of the cleft opening is increased. The internal variation in
C is the position of this helix within the N-lobe;
C in CDact is displaced with respect to the
-sheet toward the interior of the protein.
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One approach to overcome problems with specificity, and to find more effective inhibitors, is to gain a better understanding of the physical behavior of kinases including the process of kinase conformational activation. To this end, computational studies of a Src-family member, Lyn kinase, were conducted and reported here. The sequence and structural similarities among Src kinases and protein kinases in general imply that deciphering the activation mechanism of one Src kinase will afford clues about the activation mechanism of the Src-family and other kinases. Lyn initiates (Burkhardt et al. 1991; Yamanashi et al. 1991) and down-regulates (Chan et al. 1997, 1998; Nishizumi et al. 1998; Smith et al. 1998; Hong et al. 2002) B-cell signaling. NMR studies to examine substrate recognition of Lyn for ITAM have been reported (Gaul et al. 2000).
The structures of CDdown (Sicheri et al. 1997; Xu et al. 1997) and CDact (Yamaguchi and Hendrickson 1996) provide the starting point for understanding the mechanism of kinase activation, although the static crystal structures give information on neither the order nor the interdependence of conformational changes that must occur for activation. Certain features of conformational activation have been inferred from these two end states. It has been suggested that intramolecular domaindomain contacts stabilize CDdown by either hindering
C motion, thus preventing the A-loop displacement required for activation (Schindler et al. 1999), or by stabilizing the closed conformation of the catalytic domain lobes and keeping the A-loop tyrosine inaccessible (Xu et al. 1999). The computational study reported here aims to begin to elucidate the conformational transition between CDdown and CDact and to define the interdependence between displacements in
C, the A-loop, and lobelobe orientation.
Biased molecular dynamics (BMD) was used to study the conformational transition between CDact and CDdown. The time scale for this transition has been measured for protein kinase A to be in the 56-msec range (Shaffer and Adams 1999). With BMD, a biasing potential is added to the molecular mechanics force field in order to study this transition within a computationally feasible time scale. The biasing potential moves the protein toward a target structure, and is added as a global sum over the system so that departures in local structure away from the target are allowed as long as the cumulative motion is in the desired direction. The consistent characteristics of the pathways from several trajectories can give information about possible energy barriers (Neria et al. 1996). Similar methods to study activated processes are targeted molecular dynamics (TMD) and steered molecular dynamics (SMD). For BMD, the potential is like a ratchet in that it is added only when the system moves away from the target, whereas in TMD and SMD the potential is present at all times. This feature of BMD is expected to be advantageous by allowing the system to follow the energy surface more closely. BMD has been previously used to study unfolding (Marchi and Ballone 1999; Paci and Karplus 1999; Morra et al. 2003) and dissociation (Paci et al. 2001; Li et al. 2005). TMD and SMD have been used to study the conformational changes of GroEL (Ma et al. 2000) and Ras (Diaz et al. 1997; Ma and Karplus 1997) and unbinding of avidin-biotin (Isralewitz et al. 2001a). TMD has also been used to examine certain features of the Src kinase conformational transition. These studies primarily focus on the role of the SH3SH2 linker in coupling domains (Young et al. 2001) and the structural effects of the N-terminal residues of CD in interdomain communication (Banavali and Roux 2005).
We examined the unphosphorylated, isolated catalytic domain of Lyn for this initial computational analysis of activation. The Src-family catalytic domain is constitutively active (Yamaguchi and Hendrickson 1996) and inhibited by small molecules to a similar extent as the full-length form (Zhu et al. 1999). In addition, Src kinase activity is observed in the absence of Tyr416 phosphorylation (Porter et al. 2000; Adams 2003). Therefore, the catalytic domain captures significant features of conformational activation, and a description of the transition behavior in the absence of phosphorylation on Tyr416 provides information on the underlying physical processes involving the overall structure. Computational investigations should also give insight into the structural basis for conformationally selective ligand binding (Schindler et al. 2000; Kwak et al. 2005), and thus assist in the development of new kinase inhibitors. The key result from the analysis of the BMD simulations is that the network of electrostatic interactions in CDdown switches to an alternative network in CDactso that the transition may be described as a switched electrostatic network. A set of six polar or charged residues consistently switch in a temporally short fashion between binding partners over the course of the transition. These residues are highly conserved, and some are already assigned important roles in catalysis or binding. We propose that these residues also serve central roles in the transition process by functioning as a switched electrostatic network to guide the transition as anchor points along the pathway.
| Results and Discussion |
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, and C at the end of the equilibrium simulations were ~1.5 Å relative to the initial structure for both active and down-regulated catalytic domains.
The key interactions that distinguish CDact and CDdown (Yamaguchi and Hendrickson 1996; Schindler et al. 1999; Xu et al. 1999) are summarized in Table 1 and illustrated in Figure 1, C and F. These interactions were stable throughout the equilibrium simulations. In CDact, the A-loop is extended away from the active site, in a conformation that allows substrate access to the active site. In this extended conformation, the phosphoryl group of pTyr416 on the A-loop interacts with Arg385 and Arg409. In CDdown, the A-loop is folded over the active site, and Tyr416 then forms a hydrogen bond with Asp386 in the catalytic site. Glu310 was recognized to be a key residue associated with the alternative orientations of
C (Schindler et al. 1999; Xu et al. 1999). In CDact, where
C is turned in toward the ATP binding site, Glu310 interacts with the catalytically critical residue Lys295 (Snyder et al. 1985; Kamps and Sefton 1986). Alternatively, the outward rotation of
C in CDdown places Glu310 in close contact with Arg409 and Tyr382. The A-loop and
C are located at the interface of the N- and C-lobes of the catalytic domain so that their alternative structures would influence the conformation of the third distinguishing feature, the disparate lobe orientations.
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Biased molecular dynamics
Forward and reverse transitions between CDact and CDdown were calculated with values of the pairwise force constant,
, equal to 0.0004, 0.0009, 0.0013, and 0.0022 kcal/(mol Å4) with and without ATP (Table 2). At the largest
-value, the force on a single atom of the biased set ranged from 0 to ~150 pN. This value is at the lower end of the previously reported range of 100500 pN (Paci and Karplus 1999). The initial and target structures used for the biased MD simulations of the catalytic domain were those obtained following 0.30.4 nsec of equilibrium MD. No significant effect of ATP on the conformational transition was found.
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-values is shown in Figure 2 with the transitions for activation (CDdown
CDact) on the left-hand side, and those for deactivation (CDact
CDdown) on the right-hand side. The RMSD to the target structure is plotted as a function of time for all heavy atoms (Fig. 2, bottom panel), and for a subset of residues to indicate the individual progress of the three structural features of the conformational transition (Fig. 2, top three panels). The RMSD for the three structural elements are calculated after superposition of the structures with respect to the
-helices in the C-lobe. The RMSD is averaged over heavy atoms of the element: residues 403429 for the A-loop, 304314 for
C, and 261341 excluding
C residues for the N-lobe.
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C. The biased MD method therefore can tolerate increases in the RMSD value for a subset of atoms even though the global target RMSD value [R(t)] is restrained to decreasing values. As such, transient moves away from the target are possible for local regions if dictated by the potential surface.
Conformational transition is nonuniform
Decay profiles of the RMSD progress curves calculated for a subset of residues show that the conformational transition does not occur uniformly throughout the catalytic domain. The decay profiles vary for the A-loop,
C, and the lobe orientation (Fig. 2, top three panels), as well as for the activation transition and the reverse deactivation transition (left vs. right column). The opening of the two lobes (Fig. 2C) in the activation transition occurs early, within an ~50-psec time period. Closing down of the lobes in the transition to CDdown (Fig. 2G) is considerably slower, requiring as long as 250 psec, and shows a dependence on the value of the pairwise force constant,
. The activation and deactivation transitions for
C differ in a similar fashion. The
C activation curves (Fig. 2B) decay relatively smoothly and early in the transition, whereas the progress toward CDdown (Fig. 2F), with Glu310 rotated out, is slower and shows a stronger dependence on
. The largest conformational change occurs in the A-loop. The A-loop activation transition (Fig. 2A) is interestingly more complex than the N-lobe and
C transitions are and consistently shows biphasic behavior that depends on the magnitude of
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Differences in the N-lobe and
C decay profiles shown in Figure 2 can be rationalized from a simple mechanical view of the structural changes. Comparison of the structures for CDact and CDdown finds that the N-lobe is reoriented relative to the C-lobe by a simple rigid-body motion except for the position of
C (Fig. 3). The change in
C, observed after superpositioning the C-lobes, is rotation about the helix axis and translation of the N-terminal end of
C relative to the
-sheet of the N-lobe. The lobe opening during activation occurs relatively fast, and the RMSD decays monotonically, characteristic of an unhindered hinge opening. This opening is accompanied by unimpeded inward rotation and translation of
C toward the ATP-binding site (Fig. 3, gold). This internal displacement of
C explains the slower progress for lobe closure relative to opening (Fig. 2, cf. F,G and B,C); lobe closure, to generate CDdown, depends on rotation of
C to the "out" position to allow room for the lobes to close, while lobe opening can proceed independent of the position of
C. Further, the
C-in conformation is not compatible with the A-loop conformation folded over the active site in CDdown as shown by the steric clash in Figure 3 between the gold
C and the blue A-loop. Correspondingly, folding the A-loop over the active site to reach the CDdown conformation must cooperate with rotation of
C to the out position. Thus, the kinase deactivation/activation mechanism involves interdependent displacements of
C, the N-lobe, and the A-loop (Schindler et al. 1999; Xu et al. 1999).
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. The strong dependence on
is consistent with an energy barrier to the conformational change that underlies the drop in RMSD value. Analysis of the trajectories finds the
-dependent decrease to be a helixcoil transition in the short 1.5-turn
-helix in the C-terminal end of the A-loop, residues 413422. The time dependence of the helicity, monitored from the number of residues with main-chain dihedral angles in the helical region, is shown in Figure 4. Unwinding of the short helix corresponds in time with the drop in RMSD of the A-loop. By visualization of the trajectories, the A-loop is observed to open out from the two ends, and the helix then unwinds concertedly. Further, immediately prior to helix unwinding (Fig. 2A, arrows), similar Lyn CD structures are observed independent of
, so that a consistent intermediate (Fig. 5) exists in the transition. Preceding helix unwinding, the catalytic domain main chain overlays well in all parts of the catalytic domain including the A-loop. The similarity in these intermediate structures suggests that a bottleneck in a common activation pathway involves helix unwinding of the A-loop of Lyn CD. Tyr416 is on this helix of the A-loop, and the side chain faces into the active site in the down-regulated state. Interestingly, when the A-loop opens out in the activation simulations, the Tyr416 side chain is transiently exposed to solvent. The helixcoil transition may facilitate exposure of Tyr416 to make it available for phosphorylation.
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-sheet interactions with the C-lobe are broken rapidly, with subsequent reorientation of the loop between them. Although there is a rapid drop in RMSD from 12 Å to 45 Å, the transition to the active state of the A-loop is not complete within the simulation time; the RMSD value plateaus at ~4 Å and the short helix is not formed. The incomplete folding of the A-loop over the active site may be the result of a significant energy barrier to helix formation, or may be a limitation of the methodology in view of the steric conflict with
C described above.
A switched electrostatic network links the A-loop with
C and active-site residues
Trajectories were analyzed to identify interresidue interactions that were consistently formed/broken over the course of the transitions and thus likely to serve a functional role in kinase conformational activation. Rather than independent pairwise interactions, this analysis identified a group of polar residues that form alternative networks of interaction in CDdown and CDact. One set of interactions was observed to exchange with the alternative set for these polar residues, suggesting that these residues function like an electrostatic switch to guide the activation/deactivation transition. The switch, shown schematically in Figure 6, comprises a group of six residues: the catalytic Asp386, the regulatory Tyr416 on the A-loop, Arg409 on the A-loop, Glu310 on
C, the functionally critical Lys295, and Asp404 of the metal-binding DFG sequence. The four central residuesTyr416, Arg409, Glu310, and Lys295exchange binding partners to switch between a three-way and a two-way network. These six residues are highly conserved among kinases, and some have been recognized for distinguishing the active and the down-regulated states (Yamaguchi and Hendrickson 1996; Schindler et al. 1999; Xu et al. 1999). The down-regulated state is the three-way network (Asp386Tyr416, Arg409Glu310, Lys295Asp404) (see Fig. 6B), which links the A-loop to either the N- or the C-lobe (Fig. 6A). When the A-loop opens toward the active form, these interactions switch to two alternative ones within the A-loop (Tyr416Arg409) and within the N-lobe (Glu310Lys295).
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C are large internal motions, yet the interresidue distances between the switch residues remain comparatively short and constant until the point of the exchange. The distance Glu310 to Arg409 remains short even when the A-loop opens out (Fig. 9, middle panels), then Glu310 switches to interact with Lys295 (Fig. 9, bottom panel). Thus, the side-chain interactions serve as anchor points in the transition. The short-range interactions "float" with the main-chain displacement until the exchange with the alternative partner.
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| Conclusions |
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BMD and other similar methods (TMD [Schlitter et al. 1993] and SMD [Isralewitz et al. 2001b]) that use an additional potential to overcome energy barriers and move from one state to the other in nanoseconds are useful in studying conformational transitions that may take place in microseconds to seconds in the cell. Such nonequilibrium methods make it possible to determine pathways and energy barriers for these conformational transitions. The underlying energy landscape guides the transition; however, the sequence or relative timescales of events in the pathway is dependent on the magnitude of the potential as applied to a selection of atoms, with higher forces resulting in greater loss of temporal detail (Bryant et al. 2000). We used different force constants to study the forward and the reverse transition for activation in order to obtain the consistent characteristics. Our results describe conformational features for CD activation and certain aspects of interdependence among them, rather than the specific sequence with which they take place.
We find that the activation and deactivation transition of CD progresses nonuniformly. The opening of the two lobes occurs early in the activation transition and is unimpeded. An intrinsic flexibility in the lobelobe orientation has also been deduced from crystallographic analyses of Src kinase structures whereby the B-factors associated with the N-lobe were twice as high as those of the C-lobe (Breitenlechner et al. 2005). On the other hand, a helixcoil transition in the A-loop is slower and appears to be hindered by an energy barrier. The reverse deactivation transition is complicated by the interdependence of the outward rotation of
C and the folding of the A-loop over the active site.
Elucidation of the pathway at the detailed atomic level allowed only by computation is valuable for understanding the enzymatic activity of protein kinases without A-loop phosphorylation (Porter et al. 2000; Adams 2003) and inhibition by conformationally selective compounds such as imatinib (Capdeville et al. 2002) and gefitinib (Kwak et al. 2005). Intramolecular domaindomain interactions are thought to deactivate Src kinase by locking the lobe orientation or by stabilizing the inactive conformation of
C. It has been suggested that when the lobes open, Tyr416 becomes accessible for phosphorylation (Xu et al. 1999). The fast and facile opening of the lobes observed in this study of CD without the SH2/SH3 regulatory domains indicates that this suggestion is indeed reasonable. The ease of lobe reorientation and the electrostatic switch mechanism that functions in the transition in the absence of phosphorylation suggest that the active conformation is transiently populated by kinase absent of A-loop phosphorylation and bound inhibitor. Thus, we propose that the activity of Src unphosphorylated on the A-loop (Porter et al. 2000; Adams 2003) arises from the transient formation of CDact rather than another conformation of the kinase of lower catalytic power. Stabilization of CDact relative to CDdown likely requires phosphorylation of the A-loop tyrosine. A similar behavior was observed for NtrC in which phosphorylation shifts the equilibrium rather than inducing a new structure (Volkman et al. 2001). From the interdependence of the displacements in the A-loop and
C and the time dependence of the Glu310 exchange between Arg409 and Lys295 in BMD, we conclude that phosphorylation of Tyr416 would stabilize not only the A-loop but also
C conformations in CDact.
A major outcome of this investigation is the proposal that the transition is conformationally controlled by a switched electrostatic network involving the exchange between a three-way and a two-way network of interactions among Asp386, Tyr416, Arg409, Glu310, Lys295, and Asp404. The switch residues are highly conserved in tyrosine kinases, suggesting that this switched network may play an important role in other kinases as well. The ATP-binding Lys295, metal-binding Asp404, and catalytic Asp386 are absolutely conserved. Arg409 is absolutely conserved across the Src kinase family and functionally conserved across the kinase family. Helix
C Glu310 is highly conserved if not strictly conserved across all kinases. Our analysis suggests that the same residues essential for either structural stabilization (Yamaguchi and Hendrickson 1996; Schindler et al. 1999; Xu et al. 1999) or for catalysis (Kamps and Sefton 1986; Gibbs and Zoller 1991; Porter et al. 2000) also play important roles in the transition between the two end states.
The six residues of the network exchange from one group to another when the A-loop main chain extends out and refolds, and thus serve as anchor points to guide the conformational transition. Interactions in CDdown of Tyr416 and Arg409 on the A-loop connect to active-site residues and to
C, and link the A-loop conformational change to the reorientation of the N- and C-lobes and to the displacement of
C (Fig. 9). Further, the switch centered on Glu310 is likely to be energetically significant to the conformational change of the A-loop and
C. The Glu310Arg409 interaction impedes rotation of
C and the inward positioning of Glu310 for activation. This interaction seems particularly stable since it breaks late in the activation process where
C rotates in, and forms early in the reverse deactivation process (Fig. 8). Phosphorylation of Tyr416 would likely shift the equilibrium in favor of the Glu310Lys295 position of the switch in CDact by competing to form the Try416Arg409 interaction and thus release Glu310 to interact with Lys295. The electrostatic network, therefore, offers a mechanism for conformational activation, whereby phosphorylated Tyr416 on the A-loop could influence not only the change in the A-loop conformation but also the conformational transition throughout the catalytic domain. It is of interest to know how concerted the exchanges are for the four central residues, but the concertedness could not be determined from the current sampling in the biased simulations.
The switched electrostatic network mechanism proposed here concerns the conformational activation of protein kinases in contrast to earlier discussions of electrostatic switches for equilibrium states. Previous studies on Src kinases (Xu et al. 1999) recognized the switch in interactions between the two crystallographic structures of active and down-regulated kinases and their role in stabilization of two conformational states. The current study expands the roles proposed for these critical residues to include stabilization of the conformational transition. The term "electrostatic switch" has also been used to describe a change in the binding equilibrium of Src kinases (McLaughlin and Aderem 1995), whereby phosphorylation of the N terminus was shown to enhance membrane-binding affinity and reverse the relative binding affinity between membrane-bound or cytoplasmic states of Src kinase.
Given the high conservation in the switch residues in the kinase family, the exchange pathway between active and down-regulated forms could be generally conserved in kinases. Conservation of conformational transition pathways has been suggested from evolutionary relationships for other proteins (Süel et al. 2003; Zheng et al. 2005). Slight variations in kinase catalytic domain structure, such as the A-loop conformation or relative lobelobe orientations, may result in differences in the order of events.
The presence of a switched electrostatic network in conformational activation can be tested experimentally providing conditions are established where conformational activation is a component of the rate-limiting step (Adams 2003). Kinetic assays on Src (Barker et al. 1995) and the Src-family kinase Hck (Moarefi et al. 1997) show that enzymatic activity exhibits an enzyme concentration-dependent lag phase, which can be eliminated by preincubation with MgATP. As the lag phase is likely dependent on conformational activation, dependence of the lag phase on salt concentration can provide information about the effect of the electrostatic switch on the enzyme mechanism. Similar kinetic studies to those reported are currently under way in the laboratory of our collaborator.
| Materials and methods |
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Equilibrium simulations were calculated over 0.30.4 nsec with starting structures for unphosphorylated Lyn CDact and CDdown with or without ATP and Mg. Simulations were also calculated for CDact with the A-loop Tyr416 phosphorylated. To eliminate effects that could result from the force field, the unphosphorylated equilibrated structures were the initial and the target conformations used in biased molecular dynamics. The structures used were without A-loop tyrosine phosphorylation in order to have the same chemical structure for both starting and target conformations. The use of unphosphorylated end states provides the basis for deciphering the molecular details of the activation pathway without the chemistry step.
Molecular dynamics simulations were calculated with the CHARMM program (Brooks et al. 1983) using the CHARMM22 potential energy function (MacKerell et al. 1998) for the all atom model and TIP3P water parameters (Jorgensen 1981). Phosphotyrosine parameters were those of Feng et al. (1996). Periodic boundary conditions with the particle mesh Ewald method (Darden et al. 1993) were imposed on the system, and the nonbonded van der Waals interactions were truncated at 14 Å. A time step of 1 fsec was used with the leap-frog algorithm. SHAKE was used to constrain bonds to hydrogen atoms. A uniform dielectric constant of 1 was used throughout the study. The system was energy-minimized and subsequently equilibrated with the protein atoms constrained for the first 100 psec. All calculations were performed in the NPT ensemble at a constant pressure of 1 atm and constant temperature of 300 K with the Hoover method (Hoover 1985). Coordinate sets were saved every picosecond for analysis. Twenty picoseconds of BMD calculations required ~1 d of CPU time on two IBMSP processors (RS6000 375 MHz).
Biased molecular dynamics
The conformational transition pathway was studied by biased molecular dynamics (BMD) (Marchi and Ballone 1999; Paci and Karplus 1999). Application of a biasing potential promoted a conformational transition between the given starting structure and the target structure, and the crossing of the conformational space separated by energy barriers that cannot be overcome in regular MD. The external potential depends on the difference in the internal distances in the simulation and target structures and favors the decrease in its value. The reaction coordinate, R(t), is defined as
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where rij(t) is the pairwise distance between atom i and j coordinates at time step t, and rTij is the pairwise distance between coordinates of the target conformation. N gives the number of pairs included in the biased set of n atoms. With the use of this reaction coordinate instead of the RMSD to target, removal of the rotation and translation of the center of mass at each step is avoided. A time-dependent perturbation is added to the energy function
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where the biasing parameter, Ru(t), is updated at each step to the minimum value of R(t) attained until time t. The initial value of Ru(t) is obtained using the initial and target coordinates. The force constant, A, governs the rate with which the conformational transition takes place. The force constant, A, for the whole system was chosen such that the pairwise force constant,
, was 0.0004, 0.0009, 0.0013, or 0.0022 kcal/(mol Å4). The perturbation is added to the system only when it moves away from the target. Ru(t) is updated only when V(t) is zero, making the pathway adiabatic.
The reaction coordinate to calculate the conformational transition pathway between CDdown and CDact included all Lyn catalytic domain heavy atoms between residues Lys252 and Thr523 or ~2.5 x 106 atom pairs. Initial and target coordinates were from the equilibrated systems for CD with ATP and Mg2+. The biased MD simulations were calculated for 1.5 nsec or until the overall RMSD of heavy atoms to target structure reached a limiting value.
Trajectory analysis
The RMSD of the trajectory time points or snapshots from the target structure was used to measure completeness of the calculated pathway. The overall RMSD for all heavy atoms was calculated after superimposing the snapshots on the target structure based on all heavy atoms. For calculations of local RMSD, the superposition was based on the heavy atoms of the C-lobe. The dihedral angle time profiles were used to follow the A-loop secondary structure. The helicity was calculated for residues 413422 of the A-loop by enumerating the backbone angles within the helical region of conformational space. (A residue is helical when its backbone dihedral angle is within ±30° of the ideal helix values
= 57°,
= 47° [Daggett and Levitt 1992].)
Formation and disruption of contacts along the calculated pathways were assessed from time profiles of the interatomic distances and interaction energies between two residues. The contact distance between two residues is the distance between the polar atoms of least separation. The interaction energy between two residues is equal to the nonbonded terms (electrostatic + van der Waals) for all interresidue atom pairs.
| Footnotes |
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Article published online ahead of print. Article and publication date are at http://www.proteinscience.org/cgi/doi/10.1110/ps.051999206.
Abbreviations: CD, catalytic domain; SH2, Src homology domain 2; SH3, Src homology domain 3; CDact, Lyn catalytic domain active conformation; CDdown, Lyn catalytic domain down-regulated conformation; N-lobe, N-terminal lobe; C-lobe, C-terminal lobe; MD, molecular dynamics; BMD, biased molecular dynamics; A-loop, activation loop;
C,
-helix C; RMSD, root mean squared deviation;
, pairwise force constant.
| Acknowledgments |
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