Specific amino acid recognition by aspartyl-tRNA synthetase studied by free energy simulations

J. Mol. Biol. (1998) 275, 823±846

Specific Amino Acid Recognition by Aspartyl-tRNA Synthetase Studied by Free Energy Simulations Georgios Archontis1, Thomas Simonson2*, Dino Moras2 and Martin Karplus1,3* 1

Laboratoire de Chimie Biophysique, Institut Le Bel 4 rue Blaise Pascal, Universite Louis Pasteur 67000, Strasbourg, France 2

Institute de GeÂneÂtique et Biologie MoleÂculaire et Cellulaire (UPR 9004 C.N.R.S.), 1 rue Laurent Fries 67404, Illkirch (C.U. de Strasbourg), France

3 Department of Chemistry Harvard University 12 Oxford St, Cambridge MA 02138, USA

Speci®c amino acid binding by aminoacyl-tRNA synthetases is necessary for correct translation of the genetic code. To obtain insight into the origin of the speci®city, the binding to aspartyl-tRNA synthetase (AspRS) of the negatively charged substrate aspartic acid and the neutral analogue asparagine was compared by use of molecular dynamics and free energy simulations. Simulations of the Asn ±AspRS complex showed that although Asn cannot bind in the same position as Asp, several possible Ê away from the Asp site. The binding free positions exist 1.5 to 2 A energy of Asn in three of these positions was compared to that of Asp through alchemical free energy simulations, in which Asp is gradually mutated into Asn in the complex with the enzyme. To correctly account for the electrostatic interactions in the system (including bulk solvent), a recently developed hybrid approach was used, in which the region of the mutation site is treated microscopically, whereas distant protein and solvent are treated by continuum electrostatics. Seven free energy simulations were performed in the protein and two in solution. The various Asn positions and orientations sampled at the Asn endpoints of the protein simulations yielded very similar free energy differences. The calculated Asp ! Asn free energy change is 79.8(1.5) kcal/mol in solution and 95.1(2.8) kcal/mol in the complex with the protein. Thus, the substrate Asp is predicted to bind much more strongly than Asn, with a binding free energy difference of 15.3 kcal/mol. This implies that erroneous binding of Asn by AspRS is highly improbable, and cannot account for any errors in the translation of the genetic code. Almost all of the protein contributions to the Asp versus Asn binding free energy difference arise from an arginine and a lysine residue that hydrogen bond to the substrate carboxylate group and an Asp and a Glu that hydrogen bond to these; all four amino acid residues are completely conserved in AspRSs. The protein effectively ``solvates'' the Asp side-chain more strongly than water does. The simulations were analyzed to determine the interactions that Asn is able to make in the binding pocket, and which sequence differences between AspRS and the highly homologous AsnRS are important for modifying the amino acid speci®city. A double or triple mutation of AspRS that could make it speci®c for Asn was proposed, and supported by preliminary simulations of a mutant complex. # 1997 Academic Press Limited

*Corresponding authors

Keywords: molecular recognition; genetic code; molecular dynamics; protein electrostatics

Introduction Present address: G. Archontis, Department of Natural Sciences, University of Cyprus, PO 537, CY 1678, Nicosia, Cyprus. Abbreviations used: aaRS, aminoacyl-tRNA synthetase; AspRS etc., aspartyl-tRNA synthetase etc. 0022±2836/98/050823±24 $25.00/0/mb971470

This study addresses the mechanism of the speci®c recognition of aspartic acid by aspartyltRNA synthetase. Aminoacyl-tRNA synthetases (aaRSs) catalyze the ®rst step in the translation of the genetic code, by attaching a speci®c amino acid # 1998 Academic Press Limited

824 to a cognate tRNA molecule (Meinnel et al., 1995; Cusack, 1995; Arnez & Moras, 1997). Through their amino acid recognition pocket and their large, speci®c, tRNA-binding interface, the synthetases provide the link between the amino acid identity and the identity of the anticodon of the tRNA, which ultimately interacts with a codon of a messenger RNA. The tRNA acylation takes place in two steps: ®rst the backbone carboxylate group of the amino acid reacts with ATP to form an aminoacyl adenylate, with release of pyrophosphate; then the amino acid moiety is transferred to tRNA, with release of AMP. For most aaRSs, the ®rst step can take place in the absence of tRNA (Cavarelli & Moras, 1995). Correct translation of the code requires speci®city in both steps (Fersht et al., 1985; Fersht, 1988). Because the amino acid side-chain is selected for in both steps, its speci®c interactions are ``read'' twice, which allows small differences between similar amino acids to be ampli®ed (but also can introduce error in both steps). Where this is not suf®cient, a proof-reading activity of the synthetase has evolved, so that a mischarged tRNA is deacylated by the enzyme before being released (Eldred & Schimmel, 1972; Freist et al., 1985; Fersht, 1985). Even so, while error rates for tRNA recognition are of the order of 10ÿ7, error rates for amino acid selection can be 1000 times higher. This limits the ®delity of tRNA charging and of the overall translation of the genetic code. It is thus important to understand the detailed mechanisms of amino acid selectivity. This understanding could aid in the design of antibacterial inhibitors, with possible therapeutic relevance. The present study focuses on speci®city in aspartyl-tRNA synthetase, a ``class II'' synthetase. The 20 aaRSs are known to form two structural classes of ten members each (Eriani et al., 1990). Members of each class share an overall fold, active-site topology, and ATP and tRNA recognition modes (Brick et al., 1989; Brunie et al., 1990; Cusack et al., 1990; Rould et al., 1989; Ruff et al., 1991). For example, class II aaRSs all bind ATP in the same bent conformation, which has not been observed in any other ATP or GTP-binding protein so far; the class I synthetases bind ATP in a more extended conformation. Highly conserved sequence motifs have been identi®ed in each class, associated with important ATP or tRNA-binding residues (Eriani et al., 1990). Class II aaRSs also have sequence and structural homology to several other ATP-binding proteins (Artymiuk et al., 1994), such as biotin synthetase (Eisenberg, 1973), which adenylates a carboxylate group on biotin. These proteins may descend from a common ancestor that adenylated small cofactors non-speci®cally (Artymiuk et al., 1994). Within each aaRS class, the mechanism of amino acid recognition is more diverse than that of ATP. While each aaRS must recognize and correctly position the amino acid substrate backbone carboxylate group to react with ATP, it must also select a speci®c substrate side-chain. Subclasses of higher

Aspartyl-tRNA Synthetase Speci®city

sequence homology exist, which tend to re¯ect chemical similarities between the cognate amino acid substrates. For example, the class II aspartyltRNA synthetase forms a subclass with the lysyl and asparaginyl enzymes, which recognize a charged and a highly polar side-chain. It has been pointed out that aspartic acid is a biosynthetic precursor of both lysine and asparagine, and single base changes convert the aspartic acid codon into the asparagine codon, and the asparagine codon into the lysine codon, so that one might speculate that AspRS preceded LysRS and AsnRS in evolution (Gatti & Tzagoloff, 1991). The active-site domain of AspRS has signi®cant sequence homology to asparagine synthetase (Gatti & Tzagoloff, 1991), which also binds ATP and adenylates aspartic acid. In the archaebacterium Haloferax volcanii, Asn-tRNA is exclusively produced by transamidation of Asp-tRNA, and no speci®c AsnRS exists (Curnow et al., 1996). To be successful, the translation machinery must be both speci®c and robust with respect to small variations of its components. For example, random point mutations in an aaRS active site should not easily modify the speci®city of the enzyme and lead to mistranslation of the code. Indeed, the class II amino acid recognition pocket is organized in a tight network of hydrogen bonds (Ruff et al., 1991; Poterszman et al., 1994), which is very intolerant of point mutations (Cavarelli et al., 1994), and thus effectively functions as an error correction system (i.e. in response to single mutations in the pocket, the protein becomes inactive, which is harmless to the cell, rather than mistranslating the code, which could be lethal). This has hampered attempts to engineer modi®ed speci®cities into aaRSs. Whereas the identity of several tRNAs has been modi®ed successfully by mutagenesis (Normanly & Abelson, 1989), aaRSs with arti®cially modi®ed speci®city have never been reported. For tyrosyltRNA synthetase, extensive mutation experiments have been done to determine the contributions of various residues to the binding and catalysis (Fersht et al., 1985; Fersht, 1988). Increased Tyr speci®city was obtained (de Prat Gay et al., 1993); however, no attempt was made to modify the speci®city, i.e. to produce binding of a different amino acid, such as Phe. Preliminary attempts to engineer Asn binding into AspRS by mutagenesis did not succeed (G. Eriani, personal communication). Although the active site sequences of AspRS and AsnRS are very similar (Figure 1), native AspRS does not adenylate Asn detectably, and single-site mutations in the binding pocket of AspRS have not led to any activity for Asn. Here, we analyze the amino acid selectivity of aspartyl-tRNA synthetase using computer simulations. We focus on the discrimination of AspRS against Asn. There are many microscopic factors that may contribute to the amino acid selectivity, including structural rearrangements of the protein in response to binding, long-range electrostatic interactions between protein and ligands, and the

Aspartyl-tRNA Synthetase Speci®city

825

Figure 1. Sequence alignment of aspartyl, asparaginyl and lysyl-tRNA synthetases. Sequences are from yeast (Yst), T. thermophilus (Tht), and E. coli (Eco). Residues highly conserved throughout class II aaRSs are colored brown: residues conserved in AspRSs are colored yellow. Residues interacting directly with the ligand in our simulations are boxed. Among these interacting residues, the most prominent differences between AspRS and AsnRS are highlighted in green. Residues discussed in the text are explicitly numbered (E. coli numbering). Secondary structure elements, ATP and magnesium-binding residues, and the conserved sequence motifs 2 and 3, are indicated. Motifs 2 and 3 form part of the active site and are involved in ATP binding.

need to desolvate the ligands upon binding. For example in the cognate aspartyl-adenylate ±AspRS complex, the ligand side-chain is recognized by two hydrogen bonds between its carboxylate oxygen atoms and a conserved arginine residue (Arg489 in E. coli; Poterszman et al., 1994); an arginine residue is present also at the equivalent position in AsnRS (Figure 1). Since the Asn sidechain amide group cannot make the same hydrogen bonds, its binding to AspRS would require structural rearrangements of the protein or displacement of the ligand in the active site. Thus the aspartyl enzyme may bind Asn in an unreactive geometry, and some or all of the overall selectivity could arise from a ``conformational screening'' by the enzyme, rather than unfavorable Asn binding free energy. Long-range electrostatic interactions and desolvation of the ligands may also play an important role in selectivity, since it is considerably more costly in free energy terms to desolvate aspartic acid than asparagine, due to the Asp side-chain carboxylate group. The protein must provide strong compensating interactions with the Asp side-chain, primarily of an electrostatic nature, which are intrinsically longrange and can therefore involve distant protein groups. The 320 residue AspRS active-site domain alone contains 80 charged residues. Previous computational studies have shown that the overall free energy of charged moities in proteins can arise from a sum of much larger, partially compensating interactions with many protein groups (Gao et al., 1989; Kuczera et al., 1990), and from large, mutually compensating interactions with protein and solvent (Lau & Karplus, 1994; Simonson & Perahia, 1995).

To analyze these competing factors and obtain a better understanding of the AspRS speci®city, we performed molecular dynamics simulations of aspartic acid and asparagine, both in solution and complexed with AspRS. Further, an ``alchemical'' transformation of Asp into Asn was used to calculate the binding free energy difference between the two ligands (Tembe & McCammon, 1984; Wong & McCammon, 1986; Bash et al., 1987). The ligand was reversibly transformed from aspartic acid into asparagine by a series of simulations, both bound to the enzyme and free in solution. While the free energy for this unphysical, alchemical process cannot be compared to experiment, the experimentally relevant binding free energy difference is obtained by subtracting the results in solution and in the protein complex (Tembe & McCammon, 1984). The calculations allow a detailed decomposition of the energetics of the system in terms of its structural components and their interactions (Gao et al., 1989), something that is not readily available experimentally. This component analysis of free energies has been criticized (Mark & van Gunsteren, 1994) because it depends on the choice of transformation pathway (Simonson & BruÈnger, 1992). However, it has been shown that the ``alchemical'' transformation pathway used here is speci®cally adapted to provide insight into the free energy contributions most important for binding (Lau & Karplus, 1994; Boresch et al., 1994). The component analysis is the theoretical analogue of protein engineering experiments that determine the contributions of different amino acids to binding by deleting their side-chains (X ! Ala, for example, see Fersht et al., 1985; Fersht, 1988); the effects of charged amino acids on binding have

826 been analyzed in this way in the barnase ± barstar complex recently (Frisch et al., 1997). The present analysis suggests mutations for engineering of asparagine speci®city into AspRS. Moreover, insights are obtained that increase our understanding of molecular recognition in other proteins that speci®cally bind carboxylate groups. Free energy simulations have been used to study several other aspects of protein electrostatics, including enzyme transition state stability (Rao et al., 1987; Warshel et al., 1988), electron transfer (Warshel et al., 1989) and titration of ionizable groups (Warshel et al., 1986; PreÂvost, 1996). However, very few have directly addressed molecular recognition of charged ligands (Cummins et al., 1991). The effect of ligand ± protein salt bridges on binding has been probed by charge pair reversal or deletion, i.e. by alchemically modifying a charged group on the ligand and the protein at the same time (Singh, 1988; Hwang & Warshel, 1988), and the absolute binding free energies of two positively charged benzamidine inhibitors to trypsin were calculated recently (Aqvist, 1996). The effect of an Asp ! Asn mutation on La3‡ binding by a tridecapeptide was studied (Prod'hom & Karplus, 1993), and the effect of mutations of charged residues in hemoglobin on oxygen binding and sickle ®ber formation has also been examined (Gao et al., 1989; Kuczera et al., 1990). Other studies have focussed on polar but uncharged ligands (Lau & Karplus, 1994; Wong & McCammon, 1986; Bash et al., 1987). An important point in simulations of mutations that change the charge of the system, as in comparing the binding of Asp and Asn, is that long-range electrostatic interactions must be included in the calculations to obtain accurate results. To do this we rely on a hybrid approach developed recently, which combines a microscopic treatment of the AspRS active-site region with a macroscopic continuum treatment of distant parts of the protein and bulk solvent. In a ®rst step, the mutation is introduced with a ®nite model including part of the protein and a large but ®nite number of explicit water molecules; in subsequent steps, the ®nite model is transferred into bulk solvent and the corresponding free energy change is obtained from continuum electrostatics. This approach has been presented in detail elsewhere (Simonson et al., 1997). A dif®culty in free energy simulations that compare two ligands is the possibility that the two may bind to the protein at different sites. The structures of the Asp ± AspRS and Asn ±AspRS complexes are not known; neither Asp nor Asn diffused into AspRS crystals lead to a detectable Xray diffraction signal, either because binding is too weak or because the ligand is disordered in the binding pocket. The Asp-binding position could very well differ from that seen in the crystal structures of AspRS complexed with Asp-adenylate (Poterszman et al., 1994) or tRNA (Ruff et al., 1991; Cavarelli et al., 1993; Eiler, 1997; Briand, 1997). However, a recent preliminary structure of the Ê from the archaebacAsp ±AspRS complex at 2.3 A

Aspartyl-tRNA Synthetase Speci®city

terium Pyrococcus sp. KOD1 (E. Schmitt, personal communication) suggests that the Asp position is essentially the same as in the adenylate complex, in agreement with the simulations. The present simulations predict that Asn binds to AspRS in a signi®cantly different position from Asp. Alchemical free energy simulations proceed by changing one ligand into the other in a series of simulations; if the ®nal binding position is signi®cantly different from the starting one, as here, the simulations will not necessarily converge to the correct position within a tractable simulation length. This can give rise to sampling dif®culties. Here extensive preliminary simulations were performed to identify stable Asn binding positions. One of these positions was then used as a target in a series of free energy simulations, in which the Asn was explicitly based towards the target position. The sensitivity of the results to the choice of this position was tested by performing two free energy simulations without any biasing restraints, which converged to two different binding positions Ê away), but gave a free (backbone atoms ca 1.5 A energy difference in very good agreement with the other simulations. The Asp ± AspRS and Asn ±AspRS binding constants have not been measured experimentally. Asn binding is likely to be weaker and less speci®c than that of Asp, and in fact the bound Asn ± AspRS state assumed in this work may not be signi®cantly populated experimentally. Nevertheless, by modelling such a putative bound state we expect to learn what Asn binding positions are most probable, and what interactions are important for selecting Asp over Asn. The following section decribes computational details. The third section presents the results. Simulations of the Asp ± protein and Asn ± protein complexes are described and compared. Alchemical free energy simulations are described for the Asp ! Asn mutation in the protein± ligand complex and in solution. The calculations show that the mutation in solution requires 80 kcal/mol of free energy, mainly due to the loss of electrostatic interactions of the side-chain carboxylate group with water. This result is in accord with estimates of the solvation free energy of the ionized form of acetic acid (Gilson & Honig, 1988). The mutation in the protein requires 95 kcal/mol, so that the protein± Asp interactions more than compensate for the carboxylate desolvation. In effect, the protein ``solvates'' the Asp side-chain, relative to the neutral Asn side-chain, more strongly than water does. In the ®nal section, the energy and free energy contributions of key recognition residues are considered for this mutation pathway, and mutations that may increase Asn binding af®nity are suggested.

Computational Details The computational model used in this study has been described (Simonson et al., 1997). In particu-

Aspartyl-tRNA Synthetase Speci®city

lar, a detailed method was developed to include the effect of bulk solvent in the calculation of electrostatic free energy changes, such as the free energy change for the Asp ! Asn mutation considered here. An important element of the method is that it provides a way of doing simulations on a ®nite system and correcting the results for the effect of bulk solvent. For completeness, we outline the main features of the computations. Description of the microscopic model The protein ± ligand model consists of the active site region of one dimer of the Escherichia coli aspartyl-tRNA synthetase enzyme, one ligand molecule (Asp or Asn) bound in the active site, and several hundred explicit water molecules solvating the active site. Initial protein heavy-atom positions were taken from the crystal structure of the enzyÊ resolution me ±aspartyl-tRNA complex at 3.5 A (Eiler, 1997). Although the resolution of this structure is moderate, the active site is well de®ned and in good agreement with several other structures from different sources. The initial position of the Ê aspartic acid ligand was inferred from the 2.8 A crystal structure of the homologous Thermus thermophilus enzyme complexed with an aspartyladenylate ligand (Poterszman et al., 1994), by superimposing conserved backbone segments in the active sites from the two structures. The environment of the adenylate in the T. thermophilus structure is very similar to that observed in a Ê structure from the archaebacterium recent 1.8 A Pyrococcus sp. KOD1 (E. Schmitt, personal communication). Based on these structures, only a single Asp position is likely to be signi®cantly populated, in agreement with the simulations. The protonation state of the histidine residues was inferred from inspection of hydrogen bonding in the crystal structure. Only His449 interacts directly with the ligand in the model, hydrogen bonding to its side-chain carboxylate group. This histidine residue is only weakly ordered in the crystal structure, which has the adenylate analogue AMP-PCP bound in the active site; it is not conserved in yeast or archaebacteria, and in T. thermophilus it does not hydrogen bond to the ligand. Based on these observations and on the net positive charge present in the active site, His449 was modelled here in its neutral state. An approximately spherical region of Ê radius was selected, centered on the side20 A chain of the ligand. A sphere of water molecules was overlaid on the active site, and molecules that Ê overlapped protein atoms, or were outside a 20 A sphere, were eliminated. No crystal water molecule was included, due to the only moderate resolution of the crystal structure (Eiler, 1997). Following standard procedure (Brooks & Karplus, 1989), several additional water overlays were done during the course of equilibration of the system with molecular dynamics, giving a ®nal total of 384 water molecules, mostly located in or near the deep active-site pocket. The additional water overlays

827 are necessary because there is some electrostriction of the water molecules in the neighborhood of charged side-chains of the protein. Although the water density in the pocket is not known experimentally, this solvation procedure led to reasonable water structure and mobility in the simulations. The model contains 5140 atoms in all; it is shown in Figure 2. Stable positions of the Asn ligand were constructed in two stages. In the ®rst stage, the Asn was superimposed on the Asp ligand; the energy was minimized with harmonic restraints on the protein atoms; then 5 ps of molecular dynamics were done with the same harmonic restraints. The ®nal ligand position served as input for the second stage. In this stage, the ligand position was weakly restrained, and a series of possible side-chain positions were built by systematically varying the w1 and w2 dihedrals with a 60 step. For each sidechain position, energy minimization was performed. The resulting structures were found to cluster around four possible low-energy positions. Molecular dynamics simulations were initiated from each of these four positions. Each simulation involved 25 ps of heating and equilibration with the ligand, and initially also the protein, harmonically restrained; this was followed by 25 to 75 ps

Figure 2. Schematic view (Ca trace) of the aspartyltRNA synthetase dimer. The upper part of the dimer is left out. A roughly spherical protein region (green residues) and 384 explicit water molecules (ball-and-stick models) were treated by molecular dynamics; protein atoms outside the spherical region were kept ®xed. The ligand is shown in CPK representation, near the center of the spherical region. The ¯exible loop 168± 173, on the upper left of the active site cleft, is colored blue, and residue 168 is labelled. Most of the water molecules are located in and around the deep active-site cleft; however, some form a thin layer spread over the protein surface.

828 of free dynamics, which completed the second stage. The resulting structures represent different possible Asn binding modes, which are described below. After this construction, the Asn ±protein complex that deviated least from its starting conformation was subjected to an additional 200 ps of free dynamics. In addition to the protein ±ligand complexes, the ligands were studied in solution. The solution model consisted of a single Asn or Asp molecule (with the backbone in zwitterion form, as in the Ê droplet of protein complex above) in a 20 A water. To avoid drift of the ligand, its Ca was weakly restrained to remain at the center of the droplet.

Force-field and molecular dynamics simulations Atomic charges, van der Waals, and stereochemical force-®eld parameters for protein and ligand were taken from the CHARMM22 all-atom force ®eld (A. MacKerral, et al., unpublished). Water interactions were described by a modi®ed TIP3P model (Jorgensen et al., 1983; Neria et al., 1996). Electrostatic interactions were treated without any form of truncation by using a multipole approximation Ê apart (Brooks et al., for groups more than 12 A 1983; Stote et al., 1991). The van der Waals interactions were truncated at an interatom separation Ê . Water molecules were con®ned to a of 13 A Ê radius by the stochastic spherical region of 20 A boundary method (Brooks et al., 1985; Brooks & Ê from Karplus, 1989). Protein atoms more than 15 A the center were harmonically restrained to their initial positions. Protein and water heavy-atoms Ê from the center of the located more than 15 A simulation sphere were treated by Langevin dynamics and experienced frictional and random forces that mimic a thermal bath at 293 K (Brooks & Karplus, 1984). Bond lengths to hydrogen atoms, and the internal geometry of the water molecules, were constrained with the SHAKE algorithm (Ryckaert et al., 1977). Equations of motion were integrated with the Verlet algorithm modi®ed for Langevin dynamics with a 1 fs time-step, using the CHARMM program (Brooks et al., 1983).

Free energy calculations The free energy calculations model the alchemical transformation of the native Asp substrate into an Asn molecule, either in the protein ±ligand complex or in solution. A single ligand molecule is introduced, but with two side-chains, one of each type. The mutation consists of ``growing in'' one side-chain, while ``growing out'' the other. The system is divided into three ``blocks'' (Tidor & Karplus, 1991): the Asp side-chain atoms (block 2), the Asn side-chain atoms (block 3), and the rest of

Aspartyl-tRNA Synthetase Speci®city

the system (block 1). The potential energy function has the form: nb vdw vdw nb elec U…l† ˆ Ub ‡ U11 ‡ U22 ‡ U33 ‡ l…U12 ‡ U22 † nb elec ‡ U33 † ‡ Ures …l† ‡ …1 ÿ l†…U13

…1†

where Ub represents all the bounded interactions in the system, including those involving the ligand; Unb 11 represents the non-bonded interactions within and Uelec represent the van der block 1; Uvdw ii ii Waals and electrostatic interactions within block i (ˆ2 or 3); and Unb 1i represents the non-bonded interactions between blocks 1 and i. Ures(l) is a restraint term used in most of the protein± ligand simulations. It gradually forces the ligand to move from the initial Asp-binding position into a stable Asnbinding site identi®ed in separate simulations of the Asn± protein complex (described above). These preliminary simulations indicated that Asn binds in a signi®cantly different position from Asp (1.5 Ê away). Five free energy runs were perto 2 A formed, where for each value of l (each simulation window) the ligand was explicitly biased towards a speci®c position in the binding pocket. At the Asn endpoint, the target position was that occupied during the Asn ±protein simulation. Speci®cally, runs 1, 2 and 5 used the structure attained after 60 ps of simulation, while runs 3 and 4 used the structure attained after 100 ps. These two Asn positions have an rms deviation from each other of Ê . For intermediate windows, target posonly 0.4 A itions were constructed by linear interpolation between the starting Asp position and the ®nal Asn position. The ligand was restrained to the target position by harmonic restraints applied to its heavy backbone atoms, and in some cases also its side-chain atoms. The force constant was 3 to Ê 2 depending on the run, which 5 kcal/mol per A allowed suf®cient overlap between the conformations sampled with successive values of l. Three of the runs were done in the Asp ! Asn direction and two in the Asn ! Asp direction. Two additional runs were performed without any restraints for the ligand. Starting from the Asp endpoint, the ligand position was allowed to adjust spontaneously as the Asn side-chain moiety was grown in, leading to slightly different ®nal binding positions, described below. Simulations were run with l ˆ 0.02, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.98, including 10 ps of equilibration and 30 ps of data collection for each l. The free energy derivative is given by (Kirkwood, 1935; McQuarrie, 1975):   @G @U …2† ˆ @l @l l where the brackets represent ensemble averages obtained from the simulation performed with the hybrid potential U(l). The results were then

829

Aspartyl-tRNA Synthetase Speci®city

corrected to remove the contribution of the restraints (when used) to the free energy derivative, using the relation (Valleau & Torrie, 1977):     @U @U Ures =kT ˆ =heUres =kT il …3† e @l lf @l l where the subscript f indicates a free, or unrestrained, system. In what follows, only the corrected (``free'') derivatives are reported and the subscript f is dropped for simplicity. The free energy change is obtained by numerical integration of the derivative values, as described in detail elsewhere (Simonson et al., 1997).

Free energy component analysis The contribution of an individual atom i (that is not part of the hybrid ligand side-chain) to the free energy derivative can be calculated by writing the energy function as: X X U…l† ˆ Ui0 …l† ‡ Uij ‡ Ulig …l† …4† i

i