Insights into Protein Protein Binding by Binding Free Energy Calculation and Free Energy Decomposition for the Ras Raf and Ras RalGDS Complexes

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1 doi: /s (03) J. Mol. Biol. (2003) 330, Insights into Protein Protein Binding by Binding Free Energy Calculation and Free Energy Decomposition for the Ras Raf and Ras RalGDS Complexes Holger Gohlke 1, Christina Kiel 2 and David A. Case 1 * 1 Department of Molecular Biology, The Scripps Research Institute, North Torrey Pines Road, La Jolla, CA USA 2 Abteilung Strukturelle Biologie, Max-Planck-Institut für Molekulare Physiologie Otto-Hahn-Straße 11, Dortmund, Germany *Corresponding author Absolute binding free energy calculations and free energy decompositions are presented for the protein protein complexes H-Ras/C-Raf1 and H-Ras/RalGDS. Ras is a central switch in the regulation of cell proliferation and differentiation. In our study, we investigate the capability of the molecular mechanics (MM)-generalized Born surface area (GBSA) approach to estimate absolute binding free energies for the protein protein complexes. Averaging gas-phase energies, solvation free energies, and entropic contributions over snapshots extracted from trajectories of the unbound proteins and the complexes, calculated binding free energies (Ras Raf: 215.0(^6.3) kcal mol 21 ; Ras RalGDS: 219.5(^5.9) kcal mol 21 ) are in fair agreement with experimentally determined values (29.6 kcal mol 21 ; 28.4 kcal mol 21 ), if appropriate ionic strength is taken into account. Structural determinants of the binding affinity of Ras Raf and Ras RalGDS are identified by means of free energy decomposition. For the first time, computationally inexpensive generalized Born (GB) calculations are applied in this context to partition solvation free energies along with gas-phase energies between residues of both binding partners. For selected residues, in addition, entropic contributions are estimated by classical statistical mechanics. Comparison of the decomposition results with experimentally determined binding free energy differences for alanine mutants of interface residues yielded correlations with r 2 ¼ 0:55 and 0.46 for Ras Raf and Ras RalGDS, respectively. Extension of the decomposition reveals residues as far apart as 25 Å from the binding epitope that can contribute significantly to binding free energy. These hotspots are found to show large atomic fluctuations in the unbound proteins, indicating that they reside in structurally less stable regions. Furthermore, hotspot residues experience a significantly largerthan-average decrease in local fluctuations upon complex formation. Finally, by calculating a pair-wise decomposition of interactions, interaction pathways originating in the binding epitope of Raf are found that protrude through the protein structure towards the loop L1. This explains the finding of a conformational change in this region upon complex formation with Ras, and it may trigger a larger structural change in Raf, which is considered to be necessary for activation of the effector by Ras. q 2003 Elsevier Ltd. All rights reserved Keywords: absolute binding free energy; free energy decomposition; protein protein interactions; generalized Born model; Ras Abbreviations used: MD, molecular dynamics; MM, molecular mechanics; GB, generalized Born; PB, Poisson Boltzmann; SA, surface area; rmsd, root-meansquare deviation; RBD, Ras-binding domain; PME, particle mesh Ewald. address of the corresponding author: case@scripps.edu Introduction The capability of proteins to form stable complexes is of fundamental importance for a wide range of biological processes, including hormone receptor interactions, proteinase inhibition, antibody antigen interactions, signal transduction and enzyme allostery. 1 Perturbation of protein protein /$ - see front matter q 2003 Elsevier Ltd. All rights reserved

2 892 Insights into Protein Protein Binding interactions can result in diseases such as sicklecell anaemia 2 or the formation of tumors. 3 Therefore, a promising way to interfere with biological processes is the control of protein protein interactions by means of small molecules that modulate the formation of protein protein complexes. Recent results demonstrate the feasibility of this approach in principle However, our limited understanding of the energetics and dynamics of the mutual binding of two proteins presents a severe limitation for the rational design of small, non-peptide inhibitors to modulate protein protein interactions. Investigations of crystallographically determined protein protein complexes, thermodynamic experiments and mutational studies have contributed most to the current understanding of protein protein interactions. 1,12 14 Of particular interest are properties of binding interfaces of hetero-complexes, which are often made and broken according to the environment or external factors, and involve proteins that must exist independently. 12 Results from heat capacity measurements suggest that hydrophobic interactions are less dominant in protein protein association 15 than in protein folding, 16 which points to an increased influence of (long-range) electrostatic interactions across the binding interface. Mutational studies, mostly alanine scanning mutagenesis, on protein protein interfaces have revealed that a small number of amino acid residues in contact across the interface often yield a significant contribution to the free energy of binding. 1,17 20 These occurrences of hotspots 10,21 thus lead to a distinction between the structural epitope (i.e. the interface between proteins as defined by geometrical considerations) and the functional epitope. 22 Computational and theoretical methods provide a molecular view of the structural and energetic consequences of mutations, and can address the origin of binding in terms of contributions from electrostatic and van der Waals interactions and changes in solvation. 23 Furthermore, rigorous computational approaches may be used as a means of guiding new experimental investigations. 24 Recently, it has been recognized that mutations may perturb the complex (as generally assumed), as well as the unbound states. 25 In the latter case, without additional structural information, interpreting energetic consequences of the mutations in terms of changes in binding interactions will thus be misleading. In contrast, virtual mutagenesis employing thermodynamic cycles 26 can (in principle) provide a full description of structural and energetic influences due to mutations on the bound and unbound ensembles. The systems we examine are the complexes between human H-Ras (Ras) and the Ras-binding domain of C-Raf1 (Raf) as well as between Ras and the Ras-interacting domain of RalGDS (RalGDS). Ras is a GTP-hydrolyzing protein (GTPase, 21 kda) that acts as central switch in the regulation of cell proliferation and differentiation. 27 The active and inactive states of Ras are coupled to the binding of GTP or GDP to the protein, respectively. 3 Exchange of the guanine nucleotide induces conformational transitions mainly in two regions that have been called switch I (residues 30 37) and switch II (residues 60 76). Switch I overlaps with what has been called the effector region (residues 32 40), which is involved in interactions with the effectors. 28 After activation by upstream signals of the signal transduction cascade, Ras itself activates a cascade of protein kinases, 29 the first of which is the downstream effector Raf. 30 The identification of other interaction partners (such as RalGDS 31 or phosphatidyl-inositol-3 0 -kinase 32 ) has led to the conclusion that activated Ras simultaneously induces more than one signaling pathway. 3,33 The fact that permanently activated Ras is one of the most frequent oncogenes, it is found in 30% of all human tumors, 34 underlines the importance of understanding its interactions with downstream effectors Molecular structures for the unbound proteins as well as for Ras RalGDS 39,40 or complexes closely related to Ras Raf 41,42 have been determined either by X-ray crystallography or by NMR spectroscopy. They show that the Ras-effector interactions involve mainly an inter-protein b-sheet, resulting in interface sizes of Å. 2,3,39 With respect to both effectors, the interaction sites on Ras mutually overlap to a large extent, but RalGDS is rotated by <358 when viewed from the direction of the Ras moiety compared to Raf, resulting in a shift of interaction contacts towards the switch I and switch II region of Ras. 39 For the Ras RalGDS case, comparison of the components of the complex structure with the unbound molecules indicates small (,0.5 Å rmsd of C a atoms) or moderate (1.5 Å rmsd of C a atoms) changes of the protein structures upon binding. It was also found in the complex with Raf, that one of two nearly equally populated states ( state 2 ) of free, GTPbound Ras with different conformations of the loop L2 region (in particular Y32) is stabilized. 43,44 Although Raf is the best characterized Ras effector from mammalian cells in terms of biological relevance as well as structural detail, 45 it has not been possible to co-crystallize full-length Raf with Ras or Ras-related proteins but only the independently folding domain from the conserved region 1 known as the Ras-binding domain (RBD), which has been investigated in this study. Although binding of the effector region of Ras to the RBD is the major site of GTP-dependent binding, there is clear evidence that contacts between Ras and Raf outside the RBD contribute to binding and kinase activation. 46 Along these lines, the precise molecular mechanism for Raf activation is not fully understood. The question of whether a recruitment of Raf by Ras is sufficient for activation with Ras acting as an allosteric regulator, or whether additional events such as phosphorylation

3 Insights into Protein Protein Binding 893 by membrane-bound kinases or a transphosphorylation by dimerized Raf itself is responsible, has not been resolved. 43,45,47 It is consistently proposed, however, that Raf activation requires a structural change from an inactive conformation of the protein being folded between regulatory and kinase domains to an activated, open form. 45,47 Together with the structural data, thermodynamic binding data 48 for wild-type or mutant Ras and effector proteins provide a solid basis for the validation of calculations. Ras-effector interactions have been investigated repeatedly by means of theoretical methods. Among others, studies have included molecular dynamics (MD) simulations on Ras or Rap-1A bound to Raf aimed at identification of effector domains in the Raf protein 49,50 or only of Raf to investigate conformational effects of the R89K mutation. 51 Zeng et al. 52 performed alchemical free energy calculations on the R89K mutant of Raf, while Muegge et al. 53 concentrated mainly on electrostatic contributions to the Rap-1A Raf interaction. Here, (absolute) free energies of protein protein binding have been computed with the molecular mechanics (MM)-generalized Born surface area (GBSA) approach. 54,55 In this approach, gas-phase energies, solvation free energies, and entropic contributions are summed and averaged over snapshots from MD trajectories. The related MM- Poisson Boltzmann (PB) SA approach has been applied to compare relative stabilities of different conformations of nucleic acids, 55 to identify correctly folded proteins, 56 and to estimate binding affinities of small molecules binding to proteins It has been used to predict the effects of amino acid mutations on binding affinities. More recently, electrostatic contributions to solvation free energies have been calculated by GB models. 55,63,64 Since GB is significantly faster than PB, the former is an attractive alternative. In addition, GB allows one to decompose the contributions to binding free energies on a per-residue basis which provides an interesting, structurally non-perturbing alternative to the usual computational alanine scanning approach. 60 Although a similar idea has been presented for small-molecule solvation, 65 to the best of our knowledge this is the first time that GB has been used for such an approach in the context of macromolecular association. In this work, 5 ns MD simulations were carried out for the unbound proteins Ras, Raf, and RalGDS as well as for the complexes Ras Raf and Ras RalGDS. For 150 snapshots extracted from the last 3 ns of the stable trajectories, energy and entropy contributions were calculated and averaged. Energy decomposition on a per-residue basis showed convincing consistency with experimentally determined mutagenesis data. In addition, residues apart from the binding interface could be identified to contribute to the protein protein binding (hotspots). In the Raf case, particularly, these hotspots form interaction pathways that originate in the binding interface and extend through the protein structure. Possible implications for an allosteric activation of the effector molecule are discussed. The results of this study indicate clearly the significance of the applied computational method to provide insight into binding thermodynamics of proteins on an atomic level, although limitations of the current methodology still exist. Results and Discussion Structures from MD simulations For the systems Raf, RalGDS, Ras, Ras Raf, and Ras RalGDS, MD simulations with the particle mesh Ewald (PME) method were carried out in explicit water for 5 ns. For each trajectory, the time-series of the rmsd of backbone atoms from the experimental starting structure is given in Figure 1. For all systems but Raf, these rmsd values vary between 0.7 Å and 2.0 Å. The rmsd values with respect to all protein atoms remain below 2.3 Å during the course of the simulations for these four cases. These deviations are comparable to those found in related simulations. 49,50 In the case of Raf, it should be noted that, in contrast to the four Figure 1. Time-series of rmsd of backbone atoms from the starting structures for the unbound proteins and the complexes over 5 ns of MD simulations. The equilibration phase is not included. The vertical broken line indicates the time after which snapshots were extracted for binding free energy calculations.

4 894 Insights into Protein Protein Binding systems discussed above, the starting structure was derived from NMR experiments, not X-ray crystallography. In addition, only the Ras-binding domain of the regulatory N-terminal region of this kinase is structurally known and hence was used for the simulation. Both reasons thus may explain the observed higher rmsd values of the backbone atoms for Raf (rmsd of all protein atoms: Å). As can be seen from Figure 1, however, after the initial phase of 2 ns, the Raf structure shows only small changes with respect to the time-evolution. Superimpositions of the average structures of all trajectories with their respective starting structures revealed regions of major conformational changes. In the unbound Raf case, the loop region between L101 and K109 shows the largest deviations (average rmsd of backbone atoms: 4.0(^1.0) Å), while the backbone rmsd of the other residues amounts to 1.9(^0.1) Å. It should be noted, however, that the residues of Raf are not well defined in the experimental solution structure. 66 In contrast, the same region deviates by only 2.4 Å when comparing the average bound Raf structure with that taken from the starting structure of the Ras Raf complex. For the unbound RalGDS, the biggest movements are found in the region of D26 to G28 (average rmsd of backbone atoms 3.0(^0.7) Å). In case of the unbound Ras protein, the largest conformational changes, not unexpectedly, occur in the switch I/II regions (amino acid residues and 60 76), which is demonstrated also by the average rmsd values of backbone atoms with respect to the starting structure of 1.7 Å and 1.6 Å, respectively, for these regions (Table 1). Table 1. Average rms deviations of distinct regions in Ras, Ras Raf, and Ras RalGDS Ras Raf Ras RalGDS Ras Start a Start a Unbound b Start a Unbound b 1.0 c c 0.5 c c 1.2 c c 1.8 c c GTP (0.1) (0.1) c (0.1) c Mg 2þ (0.2) (0.2) c (0.2) c Switch I d (0.5) (0.3) c (0.2) c Switch II d (0.2) (0.2) c (0.3) c Ras c c interface d (0.2) c (0.2) c Effector interface d 0.8 (0.2) e 1.6 e 1.0 (0.1) e 2.1 e The rmsd deviations are reported in Å, the standard deviations are given in parentheses. a The rms deviations were determined for snapshots taken each 5 ps over 5 ns of simulation time with respect to the starting structure. b The rms deviations were determined between average structures of the proteins in the unbound and bound states. c The rmsd was determined with respect to the Ras structure. d The rmsd of backbone atoms is given. e The rmsd was determined with respect to the effector structure. Additionally, in the Ras, Ras Raf, and Ras RalGDS systems, the rmsd of the GTP atoms is below 0.8 Å and that for the Mg 2þ is below 0.5 Å with respect to the starting structures (Table 1). Similar changes are found in the bound state. With respect to the interface regions of the complexes, the Ras part shows larger conformational changes compared to the effector parts if the starting structure is taken as reference (Table 1). Comparing the average structures of both complex trajectories, the Ras interface region shows rms deviations of 0.9 Å, where the largest differences occur in the region between N26 and E37. Average structures of the complexes were compared to the average structures of the unbound protein simulations. Here, the observation from crystal structures 67 is corroborated, in that the effector proteins show larger deviations (Raf 2.0 Å; RalGDS 1.4 Å) than the Ras structures (in Ras Raf 0.8 Å; in Ras RalGDS 0.7 Å). This also holds with respect to the interface regions (Table 1). The largest structural deviation is found in Raf, where the loop region between L101 and K109 shows an average rmsd of 4.4 Å in this case. Finally, over the course of the MD simulations, in neither system was any exchange of the two water molecules coordinated to Mg 2þ observed, which is in accordance with experimentally determined exchange rates of s ,69 Hence, considering these two water molecules as part of the solute in the subsequent free energy calculations appears to be justified. Only one water molecule with atomic fluctuations below 1 Å is found in the binding interface, which mediates interactions between E37 of Ras and R59 of Raf. In the case of Ras RalGDS, two water molecules interacting with D38, I36 (Ras) and S29 (RalGDS) as well as D33, D38, T35 (Ras) and K48 (RalGDS), respectively, show similar atomic fluctuations. In contrast, in the unbound proteins, no equally restricted water molecules can be identified. This is not unexpected in view of the rather flat epitope region. Table 2 shows the absolute and relative amount of surface area per side-chain buried upon complex formation, as calculated by the recursive icosahedra method. 70 The values were averaged over all 150 snapshots taken for binding free energy calculations, and the surface area in the unbound state was used as the reference value for the relative data. In the case of the Ras Raf interface, the side-chain surfaces of seven residues of Ras and six residues of Raf are buried by more than 50% upon complex formation, with similar values for Ras RalGDS. In both complexes, polar or charged residues show the largest relative changes in accessible surface area (Ras Y40, Raf R89; Ras D38, RalGDS S29) while those of non-polar sidechains are rather modest (except for I21 on the Ras side, as well as V69 and V88 on the Raf side). Although buried polar interactions are expected to be stronger than those formed in solvent-exposed regions, the desolvation penalty increases concomitantly. No direct interaction with Raf

5 Insights into Protein Protein Binding 895 Table 2. Surface area of interface residue side-chains buried during complex formation Ras Raf interface Ras RalGDS interface Ras SA burieda (Å 2 ) Raf a SA buried Ras SA burieda (Å 2 ) RalGDS SA burieda (Å 2 ) E3 12 (24) T57 19 (32) I21 10 (25) I14 57 (56) I21 34 (77) R59 21 (22) I24 18 (77) R16 25 (32) I24 21 (59) N64 39 (40) Q25 28 (29) N23 38 (33) Q25 38 (35) K65 50 (27) H27 11 (13) N25 32 (72) I27 37 (30) Q66 43 (82) V29 19 (29) M26 67 (45) V29 17 (22) R67 65 (47) E31 21 (17) Y27 50 (60) E31 16 (14) T68 11 (85) D33 60 (52) K28 54 (76) D33 52 (47) V69 54 (88) I36 79 (80) S29 32 (96) I36 56 (41) V70 1 (12) E37 54 (83) L31 21 (25) E37 80 (65) N71 8 (11) D38 47 (97) D47 11 (16) D38 41 (78) K84 85 (52) S39 42 (86) K48 76 (83) S39 43 (85) K87 16 (12) Y40 42 (91) N50 50 (43) Y40 42 (89) V88 58 (90) R41 47 (40) E52 9 (13) R (81) R89 55 (96) D54 2 (11) L52 4 (15) L56 6 (19) E54 5 (26) Y64 24 (35) L56 14 (28) M67 15 (19) Y71 4 (19) Values are averaged over 150 snapshots extracted at regular time-intervals from the last 3 ns of the complex trajectories. Residues are reported only if the percentage of surface area buried.10%. a The percentage of surface area burial with respect to the surface area in the unbound state is given in parentheses. involving residues in the switch II region of Ras was found. Interactions between these binding partners mediated by only one water molecule could not be detected in this region. In the Ras RalGDS case, on the other hand, several residues of the switch II region (Y64, M67, Y71) are in contact with the effector. In Table 3, hydrogen bonds observed across the binding interfaces of Ras Raf and Ras RalGDS are listed, together with their persistence during the last 3 ns of simulations. If more than one hydrogen bond is formed between two residues, only the largest occupancy value is reported. Two and three salt-bridges are formed in the Ras Raf Table 3. Hydrogen bond formation across the binding interface of Ras Raf and Ras RalGDS Ras Raf interface Ras RalGDS interface Ras Raf Occupancy a Ras RalGDS Occupancy a E3 K65 16 p I24 N23 26 H27 K87 23 D33 K48 39 p D33 K84 24 p P34 K48 38 E37 R59 44 p E37 R16 97 p E37 V69 30 E37 Y27 98 D38 T68 98 E37 S S39 R67 88 D38 S29 75 S39 R89 59 S39 M26 99 R41 N64 62 S39 Y27 26 Y40 K28 15 Hydrogen bonds were defined by acceptor donor atom distances of,3.2 Å and acceptor H-donor angles of Hydrogen bonds are reported only if they exist for.10% of the investigated time period. a Occupancy is in units of percentage of the investigated time period. If more than one hydrogen bond is formed between two residues, only the largest occupancy value is reported. Saltbridges are marked by asterisks ( p ). and Ras RalGDS case, respectively, and the most stable hydrogen bonds involve residues in the center of the effector region on Ras (residues 37 39). These regions coincide with those exhibiting the largest surface area burial upon complex formation (see above, Table 2). Polar interactions involving Ras residues outside the effector region appear for the Ras Raf case (E3 K65 and H27 K87), whereas Ras residues P34 and Y40 are involved in hydrogen bonds only in the Ras RalGDS complex. A comparison with NMR data determined for Raf binding to Ras 66 shows that hydrogen bonds were found for all polar residues (except for Q66) that showed large chemical shifts upon association. Similar results are found comparing the MD simulation with the Rap-1A Raf complex crystal structure. 41 In both cases, however, no experimental evidence was reported for the E3 K65 and H27 K87 hydrogen bonds. In case of the Ras RalGDS complex, no interactions between I24 N23, E37 Y27, and S39 M26 have been reported by Vetter et al. 39 but at least the latter two can be found in the crystal structure reported by Huang et al. 67 Hence, the interaction patterns across the interface agree to a large extent (but not perfectly) with those known from experiment. Binding free energy calculations Statistical significance of the results To obtain more detailed information about the scope and limitations of the current force-fields and solvation models, free energy calculations have been performed to complement the structural analysis. To this end, using the MM-GBSA method (equations (1) and (2)), absolute binding free energies were calculated as the sum of gas-phase

6 896 Insights into Protein Protein Binding energies (including coulombic energy, van der Waals energy as determined by a Lennard Jones potential and internal energy), solvation free energies (including a non-polar part as determined by equation (4) and an electrostatic part obtained from GB calculations) and entropic terms resulting from translational, rotational, and vibrational contributions. The gas-phase and solvation free energy values were averaged over 150 snapshots taken at 20 ps intervals from the last 3 ns of MD simulations. Figure 2 shows the time-series of the sums of gas-phase energies and solvation free energies as computed for these snapshots of the unbound proteins Raf, RalGDS, and Ras and the complexes Ras Raf and Ras RalGDS. In all cases, despite only moderate rmsd fluctuations (except for Raf), significant fluctuations in the effective energies demonstrate the sensitivity of these values to conformational details. Yet, in the case of Raf, RalGDS, and Ras Raf, effective energies appear to be converged and remain stable throughout the time-period. However, in the case of Ras and Ras RalGDS, drifts in the effective energy values ðdg gasþsolv Þ still occur, as indicated by the slopes of the linear regression lines of kcal mol 21 ps 21 (Ras) and kcal mol 21 ps 21 (Ras RalGDS), even after 2 ns of equilibration time (1 cal ¼ J). Repeating these analyses with extended trajectories of 12 ns length for Raf, Ras, and Ras Raf showed that the magnitude of the drifts remains the same for Raf and Ras Raf, while the drift of Ras reduces to kcal mol 21 ps 21. This result, together with the fact that DG gasþsolv shows oscillations over the longer time-period, which are not visible in the shorter MD runs, may point to the need of using trajectories of considerable length for related analyses in the future. Binding free energies are obtained as average values. Previous studies have shown that snapshots are sufficient to estimate mean values with reasonable precision, 62,63 since the error in the mean decreases with the square-root of the number of snapshots, provided that the sample points are independent. Here, the energy values obtained for Figure 2. Sum of gas-phase and solvation free energies calculated for 150 snapshots extracted at 20 ps intervals from the last 3 ns of MD simulations. The snapshots were taken from separate trajectories. Solvation free energies were calculated at an ionic strength of 50 mm. The slopes of linear regression lines are (values in kcal mol 21 ps 21 ): Raf, ; RalGDS, ; Ras, ; Ras Raf, ; Ras RalGDS,

7 Insights into Protein Protein Binding 897 Table 4. Binding free energy components of the Ras Raf complex calculated from separate trajectories Ras Raf Ras Raf Delta a Contrib. b Mean c s d Mean e s e Mean c s d Mean c s d H elec 210, H vdw H int H gas G np G GB G solv G gasþsolv TS trans TS rot TS vib TS total G total 212, DG exp 29.6 e 0.2 e All values are given in kcal mol 21. The standard state is taken to be 1 M. a Contribution(Ras Raf) contribution(ras) contribution(raf). b H elec ; coulombic energy; H vdw : van der Waals energy; H int : internal energy; H gas ¼ H elec þ H vdw þ H int ; G np ; non-polar solvation free energy; G GB ; polar solvation free energy; G solv ¼ G np þ G GB ; G gasþsolv ¼ H gas þ G solv ; TS trans=rot=vib ; translational/rotational/ vibrational entropy; TS total ; total entropy contribution; G total ¼ G gasþsolv þ H trans=rot 2 TS total : c Average over 150 (15 in the case of entropy contributions) snapshots. d Standard error of mean values. e Values were determined by isothermal titration calorimetry adjacent snapshots extracted from 3 ns of production runs should be nearly uncorrelated, since the correlation times for relaxation of effective energy fluctuations (1 ps) are shorter than the time-interval (20 ps) used for snapshot extraction. Hence, mean values of DG gasþsolv values can be estimated to within a standard error of 5.4 kcal mol 21 and 5.6 kcal mol 21 in case of Ras Raf and Ras RalGDS, respectively (Tables 4 and 5). Absolute binding free energies and analysis of contributions To obtain insights into different contributions to the affinity of effector proteins binding to Ras, absolute binding free energies were computed for the Ras Raf and Ras RalGDS complexes (equation (1)). To coincide with experimental conditions used for affinity determinations, these calculations were performed at 50 mm ionic strength. The dependence of the solvation free energy calculations on salt will be assessed below. Tables 4 and 5 contain the contributions to binding free energy (i.e. gas-phase energies, solvation free energies, and contributions due to changes in the translational, rotational, and vibrational degrees of freedom of the solute molecules) for Ras Raf and Ras RalGDS, respectively, as calculated using snapshots from separate simulations for Ras, the effector proteins, and the complexes. Calculation of absolute binding free energies provides a stringent test of the underlying methodology used to obtain energy contributions, since cancellation of errors, as it advantageously occurs Table 5. Binding free energy components of the Ras RalGDS complex calculated from separate trajectories Ras RalGDS Ras RalGDS Delta Contrib. Mean s Mean s Mean s Mean s H elec H vdw H int H gas G np G GB G solv G gasþsolv 210, TS trans TS rot TS vib TS total G total 213, DG exp For details, see the legend to Table 4.

8 898 Insights into Protein Protein Binding for traditional relative free energy determinations, is lacking. Even relatively small errors in the individual free energy values might have a large impact on the (small) final difference values. In this respect, the calculated binding free energies obtained with GB (Ras Raf: kcal mol 21 ; Ras RalGDS: kcal mol 21 ) are in fair agreement with experimental binding free energies as determined by isothermal titration calorimetry (Ras Raf: 9.6 kcal mol 21 ; Ras RalGDS: 28.4 kcal mol 21 ) (C. Herrmann, personal communication). 48 Together with uncertainties in the mean values of approximately 6 kcal mol 21, the success of these calculations should thus be measured as being close to the right answer. Calculation of the binding free energy was repeated in the Ras Raf case for 500 snapshots extracted from separate trajectories of Raf, Ras, and Ras Raf of 12 ns length (not considering 2 ns of unrestrained equilibration) and yielded kcal mol 21 with an estimated standard error of the mean of 3.4 kcal mol 21. Compared to DG total ¼ 215:0 kcal mol 21 found for the 5 ns trajectories (Table 4), the difference is within the errors of the calculations, which again demonstrates the significance of our results. The calculated binding free energy values are encouraging in light of the balance of energy terms contributing to them. The proteins as modeled here carry total charges of 6 þ (Raf), 4 2 (RalGDS), and 8 2 (Ras including GTP and Mg 2þ ). Hence, complex formation between Ras and Raf involves oppositely charged molecules (total charge of Ras Raf 2 2 ), whereas the Ras RalGDS complex (total charge 12 2 ) is built from like-charged structures. These differences are, however, less pronounced in the interface: among residues that form polar interactions with Ras, only R89 in Raf has no equivalent analogue in RalGDS. 48 Long-range electrostatic influences on the binding equilibrium can involve residues not located in the binding epitope. 24 To adequately capture these influences during the calculations, the contributions of the gas-phase electrostatic energy and the polar part of the solvation free energy must be well balanced. This becomes obvious from Tables 4 and 5: while for Ras Raf, the gas-phase term of kcal mol 21 faces a polar solvation contribution of kcal mol 21, hence resulting in DH elec þ DG GB ¼ 25:1 kcal mol 21 ; the respective terms for Ras RalGDS are 55.0 kcal mol 21, kcal mol 21, and 1.0 kcal mol 21. Overall, electrostatic interactions thus disfavor the protein protein binding in both cases (although this finding is weak in the case of Ras RalGDS in view of the errors in the calculations), which is in agreement with other MM-PBSA studies. Furthermore, recent theoretical and computational work has demonstrated that (natural) receptor ligand pairs often show sub-optimal electrostatic interactions that may be optimized, leading to 24,71 73 increased affinity. Two studies of the Rap- 1A Raf complex, which is related to the Ras Raf complex described here, find that electrostatic contributions favor the protein protein association. 53,74 Although a direct comparison to our study is difficult due to the use of different solvation models, ionic strengths of the solutions, and dielectric constants for the solute regions, one reason for this finding may be that both studies extract the structures of the unbound proteins from the complex structure and allow none, 74 or only a limited, 53 relaxation of these. In contrast, Noskov & Lim 75 performed single-point calculations for two protein protein complexes for which crystal structures of the complexes as well as the unbound components are available. Using either GB or PB calculations to determine the polar part of solvation free energy, which yields very similar results, the total electrostatic contribution to the binding free energy has been determined to be disfavorable for both complexes. In both cases, van der Waals interactions contribute favorably to the binding affinity of the proteins, as does the non-polar part of solvation free energy, again in agreement with other studies mentioned above. The contribution from internal energy, however, is disfavorable for Ras binding to Raf and RalGDS (Ras Raf: DH int ¼ 1:9 kcal mol 21 ; Ras RalGDS: DH int ¼ 8:7 kcal mol 21 ), indicating conformational changes of the binding partners upon complex formation that lead to internal strain. Although this term was considered to contribute to what was termed structural noise, 62 the estimated statistical error in the mean values of our calculations are actually quite small. Neglecting these structural changes, and consequently DH int ; would have led to an even greater overestimate of binding affinity. While the continuum solvation models provide estimates of the free energy of solvation and thus include entropic contributions of the solvent, changes in the entropy of the solute molecules must be determined to complete the estimation of absolute binding free energies. Normal-mode analysis was used to calculate frequencies of vibrational modes based on a harmonic approximation after energy minimization of the snapshots. We averaged these entropy contributions over 15 snapshots to obtain an estimate of the error. The mean values for TDS vib in Tables 4 and 5 show rather small errors, indicating that for structures at different local energy minima, similar estimates of vibrational energies are obtained. Drawbacks of this method include the neglect of anharmonic motions, which might be overcome by quasiharmonic analysis of the trajectories, 76 and the use of a distance-dependent dielectric constant for these calculations to approximate the screening of electrostatic interactions. Changes in conformational entropy occurring due to restrictions of rotamer states on burial 77 are not considered here. Compared to folding processes, this assumption may be justified, because residues in the binding

9 Insights into Protein Protein Binding 899 interface reside in contact to neighboring residues; hence their conformational space is already restricted prior to the complex formation. Contributions of vibrational entropy are commonly assumed to dominate over contributions of conformational entropy for side-chains. 78 Taken together, values of entropic contributions to the binding free energy should be interpreted cautiously. Salt-dependence of solvation models Upon complex formation of Ras Raf and Ras RalGDS, polar and charged residues become (partially) buried (Table 2) and form new interactions (Table 3). The energetics of these interactions depends strongly on the screening properties of the surrounding medium, which in turn are related to its ionic strength. To test the effects of different concentrations of salt on the free energies of binding, calculations of the polar contribution to solvation free energy at concentrations of 0 mm (i.e. no Debye Hueckel screening), 50 mm (see above) and 100 mm 1 1 mobile counterions were performed applying an extension 79 to the MGB model, as described in Methods. Although this is not a perfect model for salt effects in a strict sense, good agreement with PB results has been reported for low concentrations of salt. 79 Results are given in Table 6. As expected, 80,81 binding of oppositely charged molecules (Ras and Raf) is disfavored by increasing concentrations of salt, whereas that of similarly charged molecules (Ras and RalGDS) is favored. The binding affinity of Ras Raf is overestimated under zero salt conditions, whereas better agreement with experimental results occurs if the experimental ionic strength is applied. Structural determinants of binding free energy Free energy decomposition as non-perturbing alternative for (computational) alanine scanning mutagenesis Insight into the origin of binding on an atomic level may be obtained by decomposing DG total in terms of contributions from structural subunits of both binding partners. The experimental method of choice for analyzing protein-binding interfaces in this context is alanine scanning mutagenesis, which has been mimicked as computational Table 6. Effects of salt contributions on the calculated binding free energy DG total (kcal mol 21 ) a Salt concentration (mm) Ras Raf Ras RalGDS a The standard state is taken to be 1 M. alanine scanning in the realm of MM-PBSA studies. 60 Investigations of protein interface energetics by both techniques, however, inevitably leads to perturbations of the systems under consideration. 25,82 In the Ras case, e.g. minor changes in the switch region, such as removing the side-chain methyl group of T35, affect dynamic behavior of the protein and, in turn, interaction with effectors, 83 while the R89K mutant of Raf was found to influence the conformation of residues with adverse effects for the binding of Ras. 51 Noticeably, in both cases the state of the unbound protein is disturbed, not only the ensemble of the complex, as is often assumed in interpreting mutagenesis results. Here, a non-perturbing alternative to determine the contribution of each residue to the binding free energy is pursued by means of component analysis. Contributions to gas-phase energies and solvation free energies are attributed to the atom that participates in the respective interaction (see Methods). Summing over atoms of a residue then yields the contribution to the binding free energy, complemented for selected residues by estimates of entropic contributions. Most importantly, these values are obtained without the need to make structural modifications in the binding partners. Thus, contributions due to non-mutatable functional groups (such as backbone atoms) can be calculated. It should be noted, however, that while the total free energy is a state function (and as such independent of the pathway used to calculate it), free energy components (whether they be from force-field decomposition or residue-based decomposition), in general, are not. Hence, the values of these contributions are sensitive to the decomposition scheme chosen in the case of (classical) molecular dynamics free energy component analyses The decomposition scheme proposed here, however, depends only on the endpoints considered, i.e. individual components do not depend on the choice of a specific pathway. 87 In addition, the residue or side-chain/backbone-based description follows a natural choice and provides a decomposition, which helps toward understanding the influence on the binding free energy due to substructural elements of the binding partners. The treatment of the (non-electrostatic) gasphase part in our decomposition scheme follows a break-down of the Hamiltonian that has been described earlier in the context of free energy component analyses by thermodynamic integration techniques. 88 A fully systematic component analysis of binding free energies in the context of PB calculations to estimate polar contributions to the solvation free energy has been presented recently by Hendsch & Tidor. 89 Free energy components determined by this approach have been compared to results from alchemical MD free energy simulations. 87 Applying the linearized PB equation, the electrostatic potential at any point equals the sum of contributions from individual charges. Thus, contributions of a group (such as a

10 900 Insights into Protein Protein Binding side-chain) to the electrostatic free energy can then be calculated by summing half of the charge at all atom positions times the potential at these atoms due to the respective group. Finally, the contribution of the group to the electrostatic binding free energy is determined by calculating the difference of the electrostatic free energy contribution in the complex minus the contribution in the unbound component. Recently, it has been noted that, since the total electrostatic work of creating a given charge distribution within a solute embedded in a solvent is a quadratic function of charges in the GB formula, a GB analogue of the electrostatic potential can be defined at the position of each atom (equation (7)), 90 which can then be used to determine group contributions, analogously to the case of PB calculations described above (equation (8)).To the best of our knowledge, this is the first time that GB calculations have been applied for such a decomposition in the context of macromolecular association. In the case of PB calculations, for each residue of interest, a separate (time-consuming) computation has to be performed to obtain the potential at all atom positions due to the charges of the group of interest. In contrast, the GB approach allows us to screen all residues at once with respect to their contributions to binding free energy, hence leading to a remarkably lower computational demand. From equation (8), further subdivision into desolvation (i.e. loss of solvation free energy of the group upon binding), direct (i.e. solvent-screened coulombic interactions of the group with the charges of the other molecule), and indirect (i.e. changes in the interactions of the group with the other charges of the same molecule due to the presence of the binding partner) terms 87,89,91 is possible, but has not been pursued in this study. Calculated effective energy ðdg gasþsolv Þ contributions per side-chain are compared to binding free energy differences ðddg total Þ obtained from isothermal titration calorimetry data for several alanine mutants of Ras Raf and Ras RalGDS with respect to the wild-type proteins (C. Herrmann, personal communication). The DG gasþsolv values were calculated according to equation (5) using 150 snapshots extracted from separate trajectories. The maximal error in these mean values is 0.4 kcal mol 21. The experimental DDG total values were determined in one laboratory, 48 and the experimental error of these values is 0.3 kcal mol 21. Figure 3 shows plots of the calculated DG gasþsolv energies per side-chain versus DDG total values, whereby favorable contributions to the binding free energy of a side-chain result in negative DG gasþsolv energies but positive DDG total values. Prior to discussion of these data, it has to be noted that perfect correlations cannot be expected here. On the one hand, DG gasþsolv lacks entropic contributions due to changes in internal and external degrees of freedom. Especially for E37 and Figure 3. Plots of calculated contributions DG gasþsolv to the binding free energy obtained per side-chain by component analysis (see Methods) versus experimentally determined 48 binding free energy differences DDG total for alanine mutants of (a) Ras Raf and (b) Ras RalGDS. Residues located on Ras are marked with plain text, those located on the effector proteins are marked in italics. The linear regression in the Ras Raf case was calculated without considering I36 or R67. In the Ras RalGDS case, N25 was excluded from the statistical analysis. For selected residues, estimates of entropic contributions due to changes in the internal and external degrees of freedom were added to DG gasþsolv (data points: x). It should be noted that binding free energy differences for Ras Raf involving Ras mutants I36A, E37A, D38A, and V45A were determined experimentally at 308 K, while all other reported values were measured at 298 K. For experimental binding free energy differences that were determined at both temperatures, deviations of up to 1.5 kcal mol 21 were reported (C. Herrmann, personal communication). D38 of Ras in Ras Raf, a decrease in atomic positional fluctuations in the bound state compared to the free state was found. The entropic contribution of the side-chains of these residues was estimated by repeating the normal mode analysis with vanishing masses for the respective atoms. 92 This removes from the vibrational entropy the entropy pertaining to motions of these side-chain atoms, since the vibrational entropy of a massless particle

11 Insights into Protein Protein Binding 901 is zero. The difference between this value and the value obtained by normal mode analysis with the normal masses, finally, yields the contribution of the side-chain to the total vibrational entropy of the considered molecular species. The sum of these contributions and DG gasþsolv is shown as crosses in Figure 3. For E37 and D38, entropic contributions of TDS total ¼ 22:2 kcalmol 21 and 26.0 kcal mol 21 (for T ¼ 300 K) are obtained, which reduce the overall contribution of the sidechains of these residues to the binding free energy. Although ideally similar calculations should be performed for all residues, this is not feasible computationally. Finally, one has to consider that a side-chain mutation leads to e.g. the loss of all partial atomic charges, which results in a loss of all interactions with surrounding residues (i.e. interaction of the (mutated) residue X with residue Y, but also of Y with X). Taking the total loss into account for a single residue, however, yields contributions which, when summed, would lead to double counting of the interactions, as has been pointed out by Hendsch & Tidor, 89 and more recently by Sheinerman & Honig. 74 In the decomposition scheme used here, by definition, only half of the interaction between X and Y is attributed to either X and Y. Thus, in our study, the sum of the per-residue contributions will equal the total binding free energy. Considering I36 and R67 (residues of effector proteins are given in italics) in the Ras Raf case and N25 in the Ras RalGDS case as outliers, correlation coefficients r 2 of 0.55 and 0.46 are found, respectively. In the latter case, however, one has to notice that the experimental data are spread over only 3 kcal mol 21. Encouragingly, the contributions per side-chain in terms of favoring or disfavoring complex formation were predicted correctly for all but three residues (I36, R67, V88) for the Ras Raf system. It is interesting to note that in case of the R67 mutant of Raf, close-to-normal Raf activation was measured with a Ras-G12V/E37G mutant, but not with a Ras-G12V mutant. 93 Hence, indirect effects may be responsible for the positive DDG total value found for the Raf-R67A mutant bound to wild-type Ras. 94 In the case of Ras RalGDS, taking into account experimental and computational errors, the influence of only two residues (R41 and H49) was predicted wrongly. In this context, it is remarkable that even for side-chains involved in polar or charged interactions (such as D33, E37, or D38 of Ras, K84 and R59 of Raf, and R16 and K48 of RalGDS), only moderate DG gasþsolv values were found here using the component analysis (in agreement with experimental results) as opposed to a recent study applying computational alanine scanning to snapshots of a wild-type trajectory. 62 In the latter case, as well as in its experimental analogue, mutation of one of the interaction partners to alanine results in the (disfavorable) loss of interaction and can lead to a desolvation penalty due to the remaining, non-saturated interaction site. On the other hand, binding free energy differences obtained by experimental mutagenesis can be influenced by structural responses of the binding partners 82 and mimicking of deleted side-chains by water molecules. Ideally, experimental mutation data should be compared to calculation results that are based on separate trajectories for each mutation. This, however, is feasible for only a small number of cases. One of the problems in binding free energy calculations is the sensitivity of the results to conformational details of the underlying structures. In this connection, it has been shown that the loop L2 region of Ras (with Y32 as the key residue) undergoes a conformational transition upon complex formation. 43,44 Y32 is located in close proximity to the phosphate groups of the nucleotide (state 2) in the bound state, whereas a different conformation (state 1) is preferred in unbound Ras. 44,95 During the course of the MD simulations, no transition between state 1 and state 2 is observed in the unbound Ras or in either of the complexes. This is in agreement with the experimentally determined exchange rates. 43 Although in the Rap1A Raf crystal structure (after modifications used as starting point for the Ras Raf complex) the aromatic ring of Y32 is close to the b-phosphate moiety of the nucleotide, this position is occupied by Y32 of a neighboring Ras molecule in the Ras RalGDS crystal structure. Thus, using the unmodified Ras RalGDS crystal structure as a starting point for the simulation, the complex will remain in the (wrong) state 1 orientation. Energy decomposition for D33 using snapshots with the correct Y32 orientation resulted in a contribution to DG gasþsolv of kcal mol 21 (the experimental binding free energy difference in the case of a D33A mutation is 1.1 kcal mol 21 ). Repeating the energy decomposition on snapshots extracted from the simulation with the wrong Y32 state, however, yields a DG gasþsolv value of 27.0 kcal mol 21. This finding clearly indicates that errors in the structures may affect the outcome of free energy calculations. In view of the fact that simulations of current standard lengths would not have been able to yield a transition between both states, it points to the requirement for good starting structures. Energetic and entropic contributions of interface and non-interface residues Computational and experimental analysis of the contributions of single residues to the binding affinity is often restricted to residues located in the binding epitope. In the case of computational studies, this restriction is used to justify the rigidbody approximation of binding. Here, influences on binding are studied by comparing the complex structure to unbound molecules extracted from the complex. There is increasing evidence, however, that residues even further apart from the interface can influence the binding equilibrium strongly, 96 and that this influence is propagated

12 902 Insights into Protein Protein Binding Figure 4. Color-coded projection onto the Ras Raf structure of the residue-based effective energy contributions ðdg gasþsolv Þ to the binding free energy of the complex as calculated with equation (5). Dark red color represents contributions #25 kcal mol 21, dark blue color those of $5 kcal mol 21. White stands for zero contribution. In addition, backbone atoms of the residues that contribute #21.5 kcal mol 21 are given as spheres. Residues discussed in the text are additionally marked. The bottom part is rotated by 908 with respect to the top part around the axis connecting the center of mass of both proteins. through the respective molecules in a cooperative manner. 97,98 Ultimately, this has contributed to a novel view of allosteric effects. 99 To examine this, we used the free energy decomposition scheme (equation (5)) to investigate the contribution of all residues of both proteins to the binding free energy. As Figure 4 strikingly reveals, residues of Ras Raf contributing to the binding free energy are by no means found exclusively in the proximity of the binding interface. Instead, residues as far as 25 Å and more apart from the epitope show a significant (i.e. ldg gasþsolv l $ 0:5 kcal mol 21 Þ change in effective energy. Though the effective energy contribution of all epitope residues (i.e. whose surface is buried upon complex formation by residues of the counterpart molecule) is 242 kcal mol 21, residues that are not in the interface contribute 25 kcal mol 21. It can be anticipated, however, that changes in the degrees of freedom of binding interface residues will more strongly oppose binding than those of non-interface residues. Along these lines, entropic contributions of epitope residues were found to be as large as 26.0 kcal mol 21 per residue, as described above for D38 of Ras. In contrast, e.g. for Q99 and Y32 of Ras in Ras Raf (neither forms direct interactions across the interface but both show contributions to DG gasþsolv,26 kcal mol 21 and the largest reductions in the magnitude of atomic fluctuations upon binding (see below)), the change in the degrees of freedom leads to values of TDS total of only kcal mol 21 and kcal mol 21, respectively. A similar picture emerges from Figure 5 for Ras RalGDS. Here, residues in the epitope contribute 249 kcal mol 21 to DG gasþsolv ; while non-interface residues in total contribute only 21 kcal mol 21. Compared to the Ras Raf case, the switch II region shows considerably larger contributions in the Ras RalGDS case. These contributions can be deemed to be the change of free energy (or more precisely effective energy, since entropic contributions due to changes in internal and external degrees of freedom are missing) that these residues experience upon complex formation. As will be discussed in more detail below, Figures 4 and 5 show that changes in DG gasþsolv are not distributed uniformly over non-epitope residues but rather are regional. Although the overall contribution to the binding free energy by these residues is small, this finding may have consequences for the explanation of the function of the systems. Analysis of mutant data together with static crystal structures have led to the picture of hotspot residues (i.e. those contributing a significant Figure 5. Color-coded projection onto the Ras RalGDS structure of the residue-based effective energy contributions ðdg gasþsolv Þ to the binding free energy of the complex as calculated with equation (5). For an explanation of the color code, see the legend to Figure 4.

13 Insights into Protein Protein Binding 903 amount to binding free energy) that tend to cluster in the center of interfaces. 10 Often, these hotspots are surrounded by a solvent-excluding O-ring of energetically unimportant residues. It is not clear, however, whether the explanation of this O-ring is related directly to binding free energy or if it is just a consequence of the fact that interactions of mutated residues in this outer region might be replaced more easily by water (and hence show less influence on DG total upon mutation) than those in the center of the binding interface. 100 E37, D38, S39, and Y40 account for 70% and 54% of the contributions to DG gasþsolv with respect to all residues that become (partially) buried during complex formation of Ras Raf and Ras RalGDS, respectively. In that sense, they may be considered to form the functional epitope 22 or the hotspot. 10,19 Taking into account the distribution of other residues favorably contributing to DG gasþsolv in the interface and even apart therefrom, however, a so-called O-ring cannot be identified. Accordingly, K5, Y32, D47, D57, Q99, R164, and H166 of Ras in the Ras Raf case, K5, D30, Y32, P34, D57, E62, R73 of Ras in the Ras RalGDS case, D113 of Raf, and E60, Q63 of RalGDS contribute,23 kcal mol 21 to the effective energy, yet they are not in the binding interface. Together with entropic contributions stated above, this amounts to contributions to the binding free energy of,23 kcal mol 21 in the Q99 and Y32 cases of Ras Raf. As mentioned above, Y32 is the key residue in the conformational transition of loop L2 of Ras upon complex formation. In the bound state, Y32 is located in close proximity to the phosphate groups of the nucleotide (state 2). 44,95 A similar orientation exists in the snapshots of the Ras Raf and Ras RalGDS complexes, which explains the favorable contribution of this residue to the effective energy with the charge-assisted hydrogen bond between the Y32 hydroxyl group and the g-phosphate group of GTP, which does not occur in the snapshots of the unbound Ras (state 1). Along these lines, a Y32R mutation in Ras (which stabilizes state 1) reduces the Ras Raf binding affinity by more than 40 times. 101 On the other hand, in the case of D57, which is bound to a water ligand of the magnesium ion, only very minor structural changes occur upon protein protein association. Nevertheless, its contribution to DG gasþsolv amounts to,23.5 kcal mol 21 (largely due to electrostatic contributions) in both the Ras Raf and Ras RalGDS cases, which stems in equal measures from backbone and side-chain atoms. Hence, changes in the environment of a residue can lead to marked DG gasþsolv values. An indirect evidence for the importance of this residue for the function of the Ras protein comes from the seed sequence alignment for the Ras family taken from the PFAM 7.2 data base. 102 In all 61 sequences, D57 is absolutely conserved. Similarly, a more than 98% of conservation is also found for K5, which is more than 6 Å apart from any residue of Raf or RalGDS, yet contributes 25 kcal mol 21 to DG gasþsolv : Considering only the Ras/Rap subfamily within the seed sequence alignment (13 sequences), for other residues showing contributions to DG gasþsolv,23 kcal mol 21 that are not located in the binding interface, sequence identity is found for Y32, P34, D47, and E62, while R73 and Q99 are highly conserved. No conservation is found, however, for R164 and H166 of Ras or for hotspots of Raf and RalGDS not residing in the interface. Decomposition of effective energies on a perresidue basis To gain additional insight into the contributions to the binding free energy change, Figure 6 depicts Figure 6. Decomposition of DG gasþsolv on a per-residue basis into contributions from internal energy (Int), van der Waals energy (vdw), sum of Coulomb interactions þ polar solvation free energy (Coul þ GB), and the nonpolar (NP) part of solvation free energy for residues of (a) Ras Raf and (b) Ras RalGDS for which ldg gasþsolv l $ 3 kcal mol 21 : Crosses above the residue identifier indicate the residues that are located in the binding interface.

14 904 Insights into Protein Protein Binding the decomposition of DG gasþsolv values on a perresidue basis into contributions from internal energy, van der Waals energy, the sum of coulombic interactions and polar solvation free energy, and the non-polar contribution to solvation free energy for residues with ldg gasþsolv l $ 3 kcal mol 21 of Ras Raf and Ras RalGDS. The sum of electrostatic interactions in the gas-phase plus the change of the polar part of the solvation free energy is shown instead of the separate contributions, since, in most of the cases, both numbers are strongly anti-correlated. Qualitatively, no major differences are obvious between residues located in the binding interface and those further apart. For the vast majority of residues, DH elec þ DG GB contributes mainly to DG gasþsolv : Exceptions are found e.g. for S39 and especially Y40. Here, changes in the van der Waals energy are largest. The overall contribution to DG gasþsolv by D38 is dominated by the sum of coulombic interactions and polar solvation in the Ras Raf case; however, in the Ras RalGDS case, van der Waals interactions prevail. This can be explained by the different interaction partners on the effector side. For those residues showing strong unfavorable contributions to DG gasþsolv (Ras: Y4, K16, I36, E153, R161; Raf: F99, E125; RalGDS: S18, D22), unfavorable coulombic interactions dominate the electrostatic part. Only in the case of E153 in the Ras Raf complex, is a gain in favorable electrostatic interactions overcompensated by unfavorable contributions from polar solvation free energy. Contributions from changes in internal energy upon complex formation or contributions from the non-polar part of solvation free energy play an inferior role in all cases. Dynamic and conformational changes of hotspot residues upon binding It is interesting to note where in the respective proteins residues are located that show significant changes of effective energy upon protein protein association, yet are not in the binding epitope. Considering K5, D30, Y32, P34, D47, D57, E62, R73, Q99, R164, and H166 of Ras, D113 of Raf, and E60, Q63, and R96 of RalGDS (in all cases DG gasþsolv #23kcal mol 21 Þ; these residues exist on the surface of the proteins and show a significant exposure to the solvent, with the exception of D57. This can be explained, in part, in view of the fact that these residues are either polar or charged. Other continuum electrostatic calculations have shown that for isolated pairs of interacting polar or ionized groups buried below the surface, the coulombic interactions are generally not strong enough to compensate for unfavorable desolvation effects, hence leading to an overall disfavorable change in effective energy. 74 A different view emerges from the new understanding that proteins do not behave as all-or-none cooperative entities but have a structure in which Figure 7. Frequency distribution of mass-weighted averages of atomic fluctuations for each residue of Ras ( ), Raf (þ), and RalGDS ( p ) in the unbound state. Below, the mass-weighted averages of atomic fluctuations for hotspot residues ðdg gasþsolv # 21:5 kcal mol 21 Þ found in the complexes of Ras ( ), Raf (þ) and RalGDS ( p ) are given. multiple regions are able to undergo local unfolding. 103,104 Energy perturbations at one site then can be propagated to remote locations by altering the dynamic network of interactions in the protein This propagation effect, however, requires the presence of residues with low structural stability in the unbound state. Indeed, Figure 7 confirms that, to a large extent, residues that show changes of DG gasþsolv #21:5kcal mol 21 upon binding, also show large atomic fluctuations in the unbound state. Thus, they reside in structurally less stable regions. The averaged difference in atomic fluctuations per residue for residues with DG gasþsolv #21:5kcal mol 21 upon binding amounts to (^ 0.44) Å (20.19(^0.41) Å) for Ras Raf (Ras RalGDS) and to 20.29(^0.49) Å (20.13(^0.43) Å) if only those residues not in the binding epitope are considered. Importantly, both values are very similar, indicating that there is no qualitative difference between hotspots in the binding interface and those at remote locations. In contrast, for all other non-hotspot residues of Ras Raf (Ras RalGDS), the decrease in the atomic fluctuation upon binding is only 20.05(^0.22) Å (0.00(^0.21) Å). Assuming independence of the respective data samples, a two-population Student s t-test indicates (with a significance level of ) that these mean values are significantly different from the mean values found for the hotspot residues. Protein protein association thus leads to a tightening of the probability distribution of protein states. 108 Similar observations have been made for the binding of antibodies to lysozyme. 109 Although hotspot residues, in general, show reduced conformational fluctuations upon protein protein association, no strict correlation between the amount of decrease in atomic fluctuation and the change in DG gasþsolv per residue upon binding is found.

15 Insights into Protein Protein Binding 905 As another consequence of shifts in the energy landscape, conformational changes between unbound and bound state of the binding partners may occur. However, the difference in the magnitude of the conformational changes between hotspot and non-hotspot residues was found to be less significant than in the case of atomic fluctuations (data not shown). Pair-wise interaction analysis and pathways of energetic coupling In the previous sections we have shown by free energy decomposition that the binding event of two proteins leads to changes in the effective energy even for residues apart from the binding interface and that these changes are mostly regional, not global. The finding raises the question of how these interferences occur, i.e. whether longrange (electrostatic) interactions or rather local perturbations contribute most. For Raf in the Ras Raf case, a visual inspection of Figure 4 suggests that one pathway of favorable interactions runs along helix a1 to the end of b4, while a second pathway appears to involve residues on b2, b1, the beginning of b5, and b3. To obtain a more quantitative result, a pair-wise decomposition of interactions (see Methods) was performed. The resulting interaction matrix is rather sparse (i.e. most of the pair interactions show values of ldg gasþsolv l, 0:5 kcal mol 21 Þ (data not shown) and a detailed analysis considering the protein structures reveals that sizeable interaction energies occur only between spatially adjacent residues. This means that even the charged residues of the interface regions interact most with their immediate counterparts of the binding partner, and that interactions arising from the binding process evolve as local perturbations. We then searched the interaction matrix for the longest paths of pair-wise interactions originating from the Ras side, where we were mostly interested in pathways that do not involve sequentially adjacent residues. Imposing the additional criterion that all pair-wise interactions must have DG gasþsolv #21:0kcal mol 21 ; only the pathway E37-R59-L126 (residues of Raf are given in italics) is identified, i.e. involving Raf residues on b1 and the beginning of b5. Attenuating the effective energy criterion to DG gasþsolv #20:5kcal mol 21 did not result in elongation of this path towards b3, but included more sequentially adjacent residues. In addition, the path along a1 originating from I24 or Q25 and involving R89, L86, and M83 is identified. Interestingly, the longest pathway through Raf is found in the case of disfavorable interactions between two residues. Originating from D38, it involves R89, Q66, F61, Q127, L101, and K106, and, hence, extends from a1 over b2, b1, b5 into the loop region between L101 and K109, whereby interactions between Raf residues show DG gasþsolv. 1:0 kcal mol 21 (Figure 8). Since this Figure 8. Pathway of disfavorable interactions between residues in Raf originating from binding to Ras. For an explanation of the color code, see the legend to Figure 4. pathway is the only one found with significant interactions between the residues that extends from the binding interface into the loop region, it seems that the difference in the loop region of Raf between the unbound and bound protein structure (rmsd ¼ 4.4 Å) may be largely influenced by it. The observed conformational change of loop region L101 to K109 of Raf, triggered by the binding to Ras as suggested by the interaction pathways that originate at the binding interface, may itself lead to a structural change between regulatory and kinase domain, which is consistently proposed to be a requirement for Raf activation. 45,47 An interesting alternative might be to perform mutational studies on Raf residues proposed here to be part of interaction pathways that are not involved in direct interactions with Ras. While effects on binding to Ras may be small (as shown for single alanine mutations of residues in Raf 110 ), disruption of pathways may have larger effects on Raf activation. Conclusion Absolute binding free energies have been calculated for the association of Ras with Raf or RalGDS, which are in fair agreement with experimental data. Following the MM-GBSA approach, gasphase energies and entropy contributions by the solute have been complemented by solvation free energies obtained from a generalized Born model. The analysis of energetic contributions to the (absolute) binding free energy has revealed that van der Waals interactions together with nonpolar contributions to the solvation free energy aid