Structure-based stabilization of insulin as a therapeutic protein assembly via enhanced aromatic–aromatic interactions

Key contributions to protein structure and stability are provided by weakly polar interactions, which arise from asymmetric electronic distributions within amino acids and peptide bonds. Of particular interest are aromatic side chains whose directional π-systems commonly stabilize protein interiors and interfaces. Here, we consider aromatic–aromatic interactions within a model protein assembly: the dimer interface of insulin. Semi-classical simulations of aromatic–aromatic interactions at this interface suggested that substitution of residue TyrB26 by Trp would preserve native structure while enhancing dimerization (and hence hexamer stability). The crystal structure of a [TrpB26]insulin analog (determined as a T3Rf3 zinc hexamer at a resolution of 2.25 Å) was observed to be essentially identical to that of WT insulin. Remarkably and yet in general accordance with theoretical expectations, spectroscopic studies demonstrated a 150-fold increase in the in vitro lifetime of the variant hexamer, a critical pharmacokinetic parameter influencing design of long-acting formulations. Functional studies in diabetic rats indeed revealed prolonged action following subcutaneous injection. The potency of the TrpB26-modified analog was equal to or greater than an unmodified control. Thus, exploiting a general quantum-chemical feature of protein structure and stability, our results exemplify a mechanism-based approach to the optimization of a therapeutic protein assembly.

aromatic rings is of particular interest in relation to the organization of protein cores and subunit interfaces (2). Aromaticaromatic interactions are governed by quantum-chemical properties, which underlie dispersion forces and give rise to asymmetric distribution of partial charges. Whereas aromatic stacking is prominent in nucleic acid structures, pairs of aromatic side chains in proteins more often exhibit edge-to-face (ETF) 4 contacts (3). Can such contacts be exploited in therapeutic protein engineering? Here, we have analyzed aromaticaromatic interactions in the insulin hexamer (4) as a basis for designing improved long-acting (basal) analogs. This class of analogs is central to the treatment of Type 1 and Type 2 diabetes mellitus (5).
Classical crystal structures of insulin hexamers (6,7) immediately suggested a pathway of assembly (4). Pertinent to the mechanism of storage in the secretory granules of pancreatic ␤-cells (8), such assembly is also of pharmacologic importance (9). Insulin assembly both protects the hormone from degradation in pharmaceutical formulations and modulates its pharmacokinetic properties (10). Indeed, the first use of insulin analogs in diabetes therapy reflected efforts to destabilize the insulin hexamer and thereby accelerate absorption of monomers and dimers from the subcutaneous (SQ) depot (summarized in Fig. S1 (11,12)). Because it is more straightforward to introduce unfavorable substitutions than favorable ones, such engineering (corresponding to rapid-acting analogs) was more successful than complementary efforts to enhance the thermodynamic (and kinetic) stability of the insulin hexamer (13). There are presently three rapid-acting insulin analogs in clinical use (14), but no basal products designed on the basis of enhanced hexamer assembly despite extensive efforts (15). These difficulties were circumvented by alternative mechanisms of protracted action (acylation and pH-dependent SQ precipitation (14) ; Fig. S2).
The dimer interface of insulin (repeated three times in the hexamer) contains a cluster of eight conserved aromatic rings (Tyr B16 , Phe B24 , Phe B25 , Tyr B26 , and their dimer-related mates in subunit D; Fig. 1, A-C). Of these, successive ETF contacts are formed by B16 -D26, B24 -B26, B24 -D24, and B26 -D16; the B25 side chain is peripheral to this network. Whereas variation at these sites is in general constrained by the structure of the hormone-receptor interface (16,17), our attention focused on the B26 side chain because of its functional tolerance to diverse substitutions (18) and because of its partial exposure in the monomer, dimer, and hexamer (4) (Fig. 1, C and D). We sought to investigate whether variant B16 -D26 and B26 -D16 ETF contacts across the dimer interface might in principle modulate, in either direction, the strength of these interactions. We hypothesized that enhanced ETF contacts at this interface might provide the long-sought approach to stabilize the insulin hexamer and so improve the pharmacokinetc properties of basal formulations.
The present study had three parts. The first employed local modeling, using the standard CHARMM empirical energy function, to probe possible effects of a Tyr B26 3 Trp substitution on aromatic-aromatic interactions within the wildtype (WT) aromatic cluster. These molecular mechanics (MM) calculations suggested that substitution of Tyr B26 by Trp could enhance dimer-related ETF contacts and yet otherwise preserve a native-like interface. We next prepared this analog to examine whether this substitution might indeed stabilize the insulin hexamer and retard its disassembly while preserving the biological activity of the monomeric hormone. The crystal structure of a [Trp B26 ]insulin analog (as a zinc-insulin hexamer) was essentially identical to that of WT insulin. Finally, we undertook studies in diabetic rats to obtain proof of principle that this approach could extend the duration of insulin action on SQ injection.  B26 3 Trp substitution is orange; and modifications in pI-shifted clinical analog glargine in purple. Our semisynthetic pI-shifted analog contained Orn (green) instead of Lys or Arg. B, structure of an insulin monomer; the A chain is shown in black and B chain in green. Tyr B26 is red, whereas Phe B24 and Tyr B16 are blue (PDB code 4INS). C, structure of zinc-coordinated insulin hexamer (T 6 state), a trimer of dimers; Tyr B26 , Phe B24 , and Tyr B16 are color-coded as in B. D, stereo view showing Tyr B26 (sticks) in a cavity within insulin dimer (extracted from T 3 R f 3 hexamer, PDB code 1TRZ). E, corresponding stick model with residues labeled.
To our knowledge, our results represent the first exploitation of aromatic-aromatic interactions to enhance the physical and biological properties of a therapeutic protein. Because standard MM calculations employ a simplified model of aromatic systems (i.e. approximating their quantum-mechanical (QM) properties via partial atomic charges (19,20)), ab initio QM simulations of the aromatic cluster and their incorporation in QM/MM simulations (21) promise to establish a rigorous foundation for therapeutic protein design, including further optimization through incorporation of modified or nonstandard amino acids (22)(23)(24). The present results suggest that insulin's conserved aromatic cluster can provide a natural laboratory for such foundational analysis and its therapeutic translation.

Molecular mechanics calculations suggested that augmented aromatic-aromatic interactions are possible at the Trp B26 dimer interface
MM simulations were employed to estimate the strength of aromatic-aromatic interactions of Trp B26 at the insulin dimer interface in relationship to those of the native Tyr. These calculations employed the CHARMM empirical energy function in which aromatic rings contain partial atomic charges, parametrized to mimic the electrostatic properties of the -system (19,20). Working models of the variant dimer were obtained by local energy minimization (see "Experimental procedures").
Energies of interaction between the eight aromatic residues at the insulin-dimer interface (Tyr B16 , Phe B24 , Phe B25 , Tyr B26 , and their symmetry-related mates) were calculated using local models in which Trp B26 was substituted within WT T 2 , R 2 , and TR f reference dimers (extracted from PDB structures 4INS, 1ZNJ, and 1TRZ) (25). The total interaction energy between B26 and the other aromatic residues at the Trp B26 interface, which was calculated using the full CHARMM potential energy function, was augmented by 2.0 and 0.8 kcal/mol relative to the minimized WT interface in the context of R 2 and TR f structures, respectively, and diminished by 1.5 kcal/mol in the context of the T 2 structure. Results are summarized in Table S1.
A minimal model was utilized to further evaluate the potential impact of a Trp B26 substitution on aromatic-aromatic interactions at the dimer interface. To this end, a structural model of the dimer interface (extracted from a T 6 insulin hexamer; PDB code 4INS) was first built containing residue B26 (Tyr B26 or Trp B26 ) and its nearest aromatic neighbors (Phe B24 , Phe D24 , or Tyr D16 ). Simulations predicted the orientation of the B26 ring corresponding to free-energy minima of electrostatic interactions between the aromatic residues (the partial-charge parametrization of aromatic residues in CHARMM is shown in Fig. S3) (23). When substituted at position B26, Trp displayed improved electrostatic interactions with its three aromatic neighbors (relative to the WT Tyr) over a broad range of conformations (Fig. 2). This trend extended to conformations that are sterically permitted in the context of the WT insulin hexamer.

Trp B26 analog exhibited markedly decreased hexamer dissociation rate
The effect of the Trp B26 substitution on the lifetime of insulin hexamers under formulation conditions was assessed in the context of [Orn B29 ]insulin, a structural equivalent of WT insulin that is amenable to production by trypsin-catalyzed semisynthesis (26). The lifetime of Co 2ϩ -substituted, phenol-stabilized (R 6 ) hexamers of [Trp B26 ,Orn B29 ]insulin was assessed at equilibrium in relationship to native [Tyr B26 ,Orn B29 ]insulin. Optical absorbance spectra of these analogs (characteristic of Co 2ϩ with tetrahedral coordination) were similar to WT (Fig. 3,  A and B). Assessment of R 6 dissociation rates (summarized in Table 1) revealed a 150-fold increase in hexamer half-life of the Trp B26 analog relative to its parent [Orn B29 ]insulin (Fig. 3, C and D). This increase is remarkable given that the difference between the half-lives of a rapidly dissociating analog in clinical use (lispro) 5 (27)(28)(29) and WT is Ͻ2-fold (Table 1).

Trp B26 imposed kinetic barriers to the dissociation of hexamers into monomers
R 6 dissociation kinetics were further examined by size exclusion chromatography (SEC). The Trp B26 analog (formulated in the presence of phenol and zinc ions) was injected onto an SEC column using a zinc-and phenol-free mobile phase. Subsequent dissociation of the R 6 hexamers was monitored in the chromatograms (Fig. 4A, Table 1). Absence of a void volume signal (V 0 ) indicated that none of the proteins formed large nonspecific aggregates. Whereas WT and [Orn B29 ]insulin eluted as a broad peak representing an association state intermediate between monomer and dimer (9.7 and 8.2 kDa, respectively) and insulin lispro eluted essentially as a monomer (5.1 kDa), [Trp B26 ,Orn B29 ]insulin eluted in two distinct peaks. The larger peak corresponded to a trimeric or tetrameric association state (molecular mass 28 kDa), and the smaller corresponded to a monomeric state (4 kDa; Fig. 4 (69); this is associated with a greater proportion of spectroscopically attenuated T 3 R f 3 hexamer and invisible T 6 hexamer (Fig. 3B). A, aromatic-aromatic interactions across insulin's dimer interface involve Phe B24 , Tyr B16 , Phe D24 (sticks) and either Tyr D26 (left) or Trp D26 (right). Residues were extracted from T 6 structure 4INS. B, contour maps depicting empirical interaction energies between B26 (Tyr on left and Trp on right) at varying 1 and 2 angles and the other three residues shown in A. The orientation of Tyr B26 or Trp B26 in the WT or variant crystal structure is indicated by a green "x"; orientation of Tyr B26 or Trp B26 in the local model is indicated by a green asterisk.

Stabilization of insulin hexamer
for reference chromatograms of the monomer and hexamer). These findings suggest that oligomers intermediate between hexamer and dimer may delay dissociation of the Trp B26 analog; in particular, the absence of broad elution tails implies that Trp B26 imposes significant barriers to rapid dissociation.

Trp B26 analog displayed a zinc-dependent delay in onset of biological activity
Hexamer assembly delays absorption of insulin from its SQinjection site (11,12). To assess the onset and duration of [Trp B26 ,Orn B29 ]insulin relative to [Orn B29 ]insulin, the pharmacodynamics (PD) profile of these proteins (made 0.15 mg/ml, corresponding to a monomer concentration of 27 M and a putative hexamer concentration of 4.5 M) were evaluated as zinc-free solutions or as pre-assembled phenol-stabilized R 6 hexamers in the presence of excess zinc ions (0.30 mM ZnCl 2 ; 70 zinc ions per hexamer). A zinc-dependent delay in onset of activity was observed on SQ injection of [Trp B26 ,Orn B29 ]insulin but not on injection of [Orn B29 ]insulin or WT insulin ( Fig. 5C; see Fig. S5 for WT results). Whereas the latter PD profiles exhibited a nadir at about 120 min irrespective of the zinc ion concentration, the PD profile of [Trp B26 ,Orn B29 ]insulin occurred at (i) 120 min in the absence of zinc ions and (ii) 150 min in the presence of 0.30 mM zinc ions with corresponding delays in the rate of fall over the first 30 min (Fig. 5D). Together with the above in vitro results, these findings suggest that the prolonged lifetime of the Trp B26 R 6 hexamer (as inferred from the above kinetic studies of the Co 2ϩ -substituted hexamer) are responsible for the inferred zinc-dependent delay in SQ absorption.

Trp B26 protracted the PD profile of a model pI-shifted analog
Insulin analogs with isoelectric points (pI) shifted to neutral pH generally exhibit prolonged activity due to precipitation in the SQ depot (30). To determine whether Trp B26 might further prolong the activity of such analogs, this substitution was introduced into a [Gly A21 ,Orn B29 ,Orn B31 ,Orn B32 ]insulin. This "glargine-like" framework was designed to recapitulate the pI shift of glargine with greater ease of semisynthesis. 6 The proteins (formulated at 0.6 mM with 0.3 mM ZnCl 2 , corresponding to 3 zinc ions per hexamer) were each injected SQ in diabetic rats.
The pI-shifted parent analog displayed peak activity at about 120 min with blood glucose levels returning to baseline after about 360 min. By contrast, its Trp B26 derivative displayed a prolonged PD profile: peak activity occurred 180 min with slow return to baseline at Ͼ800 min ( Fig. 5E; see Fig. S6 for i.v. potency). Such a marked delay in peak activity was not observed in the parent glargine-like analog or the Trp B26 derivative when administered in the absence of zinc (Fig. S7). These results suggest that Trp B26 may favorably be incorporated into current basal analogs as a complementary mechanism of prolonged SQ absorption.

Crystal structure of Trp B26 analog demonstrated native-like dimer interface
The crystal structure of [Trp B26 ,Orn B29 ]insulin was determined as a zinc-coordinated hexamer in the presence of phenol to a resolution of 2.25 Å. Diffraction and refinement statistics are provided in Table S2. The asymmetric unit constituted a "TR f " dimer 7 (31,32). The overall structures of the T and R f protomers were essentially identical to those of WT insulin ( Fig. S8) with respective r.m.s. deviations of 1.11 Ϯ 0.30 and  Table 1. a Proteins were made 0.6 mM in a buffer containing ZnCl 2 at a ratio of 2 zinc ions per insulin hexamer and applied to SEC column as described under "Experimental procedures." Masses were calculated from the plot in Fig. 4B. b "Lispro" describes insulin analogs containing Pro B28 3Lys and Lys B29 3Pro substitutions. These substitutions impair dimerization (28, 29). c Use of Orn simplified trypsin-catalyzed semisynthesis (33).

Stabilization of insulin hexamer
1.36 Ϯ 0.30. Additional r.m.s. deviations are given in Tables S3  and S4. Side chain packing near the B26 position was largely unperturbed. In both protomers the Trp B26 indole group was oriented with its six-member ring packing against conserved core residues Ile A2 , Val A3 , and Val B12 (Fig. 6); the indole NH group is exposed to solvent in the TR dimer and T 3 R f 3 hexamer. The Trp B26 side chain in both R and T protomers also displayed dihedral angles within the range of the native Tyr in WT crystal structures (Tables S5 and S6, respectively) with a slight deviation in the positioning of the peptide backbone to accommodate the larger indole side chain.

Spectroscopic probes revealed native-like structure and thermodynamic stability of Trp B26 analogs in solution
The native-like crystal structure of [Trp B26 ,Orn B29 ]insulin is in accordance with its unperturbed circular dichroism (CD) spectrum and thermodynamic stability under monomeric conditions (Fig. 7A). Free energies of unfolding (⌬G u 3.3 Ϯ 0.1) kcal/mol at 25°C as inferred from two-state modeling of chemical denaturation (33)) were indistinguishable due to small and compensating changes in transition midpoint and slope (m value) (33, 34) (Fig. 7B, Table 2). Further evidence that the crystal structure extends to the monomer in solution was provided by 2D 1 H NMR studies of Trp B26 substituted within an engineered insulin monomer (lispro (35)). Whereas the spectrum of lispro (at pD 7.6 and 37°C) exhibits sharp resonances for each aromatic spin system (Fig. 8A), as expected for a monomeric analog (35), the spectrum of its Trp B26 derivative exhibits broadening of resonances at the dimer interface (B16, B24 -B26). The latter spin systems can be observed on TOCSY spectrum ( Fig. 8C) but not in the corresponding DQF-COSY spectrum due to antiphase cancellation. Like the aromatic ring Tyr B26 in spectra of insulin lispro (Fig. 8, A and B), the indole ring exhibited regiospecific nonlocal nuclear Overhauser enhancements (NOEs) from its six-member moiety to the methyl resonances of Val B12 and Ile A2 (Fig. 8, B-D).
The pattern of secondary shifts in the variant is similar to that in the parent monomer. In particular, the aromatic 1 H NMR resonances of Trp B26 (red cross-peaks in Fig. 8C) exhibit upfield features (relative to Trp in the isolated B23-B30 octapeptide; dashed lines) similar to those of Tyr B26 in the parent spectrum (purple cross-peaks in Fig. 8A versus dotted lines) (36). Dilution of the Trp B26 sample partially mitigated resonance broadening but preserved these trends in dispersion. Indole-specific NOEs indicated that the side chain assumes one predominant and asymmetric conformation within a native-like crevice between A-and B-chain ␣-helices (Table S7). Because Tyr B26 undergoes rapid ring rotation about the C ␤ -C ␥ bond axis ("ring flips"), analogous side chain-specific NOEs (inferred in prior studies from molecular modeling) cannot be observed directly (Table S8).

Stabilization of insulin hexamer MM calculations suggested improved aromatic-aromatic interactions within the variant crystal structure
The contribution of aromatic-aromatic interactions involving Trp B26 to the stability of the variant dimer interface of the T 3 R f hexamer was evaluated through calculation of nonbonded interaction energies among aromatic residues B16, B24, B25, and B26 in the TR f dimer. These calculations, which employed the variant crystal structure, were in overall accordance with expectations based on our initial local MM-based modeling (above). In particular, based on aromatic-aromatic interactions alone, the Trp B26 ,Orn B29 dimer displayed an increase in interaction energy of 1.4 kcal/mol relative to WT TR f reference structure PDB 1TRZ; the results of these calculations are given in Table S9, a and b. Although the standard CHARMM empirical energy function, when applied to analyze either crystallographic and MM-minimized models of [Trp B26 ]insulin, suggested that the electrostatic properties of the Trp side chain were the primary contributors to the increased stability of the dimer, this physical interpretation may reflect the limitations of the partial-charge representation (23,37). Indeed, preliminary ab initio QM simulations of a minimal model (consisting of two aromatic rings in vacuo) predicted that enhanced Van der Waals interactions may also make a significant contribution (Fig. S9) (see "Discussion").

Discussion
The physical origins of protein stability and recognition define a foundational problem in biochemistry (38) with central application to molecular pharmacology (39). The zinc-insulin hexamer provides a favorable system for structure-based design due to its long history of crystallographic investigation (40). Indeed, the hexamer's rigidity, as interrogated by NMR spectroscopy (41), renders the overall structure robust to diverse amino acid substitutions (42,43), even those that destabilize the dimer interface 8 (32,44). This rigid framework has often enabled analysis of discrete interactions without complications due to the long-range transmission of conformational change (31,32).
Our studies, stimulated by the seminal recognition of aromatic-aromatic interactions by Burley and Petsko (2) more than 30 years ago, focused on the classical dimer interface, a basic building block of the hexamer (32). Long appreciated as "a thing of beauty" (4,45), this interface contains eight aromatic residues, six of which engaged in a successive set of aromaticaromatic interactions. Quantum-chemical simulations of model systems have suggested that nearest-neighbor interactions predominate even in the presence of multiple rings (46). Pairwise dissection of insulin's dimer interface has highlighted 8 An exception is provided by a substitution at the primary zinc-binding site (His B10 3 Asp), which converts the hexamer into a novel dodecamer with zinc-coordination mediated by His B5 (26). The structure of each protomer is native-like.   Table 2.

Table 2
Thermodynamic stabilities of insulin analogs a Parameters were inferred from CD-detected guanidine denaturation data by application of a two-state model; uncertainties represent fitting errors for a given data set. b The m-value (slope ⌬(G)/⌬(M)) correlates with surface area exposed on denaturation. c Analysis of replicates of [Trp B26 ,Orn B29 ]insulin, parent [Orn B29 ]insulin, and WT samples indicated that experimental standard errors were equal to or less than the above fitting errors:

Stabilization of insulin hexamer
the potential opportunity to enhance its stability through substitution of Tyr B26 by Trp. Whereas our crystallographic analysis verified that this substitution preserves native architecture, a [Trp B26 ]insulin analog exhibited a dramatic increase in hexamer lifetime in vitro. Results of animal testing demonstrated native intrinsic potency (i.e. on i.v. bolus injection) but with prolonged activity on SQ injection, presumably due to delayed dissociation of the variant zinc hexamers in the SQ depot. Protein engineering of insulin analogs is constrained by the complexity of insulin's "conformational lifecycle": from oxidative folding intermediates and self-assembly in the pancreatic ␤-cell (8) to adoption of an active, "open" conformation on receptor binding (Fig. 9, A and B) (16). Specific residues may play distinct roles at each stage. In particular, because interfaces within the insulin hexamer overlap the hormone's receptorbinding surface, essentially invariant among vertebrates (47), modifications often impair activity (13). A given WT residue may represent a compromise among competing structural tasks. A recent survey of 18 substitutions at position B26 demonstrated that Tyr is suboptimal with respect to IR-binding affinity but enhances self-assembly relative to more active alternatives (Ala, Ser, or Glu) (18). The latter side chains destabilize the "closed" dimer interface but are favorable at the solvated B26-related edge of the open hormone-receptor interface (Fig. 9C).

Protective self-assembly is of key pharmacologic importance
Insulin self-assembly protects the hormone from degradation and toxic misfolding in pancreatic ␤-cells 9 (8,48) and in pharmaceutical formulations (49). Because the zinc-insulin hexamer exhibits delayed SQ absorption relative to monomers and dimers, mutational destabilization of the hexamer (10,12) led to development of rapid-acting insulin analogs (14). Efforts to stabilize the insulin hexamer, as a converse strategy to obtain protracted action, were less successful (13). Current long-acting insulin analogs rely instead on higher-order self-association of hexamers within the SQ depot (30) and binding acylated monomer to albumin as a circulating depot (highlighted in Fig.  S2) (50,51).
The problem of how to improve a protein interface is in general more subtle than its opposite, for destabilizing substitutions abound at conserved interfaces, whereas stabilizing substitutions can be rare (13). Structure-based candidate substitutions may encounter entropy-enthalpy compensation (EEC) (52,53) or cause unintended biological perturbations (54). The challenge posed by insulin is magnified by the struc- 9 An experiment of nature provided in vivo evidence for the relationship between zinc coordination and protection from toxic insulin misfolding: in the rodent species Octogon degus, substitution of His B10 by Asn is associated with senile amyloidosis of the islets due to insulin fibrillation (70), resulting in DM (48).

Stabilization of insulin hexamer
tural elegance of its self-assembly (as emphasized by Hodgkin and colleagues (55) in a classic review). Diverse structure-based strategies were previously undertaken with only limited success. Alternate strategies previously used to create basal insulin analogs are depicted in Fig. S2 and summarized in Table S10. One approach focused on the general nonpolar character of the dimer interface: additional hydrophobic substitutions were introduced in an effort to enhance this feature (56). Such designs were not successful and also impaired biological activity, although analogs were identified whose sparing solubility slowed SQ absorption (56). A second approach exploited the classical TR transition among insulin hexamers (57). At the pivot point of this allosteric transition (Fig. S10), an invariant glycine (Gly B8 ) was substituted by Ser in an effort to stabilize the more stable R state hexamer (58). This analog was unstable as a monomer (54) and exhibited reduced activity (58). Yet another approach sought to stabilize the hexamer by relieving electrostatic repulsion created by the internal clustering of six acidic side chains (Glu B13 ): their isosteric substitution by Gln indeed promoted assembly of zinc-free hexamers but impaired biological activity (59). Overlap between the self-assembly surfaces of insulin and its receptor-binding surfaces thus compounded the optimization problem.
The present study revisited the architecture of the insulin hexamer in light of recent insights into the hormone's receptorbinding surface (18). Prominent roles are played by a quartet of aromatic residues in the C-terminal B-chain ␤-strand: Tyr B16 , Phe B24 , Phe B25 , and Tyr B26 (33). These four residues, and the clustering of eight dimer-related side chains, have long been the focus of structure-activity relationships (60). Photoactivatable aromatic probes (para-azido-Phe) at any of these sites exhibited efficient cross-linking to the IR (61, 62). The co-crystal structure of an insulin monomer bound to a fragment of the IR ectodomain (the IR model) revealed distinct binding sites at the surface of the L1 domain of the IR ␤-subunit (B16, B24, and B26) or its ␣CT element (B24 and B25). Phe B24 packs within a nonpolar pocket near aromatic residues in L1 (residues Leu 37 and Phe 39 ) and ␣CT (residue Phe 714 ); one wall of this pocket is defined by the aliphatic side chains of Leu B15 , Cys A20 , and Cys B19 as in free insulin (16). This environment differs in detail from those in the insulin dimer but exhibits analogous general features. Although aromaticity is not required to fill the B24binding pocket (33), its specific size and shape constrain potential substitutions. Tyr B16 lies at the periphery of L1 (near Phe 39 and Lys 40 ). Its substitution by Ala or other aromatic residues preserves activity (63). Phe B25 occupies a cleft between ␣CT
We chose to focus on position B26 because of its broad functional tolerance of diverse substitutions (18). As illustrated above (Fig. 8C), Tyr B26 binds at the solvated periphery of the IR interface. Indeed, substitution of small, polar, or charged amino acids (such as Ala, Ser, or Glu) enhances receptor affinity, but at the price of impaired self-assembly and decreased thermodynamic stability with heightened susceptibility to physical degradation (16). These findings highlighted the evolutionary importance of the native dimer interface and dual role of Tyr B26 . We thus hypothesized that an aromatic substitution at the B26 position might enhance self-assembly without loss of biological activity.
The classical structure of the insulin dimer motivated study of successive aromatic-aromatic interactions as a physical mechanism of stability (6, 64). The increased stability of ETF aromatic-aromatic interactions involving Trp over those involving Tyr contributes to the increased stability of the Trp B26 hexamer. The larger size of the delocalized -orbital of Trp in relationship to that of Tyr causes a stronger negative charge to accumulate on the "face" of the indole ring. For this reason, hydrogen atoms surrounding the aromatic rings of local residues form stronger electrostatic interactions with the face of the indole ring of Trp than with the phenol ring of Tyr (65, 66). Aromatic pairs involving Trp residues are less common than those involving Tyr or Phe (1). However, the strength of aromatic-aromatic interactions involving Trp is evidenced by functional importance of Trp-based interactions; an example is provided by a Trp-Tyr aromatic "lock" that stabilizes the active conformation of the ghrelin receptor (67). Indeed, comparison of electrostatic interactions of Trp B26 and Tyr B26 within the minimized model of the B16/B24/B26 aromatic network of insulin revealed that interactions involving Trp were favored over those involving Tyr across a broad variety of orientations of the respective aromatic rings. Extension of the aromatic lock metaphor (introduced by Holst et al. (67) to describe conformational "trapping" in the GPCR structure) to the insulin hexamer highlights the kinetic effect of the B26 substitution on the rate of hexamer disassembly (as probed by the Co 2ϩ -EDTA sequestration assay), which was more dramatic than effects on equilibrium association (as probed by SEC). It would be of future interest to measure activation energies for disassembly. Insight into the structural origins of the prominent Trp B26associated kinetic lock may be provided by activated molecular dynamics simulations of hexamer disassembly.

Trp B26 side chain exhibited an orientation similar to native Tyr
The Trp B26 side chain in the crystal structure of [Trp B26 ,Orn B29 ]insulin displayed an orientation similar to that of the native Tyr. A slight main chain shift in the B24 -B28 ␤-strand (0.2 (Ϯ0.03) Å) was sufficient to enable native-like packing of the larger indole ring against the core of a protomer (Fig. S12). In both T and R f subunits, the six-membered component of the indole side chain was oriented toward Ile A2 , Val A3 , and Val B12 . Based on the classical 3.5-6.5 inter-centroid distance, residue Trp B26 (of the T protomer) showed potential interactions with residues Tyr D16 and Phe D24 . An interplanar angle of 78 degrees between Trp B26 and Tyr D16 was indicative of classical aromatic-aromatic packing within proteins (2), which generally range from 50 to 90 degrees. Trp B26 and Phe D24 displayed an interplanar angle of 36 degrees, however, this orientation is less common. Similarly, in the R f protomer, Trp D26 packed near Tyr B16 and Phe B24 . The interplanar angle between Trp D26 and Tyr B16 was 62 degrees, whereas between Trp D26 and Phe B24 was 48 degrees. Previous studies have suggested that Trp residues may form aromatic-aromatic interactions over longer distances than those formed by Tyr-Phe pairs (68). Thus, the two intra-chain aromatic pairs, Trp B26 -Phe B24 and Trp D26 -Phe D24 (respectively, separated by 7.8 and 7.1 Å) may interact more efficiently than the corresponding Tyr-Phe pairs in WT insulin (ring geometries are summarized in Table S11, a and b).
CHARMM calculations of aromatic-aromatic interactions across the dimer interface of [Trp B26 ,Orn B29 ]insulin revealed 1.4 kcal/mol increased interaction energy. Residue by residue analysis of each component of the aromatic network indicated that the increased strength of interaction across the dimer interface was the result of the interactions involving Trp D26 (see Table S9b). This result suggests that Tyr B26 3 Trp may only display stabilizing properties when in an R state protomer. If so, the T 6 hexamer formed by [Trp B26 ]insulin would be expected to have dissociation kinetics similar to WT insulin, whereas the corresponding R 6 hexamer may be expected to have markedly increased stability. The R 3 T transition, which is rapid in WT insulin on release of phenol, may represent the kinetic barrier responsible for the meta-stable association state observed in SEC experiments.
The packing of Trp B26/D26 within the respective cores of Tand R f crystallographic protomers is similar in each case to the WT Tyr B26/D26 and oriented such that the indole's nonpolar six-membered portion projects more deeply into a crevice between A-and B-chains than does its proximal heterocycle. Our 1 H NMR studies of Trp B26 within an engineered monomer (35) provided evidence that this overall conformation does not require self-assembly. Analogous partial burial of Tyr B26 and Trp B26 in the respective protein structures would in itself be expected to augment the variant's stability due to enhanced solvation free energy 10 (69) (i.e. as predicted by water-octanol transfer studies of free Tyr and Trp (69); Table S12). Guanidine denaturation nonetheless, indicated that their stabilities are indistinguishable. 11 We speculate that the predicted residue-specific differences in solvation free energy are attenuated by differences in protein dynamics leading to EEC (70). Although the two B26 side chains each exhibit upfield secondary 1 H NMR shifts and analogous inter-residue NOEs, it is possible that the substitution is associated with local or nonlocal differences in protein dynam- 10 The identification of a destabilizing Trp 3 Tyr mutation in Escherichia coli thioesterase-I demonstrated, in breach, the improved cavity-filling properties of Trp relative to Tyr (72). 11 That [Trp B26 ,Orn B29 ]insulin exhibited a greater exposure of nonpolar surfaces on denaturation in guanidine HCl than did [Orn B29 ]insulin was suggested by a change in m values in two-state modeling ( Table 2).

Stabilization of insulin hexamer
ics. It would be of future interest to investigate dynamic features by amide proton 1 H-2 H exchange and heteronuclear NMR relaxation methods (70). Because Trp B26 promotes partial dimerization of insulin lispro under NMR conditions (as indicated by concentration-dependent 1 H NMR resonance broadening), such studies may require use of an alternative monomeric template.
Given the ubiquity of EEC as a confounding general aspect of protein design (71), the profound effects of Trp B26 on the properties of the insulin hexamer seem all the more remarkable. We envision that EEC is circumvented in this case by the rigidity of the insulin hexamer (including the interlocked aromatic residues at its dimer interfaces) with efficient burial of the WT and variant B26 side chains (72). With similar internal structures and external solvation properties, the variant hexamer would gain (relative to WT) two advantages from the Tyr 3 Trp substitution: (i) greater B26-related solvation transfer free energy (73) (Table S12) augmented by (ii) an uncompensated enthalpic advantage arising from more favorable ETF aromatic interactions as next discussed.

Molecular mechanics calculations rationalized physical and pharmacologic properties
The structural rigidity of the R 6 insulin hexamer (42,74) motivated local MM-based modeling to assess the interactions contributing to the stability of the [Trp B26 ]insulin hexamers. Analysis of insulin oligomers by Raman spectroscopy revealed dampened conformational fluctuations of the R 6 hexamer in relationship to lower-order oligomers and T 6 hexamers (72). Moreover, the thermodynamic stability of the assembly was evidenced by the lack of conformational changes visualized by NMR spectroscopy over a temperature range of 10 -80°C (42). The resistance of the R 6 hexamer to structural perturbation has also been shown in the context of mutant insulin analogs: native-like X-ray crystal structures have been reported of R 6 containing a broad range of substitutions (Table S13) (17,75,76). Even substitutions that were shown to destabilize the dimer interface of insulin, such as the substitution of Phe B24 by the nonaromatic cyclohexylalanine, were shown to have little impact on the global structure of the R 6 hexamer. For this reason, the Tyr B26 3 Trp substitution was expected to affect only the local structure of the insulin hexamer. Thus, the effects of the mutation were amenable to initial analysis in simplified (eight-ring) models of the dimer interface of insulin.
Energy minimization of a local model of [Trp B26 ]insulin (i.e. as substituted into a WT insulin dimer extracted from a representative crystal structure of a T 3 R f 3 zinc hexamer) yielded a native-like framework with enhanced nearest-neighbor B26related aromatic-aromatic interactions. The partial-charge (monopole) model of the aromatic rings in the CHARMM empirical energy function, parametrized in accordance with ab initio simulations (77), predicted an increase of 0.8 kcal/mol. Although this calculation could in principle have been confounded by transmitted conformational perturbations and did not consider potential changes in conformational entropy or solvation, its conservative features were verified by X-ray crystallography. That the structure of [Trp B26 ,Orn B29 ]insulin is essentially identical to WT suggests that local properties of Trp B26 directly underlie the observed increase in hexamer stability and lifetime.
The general asymmetry of the variant TR f dimer in the crystallographic hexamer was associated with differences in the details of corresponding aromatic-aromatic interactions across the dimer interface. Although CHARMM calculations predicted an increase of a 1.4 kcal/mol in interaction energies (0.7 kcal/mol per protomer) in accordance with our initial modeling, residue by residue decomposition ascribed this increase primarily to Trp D26 (in the R f protomer) and not to Trp B26 (in the T protomer). It is formally possible that Trp B26 is only stabilizing in an R state, but additional studies would be required to resolve this issue. Our cobalt-EDTA sequestration studies focused on the R 6 state as the preferred storage vehicle in a pharmaceutical formulation. On SQ injection, rapid diffusion of phenolic ligands from the depot leads to a TR transition. That Trp B26 was found to delay subsequent absorption into the bloodstream suggests that this substitution also enhances the kinetic stability and lifetime of the T 6 hexamer.
A seeming paradox is posed by the evolutionary exclusion of Trp at position B28 of vertebrate insulins despite the evident compatibility of this aromatic side chain with native structure and function. We speculate that this exclusion reflects the biological importance of the rapid disassembly of zinc insulin hexamers on their secretion by pancreatic ␤-cells. Whereas the enhanced thermodynamic and kinetic stabilities of [Trp B26 ]insulin hexamers would seem favorable for storage within secretory granules (as within pharmaceutical formulations) (8), delayed disassembly of the variant hexamers in the portal circulation would be predicted to reduce the hormone's bioavailability on first pass through the liver, as insulin dimers and hexamers cannot bind to the IR (78). Such delayed disassembly might also decrease the delivery of free zinc ions to the liver, recently predicted to constitute a regulatory signal in its own right (for review, see Ref. 79).
The resulting impairment in hormonal regulation of hepatic metabolism (and accompanying systemic hyperinsulinemia (80)) could in principle have imposed a selective disadvantage in the course of vertebrate evolution. Although to our knowledge, such a kinetics-based mechanism has not been observed in vivo, the converse, abnormally rapid clearance of insulin, has been found on release from zinc-deficient secretory granules; presumably zinc-free insulin oligomers more rapidly dissociate on dilution in the portal circulation and so are more efficiently cleared than WT zinc insulin hexamers (81). Similarly, the exclusion of Trp at position B26 of vertebrate IGFs may reflect a disadvantageous competition between self-assembly and binding to IGF-binding proteins, which are critical to the integrated physiology of IGF function (for review, see Ref. 82). Such functional complexity may impose hidden constraints on the evolution (and so divergence) of protein sequences. The conserved "aromatic triplet" of vertebrate insulins and IGFs provides a natural laboratory to uncover such evolutionary constraints (45). These considerations further suggest that structural features of a protein pertinent to its endogenous function may in general be distinct from those biophysical properties that may be re-engineered to optimize molecular pharmacology.

Stabilization of insulin hexamer Comparison of [Trp B26 ]insulin and a corresponding iodo-Tyr analog
Design of [Trp B26 ]insulin was in part motivated by prior studies of an analog containing 3-iodo-Tyr at the B26 (17,23,83). The latter analog ("3I-Y-insulin") exhibited a variety of favorable properties: increased affinity for the IR (83), increased thermodynamic stability, and augmented resistance to fibrillation (17). Moreover, when formulated as an R 6 hexamer, this analog exhibited a decreased dissociation rate (17). Because modified amino acids raise the cost and complexity of protein manufacture, we wondered whether a natural amino acid might mimic, at least in part, the structure of 3I-Y-insulin and so confer favorable pharmacologic properties with conventional manufacturing.
This translational goal motivated our initial MM-based local modeling of [Trp B26 ]insulin. Analysis of the crystal structure of 3I-Y-insulin, determined as an R 6 zinc hexamer (23), revealed that the large, nonpolar iodo-substituent packed within the core of the insulin protomer with preservation of a native-like dimer interface. Molecular dynamics simulations, undertaken with a multipolar electrostatic model of the modified aromatic ring (23), rationalized this conformation: the iodine atom efficiently filled a cryptic packing defect in WT insulin, lined by the conserved side chains of Ile A2 , Val A3 , and Tyr A19 . The enhanced packing efficiency of the modified insulin and novel network of halogen-specific electrostatic interactions ("weakly polar" interactions (1)) appear to underlie the analog's increased thermodynamic stability and resistance to fibrillation. Whereas the standard partial-charge model of aromatic systems failed to account for the conformation of iodo-Tyr observed in the crystal structure, a multipolar electrostatic model rationalized thermodynamic stabilization of the dimer interface by this halogen "anchor" (23). Subtle changes in the geometry of aromaticaromatic interactions were observed both in the simulations and in the crystal structure. Although activated MD simulations were not undertaken to probe the process of dimer dissociation, we presume that the above mechanisms of groundstate stabilization, enhanced core packing efficiency, and a halogen-specific weakly polar network, also underlie the increased barrier to dissociation as indicated by the prolonged lifetime of the variant R 6 hexamer (23).
Although the profound QM effects of halo-aromatic substitutions, including weakly polar interactions and "halogen bonding" (84), cannot be recapitulated by natural amino acids, it seemed possible that enhanced core packing efficiency might be achieved by analogy to 3I-Y-insulin. Indeed, the steric profile of the asymmetric indole side chain of Trp is similar in size to 3-iodo-Tyr. Accordingly, we imagined that the offset six-membered portion of the bicyclic indole ring might pack within the core of insulin in a manner similar to the iodine atom. In this intuitive picture the extended -system of Trp B26 was envisioned to interact with neighboring residues to recapitulate, at least in part, the favorable electrostatic properties of iodo-Tyr B26 (23,37).
The above line of reasoning led to the present set of studies. In accordance with our original intuition and local MMbased modeling, the crystal structures of 3I-Y-insulin and [Trp B26 ,Orn B29 ]insulin exhibited similar features. Nevertheless, salient differences between the quantum-chemical properties of iodo-Tyr and Trp might make the similar structures of these B26 analogs a fortuitous outcome of distinct mechanisms. Whereas effects of 3-iodo-Tyr on aromatic-aromatic interactions at the insulin dimer interface are subtle, presumably reflecting indirect inductive effects of iodo-substitutent (23), substitution of Tyr by Trp introduces a larger aromatic surface at this interface. It is possible that this feature underlies the more marked impact of Trp B26 on insulin oligomerization relative to 3-iodo-Tyr.

Aromatic-aromatic interactions exemplify limitations of classical models
The quantum origins of aromatic-aromatic interactions are complex, and so classical electrostatic models (such as partialcharge model of Tyr in the standard CHARMM empirical energy function) can be incomplete (85). Although QM calculations more fully capture this complexity, a tradeoff is encountered between rigor and computational feasibility, especially in complex systems such as proteins (86), but even in ab initio simulations of benzene-benzene interactions (46). Standard MM and MD methods thus employ parametrized force fields to approximate quantum-chemical interactions (21). Although parameters (e.g. partial charges assigned to an aromatic ring) have been chosen to provide reasonable protein models, such use of "monopolar" electrostatics neglects the polarizability of aromatic systems and so omits dispersion forces (87). Parametrized classical models may thus mischaracterize the strength or directionality of intermolecular interactions, particularly those involving more than one aromatic group or an aromatic group and a charged moiety. Although the pioneering studies of Burley and Petsko (88) suggested that the partial-charge model of aromatic rings in proteins was sufficient for characterizing aromatic-aromatic interactions, more recent work has highlighted its limitations with respect to delineating underlying physical mechanisms (85,89). The limits of parametrized classical force fields are of particular importance when applications are sought in nonstandard systems (such as unnatural protein mutagenesis (90)) for which the parameters were not intended. Examples are provided by halogen-modified aromatic systems (widely employed in medicinal chemistry) (91), which are associated with marked changes in quantum-chemical properties (92). Formal QM/MM simulations of proteins may nonetheless be circumvented through force fields incorporating multipolar electrostatic models of aromatic-aromatic networks (85).
The correspondence between our initial local MM-based modeling and our experimental findings, however striking, may be coincidental (93): rigorous elucidation of the physics of the variant aromatic cluster at insulin's dimer interface may require application of free-energy MD-based simulations with explicit inclusion of water molecules ("molecular alchemy" (94)). This approach may also provide insights into whether or how EEC may be circumvented. Nevertheless, standard MM calculations can guide initial biochemical analysis of protein structure as a guide for protein engineering. In the present study such initial modeling reinforced our structural intuition by highlighting the plausibility that substitution of Tyr B26 by Trp might pre-

Stabilization of insulin hexamer
serve a native-like interface and in fact enhance its weakly polar properties. Because the rigid hexameric framework provided a favorable context for local modeling of amino acid substitutions at subunit interfaces and yet it is the monomer that functions as a hormone in the bloodstream, it would be of future interest to apply more sophisticated computational techniques to simulate the structure and dynamics of [Trp B26 ]insulin as a monomer in solution. Such predictions may in principle be tested through biophysical studies of an engineered insulin monomer containing Trp B26 . Although this substitution is favorable in the context of the hexamer (and so of potential pharmacologic benefit), design of a monomeric NMR model will need to overcome the confounding effects of Trp B26 , as defined in this experimental context, to promote self-association.

Concluding remarks
To our knowledge, this study represents the first exploitation of aromatic-aromatic interactions to enhance the biophysical properties of a therapeutic protein (95). Our approach may be broadly applicable in protein engineering (as ETF interactions are ubiquitous) and generalizable to nonstandard aromatic moieties. The latter would be likely to require QM/MM methods rather than classical force fields parametrized with partial charges (90). Overall effects of such substitutions on protein stability and self-assembly will require an integrated analysis of solvation free energies (86), changes in protein dynamics (96), and potential EEC (97). Three-and four-dimensional heteronuclear NMR experiments would be expected to provide higher-resolution information regarding the local and nonlocal interactions of the optimized aromatic system. In the present application, analyses of 15 N relaxation and 1 H-2 H amideproton exchange are expected to improve understanding of the molecular dynamics of the Trp B26 -modified aromatic cluster and so provide a more rigorous biophysical context for its enhanced self-association properties (70,96).
The present application to insulin demonstrates a direct relationship between stabilization of the insulin hexamer and prolonged activity of a basal analog. Continuous and flat 24-h insulin activity ("peakless" basal formulations) is of clinical interest in the treatment of Type 1 and Type 2 diabetes mellitus to reduce the risk of hypoglycemia (especially at night) at a given level of glycemic control (98). Because this mechanism is unrelated to present strategies to achieve protracted action, we envision that Trp B26 -related enhancement of dimer-specific aromatic-aromatic interactions could favorably be introduced into current basal insulin formulations. In the future a combination of orthogonal molecular strategies might enable development of a once-a-week basal insulin therapy analogous to that of GLP-1 agonists (99). Optimization of weakly polar interactions may thus assume a central place in the toolkit of molecular pharmacology.

Preparation of insulin analogs
Variant insulins were prepared by semisynthesis (101). In brief, synthetic peptides were coupled to a tryptic fragment of insulin (des-octapeptide [B23-B30]insulin) in aqueous/organic solvent using trypsin as a catalyst. Following RP-HPLC purification, predicted molecular masses were confirmed by MS (33).

Hexamer disassembly assays
Disassembly of phenol-stabilized (R 6 ) Co 2ϩ -substituted insulin hexamers was monitored as described (102). In brief, WT insulin or variants were made 0.6 mM in buffer containing 50 mM Tris-HCl (pH 7.4), 50 mM phenol, and 0.2 mM CoCl 2 (18) and incubated overnight at room temperature to attain conformational equilibrium. Spectra (400 -750 nm) were obtained to monitor tetrahedral Co 2ϩ coordination (27) through its signature absorption band at 574 nm (27). Co 2ϩ sequestration was initiated by addition of EDTA to a concentration of 2 mM. Dissociation was probed via attenuation of a 574-nm band (27); data were fit to a monoexponential decay equation (29).

Protein crystallography
Crystals were obtained by hanging drop vapor diffusion at room temperature in the presence of a 1:1.7 ratio of Zn 2ϩ to protein monomer and a 3.5:1 ratio of phenol to protein monomer in Tris-HCl. Diffraction was observed using synchrotron radiation at a wavelength of 0.9795 Å at the Stanford Synchrotron Radiation Light Source (beamline BL7-1); crystals were flash frozen to 100 K. Structure determination was carried out using molecular replacement using CCP4 (103) and Phenix structure-determination suites (104). The resulting structure was validated using a PDB Redo server (105). The lattice contained one TR f dimer per asymmetric unit. The main chain conformations of the 97 residues in the refined model of the TR f dimer in the asymmetric unit (excluding 2 Thr, 1 Orn, and 1 Phe residues) each resided in a most favored Ramachandran region.

Receptor-binding assays
Analog affinities for detergent-solubilized IR-B holoreceptor were measured by a competitive-displacement assay (18). Successive dilutions of WT insulin or analogs were incubated overnight with wheat germ agglutinin-SPA beads (PerkinElmer Life Sciences), receptor, and radiolabeled tracer before counting (18). To obtain dissociation constants, competitive binding data were analyzed by nonlinear regression by the method of Wang (106).

Stabilization of insulin hexamer
were injected SQ with 3.44 nmol of insulin or insulin analogs (ϳ12-13.7 nmol).
Animals used in this study were housed in the Association for Assessment and Accreditation of Laboratory Animal Care (AAALAC)-accredited facilities of Case Western Reserve University (CWRU) School of Medicine. All procedures were approved by the Institutional Animal Care and Use Committee (IACUC) Office at CWRU, which provided Standard Operating Procedures and reference materials for animal use (in accordance with the NIH Guide for the Care and Use of Laboratory Animals). The animal health program for all laboratory animals was directed by the CWRU Animal Resource Center. Animal care and use was further monitored for Training and Compliance issues by Veterinary Services.

Spectroscopy
CD spectra were acquired in 10 mM potassium phosphate (pH 7.4) and 50 mM KCl (33). Free energies of unfolding (⌬G u ) were inferred at 25°C from two-state modeling of protein denaturation by guanidine HCl (33,34). 1 H NMR spectra were acquired at 700 MHz at pH 8.0 or pD 7.6 (direct meter reading) at 37°C (36). Chemical shifts of aromatic protons in residues B24 -B24 (Phe-Phe-Tyr or Phe-Phe-Trp) were evaluated in relationship to corresponding chemical shifts in respective octapeptides B23-B30, presumed to represent random-coil shifts.

Molecular mechanics calculations
Calculations were performed using CHARMM (kindly provided by Prof. M. Karplus). Its standard empirical energy function was employed (in whose development aromatic rings were parametrized by partial atomic charges in accordance with ab initio QM simulations (21)). Representative WT insulin dimers were obtained from PDB entries 4INS, 1ZNJ, and 1TRZ. These structures and corresponding Trp B26 homology models were subjected to local energy minimization (100 steps of steepest descent followed by Adopted Basis Newton-Raphson with gradient tolerance tolg 0.0008/10,000 steps). Minimizations were halted either at 1,000 steps or when the above tolerance was reached. Changes in conformation were allowed only to eight side chains (Tyr B16 , Phe B24 , Phe B25 , Tyr B26 (or Trp B26 ), and their dimer-related mates; the remaining atoms in the respective dimers were fixed. Total interaction energies and respective electrostatic components were obtained between the side chain of residue B26 and the neighboring three aromatic side chains (Phe B24 and dimer-related Tyr D16 and Phe D24 ). Following this survey of crystallographic dimers, such energies were further evaluated in a simplified molecular model that con-tained only the side chains of residues Tyr B26 (or Trp B26 ) and the same neighboring three aromatic residues as extracted from PDB entry 4INS; this yielded the electrostatic interaction energy map shown in Fig. 2, in which B26 1 and 2 dihedral angles were systematically varied without energy minimization.

Quantum mechanics calculations
Electron density and molecular electrostatic potential of Tyr and Trp side chains were calculated with B3LYP and 6-31G(d) basis sets using Gaussian utility Cubegen in Gaussian09 (77). The isosurface map was generated using Jmol (107). Ab initio energies of interaction between pairs of isolated aromatic rings were determined by calculating interaction energies using the MP2 method with the aug-cc-pVDZ basis set in Gaussian 09 (77).