13
Backbone Dynamics of the EGF-like Domain of Heregulin- a Wayne J. Fairbrother 1 *, Jun Liu 2 , Paul I. Pisacane 3 , Mark X. Sliwkowski 3 and Arthur G. Palmer III 4 1 Departments of Protein Engineering, 2 Pharmaceutical Research & Development and 3 Protein Chemistry, Genentech Inc., 1 DNA Way, South San Francisco, CA 94080, USA 4 Department of Biochemistry and Molecular Biophysics Columbia University 630 West 168th Street New York, NY 10032, USA The backbone dynamics of the 63 residue epidermal growth factor (EGF)- like domain of heregulin-a (HRG-a) have been characterized by measure- ment of longitudinal relaxation rate constants (R 1 ), transverse relaxation rate constants (R 2 ), and steady-state { 1 H}- 15 N nuclear Overhauser effects for the 15 N nuclear spins using proton-detected heteronuclear NMR spectroscopy. Analysis of the R 2 /R 1 ratios in conjunction with the known structure of the HRG-a EGF-like domain yields a rotational correlation time of 8.4 ns, suggesting that the protein aggregates under the solution conditions used (3.8 mM protein, 50 mM sodium acetate, pH 4.5, 20 C), and that it tumbles with an axially symmetric diffusion tensor (D k /D ? 1.4). Sedimentation equilibrium experiments confirm that the EGF-like domain of HRG-a undergoes weak self-association under these conditions and are consistent with a simple monomer-dimer equilibrium with a dimer-dissociation constant K d 1.6(0.4) mM. The relaxation data were analyzed using a reduced spectral density mapping approach to avoid systematic effects of aggregation on the usual model-free formal- ism. The reduced spectral densities show that residues near the N termi- nus (residues 3 to 5 and 7 to 12), in the -loop between b-strands 2 and 3 (residues 24 to 31), and in particular the C-terminal 13 residues (resi- dues 51 to 63), have significant mobility on a picosecond/nanosecond time-scale. In addition, conformational exchange on a microsecond time- scale was identified for residues 44 to 46 on the basis of observed differ- ences in R 2 at 11.7 and 14.1 T. The mobility identified near the N termi- nus and in the vicinity of residues 44 to 46 may be important in allowing the interactions of heregulin with multiple receptors. # 1998 Academic Press Keywords: protein dynamics; heregulin; 15 N-spin relaxation; NMR spectroscopy *Corresponding author Introduction The heregulins (HRGs, also known as neu differentiation factors, NDFs, or neuregulins, NRGs) are a family of alternatively spliced proteins that were initially isolated by monitoring their abil- ity to stimulate ErbB-2 tyrosine phosphorylation in breast tumor cell lines (Holmes et al., 1992; Peles et al., 1992). Subsequent studies have revealed that ErbB-3 and ErbB-4 are low-affinity receptors, and ErbB-3/ErbB-2 and ErbB-4/ErbB-2 heterodimers are high-affinity receptors for HRG (Plowman et al., 1993; Carraway et al., 1994; Kita et al., 1994; Sliwkowski et al., 1994; Tzahar et al., 1994; Karunagaran et al., 1996). These receptor tyrosine kinases are overexpressed in a number of human cancers and therefore are potential therapeutic targets for the development of receptor antagon- ists. A common feature of all the HRG/NDF isoforms is a region with a high level of homology to epidermal growth factor (EGF) within a multi- domain structure (Holmes et al., 1992; Wen et al., 1992). The EGF-like domain of HRG (originally described as residues 177 to 239 of HRG-a or 177 to 244 of HRG-b1) is sufficient for stimulation of ErbB-2 tyrosine phosphorylation and can mediate the known biological activities of HRG (Holmes et al., 1992; Carraway et al., 1994). The three-dimensional solution structure of the 63 residue EGF-like domain of HRG-a has been Abbreviations used: EGF, epidermal growth factor; HRG, heregulin; NOE, nuclear Overhauser effect; ppm, parts per million; r.m.s.d., root-mean-square deviation; BPTI, bovine pancreatic trypsin inhibitor; TGF, transforming growth factor. Article No. mb981837 J. Mol. Biol. (1998) 279, 1149–1161 0022 – 2836/98/251149–13 $30.00/0 # 1998 Academic Press

Backbone dynamics of the EGF-like domain of heregulin-α

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Article No. mb981837 J. Mol. Biol. (1998) 279, 1149±1161

Backbone Dynamics of the EGF-like Domainof Heregulin-aaa

Wayne J. Fairbrother1*, Jun Liu2, Paul I. Pisacane3, Mark X. Sliwkowski3

and Arthur G. Palmer III4

1Departments of ProteinEngineering, 2PharmaceuticalResearch & Development and3Protein Chemistry, GenentechInc., 1 DNA Way, South SanFrancisco, CA 94080, USA4Department of Biochemistryand Molecular BiophysicsColumbia University630 West 168th StreetNew York, NY 10032, USA

Abbreviations used: EGF, epideHRG, heregulin; NOE, nuclear Ovparts per million; r.m.s.d., root-meBPTI, bovine pancreatic trypsin intransforming growth factor.

0022±2836/98/251149±13 $30.00/0

The backbone dynamics of the 63 residue epidermal growth factor (EGF)-like domain of heregulin-a (HRG-a) have been characterized by measure-ment of longitudinal relaxation rate constants (R1), transverse relaxationrate constants (R2), and steady-state {1H}-15N nuclear Overhauser effectsfor the 15N nuclear spins using proton-detected heteronuclear NMRspectroscopy. Analysis of the R2/R1 ratios in conjunction with the knownstructure of the HRG-a EGF-like domain yields a rotational correlationtime of �8.4 ns, suggesting that the protein aggregates under the solutionconditions used (3.8 mM protein, 50 mM sodium acetate, pH 4.5, 20�C),and that it tumbles with an axially symmetric diffusion tensor(Dk/D? � 1.4). Sedimentation equilibrium experiments con®rm that theEGF-like domain of HRG-a undergoes weak self-association under theseconditions and are consistent with a simple monomer-dimer equilibriumwith a dimer-dissociation constant Kd � 1.6(�0.4) mM. The relaxationdata were analyzed using a reduced spectral density mapping approachto avoid systematic effects of aggregation on the usual model-free formal-ism. The reduced spectral densities show that residues near the N termi-nus (residues 3 to 5 and 7 to 12), in the -loop between b-strands 2 and3 (residues 24 to 31), and in particular the C-terminal 13 residues (resi-dues 51 to 63), have signi®cant mobility on a picosecond/nanosecondtime-scale. In addition, conformational exchange on a microsecond time-scale was identi®ed for residues 44 to 46 on the basis of observed differ-ences in R2 at 11.7 and 14.1 T. The mobility identi®ed near the N termi-nus and in the vicinity of residues 44 to 46 may be important in allowingthe interactions of heregulin with multiple receptors.

# 1998 Academic Press

Keywords: protein dynamics; heregulin; 15N-spin relaxation; NMRspectroscopy

*Corresponding author

Introduction

The heregulins (HRGs, also known as neudifferentiation factors, NDFs, or neuregulins,NRGs) are a family of alternatively spliced proteinsthat were initially isolated by monitoring their abil-ity to stimulate ErbB-2 tyrosine phosphorylation inbreast tumor cell lines (Holmes et al., 1992; Peleset al., 1992). Subsequent studies have revealed thatErbB-3 and ErbB-4 are low-af®nity receptors, andErbB-3/ErbB-2 and ErbB-4/ErbB-2 heterodimers arehigh-af®nity receptors for HRG (Plowman et al.,

rmal growth factor;erhauser effect; ppm,an-square deviation;hibitor; TGF,

1993; Carraway et al., 1994; Kita et al., 1994;Sliwkowski et al., 1994; Tzahar et al., 1994;Karunagaran et al., 1996). These receptor tyrosinekinases are overexpressed in a number of humancancers and therefore are potential therapeutictargets for the development of receptor antagon-ists. A common feature of all the HRG/NDFisoforms is a region with a high level of homologyto epidermal growth factor (EGF) within a multi-domain structure (Holmes et al., 1992; Wen et al.,1992). The EGF-like domain of HRG (originallydescribed as residues 177 to 239 of HRG-a or 177to 244 of HRG-b1) is suf®cient for stimulation ofErbB-2 tyrosine phosphorylation and can mediatethe known biological activities of HRG (Holmeset al., 1992; Carraway et al., 1994).

The three-dimensional solution structure of the63 residue EGF-like domain of HRG-a has been

# 1998 Academic Press

Figure 1. A, The ribbon diagram shows the structure of residues 1 to 50 of the 63 residue EGF-like domain of HRG-a.B, The stereodiagram shows the main-chain atoms of the ensemble of 20 NMR-derived structures of the EGF-likedomain of HRG-a (Jacobsen et al., 1996). The superposition was optimized using residues 3 to 23 and 31 to 49,shown in cyan; the disordered residues, 1±2, 24 to 30 and 50 to 63 are highlighted in violet. The Figure was pro-duced using the program MOLMOL (Koradi et al., 1996).

1150 Backbone Dynamics of Heregulin-�

determined independently by two groups (Nagataet al., 1994; Jacobsen et al., 1996). As shown inFigure 1, the structure is well de®ned, with theexception of the ®rst two residues, an -loopbetween the second and third b-strands, and the 13C-terminal residues. The more ordered region ofthe protein, corresponding to residues 177 to 226of native HRG-a (Figure 1A), recently has beenshown to be the minimal domain competent forbinding to cellular receptors and for stimulation ofErbB-2 phosphorylation (Barbacci et al., 1995).Indeed, the 50 residue fragment is about tenfoldmore potent that the 63 residue fragment originallydescribed (Barbacci et al., 1995); we have specu-lated previously that a ¯exible C-terminal tail mayinterfere sterically with receptor binding (Jacobsenet al., 1996).

The apparent disorder observed in the solutionstructure may be due to inherently greater mobilityin these regions of the polypeptide, relative to themore ordered regions, leading to fewer mediumand long-range NOE distance restraints for struc-ture calculation. Alternatively, the disorder mayresult from a lack of experimental restraints due tospectral overlap or unique conformations thatresult in few NOE correlations. The present studyuses 15N relaxation measurements to describe theinternal dynamics of the EGF-like domain of HRG-a, and to distinguish between these possibilities.The relaxation data were analyzed using reducedspectral density mapping (Farrow et al., 1995a,b)rather than the usual model-free formalism (Lipari& Szabo, 1982a,b) because the sample was foundto aggregate signi®cantly under the solution con-ditions used; the model-free approach has beenshown to yield unreliable internal motion par-

ameters for aggregated systems (Schurr et al.,1994). The data reveal several regions exhibitingsigni®cant internal motions with time-scales ran-ging from sub-nanosecond to microsecond. Theresults are discussed with respect to both structuraland functional data.

Results

Relaxation measurements

The backbone amide 1H and 15N resonanceassignments for the 63 residue EGF-like domain ofHRG-a have been reported (Jacobsen et al., 1996).The longitudinal relaxation rate constant, R1, thetransverse relaxation rate constant, R2, and thesteady-state {1H}-15N nuclear Overhauser effect,NOE, were obtained for 57 of the 60 protonatedbackbone 15N nuclei by analysis of 1H-detectedtwo-dimensional 1H-15N correlation spectra, asdescribed in Materials and Methods. Data for resi-dues Ser1 and His2 were not obtained, because noamide cross-peak was observed for these residues;data for Glu47 could not be ®t adequately, due tooverlap between the broad cross-peak for Glu47and the sharp Glu61 crosspeak; and residues 29, 38and 50 are proline. Representative R1 and R2 relax-ation decay curves for data obtained at 11.7 T arepresented in Figure 2.

The experimental values of R1, R2 and NOE at11.7 T and R2 at 14.1 T are plotted versus residuenumber in Figure 3. The value of R1 does not varydramatically with sequence position and has anaverage value of 1.75(�0.12) sÿ1 (mean � one stan-dard deviation). The average R2 values for residues3 to 23 and 31 to 43, which are well de®ned in the

Figure 2. Normalized (A) R1 and (B) R2 relaxation decaycurves for residues Phe21 (~), Ser27 (*), and Glu60(&). The curves represent the best ®ts to monoexponen-tial decays. The uncertainties are smaller than the size ofthe plotted symbols and are not shown.

Figure 3. Relaxation parameters (A) R1 (11.74 T), (B) R2

(11.74 T), (C) R2 (14.1 T); and (D) NOE (11.74 T) for the63-residue EGF-like domain of HRG-a plotted as a func-tion of residue number. Error bars are plotted, but inmost cases the uncertainties are less than the size of theplotted symbols.

Backbone Dynamics of Heregulin-� 1151

solution structure (Figure 1B), are 10.7(�1.1) and10.9(�1.4) sÿ1 at 11.7 and 14.1 T, respectively. Atboth frequencies, discernible reductions in the R2

values are observed for residues 24 to 31 in the dis-ordered -loop region and for residues 51 to 63 inthe highly disordered C terminus, indicating thatthese regions are more ¯exible than the remainderof the protein on the picosecond/nanosecond time-scale. Residues Arg44, Cys45 and Thr46 have R2

values signi®cantly greater than the average at11.7 T and exhibit increases in R2 signi®cantlygreater than the average between 11.7 and 14.1 T.As noted above, Glu47 also has a greater than aver-age linewidth, although the relaxation rate par-ameters could not be determined for this residue.These residues are likely involved in conformation-al exchange processes occurring on a microsecond/millisecond time-scale. Interestingly, the confor-mations of these residues are de®ned precisely inthe solution structure (Figure 1). The NOE valuesrange from approximately 0.5 to 0.75 for the struc-tured residues 3 to 23 and 31 to 48, decrease toapproximately 0.4 for residues 24 to 30 in the disor-

dered -loop region and are negative for residues51 to 63 in the highly disordered C terminus. Thedecreases in the NOE observed for the -loop and

Figure 4. Rotational diffusion anisotropy. A, Schematicrepresentation of the EFG-like domain of HRG-aoriented so that the symmetry axis of the diffusion ten-sor is vertical. The Figure was produced using the pro-gram MOLSCRIPT (Kraulis, 1991). B, The local diffusionconstants, Di, are plotted versus P2(cosyi), in which yi isthe polar angle between the ith N-H bond vector andthe symmetry axis of the diffusion tensor. The plottedvalues of P2(cosyi) are taken from the minimized meansolution structure, while the horizontal error bars rep-resent the sample deviation in P2(cosyi) calculated overan ensemble of 20 structures (Jacobsen et al., 1996). Thelinear least-squares ®t to the data is shown for illus-tration.

1152 Backbone Dynamics of Heregulin-�

the C terminus mirror the pattern obtained for R2

and indicate increased felixibility for these regionson the picosecond/nanosecond time-scale.

Rotational diffusion tensor

The inertia tensor calculated for the core residues(3 to 49) of the EGF-like domain of HRG-a usingthe atomic coordinates of the minimized meanstructure (PDB accession code 1HAF) has principalvalues in the ratio 0.38:0.95:1.00. The rotationaldiffusion tensor was characterized from the R2/R1

ratios at 11.7 T for 31 well-ordered residues usingthe local diffusion approximation as described inMaterials and Methods (BruÈ schweiler et al., 1995;Lee et al., 1997). Using the atomic coordinates ofthe minimized mean structure, the optimizedvalues of Diso � (Dk � 2 D?)/3 � 1.94(�0.01) �107 sÿ1 and Dk/D? � 1.43(�0.03). The symmetryaxis of the diffusion tensor is oriented witht � 87(�2)� and f � 37(�2)� with respect to thecoordinate system of the PDB ®le, and is within30� of the principal axis of the interia tensor withthe smallest moment of interia. A statistical F-testindicated that an axially symmetric diffusion ten-sor described the experimental data signi®cantlybetter than an isotropic tensor (F � 19.2,p � 3�10ÿ7). Identical results, within experimentaluncertainties, were obtained by averaging par-ameters for individual members from the ensembleof 20 structures (PDB accession code 1HAE). Theorientational dependence of the local diffusion con-stants is presented in Figure 4. Residues Cys6 andThr12 have somewhat reduced R1 values and elev-ated R2 values (Figure 3). The NH bond vectors forthese residues are oriented preferentially along thesymmetry axis of the diffusion tensor with P2(cosy) � 0.99 and 0.92, respectively; consequently,relaxation for these residues is dominated by rela-tively slow diffusion about the perpendicular axes.

The overall rotational correlation time,tm � (6Diso)ÿ1 � 8.4 ns, is larger than the theoreti-cal value tm � 4.0 ns calculated for an isotropicallytumbling protein of 63 residues, assuming a3 AÊ hydration layer (Venable & Pastore, 1988).Such a result probably re¯ects aggregation underthe conditions used to perform NMR spectroscopy.In support of this hypothesis, a 15N-spin relaxationstudy of hTGF-a yielded a rotational correlationtime of 3.76 ns at 30� C (Li & Montelione, 1995);the 50 residue hTGF-a is structurally similar to thecore of the EGF-like domain of HRG-a (Jacobsenet al., 1996).

The effect of aggregation on the effectiverotational diffusion tensor derived from the 15N-spin relaxation measurements is dif®cult to assess,because multiple species may exist if the oligomeri-zation is non-speci®c and the structures of any oli-gomeric species are unknown. For comparison,analysis of the R2/R1 ratios for 27 residues ofhTGF-a (6, 8, 13, 15 to 20, 25 to 29, 31 to 36, 38, 40and 43 to 47; Li & Montelione, 1995) using theatomic coordinates reported by Harvey et al. (1991;

PDB accession code 2TGF) gives a diffusion aniso-tropy Dk/D? � 1.52 � 0.34, in approximate agree-ment with the present results.

Sedimentation analysis

Sedimentation equilibrium experiments con®rmthat the EGF-like domain of HRG-a undergoes

Backbone Dynamics of Heregulin-� 1153

weak self-association under the conditions usedfor the relaxation measurements (i.e. 50 mMsodium acetate (pH 4.5), 20�C). Fitting thedata to a simple monomer-dimer equilibriummodel yields a dimer-dissociation constantKd � 1.6(�0.4) mM (Figure 5); this model consist-ently provided good ®ts to the data at all concen-trations, rotor speeds and wavelengths used. Atthe concentration used for the relaxation measure-ments, self-association results in an equilibriumratio of monomer to dimer of approximately0.37:0.63 (w/w).

Reduced spectral density functions

Because aggregation affects substantially theusual model-free analysis of 15N-spin relaxationdata (Schurr et al., 1994), the reduced spectral den-sity mapping formalism (Farrow et al., 1995a,b) hasbeen applied instead. Under the condition thatexchange between monomeric and dimeric states isfast compared to the relaxation rates R1, R2, andthe cross-relaxation rate constant (s � (NOE ÿ 1)R1gN/gH) the derived values of the reduced spec-tral density functions represent populationweighted averages of the reduced spectral densityfunctions for monomeric and dimeric species.

Values for the spectral density function at threefrequencies o � 0, oN and 0.87oH, were derivedfrom the values of R1, R2 and NOE at 11.7 T, asdescribed in Materials and Methods. The resultingvalues and uncertainties are plotted versus residuenumber in Figure 6. As has been noted (Farrowet al., 1995a; Ishima & Nagayama, 1995; LefeÁvre

Figure 5. Non-linear least-squares analysis of sedimen-tation equilibrium experiments. The protein concen-tration, represented by absorbance at 290 nm, is plottedas a function of R2/2, where R is the radial distance inthe centrifuge. The data were collected at 20,000 (*),25,000 (&), and 35,000 (~) rpm at 20�C. The data wereglobally ®t to a simple monomer-dimer equilibriummodel to obtain the dimer-dissociation constant.

Figure 6. Reduced spectral densities. The values of (A)J(0), (B) J(oN) and (C) J(0.87oH) calculated from therelaxation data acquired at 11.74 T are plotted as func-tions of residue number for the 63 residue EGF-likedomain of HRG-a. Error bars are plotted, but in mostcases the uncertainties are less than the size of theplotted symbols.

et al., 1996), the trends observed for Je(0), J(oN),and J(0.87oH) are similar to the trends in R2, R1,and (1 ÿ NOE), respectively. The Je(0) values arethus sensitive to both fast and slow dynamicprocesses; values signi®cantly less than the meanvalue indicate internal motions on the picosecond/nanosecond time-scale, while values signi®cantlygreater than the mean indicate contributions fromconformational exchange on the microsecond/millisecond time-scale. The higher-frequencymotions are also indicated by greater than averagevalues for J(0.87oH) and, to a lesser extent, lowerthan average values for J(oN).

1154 Backbone Dynamics of Heregulin-�

Slow conformational exchange

Slow conformational exchange has been ident-i®ed qualitatively by comparison of R2 valuesacquired at 11.7 and 14.1 T. Residues Arg44, Cys45and Thr46 are identi®ed as subject to conformation-al exchange as detailed in Materials and Methods.Residue Thr12 also has anomalous R2 values; how-ever, as discussed above, effects of anisotropicrotational diffusion are signi®cant for this residue.The differences in R2 at 11.7 and 14.1 T observed forresidues 44, 45 and 46 indicate an exchange contri-bution Rex � 7 sÿ1. Using pA � 0.95 and pB � 0.05and an upper limit for �o � 3.5 ppm, equation (10)yields (see Materials and Methods) a lifetimetex � 200 ms for the conformational exchange pro-cess. The values pA � 0.95 and pB � 0.05 were cho-sen to be consistent with 1H-1H NOE and otherexperimental data that predict a ``unique'' confor-mation for this region (Jacobsen et al., 1996). Valuesof tex < 200 ms require that �o be greater than3.5 ppm or that pA be less than 0.95. Values oftex > 500 ms are physically unrealistic, because theresulting free-precession linewidths of the reson-ances would preclude observation in conventional1H-15N correlation spectra.

The presence of the disul®de bond between resi-dues Cys36 and Cys44 suggests that the confor-mational exchange process extant in this region ofthe molecule may arise from isomerization of thedisul®de linkage; however, the estimated exchangetime is approximately tenfold faster than thatobserved for disul®de bond isomerization in basicpancreatic trypsin inhibitor (BPTI; Otting et al.,1993; Szyperski et al., 1993). Alternatively, the con-formational exchange process may involve relativereorientation of the two b-sheet subdomains on themicrosecond time-scale. In either case, differentialring current shifts from residues Phe14 and/orPhe40 may contribute to the observed 15N exchangeline-broadening for residues 44, 45 and 46.

Discussion

The dynamical properties of the main-chain15N-1H bond vectors of the EGF-like domain ofheregulin-a have been characterized by measure-ment of 15N relaxation parameters. Analysis of theR2/R1 ratios suggested that the protein sampleaggregates under the solution conditions used(3.8 mM protein, 50 mM sodium acetate (pH 4.5),20�C) and that it tumbles with an axially sym-metric diffusion tensor (Dk/D? � 1.4). Sedimen-tation analysis was used to con®rm the presence ofaggregation; the ratio of monomer to dimer in thesolution used for relaxation measurements wasestimated to be �0.37:0.63 (w/w). The precisenature of the dimeric species is not apparent fromthe structural data; all of the assigned NOEsresulted in distance restraints that were well satis-®ed by the calculated monomeric structure (themaximum NOE distance restraint violation was0.12(�0.01) AÊ ; Jacobsen et al., 1996). As suggested

previously, however, the observed clusters of sur-face-exposed hydrophobic side-chains may resultin non-speci®c aggregation of the protein (Jacobsenet al., 1996). Because aggregation affects the use ofthe model-free formalism for analysis of relaxationdata, the reduced spectral density mappingapproach was used instead. An additional advan-tage of spectral density mapping relative to theusual model-free analysis is that it does not requirethe a priori assumption of isotropic tumbling.

Correlation of dynamics with structure

The reduced spectral densities (Figure 6) clearlyindicate the regions of HRG-a experiencing eitherfast or slow internal motions. In particular, higherthan average values for J(0.87oH) indicate motionson a picosecond-nanosecond time-scale for resi-dues near the N terminus (residues 3 to 5 and 7 to12), in the -loop between b-strands 2 and 3 (resi-dues 24 to 31), and the C-terminal 13 residues (resi-dues 51 to 63). The values of J(0.87oH) are mappedonto the protein structure in Figure 7 by varyingthe tube radius in proportion to the spectral den-sity. The values of J(0.87oH) and the average perresidue r.m.s.d. for the backbone atoms of HRG-a(Jacobsen et al., 1996) are strongly correlated, withthe most poorly de®ned regions of the protein hav-ing the highest values of J(0.87oH) (Figure 8). Theaverage r.m.s.d. values are also distinctly corre-lated with the number of NOE-derived distancerestraints per residue, with the poorly de®nedregions having fewer medium and long-rangedistance restraints (Jacobsen et al., 1996). The lackof experimental restraints and the resultant poorstructural de®nition for these regions of the proteintherefore re¯ect increased conformational disorderon a picosecond/nanosecond time-scale. NOEinteractions may be absent in a ¯exible region of apolypeptide chain for two reasons: ®rst, the popu-lation of any conformation in which the proton-proton distance is suf®ciently close (<5 AÊ ) may below, and second, the time-dependence of the localdynamics of the inter-proton vector may approachthe cancellation condition for the NOE (otc � 1.12).The effects of intramolecular dynamics on the NOEhave been discussed extensively (BruÈ schweileret al., 1992; Palmer & Case, 1992; Post, 1992).

An interesting exception to the above obser-vation occurs in the N-terminal region of the pro-tein (residues 3 to 5 and 7 to 12), where slightlygreater than average values of J(0.87oH) are foundeven though this region appears well de®ned inthe solution structures presented by both Nagataet al. (1994) and Jacobsen et al. (1996). ResiduesLeu3 to Lys5 form the N-terminal b-strand 1, whileresidues Ala7 to Thr12 are part of the helicalregion. The b-strand is de®ned by 41 long-rangeNOE distance restraints involving residues 3 to 5,while the number of long-range restraints invol-ving residues 7 to 12 is limited to 13 (three fromGlu10 and ten from Lys11); the helical region isfurther de®ned, however, by an average of about

Figure 7. Structural dependence of dynamical proper-ties. A Ca chain trace of the 63 residue EGF-like domainof HRG-a is depicted as a tube with radius proportionalto J(0.87oH). The radius is interpolated for residues forwhich experimental values of J(0.87oH) were not deter-mined. As in Figure 1B, residues ordered in the ensem-ble of NMR solution structures are shown in cyan anddisordered residues are shown in violet. Residues 44 to46, which are ordered in the ensemble of NMR solutionstructures but experience conformational exchange onthe microsecond/millisecond time-scale, are shown inred. Disul®de linkages are shown in yellow. TheFigure was produced using the program MOLMOL(Koradi et al., 1996).

Figure 8. Correlation between structural and dynamicparameters. The average backbone heavy-atom r.m.s.d.values of the 20 re®ned solution structures about themean coordinates for residue i (Jacobsen et al., 1996) areplotted versus J(0.87oH)i. The curve represents anunweighted best ®t to a monoexponential function(y�0.05921e(166.21x); R�0.972).

Backbone Dynamics of Heregulin-� 1155

ten medium-range NOE distance restraints perresidue (Jacobsen et al., 1996). Similar numbers ofNOE distance restraints for these residues werereported by Nagata et al. (1994). Interestingly, theincreased ¯exibility found in the N-terminal regionof the HRG-a EGF-like domain, relative to theremaining b-strands, is consistent with structuresreported for EGF and TGF-a in which the N-term-inal regions are disordered or thought to beinvolved in a conformational equilibrium betweendisordered and hydrogen-bonded states (Kline

et al., 1990; Harvey et al., 1991; Hommel et al., 1992;Kohda & Inagaki, 1992; Montelione et al., 1992;Moy et al., 1993; Li & Montelione, 1995). In the caseof the HRG-a EGF-like domain, the amplitude ofthe motion is likely to be smaller, based on thenumber and magnitude of the observed NOEs,with the dynamic equilibrium being weighted sig-ni®cantly towards the more structured state. Resi-dues Cys6, Lys9 and Thr12 appear to haveanomalously low values for J(oN) and high valuesfor Je(0) when compared to the values observed forJ(0.87oH). These results remain dif®cult to interpretbecause, as discussed above, the NH bond vectorsfor these residues are oriented along (within 35�)the symmetry axis of the axial diffusion tensor:P2(cos y) � 0.99, 0.53 and 0.92, respectively.

Conformational exchange on a microsecond/millisecond time-scale was identi®ed for residuesArg44, Cys45 and Thr46 on the basis of theobserved differences in R2 at 11.7 and 14.1 T. Resi-dues 44 and 45 are part of the type I b-turnbetween b-strands 4 and 5, while residue 46 formsa b-bulge at the N-terminal end of b-strand 5; thelocations of these residues are highlighted in red inFigure 7. Residue Glu47 also can be assumed to besubject to conformational exchange, because itexhibits signi®cant line-broadening; the relaxationparameters for this residue could not be deter-mined accurately due to spectral overlap with thesharp resonance of Glu61. As with the N-terminalregion discussed above, this b-turn region is wellde®ned in the NMR solution structure; residues 44,45, 46 and 47 are restrained by 16, 14, 16 and 17long-range NOE distance restraints, respectively(Jacobsen et al., 1996). Consistent with the observedNOEs, this region of the C-terminal subdomain hasextensive interactions with the N-terminal subdo-

1156 Backbone Dynamics of Heregulin-�

main that presumably help to stabilize the relativeorientations of the two subdomains. These inter-actions include hydrogen bonds (Val15 HN-Arg44O, Asn16 Hd21-Cys45 O, Arg44 HZ21-Thr12 O, andArg44 He-Phe13 O) and hydrophobic interactionsbetween the side-chains of Arg44 and those ofPhe13 and Val15 (Jacobsen et al., 1996).

The precise nature of the conformational statescontributing to the observed exchange line-broad-ening is not provided by the reduced spectral den-sities and cannot be deduced directly from theavailable solution structures. As mentioned above,one possible conformational exchange process thatcould account for the observed relaxation data isisomerization (about w3) of the disul®de bondbetween Cys36 and Cys45. Disul®de bond isomeri-zation has been demonstrated for BPTI (Ottinget al., 1993; Szyperski et al., 1993). The values of Rex

depend on the chemical shift differences, equili-brium populations and exchange rates between thedifferent conformations (equation (10)). Althoughthese parameters are unknown in the present case,the life-time for the exchange process was esti-mated to be �200 ms by assuming a two-stateexchange model weighted towards the NMR-derived solution structure (pA � 0.95, pB � 0.05)and an upper limit for the chemical shift differenceof �o � 3.5 ppm. This value for the exchange timeis about an order of magnitude smaller than thatfound for disul®de bond isomerization in BPTI(Otting et al., 1993; Szyperski et al., 1993).

The exchange line broadening may result alsofrom motion of the two subdomains with respectto each other. Such motion, frequently referred toas hinge-bending, has been postulated to occur inboth EGF and TGF-a molecules (Ikura & Go, 1993;Moy et al., 1993; Celda et al., 1995; Li &Montelione, 1995). Indeed, these data together witha comparison of available structures for EGF andEGF-like domains have led Montelione and co-workers to suggest that in any EGF-like moleculethere are multiple orientations of the two subdo-mains in dynamic equilibrium (Tejero et al., 1996).The relaxation data for the EGF-like domain ofHRG-a appear consistent with this hypothesis.However, as with the N-terminal region, the den-sity of intersubdomain NOEs observed for HRG-asuggests that the amplitude of any hinge-bendingmotion is smaller than that for EGF or TGF-a.

Finally, the exchange line-broadening couldpotentially be related to the monomer/dimer equi-librium observed by sedimentation analysis. If thiswere the case, however, the chemical shifts of resi-dues 44 to 47 would be dependent on the relativepopulations of monomer and dimer in solution,and hence on the total protein concentration. Com-parison of heteronuclear single quantum coherence(HSQC) spectra acquired at 3.8 and 1.9 mM revealsno difference between the chemical shifts of theseresidues within the precision of the measurement(data not shown). The equilibrium population ofmonomer increases from �37 to �47 % upon two-fold dilution of the sample. The expected chemical

shift change would thus be �0.1�o, where�o�1.5 ppm is the chemical shift differencebetween the Larmor frequencies of the two statesconsistent with the measured values of Rex for theseresidues, and tex � 200 to 500 ms as estimatedfrom the dimer-dissociation constant by assumingdiffusion controlled association, kon � 5 � 105 to10 � 105 Mÿ1 sÿ1. These data therefore suggest thatthe observed exchange line-broadening is unlikelyto be due to exchange between monomer anddimer states.

Both disul®de bond isomerization and inter-subdomain hinge-bending, together with internalmotions involving the N-terminal b-strand, havebeen suggested previously to account for apparentslow conformational exchange observed through-out hTGF-a (Li & Montelione, 1995). These authorsutilized the conventional model-free formalism,incorporating an isotropic rotational diffusionmodel, in their analysis of 15N-relaxation data forhTGF-a. Recent results indicate that conformationalexchange contributions can be introduced into themodel-free analysis by unrecognized rotationaldiffusion anisotropy (Schurr et al., 1994; Tjandraet al., 1995; Mandel et al., 1996). Results forthe HRG-a EGF-like domain, and re-analysis ofthe previously reported data for the hTGF-adomain (Li & Montelione, 1995) show that therotational diffusion anisotropy may be signi®cant(Dk/D? � 1.4 to 1.5) for these molecules. Thus,slow conformational exchange in hTGF-a mightnot be as pervasive as suggested by resultsobtained using an isotropic diffusion model.

Correlation of dynamics with function

The highest-frequency motions in the HRG-aEGF-like domain are localized to the C-terminal 13residues and the -loop between b-strands 2 and3. Neither region appears to be important forfunction. Removal of the C-terminal 13 residues toproduce a 50 residue fragment results in about atenfold increase in potency (Barbacci et al., 1995),suggesting that the ¯exible C-terminal tail actuallyinterferes with receptor binding, possibly througha steric effect. Replacement of residues 21 to 33 ofthe HRG-b EGF-like domain with residues 21 to 30from hEGF, which constitutes a three residuedeletion in the -loop, has a minimal effect onreceptor binding or ErbB-2 phosphorylation(Barbacci et al., 1995). Additionally, deletion of resi-dues 26 to 28 from HRG-b gives a variant thatbinds ErbB-3 with an af®nity similar to wild-type(Ballinger et al., 1998), while mutation of the-loop residues to alanine only slightly perturbsbinding to both ErbB-3 and ErbB-4 (with the excep-tion of S27A and P29A, which bind ErbB-3 andErbB-4, respectively, about tenfold tighter thanwild-type; Jones et al., 1998).

Signi®cant ¯exibility is detected in the N-term-inal region of the HRG-a EGF-like domain. Thisregion has been shown to be important for bothreceptor binding and speci®city (Barbacci et al.,

Backbone Dynamics of Heregulin-� 1157

1995; Tzahar et al., 1997; Jones et al., 1998). Replace-ment of the ®ve N-terminal residues of hEGF(NSDSE) with the corresponding residues from theHRG EGF-like domain (SHLVK) results in abifunctional agonist that binds with high af®nity toboth HRG and EGF receptors (Barbacci et al., 1995;Tzahar et al., 1997). Also, alanine-scanning muta-genesis has been used to show that HRG residuesHis2 and Leu3 are important determinants forbinding to ErbB-3 (Jones et al., 1998).

The region undergoing slow conformationalexchange (residues Arg44, Cys45 and Thr46) hasbeen demonstrated to be critical for HRG-b bind-ing to both ErbB-3 and ErbB-4. Mutation of eitherArg44 or Gln46 to alanine in the HRG-b EGF-likedomain (note that in HRG-a residue 46 is threo-nine) resulted in a �20 to >100-fold loss in af®nityfor ErbB-3 and ErbB-4 in both phage ELISA andsoluble receptor-binding assay formats (Jones et al.,1998); both residues consensed to wild-type inmonovalent phage optimization of the HRG-bEGF-like domain for binding to ErbB-3 (Ballingeret al., 1998). The highly conserved residue Arg44has been shown to be absolutely required for bind-ing of EGF to its receptor (Engler et al., 1990;Hommel et al., 1991).

The observation of ¯exibility on both fast(picosecond/nanosecond) and slow (microsecond/millisecond) time-scales in regions of the proteinthat are clearly important for function suggests arole for dynamics in the heregulin/receptor recog-nition process. Heregulin can interact with ErbB-3,ErbB-4 and the heterodimeric receptors ErbB-3/ErbB-2 and ErbB-4/ErbB-2 with high af®nity, butdoes not bind tightly to the EGF receptor (EGFR).ErbB-3 and ErbB-4 share signi®cantly more hom-ology with each other (�65%) than with eitherEGFR or ErbB-2 (41 to 46%; Carraway & Cantley,1994). The receptors are thus thought to use similarbinding determinants in their interactions withheregulin (Ballinger et al., 1998), although alanine-scanning mutagenesis of HRG-b suggests that ErbB-3 has more stringent requirements for binding thanErbB-4 (Jones et al., 1998). The interactions of here-gulin with multiple receptors may be mediated, inpart, by the ability of the EGF-like domain to accesssomewhat different conformational states. Thisincludes higher-frequency motions in the N-term-inal region, which appears more important forbinding to ErbB-3, and the lower-frequency motionsobserved around Arg44, a region that is critical forbinding to both receptors.

Materials and Methods

Sample preparation

Expression and puri®cation of uniformly 15N-labeledHRG-a EGF-like domain (residues 177 to 239 of nativeHRG-a) were carried out as described (Jacobsen et al.,1996). The NMR sample was prepared in 90% H2O/10%2H2O solution (50 mM sodium acetate-d3 (pH 4.5),1.0 mM NaN3) at a protein concentration of 3.8 mM. An

additional unlabeled sample was prepared for sedimen-tation equilibrium experiments.

Analytical ultracentrifugation

Sedimentation equilibrium experiments were con-ducted in a Beckman XLA/I analytical ultracentrifuge.Samples of HRG-a EGF-like domain (110 ml) at approxi-mately 0.67 and 2.0 mM, in 50 mM sodium acetate(pH 4.5), were loaded into 3 mm charcoal-®lled Eponsix-channel cells. The experiments were conducted at20,000, 25,000, and 30,000 rpm. The concentration gradi-ent of protein formed at equilibrium at 20�C wasmeasured at 290 nm and 300 nm using an absorptionoptical system; extinction coef®cients, e290 � 0.208 mlmgÿ1 cm and e300 � 0.058 ml mgÿ1 cm, were determinedspectrophotometrically. The partial speci®c volume,0.723 ml gÿ1, was calculated from the amino acid com-position (Perkins, 1986). The data were edited to removethe noise on the bottom and top of the cell using a PCprogram REEDIT (D. A. Yphantis, University of Connec-ticut). The edited data were analyzed using a non-linear,least-squares ®tting program NONLIN to obtain theweighted average molecular mass and self-associationconstant (Johnson et al., 1981).

NMR spectroscopy

A series of 1H-detected two-dimensional 1H-15N corre-lation spectra for determining backbone 15N longitudinaland transverse relaxation rate constants, R1 and R2,respectively, and {1H}-15N steady-state heteronuclearNOEs were acquired at 20�C on a Bruker AMX-500 spec-trometer with a static magnetic ®eld strength of 11.7 Tand a 1H Larmor frequency of 499.87 MHz. Transverserelaxation rate constants also were measured at 20�Cusing spectra obtained on a Bruker AMX-600 spec-trometer with a static magnetic ®eld strength of 14.1 Tand a 1H Larmor frequency of 600.13 MHz.

The pulse sequences used to measure R1, R2, and{1H}-15N NOEs for the 15N nuclei were essentially asdescribed (KoÈrdel et al., 1992; Stone et al., 1992; Skeltonet al., 1993), except that the sensitivity enhancement inthe R1 and R2 experiments was achieved using the PEP-Z modi®cation described by Akke et al. (1994). The twopure-phase data sets obtained by deconvoluting theorthogonal magnetization components recorded in theunmodi®ed PEP-{1H}-15N NOE experiment were treatedas independent duplicates (i.e. the NOE was calculatedseparately for each orthogonal component). For all spec-tra obtained using the AMX-500 spectrometer, a total of2048 complex points were acquired in t2, with a spectralwidth of 6250 Hz and the 1H carrier set to the waterfrequency; 512 complex points were collected in t1, usinga spectral width of 1388.9 Hz with the 15N carrier at117.7 ppm. Spectra obtained using the AMX-600 spec-trometer were acquired similarly, but with spectralwidths of 7575.8 and 1677.9 Hz in t2 and t1, respectively.The R1 and R2 experiments were acquired using a totalof 16 transients per t1 increment. The NOE experimentswere acquired using 64 transients per t1 increment. Theinitial t1 sampling delays were adjusted to half the valueof the t1 increment in order to eliminate phase errors andbaseline distortions (Zhu et al., 1993). Solvent suppres-sion in all experiments was achieved by the use ofspin-lock purge pulses (Messerle et al., 1989) and post-acquisition convolution of the time-domain data (Marionet al., 1989).

1158 Backbone Dynamics of Heregulin-�

For measurements of R1 and R2, recycle delays of 4.2and 4.0 seconds, respectively, were used between transi-ents to allow essentially complete recovery of 1H magne-tization. For measurements of the {1H}-15N NOE, arecycle delay of 4.0 seconds, or approximately 7/R1, wasused to ensure maximal development of NOEs prior toacquisition. For R1 measurements, 16 spectra wererecorded using relaxation delays of 4 (�2), 48, 80 (�2),201, 301 (�2), 402, 603, 803, 1338 (�2), 2008 and 3013(�2) ms (where duplicate acquisitions are indicated by�2). A train of 1H 180� pulses at 4 ms intervals wasapplied during the relaxation period of the R1 exper-iment to eliminate the effects of dipolar cross-relaxationand cross-correlation between dipolar and anisotropicchemical shift relaxation mechanisms upon the 15N longi-tudinal relaxation (Boyd et al., 1990). For R2 measure-ments, 15 spectra were recorded using relaxation delaysof 4 (�2), 23, 45 (�2), 66, 87 (�2), 194 (�2), 257, 428 (�2)and 640 (�2) ms. The interval between the refocusingpulses in the 15N CPMG sequence was 1 ms. The effectsof cross-correlation upon the 15N transverse relaxationwere eliminated by application of 1H 180� pulses syn-chronously with every second echo in the 15N CPMGsequence (Kay et al., 1992; Palmer et al., 1992). For the{1H}-15N NOE measurements, two spectra, acquired withor without saturation of protons during the recycle delay(corresponding to the presence or absence of the{1H}-15N NOE, respectively), were recorded in an inter-leaved manner in order to minimize systematic differ-ences between the two. Proton saturation was achievedusing GARP-1 phase modulation (Shaka et al., 1985),with a ®eld-strength of 1.22 kHz.

Data analysis

Spectra were processed on a Silicon Graphics Indigo 2workstation using FELIX 2.3.5 (Biosym Technologies,Inc., San Diego). For each spectrum, a cosine bell fol-lowed by either a 2 Hz exponential apodization functionor a weak Lorentzian-to-Gaussian transformation wasapplied in t2; in each case, a cosine bell followed by aLorentzian-to-Gaussian transformation was applied in t1.The data were zero-®lled once in each dimension priorto Fourier transformation. A third-order polynomialbaseline correction was subsequently applied in the F2

dimension.Individual peak heights were measured from the

spectra using FELIX macros written by Dr M. Akke(Lund University). For R1 and R2 measurements, theuncertainties in the measured peak heights were esti-mated from the duplicate spectra as described (Stoneet al., 1992; Skelton et al., 1993). For NOE measurements,uncertainties in the peak heights were taken as thestandard deviation of the baseplane noise in the spectra.The R1 and R2 values and related uncertainties weredetermined by non-linear, least-squares ®tting of theexperimental data to monoexponential functions asdescribed (Palmer et al., 1991; Stone et al., 1992). The stea-dy-state NOEs were calculated as the ratios of peakheights in the spectra recorded with and without protonsaturation; the NOE uncertainties were obtained by pro-pogating the uncertainties in the peak heights. Theexperimental uncertainties were used as weighting fac-tors when averaging the replicate NOEs obtained fromthe two orthogonal data sets.

The relaxation of a protonated 15N nucleus is domi-nated by the dipolar interaction with its directly attachedproton and by chemical shift anisotropy. The relaxation

parameters are related to the spectral density function ofthe NH bond vector by the following eqations(Abragam, 1961):

R1 � �d2=4��J�oH ÿ oN� � 3J�oN�� 6J�oH � oN�� � c2J�oN� �1�

R2 � �d2=8��4J�0� � J�oH ÿ oN� � 3J�oN�� 6J�oH� � 6J�oH � oN��� �c2=6��4J�0� � 3J�oN�� � Rex �2�

NOE � 1� �d2=4R1��gH=gN�� �6J�oH � oN� ÿ J�oH ÿ oN�� �3�

in which d � [m0hgHgN/8p2]hrÿ3NHi, c � oN�s/

���3p

, m0 isthe permeability of free space; h is Plank's constant;gH and gN are the gyromagnetic ratios of the 1H and 15Nnuclei, respectively; oH and oN are the Larmor frequen-cies of the 1H and 15N nuclei, respectively; rNH is theinternuclear 1H-15N distance (1.02 AÊ ); �s is the chemicalshift anisotropy (ÿ160 ppm; Hiyama et al., 1988); andJ(o) is the value of the spectral density function at fre-quency o. Rex is a term introduced to account for otherpseudo-®rst-order processes contributing to R2 that arenot eliminated by the CPMG pulse train, such as confor-mational averaging on the microsecond/millisecondtime-scale. The three measurable relaxation parametersare insuf®cient to determine uniquely the values of thespectral density function at the ®ve frequencies inequations (1) to (3) [J(0), J(oN), J(oH ÿ oN), J(oH), andJ(oH�oN)]; the values of the spectral density function atthree frequencies, o � 0, oN and 0.870oH, can be deter-mined explicitly from the three measured relaxation par-ameters by using a reduced spectral density mappingapproach (Farrow et al., 1995a,b; Ishima & Nagayama,1995). By assuming that dJ(o)/do2 is relatively constantbetween o � oH � oN and o � oH ÿ oN (Peng &Wagner, 1992a,b) the linear combinations of J(oH ÿ oN),J(oH), and j(oH � oN) in equations (1) to (3) can bereplaced with a single equivalent spectral density term,giving simpli®ed expressions for the 15N relaxation par-ameters (Farrow et al., 1995b):

R1 � �d2=4��3J�oN� � 7J�0:921oH�� � c2J�oN� �4�

R2 � �d2=8��4J�0� � 3J�oN� � 13J�0:955oH��� �c2=6��4J�0� � 3J�oN�� � Rex �5�

s � �NOEÿ 1�R1gN=gH � �d2=4��5J�0:870oH�� �6�In which s is the 1H-15N cross-relaxation rate constant.The value of J(0.870oh) is obtained directly from R1 andNOE using equation (6). Values of J(0) and J(oN) areobtained by substitution of J(0.921oH)�(0.870/0.921)2

J(0.870oH) and J(0.955oH)�(0.870/0.955)2 J(0.870oH) intoequations (4) and (5) as described by Farrow et al. (1995b):

J�0:87oH� � 4s=�5d2� �7�

J�oN� � �4R1 ÿ 5:00s�=�3d2 � 4c2� �8�

Je�0� � J�0� � 6Rex=�3d2 � 4c2�� �6R2 ÿ 3R1 ÿ 2:72s�=�3d2 � 4c2� �9�

Backbone Dynamics of Heregulin-� 1159

As shown by equation (9), the effective value of thespectral density at 0 frequency, Je(0), is increased bycontributions from conformational exchange on micro-second/millisecond time-scales, Rex:

Rex � �o2pApBtex�1ÿ �2tex=tcp�tanh�tcp=2tex�� �10�in which pi, oi, and si are the populations, Larmor fre-quencies and chemical shifts, respectively, for the spins insite i (�A or B); �o � oA ÿ oB � B0(sA ÿ sB) is thechemical shift difference between the Larmor frequenciesof the two sites; B0 is the static magnetic ®eld strength, tcp

is the inter-pulse delay in the CPMG spin echo sequence;and tex � (kA!B � kB!A)ÿ1 is the time constant for theexchange process. More precise identi®cation of exchangeprocesses is possible by performing reduced spectral den-sity mapping (Farrow et al., 1995b) or by measuringR2 ÿ (R1/2) as functions of static magnetic ®eld to deter-mine dRex/dB0 (Phan et al., 1996). In the present instance,15N spins subject to conformational exchange were ident-i®ed qualitatively by examining the ratio [R2 ÿ hR2i]14.1/[R2 ÿ hR2i]11.7 for residues with [R2 ÿ hR2i]11.7 > 2s11.7, inwhich hR2i and s are the 10% trimmed mean and sampledeviation of R2 for residues 3 to 49 and the subscriptdenotes the static magnetic ®eld strength.

The reduced spectral density approach does notrequire the overall molecular tumbling to be isotropic.The rotational diffusion anisotropy of the 63 residueEGF-like domain of HRG-a was determined using thelocal diffusion approximation (BruÈ schweiler et al., 1995;Lee et al., 1997). Local diffusion constants, Di � (6tmi)

ÿ1

for the ith residue, were determined from the R2/R1

ratios for the well ordered (on both picosecond/nanose-cond and microsecond/millisecond time-scales) residues4 to 23, 33 to 43 and 48 using an isotropic spectral den-sity function, Ji(o) � tmi/(1 � o2t2

mi). The diffusion ten-sor, D, was determined by least-squares solution of theequation (BruÈ schweiler et al., 1995; Lee et al., 1997):

Di � ~eTi ADAÿ1~ei �11�

in which ~ei is the unit vector de®ning the orientation ofthe ith N-H bond vector (taken from the atomic coordi-nates of the energy-minimized mean NMR solutionstructure in the PDB ®le 1HAF or from atomic coordi-nates of the ensemble of 20 structures in the PDB ®le1HAE); A is the transformation matrix relating themolecular reference frame and the principal axes of thediffusion tensor; and D is a diagonal matrix with values(Dk � D?)/2, (Dk � D?)/2, and D?. The two diffusionconstants for an axially symmetric diffusion tensor areDk and D?. For a spherically symmetric diffusion tensor,Dk � D?. Axially and spherically symmetric diffusionmodels were compared using F-statistical testing (Leeet al., 1997). For an axially symmetric diffusion tensor,the local diffusion constants are given by:

Di � Diso ÿ P2�cosyi��Dk ÿD?�=3 �12�in which Diso � (Dk � 2D?)/3, P2(cos yi) � (3cos2yi ÿ 1)/2, and yi is the polar angle between the N-H bond vectorand the symmetry axis of the diffusion tensor.

Acknowledgments

We thank Nicholas Skelton (Genentech) for valuablediscussions and critical reading of the manuscript,Joseph Pease (Roche Biosciences) for time and assistance

on the 600 MHz spectrometer, and Mikael Akke (LundUniversity) for FELIX macros used to extract peakheights from the 2D NMR spectra. A.G.P. gratefullyacknowledges support from the Arnold and Mabel Beck-man Foundation and an Irma T. Hirschl Career ScientistAward.

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Edited by P. E. Wright

(Received 29 January 1998; accepted 24 February 1998)

http://www.hbuk.co.uk/jmb

Supplementary material comprising two Tables isavailable from JMB Online.