Stability and specificity of protein-protein interactions: The case of the trypsin-trypsin inhibitor complexes

J. Mol. Biol. (1976) 100, 197-211

Stability and Specificity of Protein-Protein Interactions: The Case of the Trypsin-Trypsin Inhibitor Complexes JoiiT, J ~ r N ~ D CYRUS CEOTHL~

Service de Biochimie Cellulaire Institut Pasteur 28 rue du Docteur Roux 75724 Paris, Cedex 15, .France (Received 6 June 1975, and in revised form 15 September 1975) Atomic co-ordinates of the crystalline complexes of trypsin with pancreatic trypsin inhibitor and with soybean trypsin inhibitor were used to calculate the protein surface area buried in the complexes. This gives a value of the hydrophobic contribution to the free energy of dissociation, a quantity directly related to the sLtrface area accessible to water. Most of the buried sLu'face area is provided by a dozen trypsin amino acid residues and by the binding loops of the inhibitol~. These residues form close-packed interfaces, though the packing is quite different in the two complexes. The large loss of translational and rotational entropy which occurs upon complex formation is balanced by the hydrophobic free energy due to the smaller surface area accessible to the solvent. While the contribution of polar interactions to the free energs~ of dissociation is small compared to that of hydrophobicity, the ability to form close-packed interfaces, with the polar atoms properly positioned to give hydrogen bonds, plays an essential part in trypsin specificity. 1. I n t r o d u c t i o n Proteins are made to form specific and stable complexes with their ligands. These complexes rarely involve the formation of new covalent bonds, and w h e n they do these bonds are often only present as transitory intermediates. On the other hand, the so-called weak chemical bonds are always present: electrostatic attractive forces between polar groups forming hydrogen bonds or ion pairs, and van der Waals' forces between neighbouring atoms. These forces are the same as those which stabilize crystals of small organic molecules. As most biological interactions are made in an aqueous environment, one must also consider the existence of "hydrophobic interactions", a misleading term used to describe the free energy derived from the macroscopic properties of water as a solvent. I t should not be thought that hydrophobicity results from actual interactions between atoms of the solute, but only t h a t the removal of these out of solution is generally accompanied by a favourable increase in solvent entropy. We study here the association of trypsin with two proteins which interact specifically with it, the pancreatic trypsin inhibitor and the trypsin inhibitor from soybean. The crystal structure of the complex made by P T I t with bovine trypsin has been ~Abbreviations used: PTI, pancreatic trypsin inhibitor; STI, soybean trypsin inhibitor; PTI complex, complex of bovine trypsin with pancreatic trypsin inhibitor; STI complex, complex of porcine trypsin with soybean trypsin inhibitor. 14"

197

198

J. JANIN AND C. CHOTHIA

established by Riihlmann et al. (1973) and Huber et al. (1974) and that of the region of interaction between STI and porcine trypsin by Sweet et al. (1974). While the two trypsins are closely related both in their amino acid sequences and in their three-dimensional structures, PTI and STI are not. The two inhibitors have been shown by biochemical studies (reviewed by Laskowski & Sealock, 1971) to interact with the active site of trypsin and to bind in the same manner as normal substrates (Stroud et al., 1971; Blow et al., 1972; Bode et al., 1975). We calculate the protein surface area which is buried when two trypsin-inhibitor complexes form and apply an empirical correlation established between hydrophobic free energy and surface areas accessible to solvent (Chothia, 1974) to show that hydrophobicity is the major factor in stabilizing the complexes. The specificity of trypsininhibitor association results from the ability of these molecules to form close-packed interfaces and to replace weak chemical bonds normally made with water on the protein surface by similar bonds made in the complexes. 2. Methods and Results (a) Atomic co-ordinates and energy refinement Atomic co-ordhlates for the crystalline PTI complex have been obtained by Huber et al. (1974) from a 1.9 • electron density map. They include all trypsin non-hydrogen

atoms, the PTI molecule except residues 1' and 58'~, and water molecules. These crystallographic atomic co-ordinates were subjected to "energy refinement" (Levitt & Lifson, 1969; Levitt, 1974) using a program of Levitt. Very few dihedral angles and van der Waals' contacts had high energies in the PTI complex. This confirms the high precision of the atomic co-ordinates generated by the phase refinement procedure of Huber et al. (1974). The root-mean-square movement of atoms during energy refinement was 0-134 /~, within the 0.15 A estimate given by Huber et al. (1974) for the standard deviation of the atomic positions. Atomic co-ordinates for the STI complex have been derived from an electron density map at 2.6 A resolution (Sweet et al., 1974). They include half of the inhibitor sequence (residues 1' to 93') and the following 43 residues of porcine trypsin out of 222:37 to 43, 54 to 61, 97 to 104, 150 to 152, 189 to 198 and 213 to 220. Because structural data were available for only part of the structure, energy refinement was applied to it with a potential binding elastically each atom to its initial position, in order to prevent spuriously large shifts which would affect atoms missing neighbours. The root-mean-square movement during refinement was 0.28 A, within the limit given by Sweet et al. (1974) for the precision of their data (0-4 A). Because of the improved geometry of non-bonded interactions, the energy refined co-ordinates of the STI complex were used for the rest of this work. To compare the geometry of the two trypsin-inhibitor complexes, a rigid body rotation was applied to the PTI complex. A transformation matrix was determined by a least-squares fit of the trypsin main-chain atoms (McLauchlan, 1972). Like Huber et al. (1974), we noted discrepancies between the two trypsin structures at residues 37, 97 to 98, and in the 217-219-220 loop. The positions of the main-chain atoms agree well for the remaining trypsin residues. The root-mean-square distance between equivalent carbon and nitrogen atoms was 0-53/~, which, taken together with t Trypsin residues are numberocl following the chymotrypsinogen sequence. Inhibitor residues are indicated by primes.

T R Y P S I N - I N H I B I T O R COMPLEXES

199

the precision estimates for the two sets of co-ordinates, means that these sections of trypsin are identical in the two complexes, though differences m a y exist at residues 97 and 219 (see below). (b) The surface area buried in the trypsin-inhibitor complexes We define the surface area accessible to solvent for a protein atom as the area over which the centre of a supposedly spherical water molecule can be placed so that it makes a van der Waals' contact with this atom without penetrating a n y other protein atom (Lee & Richards, 1971). A program written by Levitt was used to calculate the accessible surface area of the P T I complex from the atomic co-ordinates. The P T I moiety and the trypsin moiety were then taken separately and their accessible surface area calculated. The surface area buried in the complex is the sum of the accessible surface areas of the two moieties minus that of the complex (Chothia & Janin, 1975). The surface area buried in the STI complex was calculated in the same manner. Its value as a difference is not affected by the absence of part of STI and of most of porcine trypsin, as long as none of the missing residues participates in the interaction. The total accessible and buried surface areas of the P T I and STI complexes are given in Table 1. We see t h a t nearly the same surface area becomes inaccessible to TABLE 1

Change of accessible surface area Surface area PTIt Bovine trypsin Complex STI:~ Porcine trypsin Complex

Accessible (A2) 3586 8920 11,109 6328 4067 8947

Buried in complex

(_~2)

754 643 1397 790 658 1448

t Residues 1' and 58' are missing. The surface area accessible to solvent is 3705 •2 for the complete PTI molecule using atomic co-ordinates from Dcisenhofer & Steigemann (1974). :~Due to the large number of missing residues, the values quoted for the surface areas accessible to solvent are not significant concerning STI, porcine trypsin and their complex. Buried surface areas are meaningful nevertheless. water when the two complexes form: about 1 4 0 0 / I 2, of which 650 /l 2 are trypsin surface area and somewhat more than 750 /~2 inhibitor surface area. Moreover, homologous trypsin residues make very similar contributions in the two complexes (Fig. l(a)). On the inhibitor side (Fig. l(b)), the six residues of the "binding loop", occupying the positions P3 to P3' of the Schechter-Berger notation (Schechter & Berger, 1967) around the essential P 1 - P I ' peptide bond, provide 70% of the surface area buried on PTI, and 77~/o on STI. The residue at position P1 (Lys 15' of STI or Arg 63' of PTI) buries its charged side-chain nearly completely in the specificity pocket of trypsin, thus losing about 2 0 0 / l 2 of accessible surface area: more than one quarter of the surface area buried on the inhibitors.

J. JANIN

200 2oo~

AND

C. C H O T H I A

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o ioo

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his

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: :

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99

151

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189 asp

190 set

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193

195

ZI4

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216

217

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ser

set

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250

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9

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2'

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asp phe osn

13"

pro 6t' ~e9

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15'

lys

65" or(]

16'

17'

olo

arq 64' lie

65" or(]

18'

lie

66'

phe

19'

lie

34" 37" 3 g

val 91y r

olher

39'

arg

71' 72' his i~ro

FIe. 1. Surface area of individual residues. The empty bars represent the surface area remaining accessible to the solvent in the complexes. The area becoming buried in the PTT complex is shaded lightly, and more strongly for the STI complex. The value of the accessible surface area of ~hose residues of porcine trb~psin whose neighbours are missing in the incomplete set. of coordinates which was used is grossly overestimated (dashed lines). Residues with less than 10 A 2 of buried surface area are listed as other. They are : bovine trypsin, Cys 42, Cys 58, Tyr 94, Thr 98, Thr 149, Cys 191, Val 213, Gly 219, Cys 220, Gly 226; porcine trypsin, Cys 42, Cys 58, Asp 102, Cys 191, Cys 220; PTI, Gly 12', Arg 20'; and STI, Pro 10', G[u I2', Pro 60', Ale 68', Gly 70'.

(c) Packing of residues in the interface Those residues which see their accessibility to water change significantly in the trypsin-inhibitor complexes constitute the interface. The volume occupied by individual atoms in these residues is defined as the volume of the smallest polyhedron (Voronoi polyhedron) formed by a set of planes which separate this atom from each of its neighbours in the structure. It has been shown that the inside of proteins is close-packed (Richards, 1974), each residue occupying precisely the same volume as in the crystal of the corresponding amino acid (Chothia, 1975). Using the atomic co-ordinates for the complexes, we calculate in this manner the volumes occupied by residues of the trypsin-inhibitor interfaces and compare them to average values observed for the same residues inside proteins (Fig. 2). The two sets of values agree rather well, especially for the PTI complex, for which we have more precise atomic co-ordinates. In both complexes, Set 195 occupies about 12 A a (1.6 S.D.) less than average serine residues. This results from the short distance between its sidechain and the earbonyl group of Lys 15' or Arg 63'. However, its exact volume depends on the details of the atomic structure at the active site of trypsin (Bode et al., 1975). Since a loose packing would result in larger volumes for the residues in the interfaces, Figure 2 demonstrates that the trypsin-inhibitor interfaces are close-packed,

TRYPSIN-INHIBITOR

COMPLEXES

201

250 (a)

2OO m

E 150

~

,,,.~

,X"<

0

he"

Phe 41 250

His 57

Leu 99

Ser i95

Gin 192

Trp215

Gly216

(b) P3

P1

P2

. P l"

P3'

P2'

200 A

"10

a:

50

.,x,, N

0 P ro 13'

250

C ys 14'-38"

Lys 15"

. AIo 16"

Arg 17'

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P2

Ser61'

Tyr62'

PI

PI'

P~.'

P3'

Arg65"

Phe66"

200

E

~5o

0

I00

oc

50

0 Arg63"

Ile64 ~

FIG. 2. Volume occupied b y residues in the interface. We represent the ,volumes of those residues (a) of bovine (shaded lightly) a n d porcine (shaded more strongly) trypsin, of P T I (b) a n d of STI (e) which become buried or nearly buried in the complexes. The volume calculation is somewhat uncertain for several porcine trypsin residues, because of missing neighbours; those are dashed or not given (Trp 215). The average volume occupied b y residues buried in a sample of 15 protein structures (Chothia, 1975) is represented b y e m p t y bars, with its s t a n d a r d deviation. This sample contains no arginine ; the volume occupied by arginine residues is t a k e n from Chothia & J a n i n (1975).

J. J A N I N AND C. C H O T H I A

202

like protein interiors and like crystals of small organic molecules. The surface involved is the same on the trypsin side, and one may ask how such different molecules as P T I and STI pack equally well against it. This question can partly be answered b y comparing the P T I and STI complexes once they have been rotated into similar orientations. Using the rigid-body rotation described above, which superimposes the trypsin parts of the two complexes, the main-chain atoms of the inhibitors also superimpose at positions P3 to P I ' of the binding loops, with a root-mean-square distance of 0.65 A and the main-chain conformation is the same (Blow et al., 1974). While the side-chains of Lys 15' and Arg 63' at position P1 superimpose up to the end of the lysine side-chain, the two extra nitrogen atoms (N~) of the arginine require an additional 12 /~, which m a y need a rearrangement of the trypsin conformation (see Fig. 6) at Gly 219, which is placed at the bottom of the binding pocket. At position P3, the side-chain of Ser 61' is folded on itself to occupy the same position as Pro 13' of PTI. Comparing the eystine residue (Cys 14'-Cys 38') at position P2 of PTI, with Tyr 62' of STI, we find that the disulphide, in close contact with Leu 99 of trypsin, fills only part of the volume occupied by the phenol ring of the tyrosine (Fig. 3); the close packing is maintained by the leucine side-chain having a different conformation in the two complexes.

Y

cys 38'

L

14'

(o)

(b)

FIe. 3. Residue P2 (on the amino side of the lysine or arginine placed in the specificity pocket of trypsin) is acystine in PTI (a) and a tyrosine in STI (b) ; both are quite accessible to solvent in the free inhibitors, and buried (or nearly buried, see Fig. 1) in the complexes. They are close-packed, occupying volumes similar to those observed inside proteins (see Fig. 2) and in crystals of cystine or tyrosine. The P2 side-chain makes contacts with His 57 of trypsin, and also with Leu 99. This rotates around its Ca--Ce bond to make room for the phenol ring of the tyrosine. The P2 site is mostly hydrophobic, although the hydroxyl group of Tyr 62' may form a hydrogen bond with the side-chain of ASh 97 (Sweet et al., 1974). The two complexes are oriented the same way, after applying a rigid body rotation as indicated in the text. The co-ordinates system is that of the STI complex (Sweet et al., 1974); the scale is given by the bars (corresponding to 1 A). Nitrogen (O); oxygen (O); sulphur (D)-

TRYPSIN-INHIBITOR

COMPLEXES

203

On the leaving group side, the side-chain of Ile 64' at position PI' of STI is also significantly bigger than that of Ala 16' of PTI, but it points towards the inside of the inhibitor. At position P2', both inhibitors have an arginine residue, which makes similar contacts with trypsin (Janin et al., 1974). Residues at position P3' and beyond have completely different conformations in the two complexes, and the comparison of the two structures becomes of little use. (d) Polar interactions in trypsin-inhibitor complexes Breaking down surface areas into contributions of non-polar (that is carbon) and polar atoms, we calculate that the non-polar provide 53.40//0 of the accessible surface area of trypsin and 56.8% of that of PTI (Table 2). Non-polar carbon atoms also TABLE 2

Chemical nature of the interface Surface

P r o p o r t i o n of area (%) Non-polar t Polar:~ Charged

Accessible in: Bovine trypsin PTI P T I complex

53.4 56-8 54-2

38.4 23-0 34.3

8.2 20.2 11.5

Buried in: P T I complex STI complex

55.6 59.4

31.9 29.8

12.5 10.8

All carbon atoms. Oxygen, nitrogen a n d sulphur a t o m s except in charged groups.

provide 55.6% of the surface area buried in the PTI complex and 59.40//0 of that buried in the STI complex. This means that the surfaces involved in the interaction are similar in their chemical composition to the rest of the protein surface. It also means that many polar atoms become buried when the complexes form (Table 3). (i) The main-chain of the binding loop There are two hydrogen bonds forming a fl-sheet-like structure between the anti. parallel P3-P2-P1 sequence of the inhibitors and the 214-215-216 sequence of trypsin, and two hydrogen bonds linking the carbonyl group of P1 to the peptide nitrogen atoms of Gly 193 and Ser 195 (Fig. 4). The latter two bonds are supposed to play a role in the catalysis of the P I - - P I ' peptide cleavage (Steitz et al., 1969; Segal et al., 1971), while the first two have been described with substrates bound not only to proteases of the trypsin family but also to subtilisin (Robertus et al., 1972) a bacterial serine protease having a completely different structure. In the trypsin-inhibitor complexes, an additional hydrogen bond involves the carbon.yl group of P2 and the side-chain of Gla 192 (Fig. 5).

J. JANIN

204

A N D C. C H O T H I A TABLE 3

Polar atoms buried in trypsin inhibitor complexes t Buried atoms of trypsin

Interacting with PTI

His 40: O

Ny Arg 17'

Phe 41 : O

N Arg 17

Cys 42: Sv

STI N~, Ne Arg 65' :~

--

His 5 7 : 0

--

w

Nr His 71'

Gly 193: N

O Lys 15'

O Arg 63'

Ser 195: N

O Lys 15'

O Arg 63'

Gly 216: N

O Pro 13'

O Ser 61'

Buried atoms of: PTI

STI

Interacting with

P2 Cys 14': 0 Cys 14': Sv

Tyr 62': O --

Nc Gin 192 --

P1 Lys 15': N~ Lys 15": N Lys 15': O

Arg 63': Ne, N~? Arg 63': N Arg 63': O

(see Fig. 6) O Ser 214 N Gly 193, N Ser 195

P I ' Ala 16': O

Ile 64': O

N Gly 193

P2' Arg 17': N Arg 17': 0

Arg 65': N:~ Arg 65': 0 Arg 65': N~, N~

O Phe 41 O His 40 82

t Polar atoms accessible to solvent in free trypsin or inhibitor and buried in the complex (zero accessible surface area). Only those which do not form hydrogen bonds within their own subunit are listed here. (A total of 29 polar atoms become buried in the P T I complex.) H y d r o g e n bonds are accepted between atoms 3.9 A apart provided the angular geometry is correct. All interactions quoted here are shorter t h a n 3.5 A. ~: The distance between O Phe 41 and N Arg 63' is 4.5 A in the STI complex, which makes this bond unlikely. wThis atom is accessible to water in the P T I complex. 82I n the P T I complex, the guanidinium group of Arg 17' is partly accessible to water and forms only one bond to O His 40. H2N-- Gin 192

0RPhe 41

:

] 3.o i

! o

i i

2.9,

--I

9 .,

P_~3 T N - -

P.22

Jl

0

N --P1T ,

3.2j

3.zj o'

,;

21.._66-- N T21...~5 - N

"

N -- P.!_'T N-- p2' T 0 3"I~ ".2.9

0 '3"7

0

3.r, 3.2",, :2.e \ "".i 21m_4 N--19.__55 N - - 1 9 3

0

FIe. 4. Polar interactions made by the main-chain atoms of the binding loops: hydrogen bonds made by maln-chain (peptide) oxygen and nitrogen atoms of residues 13' to 17' of P T I or 61' to 65' of STI. Distances (underlined for PTI) are calculated using crystallographic co-ordinates for the P T I complex and energy refined co-ordinates for the STI complex. Interactions made by the earbonyl oxygen atoms of residues P2 and P I ' are discussed in the text.

TRYPSIN-INHIBITOR

~ 41

29

l

(0)

COMPLEXES

205

tyslS'

gln192

(b)

FIG. 5. Interactions made by Gln 192 of trypsin. The orientation of the amide group of Gln 192 is chosen in order to make possible hydrogen bonds to the carbonyl groups of P2 (Cys 14' (a) or Tyr 62' (b)). Sweet et al. (1974) chose the reverse orientation and proposed t h a t a hydrogen bond is made to the amino group of Ile 64, which appears unlikely with the present co-ordinates. Scale and point of view as in Figure 3. Nitrogen ( Q ) ; oxygen (Q)).

On the leaving group side, it has been suggested (Fersht et al., 1973) that the carbonyl group of PI' hydrogen bonds to the nitrogen of Gly 193. The distances observed allow this (Fig. 4), but the angular geometry is poor. Then, at position P2', the carbonyl group of Arg 17' or Arg 65' appears to move from solution to a completely apolar environment in the complex. Except for the sulphur atoms of Cys 42 and Cys 14', which would give weak hydrogen bonds anyway, the P2' carbonyl oxygen is probably the only polar atom buried in the trypsin-inhibitor complexes which cannot form polar interactions. (ii) The specificity pocket of trypsin A satisfactory explanation for the different primary specificities of trypsin and chymotrypsin was given when the structure of the latter was found to contain a pocket (Henderson et al., 1971), at the bottom of which was a serine residue, homologous to an aspartate residue of trypsin (Asp 189). The latter would make favourable electrostatic interactions with a positively charged side-chain carried by a substrate, thus causing trypsin to bind and hydrolyse preferentially peptides containing lysine or arginine residues. In the trypsin-inhibitor complexes, the side-chains of Lys 14' of PTI and Arg 63' of STI do interact with Asp 189, although with rather different geometries (Fig. 6). While the distal nitrogen atoms of Arg 63' are essentially in close contact with the carboxyl group of Asp 189 in the STI complex, the shorter side-chain of Lys 15' is unable to reach there. Its amino nitrogen remains at about 3.7 A from the carboxyl oxygens of Asp 189 and water is present in the binding pocket (Bode et al., 1975) partly filling the space occupied by the N~ atoms of Arg 63' in the STI complex. Figure 6 shows that the specificity pocket of trypsin provides a strongly polar environment for the positive charge of the P1 residue (Krieger et al., 1974). Hydrogen bonds are made to the earbonyl and hydroxyl oxygens of Ser 190 and to the carbonyl group of Trp 215 (Sweet et al., 1974; Bode et al., 1975).

206

J. J A N I N AND C. C H O T H I A

A

org63~

lys 1 5 ' N r ~ qly21S//

/,,.-

o

3. w 2.8_ "

"r, 2.'5 ~ "

3.~., 2.s' J

"1"

,~.3-5_

't

~.~

3.0 ~-

,2-5 ,, 3.0 ',,2-5

\/

~serl90

(b)

(o)

FIO. 6. The residue at position P1 is a lysine in PTI (a) and an arginine in STI (b). Their sidechains fill the specificity pocket of trypsin. View, up the x axis of the STI complex. Nitrogen (O); oxygen ( 9 water (W). (iii) Other polar interactions T h e P T I a n d S T I complexes also c o n t a i n o t h e r polar i n t e r a c t i o n s (Table 4). Several i n v o l v e t h e side-chain of t h e a r g i n i n e a t position P 2 ' (Arg 17' of P T I or Arg 65' of STI), which also forms a charge t r a n s f e r complex ~dth t h e p h e n o l ring of T y r 151 a n d gives h y d r o g e n b o n d s to the c a r b o n y l group of His 40 ( R i i h l m a n n et al., 1973; Sweet et al., 1974). These i n t e r a c t i o n s c a n n o t occur for m a n y other t r y p s i n - i n h i b i t o r s which do n o t h a v e a n a r g i n i n e a t this position. TABLE 4

-Polar interactions specific to the P T I and S T I complexes PTI

Bovine trypsin

Distance (A)

Arg 17': N~ Ile 19': N Arg 39': Ne, N~

O His 40 O~ Tyr 39~ O Asn 97

2.7 3-0 3-0, 2-9

STI

Porcine trypsin

Distance (A)

Asp 1': O5 A_rg 65': N~, Ny His 71': New

N~ Lys 60 O His 40 O His 57

2-4 :~ 3.1, 3.1 2.9

Residue 39 is a serine in porcine trypsin, which cannot make the same interactions as Ty~' 39. The side-chains of Asp 1" and Lys 60 are made to overlap by real-space refinement (Sweet et al., 1974) an artefact which was corrected only in part by energy refinement. wIncorrectly labelled NH in Table 6 of Sweet et al. (1974).

4. D i s c u s s i o n

(a) Thermodynamics of complex formation The association of two molecules is accompanied b y a reduction in entropy due to a loss of translational and rotational degrees of freedom. This can easily be calculated for free particles in vacuo, such as perfect gases, which however represent a

TRYPSIN-INHIBITOR

207

COMPLEXES

remote situation compared to macromolecules in aqueous solution. The theory gives reasonable estimates of the free energy of association of small organic molecules in non-polar solvents for which experimental values (extrapolated to ideal solutions) exist (Page & Jencks, 1971). For the trypsin-inhibitor systems, atomic co-ordinates can be used to calculate the partition functions and the corresponding free energies for the dissociated molecules and for the complexes. Table 5 shows that, at 27~ the dissociation releases about --27 kcal/mol of translational/rotational free energy. The enthalpy change is k T / 2 per degree of freedom, or 1.8 kcal/mol (3 R T ) . Thus, the entropy gained is about 100 cal deg-1 mol-1, a very large value, which should still increase somewhat if the entropy of side-chains were included. Indeed, the sidechains of Tyr 62' (but not that of Cys 14' in the corresponding P2 position of PTI), Arg 63' and Arg 65' in STI, those of Lys 15' and Arg 17' in PTI, are certainly mobile in the free inhibitors while they are immobilized in the complexes. TABLE 5

Translational~rotational free energies

Molecular weight Translational/rotational free energy (keal/mol)t Free energy gained in complex (kcal/mol)~:

PTI

STI

Trypsin

PTI complex

STI complex

6500

20,100

23,300

29,800

43,400

-- 27

-- 30

-- 30

-- 31

-- 32

26

28

The free energies are calculated from the translational and rotational partition functions for free particles : Zt (21rrnkT)3t2 V/h 3 and Z~ ~ 81r2(21rkT)3/2 Pl2/h3, where m is the particle mass, I the product of the three principal radii of gyration, and V the volume into which the particle is constrained. The free energy is, per moh =

G =

- - k T ln(Z~N/Ar!) -- k T ln(ZrN).

:~The free energy gained in the A B complex is Gas -- Ga -- Gs. (b) Weak chemical bonds and the role of hydrophobic free energy About 14 polar atoms of trypsin and 12 polar atoms of the inhibitors form new hydrogen bonds in the complexes. The enthalpy of breaking one of these bonds would typically be of the order of 5 kcal/mol (Kresheck & Klotz, 1969) in a non-aqueous environment. The ion pair in the binding pocket alone can provide several kcal/mol of electrostatic energy if the dielectric constant around the positive charges of Lys 15' and Arg 63' is significantly less than in water. Also, attractive van der Waals' forces exist between the m a n y atoms in contact. But interactions which are made within the complex replace similar interactions made with the solvent in the dissociated subunits. Therefore, each pair of interacting protein atoms contributes to the free energy of dissociation only what results from: A . . . H20 + B . . .

H20 - > A . . . B + H20 9 9 9 H20

208

J. JANIN

A N D C. C H O T H I A

In fact, even good amide hydrogen bonds have an enthalpy balance near zero in water. In view of the 27 kcal/mol required to compensate the loss of translational/ rotational free energy, it is safe to state that the stability of the trypsin-inhibitor complexes, like other protein-protein associations (Chothia & Janin, 1975), is an effect of solvent entropy rather than of intermolecular interactions. In short, it is hydrophobicity which maintains two proteins in association. Thanks to an empirical correlation established between free energies of transfer to water solution and accessible surface areas (Chothia, 1974) we can estimate the free energy gained from the increased disorder of water molecules, in contact with a smaller surface area in the complex. Using data from Table 1 and a value of 25 cal/mol p e r / ~ obtained by Chothia (1975), we find that hydrophobicity contributes about 35 kcal/mol to the stability of the trypsin-inhibitor complexes. Thus, the increased entropy of water overcompensates the entropy lost by the two protein molecules. Taking these results together, we may then represent the thermodynamic balance of the (trypsin + inhibitor--> complex) reaction (Fig. 7). It yields a large positive

50

O

E U

o~ t. ta.

L~ 0

FIG. 7. The free energy balance in trypsin-inhibitor complexes. Free energy terms favouring association include hydrophobieity (taken as 25 eal/mol per A of buried surface area), and the balance of polar or van der Waals' interactions made between the two molecules rather t h a n with water. Favouring dissociation: translational and rotational entropies, and possibly strain in the complex (dashed). The difference yields a value of the free energy of dissociation / t G D ~ - - R T In KD. The actual value of Z~GDis of the order of 15 kcal/mo] at neutral p H for the STI complex (Laskowski et al., I971) and somewhat more for the P T I complex (Vincent & Lazdunski, 1972). The primary specificity of trypsin is expressed by zJGel, an estimate of the effect of replacing the lysine or arginine residue in the specificity pocket of trypsin with an alanine.

free energy of dissociation /IGD, equivalent to a very low value of the dissociation constant K D. This leaves open the possibility that unfavourable interactions (i.e. strain) exist in the complex; at the active site of the enzyme for instance. (c) Trypsin specificity and catalysis The hydrophobic free energy largely responsible for the stability of this association is non-specific. Specificity does not imply that the "right" enzyme-ligand complex is extremely stable, but only that it is significantly more so than any "wrong" complex liable to occur. This requires complementarity of the surfaces involved: the

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complexes are close-packed structures, with polar atoms in position to make proper interactions. Let us change one of these and replace the amino nitrogen of Lys 15' b y a carbon atom. When this modified P T I binds, the same close-packed structure can be made, but the interactions made with water b y polar atoms of the trypsin binding pocket, including the carboxylate group of Asp 189, are destroyed without being replaced by those which the lysine nitrogen atom makes. Since each interaction represents several kcal/mol, the discrimination between a carbon and a nitrogen atom at this position is very strong. On the other hand, shortening the P1 side chain, replacing Lys 15' by, say, an alanine, would leave a hole in the binding pocket, and the complex could form with water molecules remaining inside to satisfy the requirement for polar bonds. A computer simulation indicates t h a t 120 •2 less are buried in the P T I complex with residue 15' an alanine instead of a lysine. Hydrophobieity contributes therefore about 3 kcal/mol less free energy in this case, a factor of 150 in the dissociation constant. This gives an estimate of the hydrophobic contribution to the primary specificity of trypsin. It is actually possible to replace Arg 63' of STI (Kowalski et al., 1974) or Lys 15' of P T I (Jering & Tschesehe, 1974a) with other amino acids b y a clever use of their interaction with trypsin. However, no value is given for the dissociation constant of modified inhibitors with trypsin. For amide and ester substrates of trypsin, the primary specificity is expressed b y increased rates of acylation (]Ca) as well as by lower dissociation constants Ks when the substrate contains a lysine or an arginine (Chevallier & Yon, 1966). This is in accordance with current models of enzymic activity (Page & Jencks, 1971; Satterthwait & Jencks, 1974; Fersht, 1974) and confirms that some binding energy is employed to accelerate the catalytic reaction (increasing K s in order to increase ]Ca): less of it is available with a wrong P1 structure. (d) P T I and S T I as inhibitors Riihlmann et al. (1973) and Sweet et al. (1974) proposed that a covalent bond is made between the carbonyl carbon of P1 on the inhibitors and Ser 195 of trypsin, the structure at the active site being that of a tetrahedral intermediate in catalysis. However, the distance of C Lys 15' to 0 7 Ser 195 is 2.6 A in the refined model of the P T I complex, similar to other carbon to oxygen distances observed in crystals of carbonyl compounds (Bolton, 1964) where there are strong electrostatic interactions but no significant strain. As in some model compounds (Biirgi et al., 1973), the P1 earbonyl carbon is tetrahedrally deformed (Huber et al., 1974). This allows a very close approach to the serine side-chain with relatively little energy involved in the distortion of bond angles (estimated by Huber et al., 1975) to be of the order of 1.4 kcal/mol). Strain in the P T I complex is therefore limited. The structure observed in the crystalline state and, most likely, the dominant structure in solution, is t h a t of a distorted Michaells complex, in which the conformation of the substrate at the reactive site (C Lys 15') is close to that of the first covalent intermediate in the catalytic mechanism. Huber et al. (1975) have recently found that the same distortion exists in P T I bound to a chemically modified form of trypsin, where Ser 195 has been transformed into dehydro-alanine; no covalent bond m a y exist in this case. Cleavage of the inhibitors at the P 1 - - P I ' peptide bond would release a free P I ' amino group and force the residues on the leaving group side to move away from the carbonyl group of P1. This disturbs the close-packed structure and, along with the fact that the carbonyl groups of P I ' and P2' do not form proper hydrogen bonds in

210

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the complexes, favours the departure of the leaving group. For normal substrates, this step is required (Fersht et al., 1973) if the newly formed acyl bond at the active site is to be accessible to water. The structure of the P T I complex does not allow water to reach the active site (Riihlmann etal., 1973), and this has been given as a reason why P T I is not cleaved, at least not at a measurable rate. To increase the half-life of the complex from about 10 -2 s for a normal substrate to about l0 T s (estimate of Vincent & Lazdunski, 1972) would require an energy barrier of more t h a n 12 kcal/mol. The formation of the acyl-enzyme and the departure of the P I ' to P2' residues, which leaves a free access to water, can hardly be so costly in energy. Close-packing is also observed in the S T I complex, in which the P 1 - - P I ' bond is cleaved at a measurable rate. I n fact, trypsin resynthesizes this bond when it is given the modified form of the inhibitor: at neutral pH, the free energy of hydrolysis of the Arg 6 3 ' - - I l e 64' peptide bond is near zero in free STI, and positive in the complex (l~Iattis & Laskowski, 1973). This bond is thus thermodynamically stable, and Jering & Tschesche (1974b) have shown t h a t this is also true of Lys 1 5 ' - - ~ a 16' bond of P T I . A "kinetic" explanation of trypsin intfibition b y P T I is therefore not needed. Like STI, P T I can be described as a very good ligand of trypsin which, playing the normal role of an enzyme, catalyses the reaction towards equilibrium. The native form of the inhibitors is the stable product of the reaction, a product which has a very high affinity for the enzyme and prevents new substrates from reaching its active site. We are grateful to Dr 1%. Huber for making available to us atomic co-ordinates of the P T I complex. We thank F. M. 1%iehards and M. Levitt for the gift of computer programs. One of us (C. C.) was supported by the D~16gation Gdndrale k la 1%echerche Seientifique et Technique during his work. REFERENCES Blow, D. M., Wright, C. S., Kukla, D., 1%fihlmann, A., Steigemarm, W. & Huber, 1%. (1972). J. Mol. Biol. 69, 137-144. Blow, D. M., Janin, J. & Sweet, 1%. M. (1974). Nature (London), 249, 54-57. Bode, W., Schwager, P. & Huber, 1%. (1975). In Proceedings lOth F E B S Meeting, Paris (Desnuelle, P. & Michelson, A. M., eds) vol. 40, pp. 3-20, North HoLland Publishing Co., Amsterdam. Bolton, W. (1964). Nature (London), 291, 987-989. Bfirgi, H. B., Dunitz, J. P. & Shelter, G. (1973). J. Amer. Chem. Soc. 95, 5065-5067. ChevaUier, J. & Yon, J. (1966). Biochim. Biophys. Acta, 122, 116. Chothia, C. H. (1974). Nature (London), 248, 338-339. Chothia, C. H. (1975). Nature (London), 254, 304-308. Chothia, C. H. & Janin, J. (1975). Nature (London), 256, 705-708. Deisenhofer, J. & Steigemarm, W. (1974). In Bayer Symposium V, Proteinaze Inhibitors (Fritz, H., Tschesehe, H., Greene, L. J. & Truscheit, E., eds), pp. 484-496, Springer Verlag, Heidelberg. Fersht, A. 1%. (1974). Prec. Roy. Soc. ser. B, 187, 397-407. Forsht, A. 1%., Blow, D. M. & Fastrez, J. (1973). Biochemistry, 12, 2035-2041. Henderson, 1%.,Wright, C. S., Hess, G. P. & Blow, D. M. (1971 ). Cold Spring Harbor Symp. Quant. Biol. 36, 63-70. Huber, 1%.,Kulda, D., Bode, W., Schwager, P., Bartels, K., Deisenhofer, J. & Steigemann, W. (1974). J. Mol. Biol. 89, 73-101. Huber, 1%., Bode, W., Kukla, D., Kohl, U. & 1%yah, C. A. (1975). Biophys. Struct. Mech. 1, 189-201. Janin, J., Sweet, 1%. M. & Blow, D. M. (1974). In Bayer Symposium V, Proteinase Inhibiters, (Fritz, H., Tsehesche, H., Greene, L. J. & Truscheit, E., eds), pp. 513-520, Springer Verlag, Heidelberg.

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Jering, H. & Tschesche, H. (1974a). Angew. Chem. Int. Ed. Engl. 13, 661-662. tiering, H. & Tschesche, H. (1974b). Angew. Chem. Int. Ed. Engl. 13, 662-663. Kowalski, D., Leafy, T. 1%., McKee, R. E., Sealock, 1%. W., Wang, D. & Laskowski, M. Jr (1974). In Bayer Symposium V, Protein~e Inhibitors (Fritz, H., Tschesche, H., Greene, L. J. & Truscheit, E., eds.), pp. 311-324, Springer Verlag, Heidelberg. Kresheck, G. C. & Klotz, I. M. (1969). Biochemistry, 8, 8-12. Krieger, M., Kay, L. M. & Stroud, 1%. M. (1974). J . Mel. Biol. 83, 209-230. Laskowski, M. Jr & Sealock, 1%. W. (1971). In The Enzymes (Boyer, P. D., ed.), vol. 3, 3rd edit., pp. 375-473, Academic Press, New York. Laskowsld, i~l. Jr, Duran, 1%.W., Finkenstadt, W. 1%.,Herbert, S., Hixson, FT. F., Kowalsld, D., Luthy, J. A., Mattis, J. A., McKee, 1%. E. & Niekamp, C. W. (1971). In InMrnational Research Conference on Proteinase Inhibitors (Fritz, H. & Tschesche, H., eds), pp. 117-134, W. de Gruyter, Berlin. Lee, B. & 1%ichards, F. M. (1971). J . Mol. Biol. 55, 379-400. Levitt, M. (1974). J. Mol. Biol. 82, 393-420. Levitt, M. & Lifson, S. (1969). J. ~lol. Biol. 46, 269-279. Mattis, J. A. & Laskowski, M. Jr (1973). Biochemistry, 12, 2239-2244. McLauchlan, A. D. (1972). Acta Crystollogr. sect. A, 28, 656-657. Page, M. I. & Jencks, W. P. (1971). Prec. Nat. Acad. Sci., U.S.A. 68, 1678-1683. 1%ichards, F. M. (1974). J . Mol. Biol. 82, 1-14. 1%obertus, J. D., Kraut, J., Alden, 1%. A. & Birktoft, J. J. (1972). Biochemistry, 11, 42934303. 1%fihlmann, A., Kukla, D., Schwager, P., Bartels, K. & Huber, 1%. (1973). J . Mol. Biol. 77, 417-436. Satterthwait, A. C. & Jencks, W. P. (1974). J . Amer. Chem. Soc. 96, 7018-7031. Schechter, I. & Berger, A. (1967). Biochem. Biophys. Res. Commun. 27, 157-162. Segal, D. M., Powers, J. C., Cohen, G. H., Davies, D. 1%. & Wilcox, P. E. (1971). Biochemistry, 19, 3728-3738. Steitz, T. A., Henderson, R. & Blow, D. M. (1969). J. Mol. Biol. 46, 337-348. 8troud, 1%. M., Kay, L. 1VI.& Dickerson, 1%. E. (1971). Cold Spring Harbor Syrup. Quant. Biol. 36, 125-140. Sweet, 1%.M., Wright, H. T., Janin, J., Chothia, C. G. & Blow, D. M. (1974). Biochemistry, 13, 4212-4228. Vincent, J. P. & Lazdtmski, M. (1972). Biochemistry, I1, 2967-2977.