J. Mol. Biol. (1976) 107, 357-367
Relationship between Helix-Coil Transition Parameters for Synthetic Polypeptides and Helix Conformation Parameters for Globular Proteins. A Simple Model E. SUZUKI
Division of Protein Chemistry C.S.I.R.O., Parkville, Melbourne, Victoria 3052, Australia AND B. ROBSON
Department of Biochemistry, University of Manchester, Oxford Road, Manchester M13 9PL, England (Received 25 March 1976, and in revised form 21 May 1976) (1) The Zimm-Bragg formulation for hehx-coil transitions in simple synthetic polypeptides is generalized to handle the formation of ~-helical regions during the folding of globular proteins. (2) The relation between the helix-coil transition parameters for this process and other conformational parameters (derived by statistical analysis of the sequences and conformations of globular proteins) is determined. (3) I t is shown that the generalized Zimm-Bragg model can be used graphically to predict the helix-coil transition parameters from the statistical parameters, and vice versa. (4) I t is also shown that the Zimm-Bragg co-operativity parameter a implied by the lengths of helices observed in globular proteins is of the order of 10-1, and therefore much larger than the values obtained from simple synthetic polypeptides. (5) I t is postulated that a similarly large value of a persists throughout the folding process from the moment the helical regions are "trapped" by interactions between residues far apart in the amino acid sequence, and the nature of these interactions is discussed. 1. Introduction I n a t t e m p t i n g to explain the observed conformational parameters derived b y statistical analysis of proteins of known sequence and conformations (see, for example, Robson & Suzuki, 1976), one of the more interesting correlations t h a t can be investigated is between the conformational parameters of a residue in globular proteins and the observed behaviour of the residue in simple artificial polypeptides in solution. Unfortunately, only the formation of ~-helix has been widely investigated experimentally in the artificial polypeptide case, but a n u m b e r of theories, notably those of Lifson & Roig (1961) and Zimm & Bragg (1959), have been applied to the problem of obtaining ~-helical parameters from such systems. 357
358
E. SUZUKI
AND B . R O B S O N
In the Zimm-Bragg treatment a statistical weight of s is att'~ched to each residue in the helix and of unity to the residues not in the helix. A factor a which accounts for the difficulty in initiating the helix is also assigned and the partition function constructed. The free energy of an ~-helix n residues long may be shown to be (Poland & Scheraga, 1970) AG
=
-- RTlmr
--
(n --
2)
RT
In s,
(1)
where the first term corresponds to the helix nucleation energy and the second term is the free energy of the formation of (u -- 2) hydrogen bonds. Equation (1) may be rewritten as ~G
=
--RTln
( a / s 2) - -
n.RT.ln
s.
(2)
Although Poland & Scheraga (1970) considered that (n -- 2) residues stabilize an ~r of n residues, this number is sensitive to a more detailed energetic analysis. Certainly, during the folding of a globular protein, when ~r regions are being formed and stabilized, different considerations apply. On inspection of molecular models of the native structures of globular proteins, it can be seen that many of the hydrogen bonds which can be formed are formed (see for example, Watson, 1969) and both non-helical residues and those at the ends of helices can participate in hydrogen bonds with the rest of the protein. While the determining factor in the Zimm-Bragg theory is the formation of hydrogen bonds in the ~-helical manner, other factors which contribute to the conformational energy of a residue will play a much more important role in proteins than in the homopolymer situation. A consequence of this is that the number of residues required to initiate helix formation in globular proteins may well differ from the minimum number of residues required to initiate a helix in synthetic polypeptides, and the simplest possible analogue of equation (2) which can be applied to a helix in globular proteins is the more general expression AG
~
-- R Tln
((~/si " s i + 1. 9 9 s i + , , - 1) - - R T l n ( s
. s j + 1. 9 9 s j + ~ _ 1),
(3)
where s , ' s ~ + l . . , s~+ , , - 1 is the product of the m statistical weights of residues from residue i to residue i + m - - 1 which must adopt the helical conformation before a stable helix can begin to form, and s j . s j + 1. 9 9 s j + n - 1 is the product for the n residues in the a-helix. Note that m ~- 1 is the length of the shortest possible helix. The same consideration which suggests that m + 1 may well differ from the value implied by the Zimm-Bragg theory also suggests that typical values for a in proteins are also quite different from those proposed by Zimm & Bragg (1959) for the homopolymer case. The significance of this parameter in equation (3) is essentially the same as that proposed by Zimm & Bragg (1959) for equation (1) and pertains to the statistical weight of the sequence which actually nucleates the helix at the moment of nucleation when the neighbouring residues have not yet adopted the helical conformation. In the original Zimm-Bragg model the statistical weight of such a sequence is very low because the nucleating residues possess a low conformational entropy, since they must be in the right ~-helical conformation, but a high enthalpy, since they do not yet possess an intramolecular hydrogen bond. A value of less than 10 -2 was proposed. Because of the alternative hydrogen-bonding arrangements (representing low enthalpy, low entropy structures) which are likely to be available
H E L I X CONFORMATION PARAMETERS
359
during the folding of a globular protein, however, the enthalpy and entropy changes on nucleation and propagation of the helix are likely to be very much lower. Recalling that in the Zimm-Bragg treatment the value of a is expressed relative to the statistical weight of a non-helical residue, this situation implies a considerable increase in the value of a over that proposed by Zimm & Bragg (1959). Unfortunately, it is usually not possible to apply the same kind of quantitative experimental analysis to helix-coil transitions in globular proteins as one applies to homopolymer and simple heteropolymer systems. The principal reason is t h a t the major structure transition in a globular protein is the breakdown of the compact, globular structure normally maintained by hydrophobic interactions between nonpolar side chains. This masks the helix-coil transition except in certain situations where proteins with a relatively unstable globular structure, compared with other well-studied proteins, are partially denatured (Robson & Pain, 1976a,b). I t is therefore necessary to obtain helix-coil transition parameters for proteins, including values of a and m, by indirect means, such as statistical analysis of proteins of known sequence and conformation. B y carrying out such an analysis, Chou & Fasman (1974a) derived a parameter Pa which represented the helix-forming ability of a specified type of amino acid residue. This could be directly compared with the Zimm-Bragg parameter s, which also measures this ability in helix-coil transitions. However, their arguments relating Pa and s are qualitative and not based on a quantitative helix-coil transition model applied to globular proteins. Chou & Fasman (1974a) state: "the good agreement between the experimental s values from poly-~-amino acids and the calculated -Pa values from proteins, while somewhat surprising, is not totally fortuitous. Therefore, P~ could be a parameter which measures the propensity of a residue to be in the helical conformation, as does s." In a further discussion, Chou & Fasman (1974a) noted that the fraction of helical residues observed in most globular proteins is roughly that predicted by helix-coil transition theory for artificial polypeptide chains of the length found in globular proteins. However, as noted by Chou & Fasman (1974b), the polypeptide chain of a globular protein is punctuated at intervals by clusters of strongly helix-breaking residues. The ~-helices cannot spread across such regions, and this is one of the bases of their predictive method. Hence the true lengths of the chain available to helixcoil transitions are very much shorter than the full chain because of the heterogeneity of the amino acid sequence of globular proteins. In developing a more quantitative model in this paper, we take into account the presence of strongly helix-breaking regions due to a cluster of helix-breaking residues. Because the regions in which the helix-coil transition can occur are relatively short, our conclusions concerning the value of a implied b y the native structure of globular proteins are somewhat different. 2. T h e o r y The Zimm-Bragg and related methods refer to a statistical-mechanical distribution of residue conformations, while the informational, Chou & Fasman (1974a,b) and other related methods refer to statistical sampling of data using the methods of the observational calculus. An exact relationship m a y be drawn between the two kinds of investigation if a reasonable assumption is made of identity between Boltzmann probabilities and observational probabilities and, in principle, one should be able to 24
360
E. SUZUKI AND B. ROBSON
formulate these relations so that the Zimm-Bragg parameters can be calculated indirectly b y statistical sampling of proteins of known sequence and conformation. However, the ease of a globular protein is much more complex than t h a t of the homopolypeptide and simple heteropolypeptide systems to which the Zimm-Bragg formulation applies. In practice, therefore, it is necessary to utilize approximate relations based on simplified models of the situation in globular proteins. Fortunately, useful conclusions can be draw~ concerning the application of a Zimm-Bragg-type approach to proteins b y qualitative inspection of the statistical results. In particular, the number of residues m required to nucleate an a-helix in globular proteins (see eqn (3)) is probably still in the vicinity of 2 proposed b y Zimm & Bragg (1959) for the homopolymer case. On the basis of statistical analysis and predictions based on statistical analysis, the values suggested as satisfactory for m -k 1, which implies both the range of co-operativity between residues and the minimum length of stable a-helix, are variously 3 (Pain & Robson 1970), 4 (Robson & Pain 1971), 5 (Kotelchuck & Seheraga 1968) and 6 (Chou & Fasman 1974b). In addition, the study b y Robson & Pain (1971) showed that it was possible to reconstitute the observed conformations of proteins from extracted information measures with greater than 80~/o accuracy, providing the value of m q- 1 ranged from 1 to 7, satisfactory values being 3, 4 and 5 with the optimal value 4. In order to gain a more quantitative insight into the helix-coil transition during the folding of a globular protein, we have examined a number of specific models leading to exact relations between Zimm-Bragg parameters and statistical parameters. Unfortunately, the values of Zimm-Bragg parameters calculated in this way are, to some extent, dependent on the choice of model. However, it is a common feature of these models that a is invariably of a greater magnitude than the maximum value of 10- 2 proposed by Zimm & Bragg (1959) for the homopolymer case (see above). For this reason a simple example of the type of model used is presented. A globular protein in the process of folding can be considered to consist of at least three kinds of residue categories. Note t h a t (Robson & Suzuki, 1976) these categories are not necessarily based on the side chain type of these residues alone : they relate to the situation after interactions between residues have been taken into account. H residues are residues in the helical conformation; F residues are potential helix formers not, however, in the helical conformation, and B residues are obligatory helix breakers. A helix-coil transition in a globular protein can thus be described in terms of an H ~ F transition in a run of residues bounded by B residues which are never helical. Hence, the model proposed here does not consider the helix-coil transition to occur unbounded along the full length of the polypeptide backbone of a globular protein, but to occur in relatively short lengths of chain which are segregated b y interspersed strong helix breakers. In the simplest case, category B m a y be considered as imposed by the type of side chain of each residue so that, for example, proline could be assigned this state. However, consideration suggests t h a t B residues should be assigned b y inspection of the side chain types of the near-neighbours in the primary sequence. Firstly, m A- 1 residues represent the shortest possible helix so t h a t a run of less than m -[- 1 residues bounded b y B residues must necessarily also be assigned to category B. Secondly, although evidence to date indicates that each amino acid residue has an important role in determining its own conformation, the possibility of a specific interaction between two or more side chains forcing otherwise helix-favouring residues into a
CONFOR~_ATION P A R A M E T E R S
HELIX
361
non-helical conformation cannot be excluded from every case. Finally, whether a residue belongs to category B might depend on the direction in which the helix is spreading, so t h a t proliue m a y be considered as H or F when the helix is spreading towards it from the C-terminal direction, but as B if it is spreading from the Nterminal direction. For simplicity, a number of assumptions and approximations are utilised. I t is assumed t h a t throughout the sample of runs of optionally helical residues, optionally helical residues of different helix-forming strengths are placed at random so t h a t where the helix is placed within a n y one run does not significantly affect the statistical weight of the helix. Thus the helix-coil transition is assumed to occur in a segment whose boundaries are B residues. Further, the usual approximation t h a t the statistical weights of residues are independent is invoked, and the value of a is assumed to be of approximately the same order of magnitude throughout. Finally, it is assumed t h a t the runs of optionally helical residues are sufficiently short (about 5 to 30 residues) so t h a t the appearance of more t h a n one helix at a time within each run is highly improbable. Although a considerable number of approximations has been made, they are no more drastic t h a n those normally used in the application of the helix-coil transition theory to homopolymers and simple artificial heteropolymers, and should allow order-ofmagnitude conclusions to be drawn concerning helix-coil transitions in globular proteins. Considering an ~-helix n residues long in the sequence of L optionally helical residues, the free energy of the helix can be obtained from equation (3). I f we assume t h a t all L residues have similar s values, since t h e y are helix-forming residues, then we m a y replace sj . . . . sj + L-1 b y their geometric mean =
(sj.sj + ~ . . . . . . .
~)~1~
(4)
R Tln n.
(5)
ss + ,.-
then equation (3) becomes A G
---- -- R Tln(a/ m)
--
I f we assume t h a t the value of L is not m u c h larger t h a n t h a t of n, and hence only one helix at a time is likely to occur within L residues, then the n u m b e r of degrees of freedom of this helix is L - - n and the number of ways t h a t the helix m a y be placed is W~=L--n+I,
form,,,
=
~="+~
(9)
L=m+l Since (8) m is the probability of encountering a helical residue in a dynamic population in solution, we can write for homopolypeptide sequences with distribution D L *
P'(H[R) (O) m P'(HIR)_.~I--(O), ~'
(HIR) ' pro, = In 1 - -
(10)
H E L I X CONFORMATION P A R A M E T E R S
363
where P' (HIR) is the probability of residue type R being helical. The prime in equation (101 indicates t h a t the obligatory non-helical residues (B) have not been counted. The suffix pred indicates t h a t this is the predicted value of *(H IR) obtained via equation (9) when the values of s, a, m and Dr. for different values of 15 have been specified. The corresponding observed value of *(HIR )' may be obtained from the globular protein data. Assuming t h a t the observed frequencies are sufficiently large,
*(HIR)'ob ~ = In f(H'R)
(11)
f(F,R)' where f(H,R) is the number of residues type R observed in the helical conformation and f(tV,R) the number of residues of type R which are optionally helical. The relation of *(HI R)'ob~ to the information measure I(S=H:lrI;R) (see Robson & Suzuki (1976)) is
*(HIR)'obs : I(S-~H:Iri;R) d- *(H) -- d, where
*(H) = In
(12)
f(H) _ lnf(H) f(F) d- f(B) f(F1)'
A -~ In
f(F,R) f(F,R) q- f(B,R)'
(13)
and where f(B,R) is the number of residues type R which are obligatory helix breakers. At first sight the term d would seem to take the value of zero, since an amino acid residue would appear unlikely to act as an optionally helical residue (/v) in one situation and as a strong helix breaker (B) in another. However, as already discussed, a residue can be optionally helical in one region and a strong helix-breaker in another. Although the term /1 in equation (13) cannot be greater than zero, a particular zero or negative value should be chosen after inspection of the data. 3. R e s u l t s The statistical weight s has been obtained for a number of residues from the solution studies of simple synthetic polypeptides. Although the situation in globular protein solutions is different to that in synthetic polypeptide solutions, it is instructive to calculate the statistical weights s and a for the residues in globular proteins, and compare the values with those observed for synthetic polypeptides. Equations (8) to (10) show t h a t *(HIR)',red is a function of m, s, a, L and D L. After obtaining the values of L and their distribution function DL from the globular protein data, we estimated the order of magnitude for a by comparing *(HIR)'pred and *(HIR)'ob s Then the values of s were obtained using the estimated a value. The values of *(HIR)'ob ~ were calculated via equation (12) using the information measures I(S=H:lri;R) evaluated by Robson & Suzuki (1976). The length of optionally helical residues (L) and their density distribution function Dr. can be obtained from the globular protein dat, a providing t h a t the helix-breaking residues (B) are recognized, but as discussed in Theory this is not a property which can be assigned to different amino acid residues without consideration of their
364
E. SUZUKI
AND
B. ROBSON
neighbour residues. The assumption can be made, however, t h a t the specific interactions between side chains play a relatively small role compared with the information a residue carries about its own conformation (see, for example, Robson & Pain, 1971; Chou & Fasman, 1974a,b), a n d t h a t only non-specific co-operativity effects need be considered. Hence it can be assumed t h a t two or more residues with strongly negative helix information measure totalling to a sum below a specified negative value will act as obligatory helix-breakers. I n practice we have identified this specified negative value with the decision constant (Robson, 1974). Predictions of helical regions based on a decision constant which is less t h a n an optional value for accurate prediction will predict new spurious additional regions and regions which are longer t h a n those observed to be helical. Such regions correspond to optionally helical regions in the sense used here. Preliminary inspection shows t h a t the optimal decision constant is between ~ 0 . 5 and --0.7 nats~. With the decision constant larger t h a n --0-4 nats the value of L becomes less t h a n the average length of helices in globular proteins, and below --0.8 the length suddenly becomes very long. For decision constants between --0.5 and --0.7, however, the value of L and its distribution function Dr. are not particularly sensitive to the value of the decision constant. A reasonable choice of DL was considered to be the one calculated on the basis of a decision constant in this range of --0.5 to --0-7. For each value of DL corresponding to a specified value of L, there are also possible choices of m from 1 to 5, on which *(H]R)'pred is also dependent. Since the correct value of m is not known a priori, *(H[R)'pred was plotted against s as a whole family of curves each corresponding to different values of a, and m. Thus despite a number of uncertainties it is possible to plot an envelope of *(H[R)'pr~d versus s curves which correspond to the range of reasonable values of parameters. The results are shown in Figure 2. The ranges of *(HIR)',r~d for different a values are shown as shaded areas. The observed values of *(HI R)' calculated from equation (12) (assuming A = 0) for residues for X which the experimental s values are known are shown as the bases of A values in Figure 2. Since A is always zero or negative, the latter points in Figure 2 indicate the smallest possible values. The insensitivity of *(HI R)'p~a to reasonable choices of z~ is shown by the apices of the triangles, where *(H]R)'p~d is calculated on the basis t h a t F ( F , R ) = f ( B , R ) , i.e. on the basis t h a t half of the residues R in the non-helical state are obligatory non-helical residues. The inspection of Figure 2 clearly indicates t h a t the optimum value of a for globular proteins m u s t be larger t h a n 10 .3 to 10 -4 which is regarded as the optimum range for the helix-coil transition in synthetic polypeptides (ef. Z i m m & Bragg, 1959). The optimum a value for a globular protein is probably in the order of 10-1. A a value of 1 • 10-1 can thus be considered as leading to predictions of the experimental s values, and vice versa. Fortunately, the properties of this helix-coil transition model at a = 10-1 are such t h a t a fairly narrow band, representing the continuum of possible curves for t h a t value of a, is formed. The deviation of experimental points from this band can thus be considered significant, and suggests e i t h e r t h a t a is not constant from residue to residue, or t h a t the relative s values of the residues in globular proteins are not identical to those in simple artificial polypeptides. JfInformation calculated using the natural Iogarithm is said to be in "natural units" cr "nats".
HELIX
CONFORMATION
PARAMETERS
365
-1
-2
-4
-5
-6
0.5
1.0
I-5
2- 0
$
FIG. 2. Predicted values o f the i n f o r m a t i o n measure * ( H ] R ) ' ~ I n ( p r o b a b i l i t y o f residue t y p e i t b e i n g h e l i c a l / p r o b a b i l i t y o f r e s i d u e t y p e R b e i n g non-helical). C o m p u t e d u s i n g different s t a t i s t i c a l w e i g h t s (s). R a n g e o f p r e d i c t e d v a l u e s lie inside a series o f e n v e l o p e s (see text). W o r k i n g d o w n w a r d s , e n v e l o p e s for (1) a = 1, (2) a = 10 -1, (3) a = 10 -2, (4) a = 10 -*. T h e c u r v e s c o n s t i t u t i n g e a c h e n v e l o p e a r e for different v a l u e s o f ~n (see t e x t ) . T h e t r i a n g l e s are t h e o b s e r v e d v a l u e s calcul a t e d b y s t a t i s t i c a l a n a l y s i s , for e a c h t y p e o f a m i n o acid r e s i d u e for w h i c h e x p e r i m e n t a l s v a l u e s are available. T h e a p e x o f e a c h t r i a n g l e is a c o r r e c t e d v a l u e a s s u m i n g h a l f o f all n o n - h e l i c a l r e s i d u e s are s t r o n g (obligatory) h e l i x b r e a k e r s . N o t e t h a t t h e e n v e l o p e for a = 1 0 - 1 is i n s e n s i t i v e t o m a n d t h a t t h e o b s e r v e d v a l u e s o f *(H/R)', u s i n g e i t h e r a s m l m p t i o n a b o u t t h e p o p u l a t i o n o f s t r o n g helix b r e a k e r s , lie a r o u n d t h i s c u r v e .
*(H) (eqn (13)) has the value --0-5 in the sample of 25 proteins. Assuming t h a t A = 0 and a = 1 • 10 -1, the predicted values of s are obtained from equation (12) and Figure 2 and are listed in column five of Table 1. Pa values calculated from the information measures via equation (3) of Robson & Suzuki (1976), the Pa values of Chou & Fasman (1974a,b), and the experimental s values, are also listed in Table 1.
4. D i s c u s s i o n
The above extension of the helix-coil model of Zimm & Bragg (1959) shows (1) that the statistical weights (s) obtained from solution studies of simple synthetic polypeptides account for the values obtained by statistical analysis in general and information theory analysis in particular, and (2) that the co-operativity parameter a is of the order 10-1 for globular proteins, i.e. considerably larger than that for most synthetic polypeptide systems.
366
E. SUZUKI
AND
B. ROBSON
TABLe. 1
Calculated and observed s values
Residue
Glu Ala Met Leu Lys Phe Val Trp His Gln Ile Asp
Arg Cys Thr Ser Tyr Ash Pro Gly
Pa of Chou & Fasman (1974a,b) (15 proteins)
Pa calculated
s observed s calculated (experimental) (helix-coil (25 proteins) (see Chou & Fasman 1974a) transition model)
1-53 1"45 1"20 1.34 1.07 1.12 1.14 1.14 1-24 1-17 1-00 0"98 0"79 0"92 0.82 0.79 0.61 0.73 0-59 0.53
1.51 1.42 1"34 1.21 1.15 1.10 1.09 1.08 1.08 1.06 1.04 1-03 0-94 0.77 0.84 0'77 0.74 0.71 0.58 0.54
1.26 1.11
1.26 1.21
1.40 1-15 1-08
1.08 1.03 1.01
1-36
1.00
0-78
0"79
0-57
0.63
Scheraga (1971), amongst others, has proposed t h a t a-helical regions form early during the folding of a globular protein and serve as nucleation sites around which the rest of the protein can rapidly fold. He also noted t h a t the time-averaged probability of finding helices of the length observed in globular proteins is very low because of the low value of a for helix-coil transitions in synthetic polypeptides. Further, it is frequently observed t h a t polypeptide sequences which are helical in the folded protein have a much lower helix content when excised and placed in an aqueous environment (see, for example, Crumpton & Small, 1967; Singhal & Atassi, 1970). S eheraga (1971) proposed t h a t a higher value of a applies during the folding of globular proteins, and t h a t the origin of this high value of a is an interaction involving residues far apart in the amino acid sequence. Such an interaction could arise between two helices, or between a helix and the non-helical p a r t of the chain, and could account for a degree of stability of the nucleating a-helices consistent with rapid folding. To account for the stability of nucleating a-helices, Robson & Pain (1971) proposed t h a t the initial stage in the folding of a globular protein is the formation of a monomolecular micelle from some of the hydrophobic side chains of a single protein molecule. Such an intermediate would have the following properties: (1) it would be compact, (2) it would be poorly solvated internally, (3) it would he structurally disordered and labile so t h a t the interior resembled a partially non-polar liquid. Such an environment would encourage the formation of stable a-helices which could orient themselves to one another and to the micelle-water interface b y virtue of specific clusters of hydrophobic and hydrophilic residues observed on the surface of protein a-helices. This extreme picture of a "micelle" or "oil-drop" model is not
HELIX
CONFORMATION
PARAMETER
367
confirmed b y recent studies on the folding of a penicillinase (Robson & Pain, 1976b). I n this system, a-helical regions are stabilized in a folding intermediate with a rather more expanded structure and a somewhat solvated interior. I f this structure is used as the basis of a " p a r t l y hydrated chain" model for the initial formation of a-helices, then this initial formation is a process which resembles even more closely the helixcoil transition of simple artificial polypeptides. Nevertheless, some of the features of the micelle model m a y still apply, although if the stabilization of nucleating a-helices is assumed to have a hydrophobie origin, the partly solvated chain model implies t h a t a relatively small number of non-polar side chains interact in a specific lock-and-key manner, so forming definite small structures, or b y a larger n u m b e r of a variety of transient non-polar associations. I n the penieillinase case (Robson & Pain, 1976a,b), the partly solvated chain intermediate with a-helices has a free energy of - - 4 kcal with respect to the finally denatured random coil in the absence of denaturant. Since hydrophobic side chains have a dehydration energy of the order of 1 kcal (measured b y transfer from water to ethanol; Nozaki & Tanford, 1970) hydrophobic stabilization is consistent with the limited degree of exposure to solvent implied by the kinetics of penieillinase folding (Robson & Pain, 1976a,b). I t is emphasized t h a t the value of a --~ 10-1 obtained in this work is deduced from native structures, and not from the nucleating intermediate state containing ahelices. However, the amount of helix observed in such an intermediate by Robson & Pain (1976a,b) is about the same as t h a t in the native state, and these authors argue t h a t the helical regions are roughly the same as those in the native state. This argument is further supported by the predictions of s from information measures derived from native structures, so t h a t helix-forming and helix-breaking regions are likely to be conserved throughout folding. I t is therefore reasonable t h a t a value of a _~ 10-1 holds throughout most of the folding process.
REFERENCES Chou, P. Y. & Fasman, G. D. (1974a}. Biochemistry, 13, 211-222. Chou, P. Y. & Fasman, G. D. (1974b). Biochemistry, 13, 223-245. Crumpton, M. J. & Small, P. A. (1967). J. Mol. Biol. 26, 143-146. Kotelchuk, D. & Seheraga, H. A. (1968). Proc. Nat. Acad. Sci., U.S.A. 62, 14-24. Lifson, S. & Roig, A. (1961). J. Chem. Phys. 34, Nozaki, Y. & Tanford, C. (1970). J. Biol. Chem. 245, 1648. Pain, R. H. & Robson, B. (1970). Nature (London), 227, 62-63. Poland D. & Scheraga, H. A. (1970). Theory of Helix-Coil Transitions in Biopolymers,
Aead~,mie Press, New York and London. Robson B. (1974). Bioehem. J. 141,853-868. Robson B. & Pain, R. H. (1971). J. Mol. Biol. 58, 237-259. Robson B. & Pain, R. H. (1974). Bioehem J. 141,883-897. Robson B. & Pain, R. H. (1976a). Biochem. J. 155, 325-330. Robson B. & Pain, R. H. (1976b). Bioehem. J. 155, 331-344. Robson B. & Suzuki, E. (1976). J. Mol. Biol. 107, 327-356. Seheraga, H. A. (1971). Chem. Rev. 71, 195-217. Singbal, R. P. & Atassi, M. Z. (1970). Biochemistry, 8, 4252-4259. Watson, H. C. (1969). Prog. Stereochem. 4, 299-320. Zimm, B. H. & Bragg, J. K. (1959). J. Chem. Phys. 31, 526-535.
Relationship between Helix-Coil Transition Parameters for Synthetic Polypeptides and Helix Conformation Parameters for Globular Proteins. A Simple Model E. SUZUKI
Division of Protein Chemistry C.S.I.R.O., Parkville, Melbourne, Victoria 3052, Australia AND B. ROBSON
Department of Biochemistry, University of Manchester, Oxford Road, Manchester M13 9PL, England (Received 25 March 1976, and in revised form 21 May 1976) (1) The Zimm-Bragg formulation for hehx-coil transitions in simple synthetic polypeptides is generalized to handle the formation of ~-helical regions during the folding of globular proteins. (2) The relation between the helix-coil transition parameters for this process and other conformational parameters (derived by statistical analysis of the sequences and conformations of globular proteins) is determined. (3) I t is shown that the generalized Zimm-Bragg model can be used graphically to predict the helix-coil transition parameters from the statistical parameters, and vice versa. (4) I t is also shown that the Zimm-Bragg co-operativity parameter a implied by the lengths of helices observed in globular proteins is of the order of 10-1, and therefore much larger than the values obtained from simple synthetic polypeptides. (5) I t is postulated that a similarly large value of a persists throughout the folding process from the moment the helical regions are "trapped" by interactions between residues far apart in the amino acid sequence, and the nature of these interactions is discussed. 1. Introduction I n a t t e m p t i n g to explain the observed conformational parameters derived b y statistical analysis of proteins of known sequence and conformations (see, for example, Robson & Suzuki, 1976), one of the more interesting correlations t h a t can be investigated is between the conformational parameters of a residue in globular proteins and the observed behaviour of the residue in simple artificial polypeptides in solution. Unfortunately, only the formation of ~-helix has been widely investigated experimentally in the artificial polypeptide case, but a n u m b e r of theories, notably those of Lifson & Roig (1961) and Zimm & Bragg (1959), have been applied to the problem of obtaining ~-helical parameters from such systems. 357
358
E. SUZUKI
AND B . R O B S O N
In the Zimm-Bragg treatment a statistical weight of s is att'~ched to each residue in the helix and of unity to the residues not in the helix. A factor a which accounts for the difficulty in initiating the helix is also assigned and the partition function constructed. The free energy of an ~-helix n residues long may be shown to be (Poland & Scheraga, 1970) AG
=
-- RTlmr
--
(n --
2)
RT
In s,
(1)
where the first term corresponds to the helix nucleation energy and the second term is the free energy of the formation of (u -- 2) hydrogen bonds. Equation (1) may be rewritten as ~G
=
--RTln
( a / s 2) - -
n.RT.ln
s.
(2)
Although Poland & Scheraga (1970) considered that (n -- 2) residues stabilize an ~r of n residues, this number is sensitive to a more detailed energetic analysis. Certainly, during the folding of a globular protein, when ~r regions are being formed and stabilized, different considerations apply. On inspection of molecular models of the native structures of globular proteins, it can be seen that many of the hydrogen bonds which can be formed are formed (see for example, Watson, 1969) and both non-helical residues and those at the ends of helices can participate in hydrogen bonds with the rest of the protein. While the determining factor in the Zimm-Bragg theory is the formation of hydrogen bonds in the ~-helical manner, other factors which contribute to the conformational energy of a residue will play a much more important role in proteins than in the homopolymer situation. A consequence of this is that the number of residues required to initiate helix formation in globular proteins may well differ from the minimum number of residues required to initiate a helix in synthetic polypeptides, and the simplest possible analogue of equation (2) which can be applied to a helix in globular proteins is the more general expression AG
~
-- R Tln
((~/si " s i + 1. 9 9 s i + , , - 1) - - R T l n ( s
. s j + 1. 9 9 s j + ~ _ 1),
(3)
where s , ' s ~ + l . . , s~+ , , - 1 is the product of the m statistical weights of residues from residue i to residue i + m - - 1 which must adopt the helical conformation before a stable helix can begin to form, and s j . s j + 1. 9 9 s j + n - 1 is the product for the n residues in the a-helix. Note that m ~- 1 is the length of the shortest possible helix. The same consideration which suggests that m + 1 may well differ from the value implied by the Zimm-Bragg theory also suggests that typical values for a in proteins are also quite different from those proposed by Zimm & Bragg (1959) for the homopolymer case. The significance of this parameter in equation (3) is essentially the same as that proposed by Zimm & Bragg (1959) for equation (1) and pertains to the statistical weight of the sequence which actually nucleates the helix at the moment of nucleation when the neighbouring residues have not yet adopted the helical conformation. In the original Zimm-Bragg model the statistical weight of such a sequence is very low because the nucleating residues possess a low conformational entropy, since they must be in the right ~-helical conformation, but a high enthalpy, since they do not yet possess an intramolecular hydrogen bond. A value of less than 10 -2 was proposed. Because of the alternative hydrogen-bonding arrangements (representing low enthalpy, low entropy structures) which are likely to be available
H E L I X CONFORMATION PARAMETERS
359
during the folding of a globular protein, however, the enthalpy and entropy changes on nucleation and propagation of the helix are likely to be very much lower. Recalling that in the Zimm-Bragg treatment the value of a is expressed relative to the statistical weight of a non-helical residue, this situation implies a considerable increase in the value of a over that proposed by Zimm & Bragg (1959). Unfortunately, it is usually not possible to apply the same kind of quantitative experimental analysis to helix-coil transitions in globular proteins as one applies to homopolymer and simple heteropolymer systems. The principal reason is t h a t the major structure transition in a globular protein is the breakdown of the compact, globular structure normally maintained by hydrophobic interactions between nonpolar side chains. This masks the helix-coil transition except in certain situations where proteins with a relatively unstable globular structure, compared with other well-studied proteins, are partially denatured (Robson & Pain, 1976a,b). I t is therefore necessary to obtain helix-coil transition parameters for proteins, including values of a and m, by indirect means, such as statistical analysis of proteins of known sequence and conformation. B y carrying out such an analysis, Chou & Fasman (1974a) derived a parameter Pa which represented the helix-forming ability of a specified type of amino acid residue. This could be directly compared with the Zimm-Bragg parameter s, which also measures this ability in helix-coil transitions. However, their arguments relating Pa and s are qualitative and not based on a quantitative helix-coil transition model applied to globular proteins. Chou & Fasman (1974a) state: "the good agreement between the experimental s values from poly-~-amino acids and the calculated -Pa values from proteins, while somewhat surprising, is not totally fortuitous. Therefore, P~ could be a parameter which measures the propensity of a residue to be in the helical conformation, as does s." In a further discussion, Chou & Fasman (1974a) noted that the fraction of helical residues observed in most globular proteins is roughly that predicted by helix-coil transition theory for artificial polypeptide chains of the length found in globular proteins. However, as noted by Chou & Fasman (1974b), the polypeptide chain of a globular protein is punctuated at intervals by clusters of strongly helix-breaking residues. The ~-helices cannot spread across such regions, and this is one of the bases of their predictive method. Hence the true lengths of the chain available to helixcoil transitions are very much shorter than the full chain because of the heterogeneity of the amino acid sequence of globular proteins. In developing a more quantitative model in this paper, we take into account the presence of strongly helix-breaking regions due to a cluster of helix-breaking residues. Because the regions in which the helix-coil transition can occur are relatively short, our conclusions concerning the value of a implied b y the native structure of globular proteins are somewhat different. 2. T h e o r y The Zimm-Bragg and related methods refer to a statistical-mechanical distribution of residue conformations, while the informational, Chou & Fasman (1974a,b) and other related methods refer to statistical sampling of data using the methods of the observational calculus. An exact relationship m a y be drawn between the two kinds of investigation if a reasonable assumption is made of identity between Boltzmann probabilities and observational probabilities and, in principle, one should be able to 24
360
E. SUZUKI AND B. ROBSON
formulate these relations so that the Zimm-Bragg parameters can be calculated indirectly b y statistical sampling of proteins of known sequence and conformation. However, the ease of a globular protein is much more complex than t h a t of the homopolypeptide and simple heteropolypeptide systems to which the Zimm-Bragg formulation applies. In practice, therefore, it is necessary to utilize approximate relations based on simplified models of the situation in globular proteins. Fortunately, useful conclusions can be draw~ concerning the application of a Zimm-Bragg-type approach to proteins b y qualitative inspection of the statistical results. In particular, the number of residues m required to nucleate an a-helix in globular proteins (see eqn (3)) is probably still in the vicinity of 2 proposed b y Zimm & Bragg (1959) for the homopolymer case. On the basis of statistical analysis and predictions based on statistical analysis, the values suggested as satisfactory for m -k 1, which implies both the range of co-operativity between residues and the minimum length of stable a-helix, are variously 3 (Pain & Robson 1970), 4 (Robson & Pain 1971), 5 (Kotelchuck & Seheraga 1968) and 6 (Chou & Fasman 1974b). In addition, the study b y Robson & Pain (1971) showed that it was possible to reconstitute the observed conformations of proteins from extracted information measures with greater than 80~/o accuracy, providing the value of m q- 1 ranged from 1 to 7, satisfactory values being 3, 4 and 5 with the optimal value 4. In order to gain a more quantitative insight into the helix-coil transition during the folding of a globular protein, we have examined a number of specific models leading to exact relations between Zimm-Bragg parameters and statistical parameters. Unfortunately, the values of Zimm-Bragg parameters calculated in this way are, to some extent, dependent on the choice of model. However, it is a common feature of these models that a is invariably of a greater magnitude than the maximum value of 10- 2 proposed by Zimm & Bragg (1959) for the homopolymer case (see above). For this reason a simple example of the type of model used is presented. A globular protein in the process of folding can be considered to consist of at least three kinds of residue categories. Note t h a t (Robson & Suzuki, 1976) these categories are not necessarily based on the side chain type of these residues alone : they relate to the situation after interactions between residues have been taken into account. H residues are residues in the helical conformation; F residues are potential helix formers not, however, in the helical conformation, and B residues are obligatory helix breakers. A helix-coil transition in a globular protein can thus be described in terms of an H ~ F transition in a run of residues bounded by B residues which are never helical. Hence, the model proposed here does not consider the helix-coil transition to occur unbounded along the full length of the polypeptide backbone of a globular protein, but to occur in relatively short lengths of chain which are segregated b y interspersed strong helix breakers. In the simplest case, category B m a y be considered as imposed by the type of side chain of each residue so that, for example, proline could be assigned this state. However, consideration suggests t h a t B residues should be assigned b y inspection of the side chain types of the near-neighbours in the primary sequence. Firstly, m A- 1 residues represent the shortest possible helix so t h a t a run of less than m -[- 1 residues bounded b y B residues must necessarily also be assigned to category B. Secondly, although evidence to date indicates that each amino acid residue has an important role in determining its own conformation, the possibility of a specific interaction between two or more side chains forcing otherwise helix-favouring residues into a
CONFOR~_ATION P A R A M E T E R S
HELIX
361
non-helical conformation cannot be excluded from every case. Finally, whether a residue belongs to category B might depend on the direction in which the helix is spreading, so t h a t proliue m a y be considered as H or F when the helix is spreading towards it from the C-terminal direction, but as B if it is spreading from the Nterminal direction. For simplicity, a number of assumptions and approximations are utilised. I t is assumed t h a t throughout the sample of runs of optionally helical residues, optionally helical residues of different helix-forming strengths are placed at random so t h a t where the helix is placed within a n y one run does not significantly affect the statistical weight of the helix. Thus the helix-coil transition is assumed to occur in a segment whose boundaries are B residues. Further, the usual approximation t h a t the statistical weights of residues are independent is invoked, and the value of a is assumed to be of approximately the same order of magnitude throughout. Finally, it is assumed t h a t the runs of optionally helical residues are sufficiently short (about 5 to 30 residues) so t h a t the appearance of more t h a n one helix at a time within each run is highly improbable. Although a considerable number of approximations has been made, they are no more drastic t h a n those normally used in the application of the helix-coil transition theory to homopolymers and simple artificial heteropolymers, and should allow order-ofmagnitude conclusions to be drawn concerning helix-coil transitions in globular proteins. Considering an ~-helix n residues long in the sequence of L optionally helical residues, the free energy of the helix can be obtained from equation (3). I f we assume t h a t all L residues have similar s values, since t h e y are helix-forming residues, then we m a y replace sj . . . . sj + L-1 b y their geometric mean =
(sj.sj + ~ . . . . . . .
~)~1~
(4)
R Tln n.
(5)
ss + ,.-
then equation (3) becomes A G
---- -- R Tln(a/ m)
--
I f we assume t h a t the value of L is not m u c h larger t h a n t h a t of n, and hence only one helix at a time is likely to occur within L residues, then the n u m b e r of degrees of freedom of this helix is L - - n and the number of ways t h a t the helix m a y be placed is W~=L--n+I,
form,,,
=
~="+~
(9)
L=m+l Since (8) m is the probability of encountering a helical residue in a dynamic population in solution, we can write for homopolypeptide sequences with distribution D L *
P'(H[R) (O) m P'(HIR)_.~I--(O), ~'
(HIR) ' pro, = In 1 - -
(10)
H E L I X CONFORMATION P A R A M E T E R S
363
where P' (HIR) is the probability of residue type R being helical. The prime in equation (101 indicates t h a t the obligatory non-helical residues (B) have not been counted. The suffix pred indicates t h a t this is the predicted value of *(H IR) obtained via equation (9) when the values of s, a, m and Dr. for different values of 15 have been specified. The corresponding observed value of *(HIR )' may be obtained from the globular protein data. Assuming t h a t the observed frequencies are sufficiently large,
*(HIR)'ob ~ = In f(H'R)
(11)
f(F,R)' where f(H,R) is the number of residues type R observed in the helical conformation and f(tV,R) the number of residues of type R which are optionally helical. The relation of *(HI R)'ob~ to the information measure I(S=H:lrI;R) (see Robson & Suzuki (1976)) is
*(HIR)'obs : I(S-~H:Iri;R) d- *(H) -- d, where
*(H) = In
(12)
f(H) _ lnf(H) f(F) d- f(B) f(F1)'
A -~ In
f(F,R) f(F,R) q- f(B,R)'
(13)
and where f(B,R) is the number of residues type R which are obligatory helix breakers. At first sight the term d would seem to take the value of zero, since an amino acid residue would appear unlikely to act as an optionally helical residue (/v) in one situation and as a strong helix breaker (B) in another. However, as already discussed, a residue can be optionally helical in one region and a strong helix-breaker in another. Although the term /1 in equation (13) cannot be greater than zero, a particular zero or negative value should be chosen after inspection of the data. 3. R e s u l t s The statistical weight s has been obtained for a number of residues from the solution studies of simple synthetic polypeptides. Although the situation in globular protein solutions is different to that in synthetic polypeptide solutions, it is instructive to calculate the statistical weights s and a for the residues in globular proteins, and compare the values with those observed for synthetic polypeptides. Equations (8) to (10) show t h a t *(HIR)',red is a function of m, s, a, L and D L. After obtaining the values of L and their distribution function DL from the globular protein data, we estimated the order of magnitude for a by comparing *(HIR)'pred and *(HIR)'ob s Then the values of s were obtained using the estimated a value. The values of *(HIR)'ob ~ were calculated via equation (12) using the information measures I(S=H:lri;R) evaluated by Robson & Suzuki (1976). The length of optionally helical residues (L) and their density distribution function Dr. can be obtained from the globular protein dat, a providing t h a t the helix-breaking residues (B) are recognized, but as discussed in Theory this is not a property which can be assigned to different amino acid residues without consideration of their
364
E. SUZUKI
AND
B. ROBSON
neighbour residues. The assumption can be made, however, t h a t the specific interactions between side chains play a relatively small role compared with the information a residue carries about its own conformation (see, for example, Robson & Pain, 1971; Chou & Fasman, 1974a,b), a n d t h a t only non-specific co-operativity effects need be considered. Hence it can be assumed t h a t two or more residues with strongly negative helix information measure totalling to a sum below a specified negative value will act as obligatory helix-breakers. I n practice we have identified this specified negative value with the decision constant (Robson, 1974). Predictions of helical regions based on a decision constant which is less t h a n an optional value for accurate prediction will predict new spurious additional regions and regions which are longer t h a n those observed to be helical. Such regions correspond to optionally helical regions in the sense used here. Preliminary inspection shows t h a t the optimal decision constant is between ~ 0 . 5 and --0.7 nats~. With the decision constant larger t h a n --0-4 nats the value of L becomes less t h a n the average length of helices in globular proteins, and below --0.8 the length suddenly becomes very long. For decision constants between --0.5 and --0.7, however, the value of L and its distribution function Dr. are not particularly sensitive to the value of the decision constant. A reasonable choice of DL was considered to be the one calculated on the basis of a decision constant in this range of --0.5 to --0-7. For each value of DL corresponding to a specified value of L, there are also possible choices of m from 1 to 5, on which *(H]R)'pred is also dependent. Since the correct value of m is not known a priori, *(H[R)'pred was plotted against s as a whole family of curves each corresponding to different values of a, and m. Thus despite a number of uncertainties it is possible to plot an envelope of *(H[R)'pr~d versus s curves which correspond to the range of reasonable values of parameters. The results are shown in Figure 2. The ranges of *(HIR)',r~d for different a values are shown as shaded areas. The observed values of *(HI R)' calculated from equation (12) (assuming A = 0) for residues for X which the experimental s values are known are shown as the bases of A values in Figure 2. Since A is always zero or negative, the latter points in Figure 2 indicate the smallest possible values. The insensitivity of *(HI R)'p~a to reasonable choices of z~ is shown by the apices of the triangles, where *(H]R)'p~d is calculated on the basis t h a t F ( F , R ) = f ( B , R ) , i.e. on the basis t h a t half of the residues R in the non-helical state are obligatory non-helical residues. The inspection of Figure 2 clearly indicates t h a t the optimum value of a for globular proteins m u s t be larger t h a n 10 .3 to 10 -4 which is regarded as the optimum range for the helix-coil transition in synthetic polypeptides (ef. Z i m m & Bragg, 1959). The optimum a value for a globular protein is probably in the order of 10-1. A a value of 1 • 10-1 can thus be considered as leading to predictions of the experimental s values, and vice versa. Fortunately, the properties of this helix-coil transition model at a = 10-1 are such t h a t a fairly narrow band, representing the continuum of possible curves for t h a t value of a, is formed. The deviation of experimental points from this band can thus be considered significant, and suggests e i t h e r t h a t a is not constant from residue to residue, or t h a t the relative s values of the residues in globular proteins are not identical to those in simple artificial polypeptides. JfInformation calculated using the natural Iogarithm is said to be in "natural units" cr "nats".
HELIX
CONFORMATION
PARAMETERS
365
-1
-2
-4
-5
-6
0.5
1.0
I-5
2- 0
$
FIG. 2. Predicted values o f the i n f o r m a t i o n measure * ( H ] R ) ' ~ I n ( p r o b a b i l i t y o f residue t y p e i t b e i n g h e l i c a l / p r o b a b i l i t y o f r e s i d u e t y p e R b e i n g non-helical). C o m p u t e d u s i n g different s t a t i s t i c a l w e i g h t s (s). R a n g e o f p r e d i c t e d v a l u e s lie inside a series o f e n v e l o p e s (see text). W o r k i n g d o w n w a r d s , e n v e l o p e s for (1) a = 1, (2) a = 10 -1, (3) a = 10 -2, (4) a = 10 -*. T h e c u r v e s c o n s t i t u t i n g e a c h e n v e l o p e a r e for different v a l u e s o f ~n (see t e x t ) . T h e t r i a n g l e s are t h e o b s e r v e d v a l u e s calcul a t e d b y s t a t i s t i c a l a n a l y s i s , for e a c h t y p e o f a m i n o acid r e s i d u e for w h i c h e x p e r i m e n t a l s v a l u e s are available. T h e a p e x o f e a c h t r i a n g l e is a c o r r e c t e d v a l u e a s s u m i n g h a l f o f all n o n - h e l i c a l r e s i d u e s are s t r o n g (obligatory) h e l i x b r e a k e r s . N o t e t h a t t h e e n v e l o p e for a = 1 0 - 1 is i n s e n s i t i v e t o m a n d t h a t t h e o b s e r v e d v a l u e s o f *(H/R)', u s i n g e i t h e r a s m l m p t i o n a b o u t t h e p o p u l a t i o n o f s t r o n g helix b r e a k e r s , lie a r o u n d t h i s c u r v e .
*(H) (eqn (13)) has the value --0-5 in the sample of 25 proteins. Assuming t h a t A = 0 and a = 1 • 10 -1, the predicted values of s are obtained from equation (12) and Figure 2 and are listed in column five of Table 1. Pa values calculated from the information measures via equation (3) of Robson & Suzuki (1976), the Pa values of Chou & Fasman (1974a,b), and the experimental s values, are also listed in Table 1.
4. D i s c u s s i o n
The above extension of the helix-coil model of Zimm & Bragg (1959) shows (1) that the statistical weights (s) obtained from solution studies of simple synthetic polypeptides account for the values obtained by statistical analysis in general and information theory analysis in particular, and (2) that the co-operativity parameter a is of the order 10-1 for globular proteins, i.e. considerably larger than that for most synthetic polypeptide systems.
366
E. SUZUKI
AND
B. ROBSON
TABLe. 1
Calculated and observed s values
Residue
Glu Ala Met Leu Lys Phe Val Trp His Gln Ile Asp
Arg Cys Thr Ser Tyr Ash Pro Gly
Pa of Chou & Fasman (1974a,b) (15 proteins)
Pa calculated
s observed s calculated (experimental) (helix-coil (25 proteins) (see Chou & Fasman 1974a) transition model)
1-53 1"45 1"20 1.34 1.07 1.12 1.14 1.14 1-24 1-17 1-00 0"98 0"79 0"92 0.82 0.79 0.61 0.73 0-59 0.53
1.51 1.42 1"34 1.21 1.15 1.10 1.09 1.08 1.08 1.06 1.04 1-03 0-94 0.77 0.84 0'77 0.74 0.71 0.58 0.54
1.26 1.11
1.26 1.21
1.40 1-15 1-08
1.08 1.03 1.01
1-36
1.00
0-78
0"79
0-57
0.63
Scheraga (1971), amongst others, has proposed t h a t a-helical regions form early during the folding of a globular protein and serve as nucleation sites around which the rest of the protein can rapidly fold. He also noted t h a t the time-averaged probability of finding helices of the length observed in globular proteins is very low because of the low value of a for helix-coil transitions in synthetic polypeptides. Further, it is frequently observed t h a t polypeptide sequences which are helical in the folded protein have a much lower helix content when excised and placed in an aqueous environment (see, for example, Crumpton & Small, 1967; Singhal & Atassi, 1970). S eheraga (1971) proposed t h a t a higher value of a applies during the folding of globular proteins, and t h a t the origin of this high value of a is an interaction involving residues far apart in the amino acid sequence. Such an interaction could arise between two helices, or between a helix and the non-helical p a r t of the chain, and could account for a degree of stability of the nucleating a-helices consistent with rapid folding. To account for the stability of nucleating a-helices, Robson & Pain (1971) proposed t h a t the initial stage in the folding of a globular protein is the formation of a monomolecular micelle from some of the hydrophobic side chains of a single protein molecule. Such an intermediate would have the following properties: (1) it would be compact, (2) it would be poorly solvated internally, (3) it would he structurally disordered and labile so t h a t the interior resembled a partially non-polar liquid. Such an environment would encourage the formation of stable a-helices which could orient themselves to one another and to the micelle-water interface b y virtue of specific clusters of hydrophobic and hydrophilic residues observed on the surface of protein a-helices. This extreme picture of a "micelle" or "oil-drop" model is not
HELIX
CONFORMATION
PARAMETER
367
confirmed b y recent studies on the folding of a penicillinase (Robson & Pain, 1976b). I n this system, a-helical regions are stabilized in a folding intermediate with a rather more expanded structure and a somewhat solvated interior. I f this structure is used as the basis of a " p a r t l y hydrated chain" model for the initial formation of a-helices, then this initial formation is a process which resembles even more closely the helixcoil transition of simple artificial polypeptides. Nevertheless, some of the features of the micelle model m a y still apply, although if the stabilization of nucleating a-helices is assumed to have a hydrophobie origin, the partly solvated chain model implies t h a t a relatively small number of non-polar side chains interact in a specific lock-and-key manner, so forming definite small structures, or b y a larger n u m b e r of a variety of transient non-polar associations. I n the penieillinase case (Robson & Pain, 1976a,b), the partly solvated chain intermediate with a-helices has a free energy of - - 4 kcal with respect to the finally denatured random coil in the absence of denaturant. Since hydrophobic side chains have a dehydration energy of the order of 1 kcal (measured b y transfer from water to ethanol; Nozaki & Tanford, 1970) hydrophobic stabilization is consistent with the limited degree of exposure to solvent implied by the kinetics of penieillinase folding (Robson & Pain, 1976a,b). I t is emphasized t h a t the value of a --~ 10-1 obtained in this work is deduced from native structures, and not from the nucleating intermediate state containing ahelices. However, the amount of helix observed in such an intermediate by Robson & Pain (1976a,b) is about the same as t h a t in the native state, and these authors argue t h a t the helical regions are roughly the same as those in the native state. This argument is further supported by the predictions of s from information measures derived from native structures, so t h a t helix-forming and helix-breaking regions are likely to be conserved throughout folding. I t is therefore reasonable t h a t a value of a _~ 10-1 holds throughout most of the folding process.
REFERENCES Chou, P. Y. & Fasman, G. D. (1974a}. Biochemistry, 13, 211-222. Chou, P. Y. & Fasman, G. D. (1974b). Biochemistry, 13, 223-245. Crumpton, M. J. & Small, P. A. (1967). J. Mol. Biol. 26, 143-146. Kotelchuk, D. & Seheraga, H. A. (1968). Proc. Nat. Acad. Sci., U.S.A. 62, 14-24. Lifson, S. & Roig, A. (1961). J. Chem. Phys. 34, Nozaki, Y. & Tanford, C. (1970). J. Biol. Chem. 245, 1648. Pain, R. H. & Robson, B. (1970). Nature (London), 227, 62-63. Poland D. & Scheraga, H. A. (1970). Theory of Helix-Coil Transitions in Biopolymers,
Aead~,mie Press, New York and London. Robson B. (1974). Bioehem. J. 141,853-868. Robson B. & Pain, R. H. (1971). J. Mol. Biol. 58, 237-259. Robson B. & Pain, R. H. (1974). Bioehem J. 141,883-897. Robson B. & Pain, R. H. (1976a). Biochem. J. 155, 325-330. Robson B. & Pain, R. H. (1976b). Bioehem. J. 155, 331-344. Robson B. & Suzuki, E. (1976). J. Mol. Biol. 107, 327-356. Seheraga, H. A. (1971). Chem. Rev. 71, 195-217. Singbal, R. P. & Atassi, M. Z. (1970). Biochemistry, 8, 4252-4259. Watson, H. C. (1969). Prog. Stereochem. 4, 299-320. Zimm, B. H. & Bragg, J. K. (1959). J. Chem. Phys. 31, 526-535.
