Possible mechanism for the dynamic stabilization of protein structure

J. theor. Biol. (1981) 90,487-493

Possible Mechanism for the Dynamic Stabilization of Protein Structure I.

SIMON

Institute of Enzymology, Biological Research Center, Hungarian Academy of Sciences,H- 1502, P.O. Box 7, Budapest, Hungary (Received 8 December 1979, and in revisedform 5 November 1980) There is an apparent contradiction between the long lifetime of the metastablestructure of native proteins and the high rate of structural fluctuations, which result from the small activation energy required to changethe native conformation. In this paper we point out that the observed stability of proteins is not a consequence

of large potential

barriers,

but a result of the continuous

reconstitutionof the degradedstructureby chain propagation.Polypeptide chainsof proteins having naturally selectedamino-acid sequenceshave regenerativeability which ensuresthe long lifetime of the native structure by makingmost of the fluctuationsreversible. A simple calculation shows that in a certain fluctuation of an average protein moleculethe probability of denaturation is lessthan lo-*‘, therefore even the most rapid, picosecond

time scale fluctuations

cause spon-

taneousdenaturation only in million year time scale.Hence, the generally observed spontaneousdenaturation in vitro is rather a consequenceof covalent structure modification or intermolecular interactions than a result of an intramolecular interconversion from the native conformation to

another conformation. Introduction It is known that a protein cannot find its native conformation by random search processeswithin a reasonable time, so that folding must be directed by a definite pathway. It is very probable that the energy minimum to which a definite pathway leads is a local one (Levinthal, 1968). Long lifetime of metastable states are quite a general feature of substanceswhere a change in there state requires a high activation energy compared to the thermal energy (kT). This simple explanation does not apply to the conservation of the native state of globular proteins, since the energy of the interactions stabilizing their conformation is so small compared with the thermal energy that the structure is in a state of continuous fluctuation (Linderstram-Lang & Schellman, 1959). Appreciable motions in certain parts of proteins have been shown by various techniques. These include H-D exchange (Hvidt & Neilsen, 1966; 487

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1. SIMON

Zavodszky, Abaturov & Varsavsky, 1966), fluorescence quenching (Lakowicz & Weber, 1973), kinetic analysis of chemical modification (Telegdi Br Straub, 1973; Vas & Boross, 1974), NMR experiments (Campbell, Dobson & Williams, 1975; Wagner & Wiithrich, 1978) and theoretical considerations (Ueda & Go, 1976; Cooper, 1976; McCammon, Gelin & Karplus, 1977; Northrup & McCammon, 1980). A metastable structure may exist for a long time not just because of large potential barriers but as a result of the continuous reconstitution of the degraded structure. In this paper we point out that polypeptide chains having naturally selected amino-acid sequences involved in fluctuations have an ability to regenerate the native conformation by chain propagation. The concept of chain propagation was suggested by Zimm & Bragg (1959) for the process of the coil-helix transition of homopolymers since the successive setting of amino-acids requires smaller activation energy than the stabilization of the same part of the chain simultaneously. It is obvious that this chain propagation is a unique pathway because of the translational symmetry of any homopolymers. The ordered structural elements of the proteins are stabilized mainly by repeated backbone H-bonds. Therefore it can be expected that these structural elements, similarly to the homopolymers, will grow by chain propagation as proposed by many authors (Levinthal, 1968; Wetlaufer, 1973; Scheraga, 1973; Ptitsyn & Rashin, 1975; Chothia, 1976; Karplus & Weaver, 1976; Lim‘& Efimov. 1976). On the other hand, most part of the chain are composed of amino-acids that are stabilized not only by backbone-backbone interactions but also by interactions of the different side-chains. Since these parts have no translational symmetry either in the amino-acid sequence or in the structure, folding of a polypeptide chain, having random amino-acid sequence, by chain propagation into a definite structure is not expected. The conformation of amino-acids, as defined by the dihedral angles (cp, $, x), in native proteins corresponds to those of the energy minima determined for the individual amino-acids in dipeptides (Pullman & Pullman, 1974; Anfinsen & Scheraga, 1975). We shall refer to the structure of any polypeptide chain segment as the native conformation if all the amino-acids are in the potential well that corresponds to the equilibrium conformation or the native protein. Short segments (4 to 10 amino-acids) of the polypeptide chains of native proteins are in the conformations corresponding to the global energy minima or to local minima the energy of which is not more than S-10 kcal/mol higher than that of the global energy minima. (Ponnuswamy, Warme & Scheraga, 1973; Howard et al., 197.5; Momany, 1976a; Simon,

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NCmethy & Scheraga, 1978). In the following we refer one of these conformations as stable oligopeptide or stable segment conformation. The number of the possible conformations of an oligopeptide of 4 to 10 amino-acid in which all amino acids are in one of its energy minima is II;= i Si (where si is the number of the stable conformations of the ith amino-acid of the n membered segment) which is in the range of 106-1014, since the average value of s, considering both the backbone and the side chain, is about 30. In fact however an oligopeptide of 4 to 10 amino-acids usually has less than 100 stable conformations as shown by energy minimization, NMR and CD studies (Ralston, De Coen & Walter, 1974; Howard et al., 1975; Burgess, Momany & Scheraga, 1975; Kang & Walter, 1976; Hurwitz & Hopfinger, 1976; Momany, 1976a,b, 1977; Miller & Scheraga, 1976; Simon et al. 1978; Anderson & Scheraga, 1978; Fitzwater, Hodes & Scheraga, 1978). In our previous studies (Simon, 1979; Simon & Asboth, 1980) arguments were found in favour of continuous folding of proteins during biosynthesis. We suggested that during biosynthesis the incoming amino-acid can only alter the conformation of the few preceding amino-acids and become stabilized by forming stable short segments. Therefore significant degree of stability of the individual segments in native proteins are expected. In this paper we shall point out that because of the small number of stable conformations of polypeptide segments of proteins, the proteins have ability to regenerate their structure by chain propagation in the course of fluctuations. This regenerative ability which has no effect on the rate of the fluctuations, ensures the long lifetime of the native structure by making most of the fluctuations reversible. Chain Propagation as a Mechanism which Leads to Definite Folding Pathway

Because of the small number of stable oligopeptide conformations even some of the dihedral angles (cp,4, x) could determine which of these few stable conformations are to be assumed, thereby determining the other dihedral angles. It is in good agreement with our previous finding that in an energy minimization study of a segment of IZ amino-acids the conformation of the terminal amino-acid is generally determined by that of the other n - 1 (cf. Simon et al., 1978, tables I, III). Therefore an amino-acid that comes next to the part of the chain which retains its original conformation in a certain fluctuation, can only be restabilized if, in its random motion, it gets into the conformation determined by the other IZ- 1 residues. In this way those parts of the polypeptide chain which take part in a certain fluctuation

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wiil be restabilized in their original conformation by chain propagation as long as the conformation of the terminal amino-acid is determined by the conformation of the preceding n - 1 ones unambiguously. Since the number of stable conformations of a segment SK II:= ,s,, the formation of a stable n membered segment in the m membered part of the polypeptide chain with a conformation different to the native one has a small probability: pl=

2 q, ‘- ’ ;[I, s,,:

where Sj and Sj,i are numbers of stable conformations of the jth R membered overlapping segment of the m membered part of the polypeptide chain, and of the ith amino-acid of the jth segment. The probability of the unambiguous chain propagation from the native conformation part of the protein is 1 -pl. Stabilization

of Folding Nuclei in Part of the Chain Involved in Fluctuation

Chain propagation will be a fast process compared to the formation of a stable oligopeptide by a random search process. In an m-membered part of the polypeptide chain the chain propagation needs on an average i Cm= 1 s, conformational changes whereas in a random process about S’ n”=, s, different conformations have to be searched through to reach one of the S stable conformations of the segment. Therefore within the time required for chain propagation the random stabilization of a segment has a probability:

where S is the average value of S. This probability is small since a segment should have at least 4 to 10 residues to be stable enough to provide a folding nucleus (Materson & Scheraga, 1978). It is important to note that the randomly stabilized folding nucleus is not necessarily different from the native one as structural information may remain in the segments taking part in the fluctuation, ensuring that a folding nucleus of the native conformation may be stabilized with higher probability. For example, the change in dihedral angles x are prevented not only by electrostatic, van der Waals and H-bond interactions, but also by the

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torsion potential which is negligible for cp and r(l dihedral angles of the backbone. The wide (120”-180”) energy minimum of the torsion potential allows considerable motions for the side chain without passing thought a torsion potential barrier UO. These barriers are at least 2-3 kcal/mol (Pullman & Pullman, 1974; Momany et al., 1975; Gelin & Karplus, 1975). This means that fluctuations in which side chain conformations do not change have an about 100 (=exp UO/RT) times higher probability than those in which one of the x dihedral angles are changed. Since a segment with original side chain conformation usually can only be stabilized in its native structure if side chain interactions take part in the stabilization, the formation of proper folding nucleus can be expected. However, there is a p3#0 probability that the conformation of the stabilized folding nucleus is different from the native one and if it can reach a certain size by chain propagation, it may cause denaturation. Termination

of Chain Propagation

The probability of the formation of a folding nucleus different from the native one in a certain fluctuation is p1 + p2p3. The question arises: what is the probability that chain propagation from such a false folding nucleus would alter the conformation of a macromolecule to such an extent to cause denaturation? Such denaturation can only occur, if the false structured part of the chain reaches the dimension of a structural domains (generally not less than 20 amino-acids), which is stable enough to resist any chain propagation starting from native folding nuclei. Chain propagation from native folding nuclei is not terminated. The existence of at least one stable conformation of the polypeptide chain in which all of the overlapping segments have significant stability, namely the native one, ensures that any residues following a segment of n - 1 aminoacids in the proper structure must have a conformation that fits the preceding n - 1 residues. Since S <
On the other hand if a domain size (m membered) part of the polypeptide chain has & stable conformations, the random stabilization of this part of

I. SIMON

the chain in a conformation different fluctuation has a very small probability:

Dynamic

from the native one on a certain

Stability and Spontaneous

Denaturation

of Proteins

According to the above simple calculation the probability of denaturation in a certain fluctuation is p = (pi +pzp7)pJ +ps. if the time between two consecutive large amplitude motion of a domain size part of the polypeptide chain is long enough for regeneration by chain propagation. In an average protein 5 is about 30, II and PII are at least 4 and 20, so as s is not more than 300, p is less than 10 “? therefore even the most rapid, picosecond time scale fluctuation cause spontaneous denaturation only in million year t 10’” ps) time scale. Therefore the generally observed spontaneous denaturation in vitro, in the circumstances corresponding to the native state, is rather the consequence of covalent structure modifications, (oxidation, desamidation, etc.) or intermolecular interactions, aggregations and precipitations of the unfolded or partly unfolded protein molecules, than a result of intramolecular interconversion from the native conformation to another stable conformation. It is important from the functional point of view that the long lifetime of the metastable native structure is ensured, not by large potential barriers but by the regeneration ability of the polypeptide chains having naturally selected amino-acid sequences, without prevented functionally important structural fluctuations. REFERENC’ES ANFINSEN, C. B. & SC‘HEKAC~A. H. A. c lY751. .-\c/t, ,v,u. (%UVU. 29. 205, ANDERSON. J. S. & SCHERA(;A. H. A. I 197X). .~~fr[,rrir,~~~/rc~~~~,s 11, 8 I?. BURGAS% A. W.. MOMANY, F. A. & SCHRKA
607. HURWITZ, F. 1. & HOPFINGER. A. J. (1976). HVIDT, A. & NIELSEN. 0. (1966). Adv. pror.

Int. J. C~CW.

Peptide PKW;~~ RK 21. 287.

8. 543.

STABILIZATION KANG,

S. &WALTER,

R. (1976).

OF

PROTEIN

Proc. natn. Acad.

STRUCTURE

Sci. U.S.A.

KARPLUS,M.& WEAVER,D.L. (1976). Narure,Lond.268,404. LAKOWICZ, J. R. & WEBER, G. (1973). Biochemistry 12.4171. LEVINTHAL,~.(~~~~). J chem.Phys.65,44. LIM,V. I. & EFIMOV, A. V. (1976). FEBSLetts 69.41. LINDERSTRIZIM-LANG,K.M.& SCHELLMAN,J. A.(1959).In

493

73, 1203.

TheEnzymes (Boyer,P.D., York: Academic Press. MATERSON,R. R. & SCHERAGA, H. A. (1978). Macromolecules 11,819. MCCAMMON,J. A.,GELIN,B. R.& KARPLUS.M. (1977). Nature,Lond.267,585. MILLER, M. H. & SCHERAGA, H. A. (1976). J. Polym. Sci. (Polymer Symposia) 54, 171. MOMANY, F. A. (1976a). J. Amer. them. Sot. 98, 2990. MOMANY, F. A. (1976b). J. Amer. them. Sot. 98, 2996. MOMANY, F. A. (1971). Biochem. biophys. Res. Commun. 75, 1098. MoMANY,F.A.,McGuIRE,R.F.,BuRGEss,A.W.& SCHERAGA,H.A.(~~~~).J. phys. Chem. 79,236l. NORTHRUP,S.H.& MCCAMMON,J. A.(1980). Biopolymers 19,lOOl. PONNUSWAMY, P. K., WARME, P. K. & SCHERAGA, H. A.(1973). Proc. natn. Acad. Sci. U.S.A. 70, 830. PTITSYN,O.B.& RASHIN,A.A.(~~~~). Biophys.Chem.3,1. PULLMAN,B.& PuLLMAN,A.(~~~~). Adv.prot. Chem.28,347. RALSTON,E.,DECOEN,J.L.&WALTER,R.(~~~~). Proc.nam.Acad.Sci. U.S.A. 71.1142. SCHERAGA,H. A.(1973). Pureappl. Chem.36,l. SIMON,~. (1979).X theor. Biol. 81,247. SIMON,~. & AsB~TH,B. (1980). J theor.Biok82.685. SIMON, I.,N~METHY,G.& SCHERAGA,H. A. (1978). Macromolecules 11,797. TELEGDI, M. & STRAUB,F. B. (1973). Biochem. biophys. Acta 321, 210. UEDA, Y. & GO, N. (1976). Znf. J. Peptide Protein Res. 8, 551. VA&M. & B0~0ss,L.(1974). Eur.J. Biochem.43.237. WAGNER,G.& W~~RTHRICK,K.(~~~~). Nature,Lond.275,247. WETLAUFER, D. B. (1973). Proc. natn, Acad. Sci. U.S.A. 70, 697. ZAVODSZKY,P.,ABATUROV,L.B.&VARSHAVSKY, Y. M.(1966). ActaBiochem.Biophys. Acad. Sri. Hung. 1, 389. ZIMM.B.H.& BRAGG,J.K.(~~~~). J chem.Phys. 31,526. Laroly,

H. & Myrback,

K. eds) p. 443, New