J. Mol. Biol. (1964) 8, 161-165 LErrers To rap Evrror ‘The Theory of Inter-allelic Complementation, are not strictly co-linear with the corresponding genetic maps. We are aware of only one publication concerned with this problem, a theoretical model for complementation in the enzyme adenylosuccinic synthetase (Kapuler & Bernstein, 1963). We present here a sketch of a different general theory of complementation (previously circulated privately, 1960), The basic idea that complementation is due to protein-protein interaction appears to have been first Suggested by Brenner ( 1959) and Fincham (1960). Recent papers dealing with in vitro complementation are Woodward (1959), Loper (1961), Schlesinger & Levinthal ( 1963), Fincham & Coddington ( 1963) and Perrin (1963). Reviews covering the subject are by Fincham ( 1960) and Catcheside (1960). TABLE ] ——___ A Bc p ee A 0 + 0 96 B + 0 0 06 Cc 0 0 60 4 D 0 6 4 9g ——— » : A Shnilar Phenomenon, specific suppression within a single peptide chain, has been reported * Helinskj & Yanofsky (1963). M 161 162 F. H. Cc. CRICK AND L. E. ORGEL We are thus driven to what is in any case a more likely hypothesis, that comple. mentation is usually due to the correction of the misfolding of one monomer (produced by the mutation) by some unaltered part of the other monomer. In other words, not that “two blacks make a white” but that “(good corrects bad”. We now proceed to develop this idea. A B Fie. 1. The complementation map resulting from the complementation pattern of Table J. This map is circular, not linear. Most sets of any four complementing mutants are found in practice to give a linear map. For simplicity, we deal only with cases in which the wild-type multimerf is madc up of monomers of only one kind; that is, of only one type of polypeptide chain. controlled by a single cistron. Now it is highly likely on general grounds that such an aggregate will have some symmetry. Although we cannot completely rule out fancy pseudo-symmetries (e.g. a shallow screw axis terminated by steric hindrance). by far the most likely symmetry elements are axes of rotation. True mirror planes and centres of symmetry are of course forbidden because proteins consist only of L-amino acids. Thus we may confidently expect that most multimers will have n-fold rotation axes, often of more than one type. Twofold axes are likely to be mon! common. We consider first the special case in which all monomers are inactive because the active site is made up of parts of two (or more) subunits. This might, for exampl. occur when two monomers form a dimer as shown diagrammatically in Fig. °. In this case we would have complementation between two monomers, one of wh had an inactive region a, and the other an inactive region b. Thus in Fig. 2 the right: hand site would be inactive, but the left-hand site would function. This may be th correct explanation in some cases, but it can hardly provide a basis for a gene™ theory of the approximate linearity of complementation maps spreading over (i! siderable lengths. Note, in passing, that complementation, as in this example. nF? often lead only to a partial restoration of activity. | For the general theory we shall make no special assumptions about the activity ©: monomers, nor about the location of the active centre. + We have used the term “multimer” to denote an aggregate of several (identical) objects wl t be ~ any implications as to their geometrical arrangement ; we prefer to retain the word “polymer form: : tems in which the aggregation is linearand involvessmall molecules held together by chemical be! ich: LETTERS To THE EDITOR , 163 Our basic structural assumptions are: (1) that certain mutations can produce a local misfolding of the protein, which in its turn prevents enzyme activity; Fic. 2. A very diagrammatic illustration of an enzyme which is a dimer and only forms the ite when the parts marked A and B come together. The Figure shows the mixed dimer formed by two complementing mutants. The upper molecule is defective at site A (marked therefore as a), the lower one at B (marked as 6). Thug the site on the right is defective while that on the left ig still active, of helix), these assumptions are plausible. Now consider Some change of an amino acid, produced by a mutation. This can have several effects, 164 ; F. H. C. CRICK AND L. E. ORGEL Thus, none of these cases will lead to complementation. To achieve complementation the misfolded region must lie so that it can only be corrected by part of the homologous regton (correctly folded) in one of the other monomers of the multimer. It is easily seen that this is most likely to occur in the regions adjacent to the axes of rotation of the multimer. ° This basic prediction can easily be seen to lead to the general type of relationship observed in complementation. Mutants affecting the same region, near a rotation axis, will often be near together on the genetic map. Thus in many cases such mutants will not complement each other. The length of a “segment” in a complementation map will be a rough measure of the length of the region misfolded by the mutants in that segment. If misfolding spreads along the length of the polypeptide chain there will be a general tendency for the genetic map and the complementation map to be co-linear, but there will be many exceptions. If it spreads not along the chain but to adjacent folded segments, the complementation map may remain linear but it may not be co-linear with the genetic map. Complicated misfoldings may easily produce non-linear, circular or spiral complementation maps. We have considered: (1) the effect of triad and higher axes of symmetry; (2) the possibility that some mutants may cause the production of a fragment of the polypeptide chain; (3) the efficiency of complementation in the various cases. It suffices to say that this has not led to anything which contradicts our basic idea. We disagree with the suggestion of Kapuler & Bernstein (1963) that because complementation maps are relatively simple “there exists a class of enzyme . . . whose tn vivo tertiary configuration is simple, and that in at least one case this configuration is approximately that of a two-turn spiral”. In our view these authors have not clearly realized that the requirements for mutants to complement are rather special and that symmetry axes are likely to be involved. Moreover, their suggestion that protein subunits are likely to aggregate into a layered stack is implausible. Com- plementation is a very common phenomenon and special explanations are unlikely to be correct. We believe, as they do, that the details of the folding of the polypeptide chain are the key to the relationship between the complementation map and the genetic map. but we do not believe that there is any simple general way of deducing these details from the supposed correspondence between the two maps. It must always be realized that while the genetic map is a linear map relatiny point mutants, the complementation map consists of segments and does not put the point mutants into a unique order. Thus one always has a certain amount of latituce in comparing the two kinds of maps, and a good deal of discretion is therefore 1¥- quired in assessing the success of a theoretical prediction. Although we believe that the general theory of complementation we have sketchc«! here is plausible, it can hardly be accepted as more than a useful working hypothes' without further experimental evidence. Unfortunately, the structure of proteins i+ so complex that we have been unable to devise any crucial experimental test of ov" theory which does not depend on an a priori knowledge of the configuration of the LETTERS TO THE EDITOR 165 protein. Such information is obtained only from lengthy X-ray studies. We believe that it is essential for any detailed test of our general theory or, indeed, of any other theory of complementation. We should like to thank the numerous workers in the field who commented on our original manuscript on this subject, and in particular Dr. Chester Partridge who sent us many detailed criticisms. The basic idea originally came to us after conversations with Dr. Norman Giles, to whom we are particularly grateful for instructing us on the facts then available. Medical Research Council Laboratory of Molecular Biology F. H. C. Cricx and Department of Theoretical Chemistry LE Cambridge University, Cambridge, England Received 6 November 1963 REFERENCES Brenner, 8. (1959). In Symposium on Biochemistry of Human Genetics, ed. by G. E. W. Wolstenholme & C. M. O’Connor, p. 304. London: Churchill. : Catcheside, D. G. (1960). In Microbial Genetics, p. 181. Cambridge: The University Press, Fincham, J. BR. S. (1960). Advanc. Enzymol. 22, 1. Fincham, J. R. S. & Coddington, A. (1963). J. Mol. Biol. 6, 361. Helinski, D. R. & Yanofeky, C. (1963). J. Biol. Chem. 238, 1043. Kapuler, A. M. & Bernstein, H. (1963). J. Mol. Biol. 6, 443. Loper, J. C. (1961). Proc. Nat. Acad. Sci., Wash. 47, 1140. Perrin, D. (1963). Cold Spr. Harb. Symp. Quant. Biol. vol. 28. Schlesinger, M. J. & Levinthal, C. (1963). 7. Mol. Biol. 7, 1. Woodward, D. O. (1959). Proc. Nat. Acad. Set., Wash. 45, 846.