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Proc. Int. Symp. Biomol. Struct. Interactions, Suppl. J. Biosci., Vol. 8, Nos 3 & 4, August 1985, pp. 669–679. © Printed in India. The mutation buffering concept of biomolecular structure MICHAEL CONRAD Departments of Computer Science and Biological Sciences, Wayne State University Detroit Michigan 48202, USA Abstract. Redundant elements in proteins and nucleic acids serve to buffer the effect of point mutations on features of conformation critical for function. Mutation buffering associated with mechanistically redundant amino acids facilitates the evolution of proteins. Such redundant amino acids accumulate by hitch-hiking along with the evolutionary advances which they facilitate. Redundancies in DNA (such as introns and repetitive DNA) prevent extraneous sequence dependent conformational effects from interfering with readout. They also facilitate regulatory evolution. According to the mutation buffering concept biological organizations are selected to facilitate evolution. As a consequence biological information processing is very different from information processing in man-made computers. The link between molecular conformation, evolutionary processes, and information processing is formulated in terms of a tradeoff principle. By utilizing mutation buffering biological systems sacrifice programmability; by achieving programmability digital computers make mutation buffering computationally expensive and hence sacrifice evolutionary adaptability. Keywords. Biomolecular conformation; biophysics of evolution; biophysics of information processing. Introduction It is useful for biophysicists to view the principles of physics and chemistry as inexorable givens. But it is also useful to recognize that biological macromolecules are the products of evolution. The sequence of nucleotides in DNA (and consequently the sequence of amino acids in proteins) is a consequence of the historical mechanism of variation and natural selection. Nucleic acids and proteins are very unlike the physical principles which govern their conformation and dynamics. What is most important about them is that they are not inexorable. I wish in this paper to present a conceptual model of biomolecular structure which unites physical and evolutionary thinking. Consider two proteins, A and A', which perform the same mechanistic function. That is, A and A' are virtually indistinguishable so far as their specificity and catalytic properties are concerned. These molecules must be capable of evolving through variation and selection. An investigator who naively views the properties of biological macromolecules as being just as inexorable as the principles of physics might be tempted to suppose that this ability to evolve is a given fact of protein chemistry, say an inherent consequence of the peptide bond. However, it is possible to propose molecular structures which are more suitable as substrates for evolution than others. Such structures contain redundant features which buffer the effects of point mutation (or other genetic changes) on conformational features critical for function. This idea of mutation buffering applies to biological systems at all levels of 669 670 Conrad organization, ranging from that of polymers such as nucleic acids and proteins to that of genotype–phenotype relations taken as a whole. My purpose in this paper is to summarize the argument for mutation buffering in proteins and nucleic acids, the best understood biological systems from the physical point of view. The mathematics which underlies the argument is reviewed in my recent book (Conrad, 1983). This book also reviews the application of the mutation buffering concept to intracellular control systems, endocrine systems, neurons and nervous systems, and to the organization of development. Structure of the argument The mutation buffering model is based on the following considerations. Rate of evolution Evolution works only if the organizational features of biological systems are such that acceptable forms are derivable by single genetic changes, such as single point mutations. This is due to the fact that evolution time scales as p–n , where n is the number of simultaneous genetic changes required to derive an acceptable form. This time becomes unacceptably small for a value of n > 1. Call f the fraction of mutations of a protein or nucleic acid which lead to an acceptable form. The threshold condition for evolution to occur can be expressed in terms of the simple condition, f N > 1 (Maynard-Smith, 1970). If a protein or nucleic acid fails to satisfy this condition we will say that it has reached an 'evolutionary bottleneck'. For detailed calculations which demonstrate that the evolution time is effectively independent of factors such as population size, mutation rate, size of the molecule, and extent of improvement (see Conrad, 1978, 1983). Elimination of bottlenecks Biological polymers cannot in general be free of evolutionary bottlenecks unless they incorporate redundancies which buffer the effect of point mutation. The reason can be appreciated in terms of the balls and springs analogy. The balls represent monomers, say amino acids, strong springs represent covalent bonds, and weak springs represent the noncovalent interactions responsible for folding. Particular spatial arrangements of the balls represent the recognition site, the active site, binding sites, or control sites. If a system is mutated by adding, deleting or replacing a ball these crucial spatial arrangements will be altered. If the number of balls in the system and the number of weak springs are increased, effects of deletion, addition, or replacement will be distributed over a larger system. The effect of any particular alteration on the critical spatial arrangements will generally be reduced. Similarly, if more types of balls are used, allowing for more graded replacements, the effect on critical spatial arrangements will be more graded. Subtle adjustments will become possible and acceptable pathways connecting different useful structures may be opened up. The increase in the number of balls and in the number of types of balls are both forms of redundancy which buffer the effect of mutation on features of shape critical for function. Mutation buffering of biomolecular structure 671 How the degree of buffering is related to the number of redundant components depends on the detailed structure of the system and on the particular addition, deletion, or replacement. As the whole structure changes in response to mutation it may happen that the system hits an evolutionary bottleneck. Possibly some subtle alteration would be useful, but no single mutation of the structure will give rise to this alteration. Or perhaps some major alteration would be desirable, but no sequence of single mutations can lead to its discovery. The condition f N > 1 fails, at least to the extent that no sequence of single mutations leads to the desired form. This is why mutation buffering is not an inexorable feature of biological polymers. By adding a sufficient amount of additional redundancy it will always be possible to patch around the bottleneck. The crucial point is that whenever a bottleneck is reached it is necessary to add more redundancy. The formal argument leading to this conclusion utilizes entropy theory. The primary structure of the polymer is treated as an information source and the tertiary structure and function is treated as a receiver. Mutation of the primary structure is the source of uncertainty, or noise. If the uncertainty (or entropy) of the receiver is kept small it is possible for the corresponding shape and function change to be small. To keep this uncertainty small it is necessary to introduce a regulator which can absorb some of the uncertainty. The degree of actual change exhibited by the receiver in response to the noise is determined by scale factors. It is these scale factors which correspond to the detailed organization in the balls and springs analogy. Since the scale factors change with the evolution of the polymer, the degree of buffering cannot be an inherent feature of the types of bonds in the system. It is always possible to hit a bottleneck, in which case the number of redundant elements necessary for regulating the expression of point mutation must be increased. For the mathematical formulation of this argument see Conrad (1979a, 1983). Patching around bottlenecks Suppose that a protein or nucleic acid reaches an evolutionary bottleneck. The time required for an evolutionary advance to occur by means of a double mutation scales as p– 2. The time required for this advance to occur by means of k f-increasing additions of redundant elements followed by a fitness increasing mutation scales as p–1 even if k is large. This is due to the fact that it is always possible to add redundancy through single genetic changes. Thus a system which patches around a bottleneck by means of k redundancy increasing mutations will always evolve faster than the system which waits for a double mutation. Redundancy increasing mutations are a cost to the organism in terms of free energy. Such mutations are slightly fitness reducing unless the redundancy subserves a mechanistic function, such as that of stabilizing the folded shape of the polymer. Nevertheless such redundancies will accumulate in the course of evolution by hitchhiking along with the evolutionary advances which they facilitate. If redundancy increasing mutations are only slightly fitness reducing it is inevitable that a population will always carry a load ofthem. Allen and Ebeling (1983) have calculated the amount of drift of fitness decreasing mutations which are possible. The quantity k, which corresponds to the amount of redundancy increasing drift, could easily become as large as five or ten. 672 Conrad This three part argument can be summed up in the slogan, "Biological systems become built for effective evolution through the process of evolution." I have used the term "bootstrapping" to describe this process (Conrad, 1979b). The process of evolution facilitates itself through the accumulation of redundancies which buffer the effects of genetic change. In effect, evolution picks itself up by its own bootstraps. Mutation-buffering in proteins The balls and springs analogy suggests the buffering mechanisms which are possible in proteins. These include: (i) Redundancy of weak bonding; (ii) Quantitative redundancy of amino acids; (iii) Redundancy of amino acid types; (iv) Specific conformational formats, such as the looped, hypervariable regions of the immunoglobin molecule; (v) Utilization of codons which are more likely to mutate to similar amino acids, for example, to amino acids with similar hydrophobicities. Solovyov and Kolchanov (1982) have formulated a useful principle: the preservation of all normal steps during the folding of a mutant tertiary structure is an indispensable condition for preventing a strong distortion of this structure. Turning the statement around, we can say that any change which preserves the sequence of steps involved in folding will allow for gradual changes with respect to point mutation. The essential features of all the redundancies listed above is that they increase the number of possible mutations which are compatible with a given sequence of steps which occur during folding. In some cases fragments of protein appear to perform about as well as the whole protein so far as specificity and catalytic speed are concerned. This is particularly evident in the Merrifield synthesis (1973). Fragments of a protein can often be synthesized which appear to duplicate relevant specificity and catalytic properties of the whole protein. Analysis of codon usage in haemoglobin suggests that the more replaceable codons are utilized more frequently (Conrad et al., 1983). In some cases the less replaceable codons are utilized more frequently. Perhaps this suggests the existence of fine and gross controls, like the fine and gross focussing controls on a microscope. However it should be recognized that the factors which control codon usage are complex. Depending on the tRNA populations which are present, different choices of codons could lead to different consequences for gene expression. Haemoglobin is a protein which must be fine tuned to a variety of environments, hence one which ought to be evolutionarily plastic. The highly conserved protein cytochrome c gives a different result. The codons which are most used are not the most replaceable ones. Mutation buffering in proteins bears on the issue of selectionist versus neutralist models of evolution (Conrad, 1977, 1982). According to selectionist models the sequence of amino acids in proteins is fine tuned by natural selection. According to neutralist models many of these details are more driven by mutation than fine tuned by Mutation buffering of biomolecular structure 673 selection (Kimura, 1968; King and Jukes, 1969). If mutation-buffering is necessary in order for sequences to arise on which selection can act effectively, a great deal of neutral or quasi-neutral variation becomes inevitable. According to the mutation-buffering model, the high degree of neutral variation exhibited by proteins is a precondition for natural selection to work effectively. Mutation buffering in nucleic acids* It is now known that DNA is not an ideal double helix. A great deal of conformational polymorphism is possible due to the flexibility inherent in the DNA structure (Sasisekharan and Pattabiraman, 1978; Gupta et al., 1980; Sasisekharan and Brahmachari, 1981). Handedness and conformation within a given handedness are influenced by base sequence and are milieu dependent. This variability of DNA conformation could conceivably subserve a number of biological functions. A plausible assumption is that it plays a role in gene expression. A large number of redundant bases appear to occur in some DNA molecules. Introns and repetitive DNA are prominent examples. Given the probable importance of conformational deviations from an ideal helical structure for readout and regulation, it is pertinent to consider whether redundant DNA serves a buffering function. First consider the features which a DNA molecule should have in order to properly perform its biological functions. Information storage Evolution of proteins should not be constrained because the DNA which codes for them is conformationally unfavourable. This would reduce the information storage capacity of DNA and would retard the rate of evolution. This retardation effect is exhibited by computer models of evolution in which the mutation probabilities are biased (Conrad, 1981). Such biasing causes genes to become trapped in subregions of the space of possible base sequences. Readout requirement Sequence dependent conformational variations in DNA structure are desirable in that they can facilitate the speed, specificity, and regulation of readout. In the classical, pure double helical model of DNA readout enzymes had to recognize single bases as if they were a string of bits on a tape. If groups of bases have distinguishable conformations the specificity and speed attainable by a readout enzyme is much greater. Isolation requirement Sequence dependent alterations in DNA conformation should not interfere with readout enzymes acting on coding sequences. Nor should they lead to extraneous * The application of the mutation buffering model to DNA is based on discussion with V. Sasisekharan and S. K. Brahmachari and has been presented elsewhere in a joint paper. 674 Conrad regulatory effects. The isolation requirement is similar to, but not identical with, the information storage requirement. Evolvability Single genetic changes should always be possible which lead to gradual variations in the conformational features of DNA responsible for gene expression and for regulating gene expression. The readout requirement conflicts with the information storage, isolation, and evolution requirements. This is due to the fact that recognizable conformational features abet readout, whereas they reduce information storage and decrease isolation. They also interfere with evolution by increasing the likelihood of unacceptable changes in readout and regulation of readout. In the classical model of DNA this conflict could not exist because recognizable conformational features did not play a prominent role. In the absence of flexibility and the consequent conformational polymorphism the readout requirement had to be met by putting an extra burden on the readout proteins. But as a matter of fact conformation contributes significantly to the specificity of readout. How can DNA meet the readout requirement and at the same time satisfy the requirements for information storage, isolation, and evolvability? This is where buffering effects of "redundant" DNA plays a critically important role. Two types of buffers are possible. Readout (or mechanistic) buffers make it possible to meet the isolation requirement. In this case redundant DNA controls the ramification of conformational effects which could interfere with readout or the regulation of readout. Introns and some other redundant components of DNA could quite conceivably serve as readout buffers. The second type of buffer are evolutionary buffers analogous to the evolutionary buffers which facilitate protein evolution. In this case redundant DNA enhances the tunability of conformation dependent regulation of gene expression. Repetitive DNA may serve as an evolutionary buffer. Readout buffers always contribute to evolutionary buffering. Similarly evolutionary buffers always contribute to readout buffering. But a particular piece of noncoding, nonregulatory DNA might make a much more prominent contribution to one or another of these two types of buffering. A pure evolutionary buffer is a selective disadvantage to the individual and therefore can only evolve by hitch-hiking selection. Its sole function is to enhance the capacity for evolution. A readout buffer is a selective advantage to the individual in that it allows for effective gene expression. Readout buffers are evolution facilitating since some combinations of regulatory and coding sequences would interfere with one another in their absence. An example of buffering has recently been observed by Azorin et al. (1984). The recognition sequence (G-G-A-T-C-C) for the restriction endonuclease BamHI may be located at different distances from a B-Z junction in negatively supercoiled plasmids. Cleavage is increasingly inhibited as the number of intervening bases between the recognition site and the junction decreases. This observation demonstrates that it is physically realistic to interpret redundant (noncoding, nonregulatory) DNA as subserving a buffering function. The redundancy observed in prokaryotes is much greater than in eukaryotes. In Mutation buffering ofbiomolecular structure 675 some viruses DNA is even used to code for multiple proteins, though this can only occur if the evolution of the proteins is buffered by the use of highly replaceable amino acids (Sander and Schulz, 1979; Conrad and Volkenstein, 1981). Selection against redundant DNA is stronger in a small DNA molecule than in a large one. This is due to the fact that optimization is increasingly difficult as the size of the optimization problem increases. This is as true for evolutionary optimization as for other forms of optimization. In bacteria genes which code for unneeded enzymes are eliminated by selection (Zamenhof and Eichhorn, 1967). But as the number of genes becomes larger the amount of variation and selection required to obtain the most efficient gene structure becomes so large that redundancy inevitably accumulates. The balance of selective disadvantages versus selective advantage of buffering DNA shifts towards the advantage side in eukaryotes. If buffering material is present greater readout and regulatory specificity is possible. It is plausible that life splits into two great regimes. The regime of prokaryotes opts for lean DNA at the expense of readout and regulatory specificity. The regime of eukaryotes opts for redundant DNA, compensating for the loss in efficiency by the gain in readout and regulatory specificity. This argument does not apply to proteins. These must evolve in the prokaryotes as in the eukaryotes. Buffering is necessary in order for this evolution to take place. Thus there is no avoiding buffering mechanisms in proteins. In metazoan organisms the regulatory mode of evolution is extremely important. The regulatory mode of evolution is probably much less important in the prokaryotes. Regulatory buffering is therefore not a prerequisite to evolution in these simple forms. Regulatory buffering has profound implications for evolutionary theory. DNA sequence changes played the major role in the diversification of the proteins and the adaptive radiation of prokaryotes. Undoubtedly this mechanism has played an important role in metazoan organisms as well. But the diversification of metazoans is probably largely a matter of regulatory evolution. The mechanism which most plausibly underlies this type of evolution is sequence dependent structural changes in DNA rather than sequence dependent structural changes in protein. The concept of regulatory buffering by redundant DNA opens up the possibility that DNA conformational changes play a major role in the evolution of higher plants and animals. DNA which accumulates such buffering material will exhibit an enormous amount of neutral or quasi-neutral conformational polymorphism. As with proteins, such neutralism is necessary in order for selection to act effectively. Mutation buffering and information processing The mutation buffering principle is clearly pertinent to the interpretation of structure-function relations in biopolymers. It is perhaps less obvious that structure-function relations in high level biological organizations must also be interpreted in the light of mutation buffering. In part this is because the argument which implies mutation buffering in biological polymers also applies to genotype-phenotype relations generally. But in part it is due to the fact that biological organization in the large must accommodate mutation buffering in individual polymers. 676 Conrad It is clear that mutation buffering is relevant to intracellular information processes such as transcription and readout of DNA. But to capture the full significance of mutation buffering for biological organization in the large I would like to consider information processing in nervous systems, an area which at first sight appears to be far removed from principles of molecular conformation. Rather than using the term "information processing" I shall use the more specific term "computing". So far as is known, all processes in nature can be described as computing processes by simulating them with well defined models of computation, such as digital computers. In this way the precise concepts of computer science can be brought to bear on processes which are mechanistically very different from those which occur in a digital computer. The salient feature of structure-function relations in present day digital computers is programmability. It is possible to prescriptively control the behaviour of such machines by setting the states and connections of their components according to a finite programmer's manual. To achieve this the engineer designs the computer to be as discrete as possible. Continuous dynamic processes, such as protein folding, play no role. As a consequence incorporation of redundancies which buffer these processes is impossible. It can only be done by using the computer to simulate buffering mechanisms, at great computational cost. As a consequence digital computers are low on evolutionary adaptability. They also tend to be computationally inefficient. This is due to their inability to learn to use their computational resources efficiently. Universal programmability means that the structure of the machine must have an arbitrary relationship to the structure of the problem which it is used to solve. Its components, unlike those of biological systems, cannot specifically adapt to the task at hand and most components are dormant at any given time since programmability requires disciplined sequential operation. The situation is summed up in a tradeoff principle: structural programmability is obtained at the cost of computational efficiency and evolutionary adaptability (Conrad, 1974a, 1984). Digital computers are built for programmability at the expense of efficiency and evolvability. But biological systems, as products of evolution, must have opted for evolutionary adaptability rather than for programmability. Evolutionary adaptability allows these systems to learn to use their computational resources efficiently. If all processes in nature are in principle simulatable by digital computers, it should be possible to simulate evolutionary processes. This can be done, but in order to do so it is necessary to pay the computational cost of simulating buffering mechanisms of the type which facilitate biological evolution. Biological systems avoid this overhead by utilizing computing mechanisms which are inherently amenable to buffering. All these mechanisms incorporate continuous dynamic features. Relatively inexpensive structural redundancies serve to buffer the effects of structural perturbation on these dynamics. Buffering is possible in proteins because folding is a continuous process. Buffering is possible in nucleic acids because conformation and conformational strain in these polymers is a folding of sorts, though a very much more flexible one than in proteins. Higher levels of buffering in cells and organisms are connected with continuous dynamic features, such as continuous control and regulatory mechanisms. The tradeoff principle creates a choice. If structural programmability is chosen continuous dynamics must be suppressed, making it necessary to simulate mutation buffering to achieve evolutionary adaptability; if Mutation buffering of biomolecular structure 677 evolutionary adaptability is chosen dynamic features must play a prominent role, implying a style of computing wholly different from that of digital computers. Mutation buffering must be incorporated and therefore it becomes impossible to interpret the relation between structure and function from a purely physiological point of view. It is possible to construct models of computing which operate on the adaptabilityfficiency side of the tradeoff principle and which illustrate the significance of molecular conformation for biological information processing (Conrad, 1974b, 1984). The term 'tactilization' captures the key features of these models. The folded shape of a protein allows it to efficiently recognize a molecular surface. This is a form of tactile (or shape dependent) pattern recognition which is difficult to simulate with a digital computer. Clearly the pattern of influences impinging on a cell, say the pattern of presynaptic input, is not the type of tactile pattern which can be directly recognized by an enzyme. But such patterns can be converted to tactile patterns by second messengers, such as cyclic AMP. This is known to be the case in some central nervous system neurons (Liberman et al., 1982). Here the pattern of cyclic nucleotide concentration can be read out by kinase and gating proteins. Other types of milieu changes, such as changes in membrane fluidity or cAMP induced chains of conformational changes in critical cytoskeletal or membrane bound proteins, may also occur. Some evidence (Liberman et al., 1983, 1985) indicates that second messengers may trigger cytoskeletal alterations which control nerve impulse activity. Through such second messenger mediated milieu changes the powerful pattern recognition capabilities of proteins can be harnessed for the very difficult task of high level pattern recognition. The idea of tactilization need not be confined to nerve cells. All cells in the body must make decisions on the basis of the pattern of chemical influences impinging on them. The process of tactilization is highly amenable to evolution. The proteins and cellular regulatory mechanisms which participate in the tactilization process can all be buffered to facilitate evolution. The intervention of a kinase between cyclic AMP and the effector protein is itself an evolution-facilitating redundancy (Kirkpatrick, 1979). The confusing superfluity of such cellular regulatory mechanisms corresponds to the evolution-facilitating superfluities of protein and nucleic acid structure. The biological implications of molecular conformation The mutation buffering concept clarifies the significance of biomolecular conformation for fundamental biological processes such as evolution and information processing. Features of protein and nucleic acid conformation are directly pertinent to the process of evolution. Admittedly it is a long step from protein shape to cellular information processing and brain function. But the idea of tactilization shows in principle how biophysical principles of conformation, including the principle of buffering, provide the underpinning of biological computing. The early history of molecular biology was dominated by a naive computer analogy. The mechanisms of heredity and gene expression were pictured in terms of bit by bit tape reading and tape writing. Much of the original excitement engendered by the double helical model of DNA resided in the belief that hydrogen bonds were sufficient 678 Conrad to account for the specificity of base pairing. Eventually it was realized that the specificity for pairing is mainly due to enzymes and that all the tape reading and tape writing processes involve shape-dependent pattern recognition on the part of enzymes. But enzymes need not confine themselves to recognizing the shapes of individual nucleotides. They can look at shapes of groups of nucleotides. The analogy to bit by bit operations in a computer breaks down even at this elementary level. The process of tactilization involves a hierarchy of exotic dynamics which leads very much further away from the simple digital computer analogy. Some new styles of biophysical thinking are going to be necessary to account for biological information processing. It is necessary to integrate the principles of biomolecular conformation with dynamical analyses of cellular processes. The digital computer is not a very good metaphor for this type of system; but it will certainly play an important role as a simulating tool. Seen in the light of mutation buffering, the ideas which have been painstakingly developed about the conformation of proteins and nucleic acids will perhaps find their full implication in the related phenomena of evolution and information processing. Acknowledgements This paper was prepared during a sabbatical visit to the Molecular Biophysics Unit at the Indian Institute of Science, Bangalore. Support from the Institute and from National Science Foundation grants INT-83-11410 and MCS-82-05423 are gratefully acknowledged. I am indebted to both the faculty and students of the Molecular Biophysics Unit for valuable discussions. References Allen, P. M. and Ebeling, W. (1983) BioSystems, 16, 113. Azorin, F., Hahn, R. and Rich, A. 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