Download The mutation buffering concept of biomolecular structure

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
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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.
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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.
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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
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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.
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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
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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.
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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
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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
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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.
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