Abstract
Aren’t most mutations harmful
Are there any favorable mutations?
Don’t mutations reduce specificty?
Types of mutation and their effects
Mutation Studies by Joe Boxhorn
Notes
Appendix I – mutation rates
Appendix II – Atherosclerosis resistance
Appendix III – Atherosclerosis resistance
Appendix IV – HIV resistance
References
Acknowledgements
Abstract
People often ask questions such as “Doesn’t evolution depend on mutations, and aren’t most mutations harmful?” and “Are there favorable mutations?”. In this FAQ we try to answer these questions. Briefly:
Q: Doesn’t evolution depend on mutations and aren’t most mutations
harmful?
A: No. Most mutations are neither harmful nor helpful.
That’s the short answer. The long answer is that mutations can be neutral (neither helpful nor harmful), strictly harmful, strictly helpful, or (and this is important) whether they are harmful or helpful depends on the environment. Most mutations are either neutral or their effect depends on the environment. Let’s look at an example of a mutation which may be harmful or helpful, depending upon circumstances.
English peppered moths come in two varieties, light and dark. Before the industrial revolution dark moths were very rare. During the worst years of the industrial revolution when the air was very sooty dark moths became quite common. In recent years, since the major efforts to improve air quality, the light moths are replacing the dark moths.
This is a classic example of natural selection; the variations in a species which are better suited to the environment survive and reproduce more effectively than those which do not.
It can be very tricky to determine why some variations better fit their environments than others. The peppered moth is a good example. In a famous paper Kettlewell proposed the following explanation:
Birds eat the kind of moth they can see the best.Kettlewell’s explanation (which makes for an appealing story) has not stood the test of time. Peppered moths seldom rest on exposed areas of the trunks of trees. Moreover the distribution of dark moths might not be well correlated with tree color except in the areas which Kettlewell studied. Some more recent studies indicate that peppered moth melanism is very well correlated with the amount of SO2 (sulfur dioxide) in the air. [5]In England before the Industrial Revolution trees are often covered with light colored lichens. As a result light moths were favored because they were hard to see on the bark of trees whereas the dark moths were easy to see; birds ate the dark moths. During the worst years of the Industrial Revolution the air was very sooty so tree bark was dark because of soot. Dark moths were hard to see whereas the light moths were easy to see; birds ate the light moths. As a result the dark moths became common and the light moths became rare.
None-the-less, before the Industrial Revolution a mutation which changed light moths into dark moths was an unfavorable (harmful) mutation whereas during the dark years it was a favorable (helpful) mutation.
To see why most mutations are neither harmful nor helpful it helps to know a bit about what mutations actually are. A mutation is a change in the genetic material that controls heredity. The genetic material is contained in chromosomes. Plants and animals have two copies of each chromosome whereas bacteria only have one copy. Organisms which have two copies of each chromosomes are called diploids. Those which only have one copy of each chromosome are called haploids.
Chromosomes are divided into genes, each gene being a stretch of DNA, i.e., a sequence of nucleotides (A,G,C,T for short). The location of a gene is called a locus. (The position of a nucleotide within a gene is called a site. Don’t mix up locus and site.) At a given locus you may find that the DNA sequence is different from one critter to another in some small way. These are usually known as different alleles although sometimes they are confusingly called different genes. Let’s call them different alleles so that we don’t get confused; besides that’s the standard term.
If we look at populations of animals and plants we find that there are multiple alleles at 10-20% of the genes. In other words if we look at a given locus in all the members of a population about 10-20% of the time we will find more than one sequence at that locus. There can be more than two alleles within a population for a given gene locus.
Our peppered moths have a gene which controls whether the moth is light or dark.[1] Since moths are diploids each moth has two copies of the gene. If both copies of a given gene are the same allele then the moth is said to be homozygous for that gene. If the two copies are different alleles then the moth is said to be heterozygous for that gene. If both alleles are the same then the moth will be light or dark, depending on which allele it has. People sometimes say “which gene it has” but that is confusing because it mixes up genes and alleles. If a moth has two different alleles (i.e. if it is heterozygous) then the hue depends on which allele is dominant. In the case of peppered moths dark is dominant, i.e., a heterozygote will be dark rather than light.
Now let’s talk about how a gene might change, i.e., how one allele might change into another. There are a number of ways this might happen. We might get a point mutation, one nucleotide being replaced by another. A section might get swapped end for end. A section might be snipped out. A section might be inserted. Or the entire gene might be duplicated. See the next section for a fuller description of the different kinds of mutations and their effects.
What is the consequence when one of these things happens? Most of the time the change either has no perceptible effect at all, or it is fatal. Coding genes map into proteins using the genetic code. The genetic code is redundant (the technical term is degenerate), i.e., different triplets of nucleotides will produce the same amino acid. Because of the redundancy a point mutation may have no effect at all on the protein being coded for; these are known as silent mutations. If the sequence is altered by snipping or swapping the result is likely to be fatal because the coding sequence [the readout in terms of triplets] will be messed up. However this isn’t always true because there are processes that snip and insert sections of DNA into genes in a way that doesn’t mess up the coding sequence.
Supose we have one of these mutations that isn’t fatal but isn’t silent. What happens as a result is that we get a slightly different protein. Most of the time the new protein works very much the same as the old protein – it catalyzes the same reactions. Sometimes it’s functional capability changes; it now catalyzes a different reaction. When this happens there may be another protein which also handled the original task; in this case we’ve added a capability. If there wasn’t we lost the original capability and replaced it by a new one. Changes in enzymes (proteins that catalyze reactions) are seldom an all or nothing proposition.[3]
Gene duplication is important because it is a way to get new genes. Once a gene has been duplicated one copy can change while the other remains the same.
Genes vary a great deal with respect to how much they can be changed without the changes harming the organism. Some genes, such as those that encode the basic metabolism and the components of the replication, transcription, and translation machinery, are hard to change without harm. We see very little variation in them from one organism to another. Such genes are said to be conserved.
“What is the net result,” you may ask. Some mutations are fatal or very bad. These mutations get eliminated immediately. Some are silent and don’t count. Sometimes a mutation is definitely advantageous; this is rare but it does happen. Almost all mutations which aren’t silent and which aren’t eliminated immediately are neither completely advantageous nor deleterious. The mutation produces a slightly different protein, and the cell and the living organism work slightly differently. Whether the mutation is helpful or harmful depends on the environment; it could be either.
If you think about it, life has to work this way – mutations (changes in the genetic material) are happening all the time. The average human being has about 50-100 mutations, of which about 3 matter, i.e., they actually change a protein. If the typical mutation were deleterious life would go extinct in short order. [4]
Although most mutations are neither uniformly helpful nor harmful they may be either helpful or harmful in a particular environment. Environments are always changing, and each member of a population lives in a slightly different environment from the other members. Some organisms live; some do not. Some reproduce; some do not. The alleles of those that live and reproduce get passed on. Any difference in the organism which is favorable with respect to the environment will prosper.
It is important to realize that mutations do not occur in response to the environment. They simply happen. Quite often a mutation occurs within a population and then disappears because the organism had no offspring or didn’t happen to pass the mutation on to its offspring; this can happen even if the mutation is beneficial. Sometimes a mutation will get established within a population by chance even though it doesn’t offer an advantage; this is known as genetic drift. [8]
It is also important to realize mutations do not happen just once. They happen rarely but they keep happening over and over again within a species. In effect a mutation gets more than one bite at the apple; if it doesn’t catch on the first time it appears it gets another chance.[9]
Q: Are there favorable mutations?
A: There are, but it can be hard to tell.
For a number of reasons it is not simple to give examples of favorable mutations. First of all, as we have seen, traits [6] may be favorable or unfavorable, depending upon the environment. Secondly it is not usually known to what extent a trait is genetically fixed and to what extent it reflects a reaction to the environment. Thirdly we don’t usually know what genes effect which traits. Moreover a mutation may be favorable in the sense that it permits survival in an unfavorable environment and yet be unfavorable in a better environment.
However there are a number of good examples:
Antibiotic resistance in bacteria:
In modern times antibiotics, drugs that target specific features of
bacteria, have become very popular. Bacteria evolve very quickly
so it is not surprising that they have evolved resistance to antibiotics.
As a general thing this involves changing the features that antibiotics
target.
Commonly, but not always, these mutations decrease the fitness of the bacteria, i.e., in environments where there are not antibiotics present, they don’t reproduce as quickly as bacteria without the mutation. This is not always true; some of these mutations do not involve any loss of fitness. What is more, there are often secondary mutations that restore fitness.
Bacteria are easy to study. This is an advantage in evolutionary studies because we can see evolution happening in the laboratory. There is a standard experiment in which the experimenter begins with a single bacterium and lets it reproduce in a controlled environment. Since bacteria reproduce asexually all of its descendents are clones. Since reproduction is not perfect mutations happen. The experimenter can set the environment so that mutations for a particular attribute are selected. The experimenter knows both that the mutation was not present originally and, hence, when it occurred.
In the wild it is usually impossible to determine when a mutation occurred. Usually all we know (and often we do not even know that) is the current distribution of particular traits.
The situation with insects and pesticides is similar to that of bacteria and antibiotics. Pesticides are widely used to kill insects. In turn the insects quickly evolve in ways to become immune to the pesticides.
Bacteria that eat Nylon:
Well, no, they don’t actually eat nylon; they eat short molecules
(nylon oligomers) found in the waste waters of plants that produce
nylon. They metabolize short nylon oligomers, breaking the nylon
linkages with a couple of related enzymes. Since the bonds involved
aren’t found in natural products, the enzymes must have arisen since
the time nylon was invented (around the 1940s). It would appear this
happened by new mutations in that time period.
These enzymes which break down the nylon oligomers appear to have arisen by frameshift mutation from some other gene which codes for a functionally unrelated enzyme. This adaptation has been experimentally duplicated. In the experiments, non-nylon-metabolizing strains of Pseudomonas were grown in media with nylon oligomers available as the primary food source. Within a relatively small number of generations, they developed these enzyme activities. This would appear to be an example of documented occurrence of beneficial mutations in the lab.
Sickle cell resistance to malaria:
The sickle cell allele causes the normally round blood cell to have
a sickle shape. The effect of this allele depends on whether a
person has one or two copies of the allele. It is generally fatal
if a person has two copies. If they have one they have sickle
shaped blood cells.
In general this is an undesirable mutation because the sickle cells are less efficient than normal cells. In areas where malaria is prevalent it turns out to be favorable because people with sickle shaped blood cells are less likely to get malaria from mosquitoes.
This is an example where a mutation decreases the normal efficiency of the body (its fitness in one sense) but none-the-less provides a relative advantage.
Lactose tolerance:
Lactose intolerance in adult mammals has a
clear evolutionary explanation; the onset of lactose intolerance
makes it easy to wean the young. Human beings, however, have taken
up the habit of eating milk products. This is not universal; it is
something that originated in cultures that kept cattle and goats.
In these cultures lactose tolerance had a strong selective value.
In the modern world there is a strong correlation between lactose
tolerance and having ancestors who lived in cultures that exploited
milk as a food.
It should be understood that it was a matter of chance that the lactose tolerance mutation appeared in a group where it was advantageous. It might have been established first by genetic drift within a group which then discovered that they could use milk. [9]
Resistance to atherosclerosis:
Atherosclerosis is principally a disease of the modern age, one
produced by modern diets and modern life-styles. There is a
community in Italy near Milan (see Appendices II and III for
biological details) whose residents don’t get atherosclerosis
because of a fortunate mutation in one of their forebearers. This
mutation is particularly interesting because the person
(Giovanni Pomaroli, born 1780 in Limone sul Garda, Italy)
who had
the original mutation has been identified.
Note that this is a mutation that is favorable in modern times because (a) people live longer and (b) people have diets and life-styles that are not like those of our ancestors. In prehistoric times this might not have been a favorable mutation. Even today we cannot be certain that this mutation is reproductively favorable, i.e., that people with this mutation will have more than the average number of descendents. It is clear, however, that the mutation is personally advantageous to the individuals having it.
Immunity to HIV:
HIV infects a number of cell types including T-lymphocytes,
macrophages, dendritic cells and neurons. AIDS occurs when lymphocytes,
particularly CD4+ T cells are killed off, leaving the patient unable to
fight off opportunistic infections.
The HIV virus has to attach
to molecules that are expressed on the surface of the T-cells. One of
these molecules is called CD4 (or CD4 receptor); another is C-C
chemokine receptor 5, known variously as CCR5, CCCKR5 and CKR5. Some
people carry a mutant allele of the CCR5 gene that results in lack of
expression of this protein on the surface of T-cells. Homozygous
individuals are resistant to HIV infection and AIDS. The frequency of
the mutant allele is quite high in some populations that have never
been exposed to AIDS so it seems likely that there was prior selection
for this allele. (See Appendix IV)
For a description of the recent literature consult the OMIM site for CCR5.
A more sophisticated version of the “mutations are always harmful” argument is the claim that mutations always destroy information in the genome, i.e., even though a mutation may provide a selective advantage it does so by destroying information. If this were so then evolution would be a process of continual degradation of the information content of the genome.
Most presentations of this argument rely on an essential vagueness in the use of the word “information” and are worthless. However Leo Spetner has presented a firmer and more definite version of this argument, to wit: Point mutations reduce the specifity of the proteins that they encode. Many (but not all) proteins act as catalysts; that is, they speed up chemical reactions. [11] Biological catalysts are often highly specific; that is, they catalyze a specific reaction with great efficiency. Spetner’s argument, then, is that although some mutations may have selective advantage they purchase this advantage at the price of degradation of biochemical efficency. Spetner writes:
“I have indicated in this chapter that there is no evidence that genetic information can build up through a series of small steps of microevolution. Mutations needed for these small steps have never been observed. By far, most observed mutations have been harmful to the organism. We have seen that there are some point mutations that, under the right circumstances, do give the organism an advantage. There are point mutations that make bacteria resistant to antibiotics. There are some that make insects resistant to insecticides. There are some that increase quantitative traits in farm plants and animals. But all these mutations reduce the information in the gene by making a protein less specific. They add no information, and they add no new molecular capability. Indeed, all mutations studied destroy information. None of them can serve as an example of a mutation that can lead to the large changes of macroevolution.”One can object that this is wrong in a trivial sense since point mutations are reversible. That is, if alleles a and b differ by a point mutation then the mutation that changes a to b is as likely as the one that carries b to a. The counter argument is that in existing organisms genes are already tuned to produce enzymes with maximum specificity. Ergo any change will reduce specificity.
Not by Chance, pp 159-160, 1997.
The counter argument rests on two fallacies, these being (a) assuming that all mutations are point mutations and (b) ignoring change in function. If all mutations were point mutations then a mutation would not change the information content (in the Shannon sense) of the genome because the length of the genome would not change. However it is not the case that all mutations are point mutations (see mutation types below.) Genes can be duplicated, sections of genes can be duplicated, genes can be fused, and DNA can be inserted into genes. In other words there are mutations that increase the information content of the genome.
Equally importantly the counter argument ignores change in function. Decreasing the specificity of an enzyme for one substrate does not mean that it is decreased for all substrates. As environments change the functional needs of organisms are altered; in consequence the relevant enzymes need to be specific for different substrates. Mutations which have selective value for the changed environment will gain specificity for the new substrates while losing specificity for the old substrates. The fallacy in the counter argument is to ignore the gain and mention only the loss.
Spetner’s argument is incorrect in principle but is it, one asks, true in practice. That is, is the case that all observed mutations involve (only) the loss of specificity. The simple answer is “no”; Spetner’s claim about observed mutations is false. Numerous examples of mutations which produce increased specifity for a substrate. These include: evolved beta-galactosidase, the 20x affinity xylitol dehydrogenase enzyme, galactitol dehydrogenase, nylonase, anyone of the vancomycin resistable genes, the sperm-specific dynenin gene, and turf13 (examples posted by Ian Musgrave).
Mutations are changes in the genome (genetic constitution). There are quite a number of ways in which mutations can happen. They also differ in the way that they impact evolution.
Mutations which occur when the genome is copied during reproduction are known as vertical transfer mutations. They are called vertical transfer mutations because they are transferred from ancestor to descendent along vertical lines of descent. In the original work on population genetics it was assumed that all mutations were vertical transfer mutations.
Horizontal transfer mutations occur when DNA is moved from one organism to another. Horizontal transfer can be a major source of evolutionary novelty. It is important because new genes can be propagated much more rapidly by horizontal transfer than by vertical transfer. If evolution is depicted by the tree, vertical genetic movement is the transmission of genes down branches; horizontal genetic movement is the transmission of genes between the branches.
Intra-organism transfer mutations occur when genes or parts of genes move around within an organism.
Strictly speaking, hybrids (mating across species) are not mutants. In many groups of species, particularly among plants, genes are transferred from to one species to another via hybrids.
Point mutations:
The most common type of copying error is the point mutation. In this
form of mutation the nucleotide at a site is replaced by a different
nucleotide. When people talk about mutation rates they are usually
talking about rates of point mutations.
Consequences of point mutations:
Point mutations in junk DNA are common but have no effect.
Sometimes point mutations in regulatory
regions have no effect and sometimes they alter the expression of some
genes.
Additions and Deletions:
During copying a segment of DNA may be deleted or a new segment may be
inserted. Typically this happens as a result of chromosome breakage
or realignment. (See below.) Additions and deletions can also be
produced by certain types of horizontal transfer.
Effects of additions and deletions:
If the length of the new or deleted segment is not a multiple of three
the translation will be garbled after the point at which the
insertion/deletion occurred because the frame reading is now
misaligned. This is known as a frameshift mutation.
In some genes there are segments that may be duplicated as a block. This is known as tandem duplication.
Chromosomal Duplication:
Sometimes one or more chromosomes are duplicated during reproduction;
the offspring get extra copies of those chromosomes.
Effects of chromosomal duplication:
Duplicating only one chromosome
is generally disadvantageous; an example in human beings is Down’s
syndrome. Having multiple copies of all of the chromosomes is known as
polyploidy. Polyploidy is rare in fungi and animals (although it does
occur) and is common in plants. It has been estimated that 20-50% of
all plant species arise as the result of polyploidy.
Gene duplication is very common; it is important because it provides a way to evolve new capabilities while retaining the old capabilities. All intermediate stages can be found in nature, from a single gene with alternate alleles to nearly identical duplicated genes with slightly different functional alleles to gene families of evolutionarily related genes with different functionalities.
Chromosomal Breakage and Realignment:
During reproduction a chromosome may break into two pieces or two
chromosomes may be joined together. A section may be moved from one
part of the chromosome to another or may be flipped in orientation
(inverted). This is the mechanism by which deletions, duplications
and transpositions my occur.
Effects of chromosomal breakage and realignment:
Quite often these types of changes do not affect the viability of the
organism (the genes are still there; they’re just in different places)
but, in sexually reproducing species, they may make it less likely for
the organism to produce viable, fertile offspring.
Retroviruses:
Certain viruses have the ability to insert a copy of themselves into
the genome of a host. The chemical that make this possible (reverse
transcriptase) is widely used in genetic engineering.
Effect of retroviruses:
Usually this is a way for the virus to get the host to do the work of
reproducing the virus. Sometimes, however, the inserted gene mutates
and becomes a permanent part of the host organism’s genome. Depending
on the position of the viral DNA in the host genome, genes may be
disrupted or their expression altered. When insertions occur in the
germline of multicellular organisms, they can be passed on vertically.
Plasmids:
Plasmids are little pieces of circular DNA that are passed from
bacterium to bacterium. Plasmids can be transferred across species
lines.
Effects of plasmid transfer:
Plasmid transfer is an important way of spreading useful genes such as
those which confer resistance to antibiotics. Plasmid transfer is an
example of horizontal transfer.
Bacterial DNA exchange:
Bacteria can exchange DNA directly. They often do this in response
to environmental stress.
Effects of bacterial DNA exchange:
Exchange is often fatal to one or both of the bacteria involved.
Sometimes, however, one or both of the partners acquires genes
which are essential for the current environment.
Higher level transfer:
Some parasites can pick up genetic material from one organism and carry
it to the next. This has been observed in fruit flies in the wild.
Effects of higher level transfer:
When this happens novel alleles can spread much more rapidly through
a species than they would for ordinary gene flow.
Symbiotic transfer:
When two organisms exist in a close symbiotic relationship one may
“steal” genes from the other. The most notable example of this are
mitochondria. In most organisms with mitochondria most of the original
mitochondrial genes have moved from the mitochondria to the nuclear
genome.
Effects of symbiotic transfer:
A major effect is that the symbiotic relationship changes from
being optional to be obligatory.
Transposons:
Transposons are genes that can move from one place in the genome
to another.
Effects of transposons:
Experimental work with bacteria, eukaryotic micro-organisms and very
small animals can tell us much about the occurrence and properties of
mutations, including beneficial mutations. Over the last fifty years or
so beneficial mutations have been observed to occur in a number of studies.
Most of these experiments were done in a continuous culture system
called a chemostat. Chemostats have been used for the last fifty
years in the study of the physiology, population biology and ecology
of bacteria and a variety of other small organisms. They are also
used widely in the commercial production of microbe produced substances.
A chemostat consists of a bottle in which the organisms grow. Growth
medium (i.e. food) is continuously pumped into the bottle and waste
products, residual medium and organisms flow out. The contents of the
bottle are well mixed so that each critter in the chemostat has an equal
chance of getting at each bit of food. Factors that affect the growth
of the organisms such as temperature are controlled, sometimes quite
rigourously. Several variations of chemostats have been developed.
They will be described as they become relevant.
Chemostats have several properties that make them useful for biological
research. Over time, the organisms in the system reach a steady state
in which organism growth equals the amount of organism flowing out of
the bottle. At this steady state the concentration of organisms, measured
as biomass, remains quite stable as does the concentration of residual
(unused) nutrient. Numbers can change somewhat due to changes in the
size of individuals. It is important to note that when the system is
in steady state, the critters are growing exponetially with their growth
rate being the dilution rate (in flow of medium/bottle volume) of the
system. The average time an organism remains in the chemostat is the
reciprocal of the dilution rate. These organisms are also in a steady
state physiologically. The population densities of organisms grown in
these continuous culture systems can be quite high. For a fast growing
bacterium like E. coli densities of 3 x 10^8 per ml are readily attainable.
Similarly small eukaryotic algae such as Chlorella vulgaris can be
easily be grown at densities of 3 x 10^7 per ml. Densities on the order
of 10^5 – 10^6 per ml are attainable for many larger unicellular and
colonial eukaryotes. The implications of this for the study of mutations
are important. Assuming reasonable mutation rates and genome sizes it is
virtually certain that a culture of this sort that has been run at steady
state for any length of time will contain some mutant individuals. This
holds even when the culture is innoculated with a strain derived from
one individual in an obligately asexual species. If, for example, we
assume the following characteristics for an E. coli chemostat containing
identical cells:
We should see 7.5 X 10^6 mutant genes produced in one day. I would note
that E. coli chemostats are generally run at dilution rates far faster
than this. Another property of this type of system is that when organisms
in a chemostat vary in their growth rates the proportion of the faster
growing forms in the population tends to increase at the expense of the
slower growing ones. Finally, the mathematical models describing growth
of bacteria and unicellular algae in these systems are reasonably well
understood and work fairly well when compared to data (see, for example,
Herbert et al. 1956, Kubitschek 1970, Pirt 1975). These models do not do
as well predicting the dynamics when larger organisms with more complicated
life cycles are grown in chemostats.
A reinterpretation by Kubitschek (1974) of work by Novick and Szilard
(1956) suggests that the argument above was reasonable. In this study
resistance to a bacterial virus was used as a marker to follow the
appearance of some mutations in a chemostat culture. Novick and
Szilard grew E. coli in a chemostat at a steady-state density of about
3 X 10^8 cells per ml. Periodically they assayed cells sampled from
the chemostat for resistance to infection by bacteriophage T5 and
calculated the density of T5 resistant cells in the culture. At no
time was phage T5 present in the chemostat nor had the cells in the
chemostat been exposed to phage T5. They found that there was always
a fraction of cells in the culture that was resistant to T5. The
density of resistant cells fluctuated betweeen 10^2 and 10^3 per ml.
It followed a pattern like the one drawn below:
It is important to note here that in this environment sensitivity and
resistance to infection by T5 is a neutral trait here. Because there
is no T5 in the environment, resistance does not provide an advantage.
But it doesn’t seem to provide much disadvantage either. If it
provided a disadvantage, the resistant cells would washout of the
chemostat. In this environment, it is selectively neutral. Mutations
in other genes cause some cells to have a higher growth rate. It
is just a matter of whether these mutations occur first in resistant
or sensitive cells that determines whether the frequency of T5
resistant cells increases or decreases. It’s a hitchhiking effect –
the T5 resistance gene just goes along for the ride with the genes
causing the fluctuations.
Now in a different environment, the value of the mutation producing
resistance to infection by a virus might have a totally different value.
Chao et al. (1977) grew wild type E. coli B in a chemostat. Once the
vessel reached steady state they innoculated it with bacteriophage
T7. The bacteria are sensitive to infection by T7. Needless to say,
T7 grew like mad on the bacteria. After a short time, though, a mutation
attributable to a single gene appeared in a cell surface receptor site
which gave the bacteria complete resistance to T7. This bacterial stain
was designated B1. Shortly after this a mutation occured in the virus
which allowed it to infect strain B1 (strain T7.1). A second mutation
occurred in B1 which made it resistant to this second virus strain as
well as to the original virus strain (strain B2). All five of these
critters happily coexisted in the same chemostat.
Now whether these mutations were favorable or detrimental depends on
which environment the critters were put in. In an environment containing
T7, E. coli B1 or E. coli B2 could survive while E. coli B suffered
tremendous mortality. But the mutant strains paid a cost. They were
not as fast at taking up nutrient as the wild type and, consequently,
could not grow as quickly. In competition experiments in phage-free
environments, E. coli B outcompeted every time. So whether a mutation
conferring resistance to T7 is beneficial depends on:
There has been a considerable amount of work on resistance of
bacteria to bacteriophage that supports this. Some of it is reviewed
in Lenski (1987).
The presence of a predator in a continuous culture system can place
strong selection upon the critters being grown. When mutations appear
in the prey that confer resistance to predations, they can spread
through the chemostat quite rapidly — in real time! This has been
seen in many of the studies whose results are reported in the continuous
culture literature.
Shikano et al. (1990) observed a major morphological change in an
unidentified gram negative bacterium when it was grown in semicontinuous
culture with a predator. Semicontinuous culture is a culture technique
where critters are grown in a mixed flask. Periodically, a set volume
of medium and organism are removed and replace by fresh medium. This
type of system reaches a pseudosteady state similar to the steady state
found in a chemostat. In this study, an amotile, short (1.5 micrometer)
rod-shaped bacterium was grown with the ciliate predator Cyclidium.
Medium transfers occurred every seventh day. After 8 to 10 transfers
long bacterial cells (up to 20 micrometers) appeared in cultures which
had the ciliate. These cells lacked crosswalls. They coexisted with a
shorter morph. After appearance of the long form, the density of ciliates
in the experimental flasks declined. Feeding experiments showed that
the ciliates fed preferentially on the shorter cells.
To test whether the change in the bacterium was a genetic change, Shikano
et al. (1990) examined size distributions of cell in 30 colonies derived
from an experimental flask. The frequency distribution of sizes of the
short cells in the the flasks were indistinguishable from those in the
controls and the parental strain. The frequency distribution of sizes
for the long cells was considerably broader. The fact that daughter
colonies derived from colonies of the long cells show the same
distribution of cell lengths as the long cell colonies from the
experimental flasks suggests that this change in morphology reflects
a genetic change.
Selection for filamentous by a phagotrophic predator seems to be
common with bacteria. Pernthaler et al. (1997) reported the appearance
of a filamentous form of an unidentified member of the beta-proteobacteria
when the predatory flagellate Bodo saltans was added to a chemostat growing
a mixed bacterial assemblage. Similar filaments have been seen to appear
when E. coli is grown in a chemostat with the predatory flagellate
Poterioochromonas malhamensis (Gillott et al. 1993). Within about 5 days
nonseptate filaments as long as 100 micrometers appeared. Many were so
long that the flagellate could not completely ingest them. (Note: I have
done some feeding study work with this strain. I have videotape of
flagellates trying to engulf a long filament, pushing the filament through
itself until the whole mess looks like a gall on a goldenrod stem and
finally pushing the filament out of itself like an arrow shooting out
of a bow.) E. coli has been known to produce filaments like this as
a result of exposure to radiaion or chemical agents for a long time
(Deering 1958, Curry and Greenberg 1962, Hoffman and Frank 1963, Adler
and Hardigree 1964). The mechanism appears to be a mutation in crosswall
formation (Begg and Donachie 1985).
Nakajima and Kurihara (1994) produced a different favorable mutation in
E. coli. They grew the bacteria in a chemostat with the predatory
ciliate Tetrahymena thermophila. Within 15 days of innoculation of the
ciliates, chains of normal-sized E. coli cells appeared. This
morphological change lasted through several platings on agar. Again,
the new form provide protection against predation.
Van den Ende (1973) introduce the ciliate predator Tetrahymena
pyriformis into a chemostat containing the bacterium Klebsiella
aerogenes growing in steady state. During the period 140 hours to
200 hours following innoculation with the predator, the bacterium’s
colony morphology changed from normal mucoid appearance to a glassy
appearance. This reflected a loss of the bacterium’s mucoid capsule.
Bacteria began to adhere to the walls of the culture vessel at this
time. No wall growth was seen in the controls. The morphological
change seems to be an adaptation that allows the bacteria to utilize
the wall as a refuge from predation. This is supported by a change
van den Ende saw in the size distribution of the ciliates. At
innoculation the ciliates showed a distribution of lengths ranging
from 40 – 200 micrometers. After 800 hours in the chemostat,
few ciliates exceeded 60 micrometers in length. This appears to be
due to starvation.
In the above cases, mutations appeared which gave resistance to
predation. Mutations which confer resistance to parasites have also
been seen in studies of bacteria growing in chemostats. Varon (1979)
introduced the parasitic bacterium Bdellovibrio into a chemostat with
the luminescent bacterium Photobacterium leiognathi growing in steady
state. Within six days a new strain of the host appeared which was
resistant to attack by the parasite. This mutant coexisted in the
culture with a form similar to the original strain. Normally P.
leiognathi grows as pairs of rod-shaped cells and forms translucent
colonies. The mutant strain grows as chains of oval cells and forms
opaque colonies. Plaque assays showed that the efficiency of plating
of Bdellovibrio suspension on lawns of the mutant was at least 10^7
times lower than on the original strain or on the wild-type cells
from the culture. Examination of mixed suspension of parasite and
host using phase-contrast microscopy showed that wild type cells were
attacked immediately upon mixing by Bdellovibrio, while mutant cells
remained untouched. Batch-culture studies showed that under similar
culture conditions, the mutant strain has a much lower growth rate
than the wild-type bacterium.
This concludes what I’m going to discuss about prokaryotes. Several
conclusions seem to emerge from these studies. First, given exponential
growth and large population sizes, lots of mutations seem to occur in
bacterial populations. When bacteria under these conditions are placed
under strong selection, by means such as the introduction of a predator
or a parasite, adaptations countering the effect of the selective agent
rapidly appear and spread through the population. This could not happen
unless mutations which confer these benefits were appearing. This
must be the case when we consider that standard practice in microbiology
is to start cultures from single colonies on agar plates – colonies
which represent the descendents of a single cell. Whether the mutation
is beneficial depends on the environment that the mutant is in. In
the presence of the selective agent (e.g. a predator), the mutation is
beneficial. In a different environment the mutation may be detrimental.
A common effect of mutations conferring resistance to predators and
parasites seems to be a lowering of the maximum growth rate of the
mutant bacteria. In at least some cases (e.g. E. coli and T phages),
this results from the same mutation producing resistance and reducing
the ability to take up nutrients. In any case, the appearance of
beneficial mutations seems to occur in continuous culture in a number
of bacterial species and is probably a general phenomenon.
It is my opinion that these conclusions also apply to eukaryotes. I’ll
discuss a few examples from work here in the Counter Culture Lab to
support this assertion.
Chlorella vulgaris is a common unicellular green alga that is used as
a “lab rat” in labs throughout the world. We’ve grown the same strain
of it for thousands of generations on agar and in liquid culture without
it losing its unicellular morphology. Dozens to hundreds of labs
have done this. Steady-state unicellular C. vulgaris cultures were
innoculated with the predator Ochromonas vellesiaca, a phagotrophic
flagellate. Within less then 100 generations a multicellular form
of the Chlorella became dominanat in the culture. (Boraas 1983b, Boraas
et al. 1998). The alga first formed globose clusters of tens to
hundreds of cells. After 10-20 generations in the presence of the
flagellate, eight-celled colonies predominated. These colonies retained
the eight-celled morphology indefinitely in continuous culture and when
plated onto agar. The basis of the change appears to be a change in
the cell wall. Cell division in normal Chlorella occurs within the
cell wall of the maternal cell. The cell undergoes 1-4 divisions to
form 2-16 daughter cell. This is followed by a split in the mother
cell wall and dispersal of the neonatal cells. In a cuture, empty
mother cell walls are interspersed with whole cells at a ratio of
about 1:4. Empty mother cell walls are not found in cultures of the
multicellular form. The colonies are enclosed in a “membrane” which
appears to be modified cell wall material.
As was seen in the bacterial cases, this mutation provided Chlorella
with resistance to predation at the cost of growth rate. Neonatal
colonies are barely small enough for Ochromonas to engulf. After
they have grown slightly they are to big to be eaten. In the presence
of the predator, the colonial form of Chlorella displaces the unicellular
form and persists. When the predator is not present, the unicellular
form displaces the colonial form. This makes sense as the colonial
form has less surface area exposed to the environment available for
nutrient uptake than the unicellular form has.
There is also evidence that mutations occur and are selected for in
animals grown in chemostats and related systems. Boraas (1983a)
observed several changes the rotifer Brachionus calyciflorus when it
was grown for 24 months in a chemostat. The mean adult body size of
the animal declined steadily over time. Rotifers ceased production
of males and resting eggs after 1-2 months in continuous culture,
suggesting that the chemostat environment selected against sexual
reproduction. After 2-3 months in the sexuality could not be induced
in animals removed from the culture. They appear to have lost the
ability to undergo sexual reproduction.
Bennett and Boraas (1988, 1989) saw even more striking changes in
the same rotifer species when it was grown in a turbidostat. A
turbidostat is a variation on the chemostat. While a chemostat is
designed for constant input of medium, a turbidostat is designed to
keep the organisms at a constant concentration. A turbidity
sensor measures the concentration of organisms in the culture.
When exceeds a preset value, additional medium is added. In
Bennett and Boraas’ study, the sensor measured the concentration of
residual food (algae) in the culture (Boraas and Bennett 1988). When
it dropped below a certain level, more was added. This type of
culture system allows the organisms to grow at the maximum rate
physiologically possible in a given environment and selects for rapid
growth rate. In a chemostat, the investigator chooses the growth
rate that the critters grow at and the population density is a
response variable, in a turbidostat the investigator chooses the
population density and the critters grow as quickly as they can.
Bennett and Boraas saw the rotifers undergo several changes. The
result of the changes was a fast-growing strain of the rotifer. Over
8 months in the chemostat the maximum growth rate of the rotifers
increased from 0.053 h^(-1) to 0.080 h^(-1). This change persisted
even when the animals were grown for over 100 generations in a
chemostat at the slow growth rate of 0.009 h^(-1). There was a
shift in fecundity to younger age classes in the fast-growing strain.
Longevity of the fast-growing strain was 28% shorter than longevity
in the parental strain. Egg development time was shorter, and egg
volume was considerably smaller in the fast-growing strain. As
seen in Boraas’ (1983a) study, the adults were smaller and sexuality
was lost.
The rotifer example show changes in life history characters which
are under genetic control. These examples suggest that the
argument made for prokaryotes can be extended to eukaryotes.
Depending on the position of insertion, transposons can disrupt or alter
the expression of host genes. In some species most mutations due to
transposon insertion. For example,
in Drosophila, 50-85% of mutations are due to
transposon insertions.
Mutation Studies
by Joe Boxhorn
The material in this section is by Joe Boxhorn. It goes into
greater depth than the material in the rest of the FAQ. It
gives a good picture of how experiments are actually run. It
also gives some examples that aren’t usually seen in the popular
literature.
Culture volume 500
ml Dilution rate 1.0 per day Genome size 5,000 genes Population density 3 x 10^8 cells per ml
Mutation rate 10^(-8) mutations per gene per individual
per generation
2,000 per ml
| *
R | *
e | *
s | * *
i | * * *
s | * * * *
t | * * * * *
a | * * * * * * * * *
n | * * *
t | * * * *
| * * * * *
c | * * * * * *
e | * * * *
l | *
l | *
s |___________________________________________________________
0
0 Generations 700
(Note: this is not the actual graph. It shows the pattern of changes
that the system went through. For the actual graph see Kubitschek 1974.)
The increases and decreases reflect the occurrance of mutations within
strains in the chemostat. The initial increase in the frequency of
resistant cells occurs because a mutation occurs within a T5 resistant
strain that makes it (and its descendents) the fastest growing cells in the
culture. As long as this strain remains the fastest growing one its
representation in the population will increase. Eventually different
favorable mutation occurs in a cell that is sensitive to T5 that makes it
(and its descendents) the fastest growing cells in the culture. This
causes the frequency of T5 resistance to decline. Later a different
mutation occurs in a T5 resistant strain that makes it the fastest
growing strain. Its frequency increases, and so on.
Notes
[1] There are actually two different varieties of dark peppered moths, with the darkness being determined by different genes.
[2] There is no note [2]. See [2] for details.
[3] Proteins are the workhorse chemicals in the cell. There are two major kinds of proteins, structural proteins and enzymes. Typically an enzyme is optimized to perform a simple chemical operation on another chemical (the substrate). However it can also perform operations with much less efficiency on other substrates. A change in an enzyme often changes its efficiency on alternate substrates; it also may change the optimal conditions in which the reaction occurs, e.g. the temperature or the pH.
Diploid organisms have two copies of each gene. When a mutation in one copy occurs the organism can have alternate alleles with different properties. In some environments organisms with copies of both alleles (they are said to be heterozygous for the gene) will have an advantage.
[4] The human genome has 3 billion base pairs. The average rate of point mutations is about 20-30 in a billion per individual. Almost all point mutations in multi-cellular organisms are strictly neutral. In human beings 90-98% of the DNA is “junk DNA” that does nothing (as best as can be determined.) One third of the changes to codons (sections of DNA that code for proteins) are silent; that is, the DNA changes, but the the amino acid coded for remains the same. Thus 93-99% of all point mutations in humans are strictly neutral.
Of the remaining 1-7% almost all of them are also neutral. A typical protein is a sequence of about 350 amino acids which folds up around a reaction site consisting of about 25 amino acids. Changes in the reaction site have a strong effect on the properties of the protein; changes elsewhere often do not unless they affect the folding pattern. As a result, less than 1% of the point mutations are subject to selection. For more details seeNote 7.
[5] Johnathan Wells has written an excellent summary
article
on the peppered moth which should not be taken as being definitive.
The topic is the subject of considerable controversy. For dissenting
commentary see:
http://www.calvin.edu/archive/evolution/199904/0100.html
and
http://www.calvin.edu/archive/evolution/199904/0103.html
A more balanced and fairly complete discussion can be found at:
http://www.tulane.edu/~guill/demonstration_module.html.
[6] A trait is a physical feature of an organism. An organism’s traits
are determined by a combination of its genes and by its responses to
its environment. The effect of genes on traits is often very indirect.
[7] Most of the numbers relating to the size of the effective genome,
the number of genes, and the average size of genes are approximate
and are still being refined.
A number of genomes, both bacterial and eukaryote, have been
completely sequenced. Protein sizes average about 350 amino
acids (1050 base pairs).
Older estimates of the number of genes in the human genome fall
in the range 50-100 thousand. More recent estimates using data from
the genome project are about 60-70 thousand.
Estimates of the size of the effective genome vary. Drake gives
an estimate of 80,000,000 base pairs of coding DNA.
The number may be as low as
3% (Drake) or as high as 10% (older estimates).
The issue is complicated by the fact that some (unknown) percentage
of the non-coding DNA is not junk.
Estimating mutation rates is not simple. It should be understood
that current estimates are extrapolations from sampled sections in
genomes. Moreover mutation rates vary for different sites. Different
techniques, however, seem to consistently produce estimates of
1 to 6 point non-silent mutations in coding DNA per individual in
humans. The total number of point mutations per individual is
much higher (Drake gives ~64; other estimates are of the same order)
but, as discussed in note 4 almost all of
these are either silent or are in non-coding (junk) DNA.
[8] The percentages of occurrences of different alleles in a
population is always fluctuating because different individuals
have different numbers of offspring. In diploid species such as
ourselves there is an additional source of randomness; each offspring
gets a different combination of genes from its parents. Not only
are the percentages fluctuating, but they can by chance drift from
one ratio to another.
This random change is what is meant by genetic drift. When a
particular allele is beneficial compared to another the fluctuation
will be biased; this biased movement of the changes in ratios is
called natural selection.
[9] If we use the numbers in appendix I the effective genome size
(for humans) is about 80,000,000 base pairs and the average number
of point mutations in the effective genome is about 4. This works
out that each base pair in the effective genome will mutate about
once in every 20,000,000 individuals.
This means that in species with large populations such as human
beings (currently) every relevant point mutation appears in the
species. On the other hand, given a small group such as a
hunter/gatherer tribe, a given mutation probably will not appear
in the tribe.
[10]
Mutations per replication of germ-cell cells is a different rate from
that of mutations per conception because there are many germ-cell
divisions in an individual. Wen-Hsiung Li estimates that for humans
the number
of germ-cell divisions
per generation in females is about 33. For males it’s (a-13)*23+45
where a is the age in years of the father.
If we assume that the mutation rate in the paternal germ-cell divisions is
the same as that in the maternal germ-cell divisions then the ratio of
paternal mutations to maternal mutations would be very high. Drake et al
assumed that the ratio was large enough that it was safe to assume that
all mutations were in the sperm and to completely ignore mutations from
the mother.
This assumption appears to be false. In his studies of a particular gene
associated with Hemophilia B Li found that mutations in this particular
gene were 3.5 times more common in the sperm than in the egg. Li also
mentioned another study that estimated a ratio of 6, and a study with mice
that estimated a ratio of 2.
[11]
Spetner confuses reaction velocity with specificity. Reaction velocity
is sometimes called “specificity” in the biochemical literature, but
it depends on two separate components, catalytic efficiency (the
actual rate at which the bound substrate is converted to the product,
which has no analog in Dr. Spetners definition of information, but is
very important to biology) and affinity (how tightly the substrate is
bound to the enzyme), which is analogous to Dr. Spetners definition
of specificity.
Equally important Spetner’s identification of specifity and information
ignores broad classes of proteins. Many proteins are structural and are
not enzymes. Hormone receptors are not enzymes. Enzymes fall into two
classes, one with a narrow range of substrates and
the other with a much broader range of relevant substrates.
When we speak of the frequency of mutations we have to distinguish
between the mutation rate for the entire genome and the mutation
rate for the effective genome (the 5% that is not junk DNA).
In Genetics 148:1667-1686, April 1998) John W. Drake et al estimate
that the average human zygote has about 64 mutations, most of which
occur in “junk” DNA.
From tables 4 and 5 in “Rates of Spontaneous Mutation”, by JW Drake et al,
Genetics 148:1667-1686 (April, 1998):
Appendix I – Frequency of Mutations
Organism | effective genome size (Ge) | mutations/Ge/replication |
bacteriophage M13 | 6.4 * 10^3 | 0.0046 |
bacteriophage lambda | 4.9 * 10^4 | 0.0038 |
bacteriophages T2 & T4 | 1.7 * 10^5 | 0.0040 |
E. coli | 4.6 * 10^6 | 0.0025 |
Saccharomyces cerevisiae | 1.2 * 10^7 | 0.0027 |
Neurospora crassa | 4.2 * 10^7 | 0.0030 |
C. elegans | 1.8 * 10^7 | 0.004 |
Drosophila | 1.6 * 10^7 | 0.005 |
Mouse | 8.0 * 10^7 | 0.014 |
Human | 8.0 * 10^7 | 0.004 |
Note that for humans, the number of cell divisions prior to sperm formation in a male of age 30 is about 400. This works out to about 1.6 mutations per sperm cell. Drake assumed that almost all mutations were in the sperm; this assumption does not appear to be correct. See note 10 for further discussion.
In the 28 January 1999 issue of Nature, in the article “High genomic deleterious mutation rates in hominids” Walker and Kneightey estimate that the mutation rate in the effective genome is a bit higher, 4.2 mutations per individual, of which 1.6 are deleterious. See note 7 for further discussion.
In the Journal :Arterioscler Thromb Vasc Biol 1998 Apr;18(4):562-567
“PAI-1 plasma levels in a general population without clinical evidence of atherosclerosis: relation to environmental and genetic determinants.” ; by Margaglione M, Cappucci G, d’Addedda M, Colaizzo D, Giuliani N, Vecchione G, Mascolo G, Grandone E, Di Minno G; Unita’ di Trombosi e Aterosclerosi, IRCCS Casa Sollievo della Sofferenza, San Giovanni Rotondo (FG), Italy.
Plasminogen activator inhibitor-1 (PAI-1) plasma levels have been consistently related to a polymorphism (4G/5G) of the PAI-1 gene. The renin-angiotensin pathway plays a role in the regulation of PAI-1 plasma levels. An insertion (I)/deletion (D) polymorphism of the angiotensin-converting enzyme (ACE) gene has been related to plasma and cellular ACE levels. In 1032 employees (446 men and 586 women; 22 to 66 years old) of a hospital in southern Italy, we investigated the association between PAI-1 4G/5G and the ACE I/D gene variants and plasma PAI-1 antigen levels. None of the individuals enrolled had clinical evidence of atherosclerosis. In univariate analysis, PAI-1 levels were significantly higher in men (P<.001), alcohol drinkers (P<.001), smokers (P=.009), and homozygotes for the PAI-1 gene deletion allele (4G/4G) (P=.012). Multivariate analysis documented the independent effect on PAI-1 plasma levels of body mass index (P<.001), triglycerides (P<.001), sex (P<.001), PAI-1 4G/5G polymorphism (P=.019), smoking habit (P=.041), and ACE I/D genotype (P=.042). Thus, in addition to the markers of insulin resistance and smoking habit, gene variants of PAI-1 and ACE account for a significant portion of the between-individual variability of circulating PAI-1 antigen concentrations in a general population without clinical evidence of atherosclerosis.
J Biol Chem 1985 Dec 25;260(30):16321-5. “Apolipoprotein AIMilano. Accelerated binding and dissociation from lipids of a human apolipoprotein variant,” by Franceschini G, Vecchio G, Gianfranceschi G, Magani D, Sirtori CR.
Abstract:
The lipid binding properties of apolipoprotein (apo) AIMilano, a molecular variant of human apolipoprotein AI, characterized by the Arg173—-Cys substitution, was investigated by the use of dimyristoylphosphatidylcholine liposomes. Both the variant AIMilano and normal AI are incorporated to the same extent in stable complexes isolated by gel filtration, showing similar dimensions and stoichiometries. A higher affinity of apo-AIMilano for dimyristoylphosphatidylcholine is suggested by the faster association rate of the variant apoprotein compared to normal AI; similarly, apo-AIMilano is more readily displaced by guanidine hydrochloride from the isolated dimyristoylphosphatidylcholine- apoprotein complexes. When the secondary structure of apo-AIMilano was investigated by spectrofluoroscopy and circular dichroism, a higher fluorescence peak wavelength and a lower alpha-helical content were detected in the variant apoprotein compared to normal AI. The substitution Arg173—-Cys in the AIMilano dramatically alters the amphipathic nature of the modified alpha-helical fragment of apoprotein AI. The association rate with lipids is accelerated by an increased exposure of hydrophobic residues. The reduced stability of the lipid-apoprotein particles is possibly mediated by a reduction in the number of helical segments involved in lipid association. The high flexibility of the AIMilano apolipoprotein in the interaction with lipids may explain its accelerated catabolism and the possibly improved uptake capacities for tissue lipids.
From the abstract of a paper by JC Stephens et al (Am J Hum Genet 1998 Jun;62(6):1507-15).
“The CCR5-Delta32 deletion obliterates the CCR5 chemokine and the human immunodeficiency virus (HIV)-1 coreceptor on lymphoid cells, leading to strong resistance against HIV-1 infection and AIDS. A genotype survey of 4,166 individuals revealed a cline of CCR5-Delta32 allele frequencies of 0%-14% across Eurasia, whereas the variant is absent among native African, American Indian, and East Asian ethnic groups. Haplotype analysis of 192 Caucasian chromosomes revealed strong linkage disequilibrium between CCR5 and two microsatellite loci. By use of coalescence theory to interpret modern haplotype genealogy, we estimate the origin of the CCR5-Delta32-containing ancestral haplotype to be approximately 700 years ago, with an estimated range of 275-1,875 years. The geographic cline of CCR5-Delta32 frequencies and its recent emergence are consistent with a historic strong selective event (e.g. , an epidemic of a pathogen that, like HIV-1, utilizes CCR5), driving its frequency upward in ancestral Caucasian populations.”
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Acknowledgements
I wish to thank Larry Moran, Rich Daniel, Tedd Hadley, Allen Gathman,
Mike Coon, Robin Goodfellow, Mike Syvanen, Joe Boxhorn, Mark Isaak,
Pete Dunkelberg, and Adam Noel Harris
for helpful suggestions and comments. I also wish to give credit to
Ian Musgrave for the examples of mutations which increase specificity.
This page was last updated February 3, 2001.