Epistasis is the phenomenon where the effect of one gene (locus) is
dependent on the presence of one or more 'modifier genes', i.e. the
genetic background. Originally the term meant that the phenotypic
effect of one gene is masked by a different gene (locus). Thus,
epistatic mutations have different effects in combination than
individually. It was originally a concept from genetics but is now
used in biochemistry, computational biology and evolutionary biology.
It arises due to interactions, either between genes, or within them,
leading to non-linear effects.
Epistasis has a large influence on the
shape of evolutionary landscapes, which leads to profound consequences
for evolution and evolvability of phenotypic traits.
2.2 Magnitude epistasis
2.3 Sign epistasis
3 Genetic and molecular causes
Epistasis between genes
Epistasis within genes
3.3.1 Heterozygotic epistasis
4 Evolutionary consequences
4.1 Fitness landscapes and evolvability
Evolution of sex
5 Methods and model systems
5.1 Regression analysis
5.2 Double mutant cycles
5.3 Statistical coupling analysis
5.4 Computational prediction
6 See also
8 External links
Understanding of epistasis has changed considerably through the
history of genetics and so too has the use of the term. In early
models of natural selection devised in the early 20th century, each
gene was considered to make its own characteristic contribution to
fitness, against an average background of other genes. Some
introductory courses still teach population genetics this way. Because
of the way that the science of population genetics was developed,
evolutionary geneticists have tended to think of epistasis as the
exception. However, in general, the expression of any one allele
depends in a complicated way on many other alleles.
In classical genetics, if genes A and B are mutated, and each mutation
by itself produces a unique phenotype but the two mutations together
show the same phenotype as the gene A mutation, then gene A is
epistatic and gene B is hypostatic. For example, the gene for total
baldness is epistatic to the gene for brown hair. In this sense,
epistasis can be contrasted with genetic dominance, which is an
interaction between alleles at the same gene locus. As the study of
genetics developed, and with the advent of molecular biology,
epistasis started to be studied in relation to Quantitative Trait Loci
(QTL) and polygenic inheritance.
The effects of genes are now commonly quantifiable by assaying the
magnitude of a phenotype (e.g. height, pigmentation or growth rate) or
by biochemically assaying protein activity (e.g. binding or
catalysis). Increasingly sophisticated computational and evolutionary
biology models aim to describe the effects of epistasis on a
genome-wide scale and the consequences of this for evolution.
Since identification of epistatic pairs is challenging both
computationally and statistically, some studies try to prioritize
Quantitative trait values after two mutations either alone (Ab and aB)
or in combination (AB). Bars contained in the grey box indicate the
combined trait value under different circumstances of epistasis. Upper
panel indicates epistasis between beneficial mutations (blue).
Lower panel indicates epistasis between deleterious mutations
Since, on average, mutations are deleterious, random mutations to an
organism cause a decline in fitness. If all mutations are additive,
fitness will fall proportionally to mutation number (black line). When
deleterious mutations display negative (synergistic) epistasis, they
are more deleterious in combination than individually and so fitness
falls with the number of mutations at an increasing rate (upper, red
line). When mutations display positive (antagonistic) epistasis,
effects of mutations are less severe in combination than individually
and so fitness falls at a decreasing rate (lower, blue
Terminology about epistasis can vary between scientific fields.
Geneticists often refer to wild type and mutant alleles where the
mutation is implicitly deleterious and may talk in terms of genetic
enhancement, synthetic lethality and genetic suppressors. Conversely,
a biochemist may more frequently focus on beneficial mutations and so
explicitly state the effect of a mutation and use terms such as
reciprocal sign epistasis and compensatory mutation. Additionally,
there are differences when looking at epistasis within a single gene
(biochemistry) and epistasis within a haploid or diploid genome
(genetics). In general, epistasis is used to denote the departure from
'independence' of the effects of different genetic loci. Confusion
often arises due to the varied interpretation of 'independence' among
different branches of biology. The classifications below attempt
to cover the various terms and how they relate to one another.
Two mutations are considered to be purely additive if the effect of
the double mutation is the sum of the effects of the single mutations.
This occurs when genes do not interact with each other, for example by
acting through different metabolic pathways. Simple, additive traits
were studied early on in the history of genetics, however they are
relatively rare, with most genes exhibiting at least some level of
When the double mutation has a fitter phenotype than expected from the
effects of the two single mutations, it is referred to as positive
epistasis. Positive epistasis between beneficial mutations generates
greater improvements in function than expected. Positive
epistasis between deleterious mutations protects against the negative
effects to cause a less severe fitness drop.
Conversely, when two mutations together lead to a less fit phenotype
than expected from their effects when alone, it is called negative
epistasis. Negative epistasis between beneficial mutations
causes smaller than expected fitness improvements, whereas negative
epistasis between deleterious mutations causes greater-than-additive
Independently, when the effect on fitness of two mutations is more
radical than expected from their effects when alone, it is referred to
as synergistic epistasis. The opposite situation, when the fitness
difference of the double mutant from the wild type is smaller than
expected from the effects of the two single mutations, it is called
antagonistic epistasis. Therefore, for deleterious mutations,
negative epistasis is also synergistic, while positive epistasis is
antagonistic; conversely, for advantageous mutations, positive
epistasis is synergistic, while negative epistasis is antagonistic.
The term genetic enhancement is sometimes used when a double
(deleterious) mutant has a more severe phenotype than the additive
effects of the single mutants. Strong positive epistasis is sometimes
referred to by creationists as irreducible complexity (although most
examples are misidentified).
Sign epistasis occurs when one mutation has the opposite effect
when in the presence of another mutation. This occurs when a mutation
that is deleterious on its own can enhance the effect of a particular
beneficial mutation. For example, a large and complex brain is a
waste of energy without a range of sense organs, but sense organs are
made more useful by a large and complex brain that can better process
At its most extreme, reciprocal sign epistasis occurs when two
deleterious genes are beneficial when together. For example, producing
a toxin alone can kill a bacterium, and producing a toxin exporter
alone can waste energy, but producing both can improve fitness by
killing competing organisms.
Reciprocal sign epistasis also leads to genetic suppression whereby
two deleterious mutations are less harmful together than either one on
its own, i.e. one compensates for the other. This term can also apply
sign epistasis where the double mutant has a phenotype intermediate
between those of the single mutants, in which case the more severe
single mutant phenotype is suppressed by the other mutation or genetic
condition. For example, in a diploid organism, a hypomorphic (or
partial loss-of-function) mutant phenotype can be suppressed by
knocking out one copy of a gene that acts oppositely in the same
pathway. In this case, the second gene is described as a "dominant
suppressor" of the hypomorphic mutant; "dominant" because the effect
is seen when one wild-type copy of the suppressor gene is present
(i.e. even in a heterozygote). For most genes, the phenotype of the
heterozygous suppressor mutation by itself would be wild type (because
most genes are not haplo-insufficient), so that the double mutant
(suppressed) phenotype is intermediate between those of the single
When two mutations are viable alone but lethal in combination, it is
Synthetic lethality or unlinked non-complementation.
In a haploid organism with genotypes (at two loci) ab, Ab, aB or AB,
we can think of different forms of epistasis as affecting the
magnitude of a phenotype upon mutation individually (Ab and aB) or in
No epistasis (additive)
AB = Ab + aB + ab
Positive (synergistic) epistasis
AB > Ab + aB + ab
Negative (antagonistic) epistasis
AB < Ab + aB + ab
AB has opposite sign to Ab or aB
Reciprocal sign epistasis
AB has opposite sign to Ab and aB
Epistasis in diploid organisms is further complicated by the presence
of two copies of each gene.
Epistasis can occur between loci, but
additionally, interactions can occur between the two copies of each
locus in heterozygotes. For a two locus, two allele system, there are
eight independent types of gene interaction.
Additive A locus
Additive B locus
Dominance A locus
Dominance B locus
Additive by Additive Epistasis
Additive by Dominance Epistasis
Dominance by Additive Epistasis
Dominance by Dominance Epistasis
Genetic and molecular causes
This can be the case when multiple genes act in parallel to achieve
the same effect. For example, when an organism is in need of
phosphorus, multiple enzymes that break down different phosphorylated
components from the environment may act additively to increase the
amount of phosphorus available to the organism. However, there
inevitably comes a point where phosphorus is no longer the limiting
factor for growth and reproduction and so further improvements in
phosphorus metabolism have smaller or no effect (negative epistasis).
Some sets of mutations within genes have also been specifically found
to be additive. It is now considered that strict additivity is the
exception, rather than the rule, since most genes interact with
hundreds or thousands of other genes.
Epistasis between genes
Epistasis within the genomes of organisms occurs due to interactions
between the genes within the genome. This interaction may be direct if
the genes encode proteins that, for example, are separate components
of a multi-component protein (such as the ribosome), inhibit each
other's activity, or if the protein encoded by one gene modifies the
other (such as by phosphorylation). Alternatively the interaction may
be indirect, where the genes encode components of a metabolic pathway
or network, developmental pathway, signalling pathway or transcription
factor network. For example, the gene encoding the enzyme that
synthesizes penicillin is of no use to a fungus without the enzymes
that synthesize the necessary precursors in the metabolic pathway.
Epistasis within genes
Just as mutations in two separate genes can be non-additive if those
genes interact, mutations in two codons within a gene can be
non-additive. In genetics this is sometimes called intragenic
complementation when one deleterious mutation can be compensated for
by a second mutation within that gene. This occurs when the amino
acids within a protein interact. Due to the complexity of protein
folding and activity, additive mutations are rare.
Proteins are held in their tertiary structure by a distributed,
internal network of cooperative interactions (hydrophobic, polar and
covalent). Epistatic interactions occur whenever one mutation
alters the local environment of another residue (either by directly
contacting it, or by inducing changes in the protein structure).
For example, in a disulphide bridge, a single cysteine has no effect
on protein stability until a second is present at the correct location
at which point the two cysteines form a chemical bond which enhances
the stability of the protein. This would be observed as positive
epistasis where the double-cysteine variant had a much higher
stability than either of the single-cysteine variants. Conversely,
when deleterious mutations are introduced, proteins often exhibit
mutational robustness whereby as stabilising interactions are
destroyed the protein still functions until it reaches some stability
threshold at which point further destabilising mutations have large,
detrimental effects as the protein can no longer fold. This leads to
negative epistasis whereby mutations that have little effect alone
have a large, deleterious effect together.
In enzymes, the protein structure orients a few, key amino acids into
precise geometries to form an active site to perform chemistry.
Since these active site networks frequently require the cooperation of
multiple components, mutating any one of these components massively
compromises activity, and so mutating a second component has a
relatively minor effect on the already inactivated enzyme. For
example, removing any member of the catalytic triad of many enzymes
will reduce activity to levels low enough that the organism is no
Diploid organisms contain two copies of each gene. If these are
different (heterozygous / heteroallelic), the two different copies of
the allele may interact with each other to cause epistasis. This is
sometimes called allelic complementation, or interallelic
complementation. It may be caused by several mechanisms, for example
transvection, where an enhancer from one allele acts in trans to
activate transcription from the promoter of the second allele.
Alternately, trans-splicing of two non-functional RNA molecules may
produce a single, functional RNA. Similarly, at the protein level,
proteins that function as dimers may form a heterodimer composed of
one protein from each alternate gene and may display different
properties to the homodimer of one or both variants.
Fitness landscapes and evolvability
The top row indicates interactions between two genes that are either
additive (a), show positive epistasis (b) or reciprocal sign epistasis
(c). Below are fitness landscapes which display greater and greater
levels of global epistasis between large numbers of genes. Purely
additive interactions lead to a single smooth peak (d), as increasing
numbers of genes exhibit epistasis, the landscape becomes more rugged
(e) and when all genes interact epistatically the landscape becomes so
rugged that mutations have seemingly random effects (f).
See also: fitness landscape and evolvability
In evolutionary genetics, the sign of epistasis is usually more
significant than the magnitude of epistasis. This is because magnitude
epistasis (positive and negative) simply affects how beneficial
mutations are together, however sign epistasis affects whether
mutation combinations are beneficial or deleterious.
A fitness landscape is a representation of the fitness where all
genotypes are arranged in 2D space and the fitness of each genotype is
represented by height on a surface. It is frequently used as a visual
metaphor for understanding evolution as the process of moving uphill
from one genotype to the next, nearby, fitter genotype.
If all mutations are additive, they can be acquired in any order and
still give a continuous uphill trajectory. The landscape is perfectly
smooth, with only one peak (global maximum) and all sequences can
evolve uphill to it by the accumulation of beneficial mutations in any
order. Conversely, if mutations interact with one another by
epistasis, the fitness landscape becomes rugged as the effect of a
mutation depends on the genetic background of other mutations. At
its most extreme, interactions are so complex that the fitness is
‘uncorrelated’ with gene sequence and the topology of the
landscape is random. This is referred to as a rugged fitness landscape
and has profound implications for the evolutionary optimisation of
organisms. If mutations are deleterious in one combination but
beneficial in another, the fittest genotypes can only be accessed by
accumulating mutations in one specific order. This makes it more
likely that organisms will get stuck at local maxima in the fitness
landscape having acquired mutations in the 'wrong' order. For
example, a variant of TEM1 β-lactamase with 5 mutations is able to
cleave cefotaxime (a third generation antibiotic). However, of the
120 possible pathways to this 5-mutant variant, only 7% are accessible
to evolution as the remainder passed through fitness valleys where the
combination of mutations reduces activity. In contrast, changes in
environment (and therefore the shape of the fitness landscape) have
been shown to provide escape from local maxima. In this example,
selection in changing antibiotic environments resulted in a "gateway
mutation" which epistatically interacted in a positive manner with
other mutations along an evolutionary pathway, effectively crossing a
fitness valley. This gateway mutation alleviated the negative
epistatic interactions of other individually beneficial mutations,
allowing them to better function in concert. Complex environments or
selections may therefore bypass local maxima found in models assuming
simple positive selection.
High epistasis is usually considered a constraining factor on
evolution, and improvements in a highly epistatic trait are considered
to have lower evolvability. This is because, in any given genetic
background, very few mutations will be beneficial, even though many
mutations may need to occur to eventually improve the trait. The lack
of a smooth landscape makes it harder for evolution to access fitness
peaks. In highly rugged landscapes, fitness valleys block access to
some genes, and even if ridges exist that allow access, these may be
rare or prohibitively long. Moreover, adaptation can move proteins
into more precarious or rugged regions of the fitness landscape.
These shifting "fitness territories" may act to decelerate evolution
and could represent tradeoffs for adaptive traits.
Rugged, epistatic fitness landscapes also affect the trajectories of
evolution. When a mutation has a large number of epistatic effects,
each accumulated mutation drastically changes the set of available
beneficial mutations. Therefore, the evolutionary trajectory followed
depends highly on which early mutations were accepted. Thus, repeats
of evolution from the same starting point tend to diverge to different
local maxima rather than converge on a single global maximum as they
would in a smooth, additive landscape.
Evolution of sex
Main article: evolution of sexual reproduction
Negative epistasis and sex are thought to be intimately correlated.
Experimentally, this idea has been tested in using digital simulations
of asexual and sexual populations. Over time, sexual populations move
towards more negative epistasis, or the lowering of fitness by two
interacting alleles. It is thought that negative epistasis allows
individuals carrying the interacting deleterious mutations to be
removed from the populations efficiently. This removes those alleles
from the population, resulting in an overall more fit population. This
hypothesis was proposed by Alexey Kondrashov, and is sometimes known
as the deterministic mutation hypothesis and has also been tested
using artificial gene networks.
However, the evidence for this hypothesis has not always been
straightforward and the model proposed by Kondrashov has been
criticized for assuming mutation parameters far from real world
observations. In addition, in those tests which used artificial
gene networks, negative epistasis is only found in more densely
connected networks, whereas empirical evidence indicates that
natural gene networks are sparsely connected, and theory shows
that selection for robustness will favor more sparsely connected and
minimally complex networks.
Methods and model systems
Quantitative genetics focuses on genetic variance due to genetic
interactions. Any two locus interactions at a particular gene
frequency can be decomposed into eight independent genetic effects
using a weighted regression. In this regression, the observed two
locus genetic effects are treated as dependent variables and the
"pure" genetic effects are used as the independent variables. Because
the regression is weighted, the partitioning among the variance
components will change as a function of gene frequency. By analogy it
is possible to expand this system to three or more loci, or to
Double mutant cycles
When assaying epistasis within a gene, site-directed mutagenesis can
be used to generate the different genes, and their protein products
can be assayed (e.g. for stability or catalytic activity). This is
sometimes called a double mutant cycle and involves producing and
assaying the wild type protein, the two single mutants and the double
Epistasis is measured as the difference between the effects of
the mutations together versus the sum of their individual effects.
This can be expressed as a free energy of interaction. The same
methodology can be used to investigate the interactions between larger
sets of mutations but all combinations have to be produced and
assayed. For example, there are 120 different combinations of 5
mutations, some or all of which may show epistasis...
Statistical coupling analysis
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Numerous computational methods have been developed for the detection
and characterization of epistasis. Many of these rely on machine
learning to detect non-additive effects that might be missed by
statistical approaches such as linear regression. For example,
multifactor dimensionality reduction (MDR) was designed specifically
for nonparametric and model-free detection of combinations of genetic
variants that are predictive of a phenotype such as disease status in
human populations. Some of these approaches have been recently
Epistasis and functional genomics
Quantitative trait locus
Interactome (Genetic interaction network)
Evolution of sexual reproduction
^ Rieger, R.; Michaelis, A.; Green, M.M. (1968), A glossary of
genetics and cytogenetics: Classical and molecular, New York:
Springer-Verlag, ISBN 9780387076683 CS1 maint: Uses authors
^ Szendro, Ivan G; Schenk, Martijn F; Franke, Jasper; Krug, Joachim;
de Visser, J Arjan G M (16 January 2013). "Quantitative analyses of
empirical fitness landscapes". Journal of Statistical Mechanics:
Theory and Experiment. 2013 (01): P01005.
^ Edlund, JA; Adami, C (Spring 2004). "
Evolution of robustness in
digital organisms". Artificial Life. 10 (2): 167–79.
doi:10.1162/106454604773563595. PMID 15107229.
^ Ayati, Marzieh; Koyutürk, Mehmet (2014-01-01). "Prioritization of
Genomic Locus Pairs for Testing Epistasis". Proceedings of the 5th ACM
Conference on Bioinformatics, Computational Biology, and Health
Informatics. BCB '14. New York, NY, USA: ACM: 240–248.
doi:10.1145/2649387.2649449. ISBN 978-1-4503-2894-4.
^ Piriyapongsa, Jittima; Ngamphiw, Chumpol; Intarapanich, Apichart;
Kulawonganunchai, Supasak; Assawamakin, Anunchai; Bootchai, Chaiwat;
Shaw, Philip J.; Tongsima, Sissades (2012-12-13). "iLOCi: a SNP
interaction prioritization technique for detecting epistasis in
genome-wide association studies". BMC Genomics. 13 (Suppl 7): S2.
doi:10.1186/1471-2164-13-S7-S2. ISSN 1471-2164.
PMC 3521387 . PMID 23281813.
^ a b Phillips, PC (November 2008). "Epistasis--the essential role of
gene interactions in the structure and evolution of genetic systems".
Nature Reviews Genetics. 9 (11): 855–67. doi:10.1038/nrg2452.
PMC 2689140 . PMID 18852697.
^ a b Domingo, E; Sheldon, J; Perales, C (June 2012). "Viral
quasispecies evolution". Microbiology and molecular biology
reviews : MMBR. 76 (2): 159–216. doi:10.1128/mmbr.05023-11.
PMC 3372249 . PMID 22688811.
^ a b c Tokuriki, N; Tawfik, DS (October 2009). "Stability effects of
mutations and protein evolvability". Current Opinion in Structural
Biology. 19 (5): 596–604. doi:10.1016/j.sbi.2009.08.003.
^ a b c He, X; Qian, W; Wang, Z; Li, Y; Zhang, J (March 2010).
"Prevalent positive epistasis in Escherichia coli and Saccharomyces
cerevisiae metabolic networks". Nature Genetics. 42 (3): 272–6.
doi:10.1038/ng.524. PMC 2837480 . PMID 20101242.
^ Ridley M (2004) Evolution, 3rd edition. Blackwell Publishing.
^ a b Charlesworth B, Charlesworth D (2010) Elements of Evolutionary
Genetics. Roberts and Company Publishers.
^ Ortlund, EA; Bridgham, JT; Redinbo, MR; Thornton, JW (Sep 14, 2007).
"Crystal structure of an ancient protein: evolution by conformational
epistasis". Science. 317 (5844): 1544–8.
doi:10.1126/science.1142819. PMC 2519897 .
^ a b Cordell, Heather J. (2002). "Epistasis: what it means, what it
doesn't mean, and statistical methods to detect it in humans". Human
Molecular Genetics. 11 (20): 2463–8. doi:10.1093/hmg/11.20.2463.
^ a b c Kauffman, Stuart A. (1993). The origins of order :
self-organization and selection in evolution ([Repr.]. ed.). New York:
Oxford University Press. ISBN 0195079515.
^ a b Bornscheuer, U. T.; Huisman, G. W.; Kazlauskas, R. J.; Lutz, S.;
Moore, J. C.; Robins, K. (9 May 2012). "Engineering the third wave of
biocatalysis". Nature. 485 (7397): 185–194. doi:10.1038/nature11117.
^ a b c Azevedo R, Lohaus R, Srinivasan S, Dang K, Burch C (2006).
"Sexual reproduction selects for robustness and negative epistasis in
artificial gene networks". Nature. 440 (7080): 87–90.
doi:10.1038/nature04488. PMID 16511495.
^ Bonhoeffer S, Chappey C, Parkin NT, Whitcomb JM, Petropoulos CJ
(2004). "Evidence for positive epistasis in HIV-1". Science. 306
(5701): 1547–50. doi:10.1126/science.1101786.
^ Weinreich, Daniel M.; Watson, Richard A.; Chao, Lin (June 2005).
Epistasis and Genetic Constraint on Evolutionary
Trajectories". Evolution. 59 (6): 1165–1174.
doi:10.1111/j.0014-3820.2005.tb01768.x. JSTOR 3448895.
^ Poelwijk, Frank J.; Kiviet, Daniel J.; Weinreich, Daniel M.; Tans,
Sander J. (January 2007). "Empirical fitness landscapes reveal
accessible evolutionary paths". Nature. 445 (7126): 383–386.
doi:10.1038/nature05451. PMID 17251971.
"Synthetic Lethal Mutations." Retrieved on 2010-01-27.
^ Lunzer, M; Miller, SP; Felsheim, R; Dean, AM (Oct 21, 2005). "The
biochemical architecture of an ancient adaptive landscape". Science.
310 (5747): 499–501. doi:10.1126/science.1115649.
^ Shakhnovich, BE; Deeds, E; Delisi, C; Shakhnovich, E (Mar 2005).
"Protein structure and evolutionary history determine sequence space
Genome Research. 15 (3): 385–92. doi:10.1101/gr.3133605.
PMC 551565 . PMID 15741509.
^ Harms, MJ; Thornton, JW (Aug 2013). "Evolutionary biochemistry:
revealing the historical and physical causes of protein properties".
Nature Reviews Genetics. 14 (8): 559–71. doi:10.1038/nrg3540.
PMC 4418793 . PMID 23864121.
^ Witt, D. (2008). "Recent developments in disulfide bond formation".
Synthesis. 2008 (16): 2491–2509. doi:10.1055/s-2008-1067188.
^ Bershtein, S; Segal, M; Bekerman, R; Tokuriki, N; Tawfik, DS (Dec
14, 2006). "Robustness-epistasis link shapes the fitness landscape of
a randomly drifting protein". Nature. 444 (7121): 929–32.
doi:10.1038/nature05385. PMID 17122770.
^ a b c Steinberg, Barrett; Ostermeier, Marc (2016-01-01).
"Environmental changes bridge evolutionary valleys". Science Advances.
2 (1): e1500921. doi:10.1126/sciadv.1500921. ISSN 2375-2548.
PMC 4737206 . PMID 26844293.
^ Halabi, N; Rivoire, O; Leibler, S; Ranganathan, R (Aug 21, 2009).
"Protein sectors: evolutionary units of three-dimensional structure".
Cell. 138 (4): 774–86. doi:10.1016/j.cell.2009.07.038.
PMC 3210731 . PMID 19703402.
^ Neet, KE; Koshland DE, Jr (Nov 1966). "The conversion of serine at
the active site of subtilisin to cysteine: a "chemical mutation"".
Proceedings of the National Academy of Sciences of the United States
of America. 56 (5): 1606–11. doi:10.1073/pnas.56.5.1606.
PMC 220044 . PMID 5230319.
^ Beveridge, AJ (Jul 1996). "A theoretical study of the active sites
of papain and S195C rat trypsin: implications for the low reactivity
of mutant serine proteinases". Protein Sci. 5 (7): 1355–65.
doi:10.1002/pro.5560050714. PMC 2143470 .
^ Sigal, IS; Harwood, BG; Arentzen, R (Dec 1982).
"Thiol-beta-lactamase: replacement of the active-site serine of RTEM
beta-lactamase by a cysteine residue". Proceedings of the National
Academy of Sciences of the United States of America. 79 (23):
7157–60. doi:10.1073/pnas.79.23.7157. PMC 347297 .
^ Phillips PC (November 2008). "Epistasis--the essential role of gene
interactions in the structure and evolution of genetic systems". Nat.
Rev. Genet. 9 (11): 855–67. doi:10.1038/nrg2452.
PMC 2689140 . PMID 18852697.
^ Poelwijk, Frank J.; Tănase-Nicola, Sorin; Kiviet, Daniel J.; Tans,
Sander J. (March 2011). "Reciprocal sign epistasis is a necessary
condition for multi-peaked fitness landscapes". Journal of Theoretical
Biology. 272 (1): 141–144. doi:10.1016/j.jtbi.2010.12.015.
^ Reetz, MT; Sanchis, J (Sep 22, 2008). "Constructing and analyzing
the fitness landscape of an experimental evolutionary process".
Chembiochem : a European journal of chemical biology. 9 (14):
2260–7. doi:10.1002/cbic.200800371. PMID 18712749.
^ Weinreich, DM; Delaney, NF; Depristo, MA; Hartl, DL (Apr 7, 2006).
"Darwinian evolution can follow only very few mutational paths to
fitter proteins". Science. 312 (5770): 111–4.
doi:10.1126/science.1123539. PMID 16601193.
^ Gong, LI; Suchard, MA; Bloom, JD (2013). "Stability-mediated
epistasis constrains the evolution of an influenza protein". eLife. 2:
e00631. doi:10.7554/eLife.00631. PMC 3654441 .
^ Steinberg, Barrett; Ostermeier, Marc. "Shifting fitness and
epistatic landscapes reflect tradeoffs along an evolutionary pathway".
Journal of Molecular Biology. 428: 2730–2743.
^ Lobkovsky, AE; Wolf, YI; Koonin, EV (Dec 2011). "Predictability of
evolutionary trajectories in fitness landscapes". PLOS Computational
Biology. 7 (12): e1002302. doi:10.1371/journal.pcbi.1002302.
PMC 3240586 . PMID 22194675.
^ Bridgham, JT; Ortlund, EA; Thornton, JW (Sep 24, 2009). "An
epistatic ratchet constrains the direction of glucocorticoid receptor
evolution". Nature. 461 (7263): 515–9. doi:10.1038/nature08249.
^ A. S. Kondrashov (1988). "Deleterious mutations and the evolution of
sexual reproduction". Nature. 336 (6198): 435–440.
doi:10.1038/336435a0. PMID 3057385.
^ MacCarthy T, Bergman A (July 2007). "Coevolution of robustness,
epistasis, and recombination favors asexual reproduction". Proc Natl
Acad Sci U S A. 104 (31): 12801–6. doi:10.1073/pnas.0705455104.
PMC 1931480 . PMID 17646644.
^ a b Leclerc R. (August 2008). "Survival of the sparsest: robust gene
networks are parsimonious". Mol Syst Biol. 4 (213): 213.
doi:10.1038/msb.2008.52. PMC 2538912 .
^ Wade, MJ; Goodnight, CJ (Apr 2006). "Cyto-nuclear epistasis:
two-locus random genetic drift in hermaphroditic and dioecious
species". Evolution; international journal of organic evolution. 60
(4): 643–59. doi:10.1554/05-019.1. PMID 16739448.
^ Horovitz, A (1996). "Double-mutant cycles: a powerful tool for
analyzing protein structure and function". Folding & Design. 1
(6): R121–6. doi:10.1016/s1359-0278(96)00056-9.
^ Moore, Jason H.; Andrews, Peter C. (2015-01-01). "
using multifactor dimensionality reduction". Methods in Molecular
Biology (Clifton, N.J.). 1253: 301–314.
doi:10.1007/978-1-4939-2155-3_16. ISSN 1940-6029.
^ Cordell, Heather J. (2009-06-01). "Detecting gene-gene interactions
that underlie human diseases". Nature Reviews. Genetics. 10 (6):
392–404. doi:10.1038/nrg2579. ISSN 1471-0064.
PMC 2872761 . PMID 19434077.
Epistasis - Methods and Protocols Jason H. Moore Springer.
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INTERSNP - a software for genome-wide interaction analysis (GWIA) of
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The development of phenotype
Norms of reaction
Fitness landscape/evolutionary landscape
Dual inheritance theory
Evolution of genetic systems
Evolution of sexual reproduction
Control of development
Regulation of gene expression
Gene regulatory network
Evolutionary developmental biology
Hedgehog signaling pathway
Notch signaling pathway
Cell surface receptor
C. H. Waddington
François Jacob + Jacques Monod
Eric F. Wieschaus
Sean B. Carroll
Endless Forms Most Beautiful
Nature versus nurture
Index of evolutionar