Wagner chapter 5
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Transcript of Wagner chapter 5
Book club
Andreas Wagner,The Origins of Evolutionary Innovations
Chapter 5
Book club presented by G. M. Dall'Olio, Pompeu Fabra, IBE-CEXS
Reminder:Genotype network
A genotype network is a set of genotypes that have the same phenotype, and are connected by single pairwise differences
Green = same phenotype = a genotype network Note: genotype network == neutral network
Chapter 5:The Origins of Evolutionary
Innovations This chapter makes some conclusions from the 4
preceding chapters Under which common principle do metabolic
networks, regulatory circuits and protein/RNA folds evolve?
Which are the basics of a theory of Innovation?
Many more genotypes than phenotypes
Metabolic networks: 2 ^ S genotypes (S: number of known reactions) 2 ^ C phenotypes (C: number of carbon sources)
Regulatory Networks: 3 ^ N ^ 2 genotypes (3: activation, repression, no
interaction; N: number of reactions) 2 ^ S phenotypes (S: number of genes)
Protein molecules: 20 ^ S genotypes (S: length of sequence) 10 ^ 4 phenotypes (lattice protein folds)
Genotypes can vary a lot, without altering the
phenotype In metabolic networks, organisms can differ for
75% of reactions, but still have the same phenotype
Some regulatory circuits can be completely different but still have the same functions (examples of GAL4 in C.albicans/S.cerevisiae, etc..)
Proteins with different sequences can have the same fold (e.g. globins, etc..)
Genotypes can vary a lot, without altering the
phenotype Same fold but different sequence (genotype
Distance = 1.0):
http://eterna.cmu.edu/
The same phenotype can be achieved by many
genotypes A corollary of the previous two slides is that the
same phenotype can be achieved by many genotypes
Why should a phenotype be reachable by more than one genotype? (open question)
Robustness of a genotype network
The robustness of a biological system is its ability to withstand changes without altering the phenotype
Not only within a genotype network. It is also important that the neighbors of points in a genotype network have “neutral” phenotypes
e.g. the neighbor of a genotype must be viable
The genotype-phenotype function
The genotypephenotype function is a function that allows to predict the phenotype of certain genotype
Flux balance analysis in metabolic networks Structure prediction in sequence networks ...
Definitions: The Genotype-Phenotype-Map
The method of representing all genotypes as a Hamming graph and defining neutral networks is also called “GenotypePhenotypeMap”
I am not sure about who invented the method, but it is well described in [1]
[1] Stadler, B.M. et al., 2001. The topology of the possible: formal spaces underlying patterns of evolutionary change. Journal of theoretical biology, 213(2), pp.241-74.
The genotype space is huge
For a protein of length 10, there are 20^10 possible sequences
It is difficult for humans to imagine how much the genotype space is big
Big genotype networks can be still small compared to
the genotype space A given RNA structure can be generated by
5*10^22 sequences Yet, this is only a tiny fraction of the genotype
space
Big genotype networks are favored by evolution
Imagine that a given biological function can be carried out by two different phenotypes:
Phenotype 1 has a big genotype network Phenotype 2 has a small genotype network
Selection will be more likely to find Phenotype 1, just because there are more genotypes that produce it
Small and big genotype networks
The two purple phenotypes have a selective advantage over white ones
However, evolution is more likely to find the light phenotype, because its genotype network is bigger
Phenotypes with small genotype networks can be
important We said that big genotype networks are more likely
to be found by evolution However, in nature we can observe phenotypes
with small genotype networks
Phenotypes involved in multiple functions can still
have big genotype networks Some systems can carry out more than one
biological function For example, many metabolisms can survive on both
glucose and mannose
The genotype network of these systems would be the intersection of the genotype networks that carry each of the functions
Yet, these genotype networks are still big
Intersection of genotype networks
Yellow can →survive on Glucose as sole carbon source
Blue can survive →on Alanine as sole carbon source
Green →intersection
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Connectivity and broadness of genotype networks
Two important properties of genotype networks are the connectivity and the broadness
These two properties are important in the search for innovations
A poorly connected genotype set
Fig a shows a set of notconnected genotype networks
They all have the same phenotype, but are not connected
In this situation, populations can not explore the genotype space efficiently, because they don't have a way to “jump” between genotype networks
(recombination and chromosomal arrangements will be discussed later)
A well connected but localized genotype network
Fig b shows a well connected genotype network
However, this network is clustered, and all its nodes are close
It is difficult for a population to find Innovations, because there is no way to get close to them
A connected and broad genotype network
Fig c represents a well connected and broad genotype network
This is the ideal situation for finding innovations
A population can explore the genotype space without having to “jump”
Connectivity and broadness
Genotype networks are highly interwoven
Genotype networks are usually close in the space Many organisms can survive on multiple carbon
sources It is possible to convert RNA structures by changing
few aminoacids
Genotype networks are highly interwoven
Yellow can →survive on Glucose as sole carbon source
Blue can survive →on Alanine as sole carbon source
Green →intersection
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The theory of innovation
In this chapter, Wagner formalizes the framework of “genotypephenotypemaps” for studying how innovations can be found
It also describe some important properties that a system must have in order to reach innovations
The theory of Innovations
Innovation is combinatorial in nature Genotypephenotypemaps allow to explore the
nature of innovations
Genotypes have many neighbors with the same phenotype
Many or all genotypes with the same phenotype are connected in genotype networks
The theory of Innovations
Genotype networks of different phenotypes are different in size
Typical genotype networks traverse a large part of genotype space
Different neighborhoods of a genotype network contain different phenotypes
Pros of this theory of innovation
Genotype networks can explain how population explore the genotype space, without altering the phenotype
This framework is valid for metabolic networks, regulatory circuits and sequences
Captures the combinatorial nature of innovation It allows to simulate that a problem can be solved
through different solutions e.g. different metabolic networks can survive on
glucose
Cons of this theory of Innovation
Difficult to get to phenotypes that are highly innovative, but have a tiny genotype network
Difficult to study systems where genotype networks are not connected or localized
The method doesn't work if there are more phenotypes than genotypes (phenotipic plasticity)
Immunity systems tend to have more phenotypes than genotypes
Take Home messages
We have seen some properties that are common for the evolution of metabolic networks, regulatory circuits and sequences
The framework of genotypephenotypemaps can be used to explore how innovations are found
There are many more genotypes than phenotypes A common property of the systems studied in the
previous chapters is that there are more genotypes than phenotypes