The document summarizes key points from Chapter 5 of Andreas Wagner's book on the origins of evolutionary innovations. The chapter examines how metabolic networks, regulatory circuits, and protein/RNA folds evolve under a common principle. It finds that there are typically many more possible genotypes than phenotypes for biological systems. Genotype networks, where genotypes differ by single mutations but share a phenotype, tend to be large, interconnected, and span a broad region of genotype space. This allows populations to explore the genotype space and facilitates the discovery of innovations through neutral drift.

1. Book club
Andreas Wagner,
The Origins of Evolutionary Innovations
Chapter 5
Book club presented by G. M. Dall'Olio,
Pompeu Fabra, IBE-CEXS

2. 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

3. 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?

4. 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)

5. 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..)

6. Genotypes can vary a lot,
without altering the
phenotype
 Same fold but different sequence (genotype
Distance = 1.0):
http://eterna.cmu.edu/

7. 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)

8. 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

9. 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
 ...

10. 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.

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. Intersection of genotype
networks
 Yellow → can 0....0 ….. ….. ….. ….. …..
survive on 0....1 ….. ….. ….. ….. …..
Glucose as sole 0...10 ….. ….. ….. ….. …..
0..1.0 ….. ….. …..
carbon source 0.1..0 ….. ….. …..
 Blue → can survive 0..... ….. ….. …..
on Alanine as ….. ….. …..
….. ….. …..
sole carbon
….. ….. …..
source ….. ….. ….. …..
 Green → ….. ….. ….. ….. ….. …..
intersection ….. ….. ….. ….. ….. …..
….. ….. ….. ….. ….. …..

18. 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

19. 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)

20. 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

21. 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”

22. Connectivity and broadness

23. 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

24. Genotype networks are
highly interwoven
 Yellow → can 0....0 ….. ….. ….. ….. …..
survive on 0....1 ….. ….. ….. ….. …..
Glucose as sole 0...10 ….. ….. ….. ….. …..
0..1.0 ….. ….. …..
carbon source 0.1..0 ….. ….. …..
 Blue → can survive 0..... ….. ….. …..
on Alanine as ….. ….. …..
….. ….. …..
sole carbon
….. ….. …..
source ….. ….. ….. …..
 Green → ….. ….. ….. ….. ….. …..
intersection ….. ….. ….. ….. ….. …..
….. ….. ….. ….. ….. …..

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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