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Robustness in biology
Eörs Szathmáry
Collegium Budapest
Eötvös University
A genotype-phenotype model
Robustness and adaptation time
The explanation
Robustness and diversity
Drosophila melanogaster
• Each segment in the adult fly is anatomically
distinct
– Characteristic appendages
Drosophila embryonic development
• Subsequent embryonic events create clearly
visible segments
– Initially look very similar
• Some cells move to new
positions
– Organs form
• Wormlike larva hatches
– Eats, grows, & molts
Drosophila early gradients
• Bicoid gene product is concentrated at anterior
end of fly embryo
– Gradient of gene product
– Essential for setting
up anterior end of fly
• Gradients of other proteins
determine the posterior end
and the dorsal-ventral axis
Drosophila segmentation genes
• Segmentation genes
– Genes of embryo
– Expression regulated by products of eggpolarity genes
– Direct the actual formation of segments after
the embryo’s major axes are defined
Three sets of segmentation genes
• Three sets of segmentation genes are
activated sequentially
– Gap genes
– Pair-rule genes
– Segment polarity genes
• The activation of these sets of genes defines
the animal’s body plan
– Each sequential set regulates increasingly fine
details
Gap genes
• Gap genes
– Map out basic subdivisions along the embryo’s
anterior-posterior axis
– Mutations cause “gaps” in the animal’s segmentation
Pair-rule genes
• Pair-rule genes
– Define pattern in terms of pairs of segments
– Mutations result in embryos having half the normal
number of segments
Segment polarity genes
• Segment polarity genes
– Set the anterior-posterior
axis of each segment
– Mutations produce
segments where part of the
segment mirrors another
part of the same segment
The segment polarity network in
Drosophila
The differential equations
Expression pattern in vivo
The normal pattern
Crisp initial conditions
Biomathematics predicts
Without the broken
connections
With the broken connections
1192 solutions found with crips
initial conditions
Solutions found with degraded
initial conditions
The degree of robustness
Epistasis of mutations
Simulated development
Formulae
Change in gene expression
states
Fitness of a genotype in
asexual reproduction
The model
Results
Evolution without mutations
Recombination favours negative
epistasis favours sex
• Only without strong directional selection
on a particular gene expression pattern
• Mutational load is lower with
recombination AND negative epistasis
• What are the possible predictions?
Unambiguous and degenerate
The structure of the genetic code
• Amino acids in
the same column
of the genetic
code are more
related to each
other physicochemically
• „The genetic code
is one in a
million”
(Freeland &
Hurst)
Central nucleotide and amino acid
properties
Constraints on codon reshuffling
for statistical investigations
Significance of some patterns
Robustness in food webs
Connectivity
• The average
connectivity of the
neighbours of the
black node with k = 3
links is < kn > = 4.
Physical interaction between
nuclear proteins
A ‘random foodweb’
Ythan esturay foodweb
Food web patterns
Food web robustness
Statistical food web properties
Secondary extinctions resulting from primary
species loss in 16 food webs ordered by
increasing connectance (C ).
Robustness of food webs
Network structure and biodiversity loss
in food webs:
robustness increases with connectance