Robustness in biology

Eörs Szathmáry

Eötvös University Collegium Budapest

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 egg-

polarity 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 statesFitness 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 physico-chemically

• „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