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Robustness and genetic networks Eörs Szathmáry Collegium Budapest Eötvös University Selected members of five gene classes • Only one segment polarity gene is shown • Most of the proteins are transcriptional activators Some regulatory interactions that esablishing gap gene expression • Krüppel is expressed in the grey region • Bicoid is an activator • Hunchback and giant are repressors • Inelegant mechanism! Cooperativity in biomolecule activity • The degree of cooperativity can be measured by the Hill coefficient: the slope at inflection point • Common in transcriptional regulation and ligandreceptor interactions Expression of segment-polarity genes in the embryo • Pair rule gene expression patterns regulate engrailed and wingless expression • 14 parasegments are thus formed at en/wg boundaries • True segment boundaries are displaced one cell to the right of the parasegment boundaries A model for the maintenance of segment polarity gene expression • Gene expression patterns (black in a) • Part of the segment polarity network (lowercase: genes, uppercase: gene products) • Each cell has one such network Space of functional segment polarity networks • 22 parameters out of 48 are shown • Gray polygons yield functional networks • Kxy: concentration of X at which activity of y is half maximal, etc.. • Mean and standard variation for polygons are shown Some insights • Extremely robust to variation in individual parameters • Also against change in netwok topology • Robust against change in concentration also A theoretical treatment Si (t jwijSj (t )) • Let us borrow a model from neural networks • Only two states: on and off • Activators and inhibitors influence the weight • Switch-like cooperativity • 60% of random changes gives the same expression pattern • One can select for networks with even higher robustness Dorsal view of the Drosophila wing • Heat-shock treatment induces the disappearance of cross-veins • One can select for or against this sensitivity • Genetic assimilation: some show the phenotype without the inducer! • Does not work with inbred lines Incidence of Hsp90-induced eye deformities • Hsp90 associates with signal-transduction molecules • Lines can be selected for tolerance of mutation of Hsp90 Many ways of building the same body: the sea urchin Larvae can be very different • Feeding pluteus (a) • A non-feeding larva (b) • Direct development (c) Evolution of developmental modes • Black bars: direct development • Most adult forms are conserved • Ecological correlates: direct development no dispersal, large eggs