Extended analyses of the Wnt/beta-catenin pathway: robustness and oscillatory behaviour.
The Wnt/beta-catenin signalling pathway is evolutionarily conserved across many species and plays important roles during embryogenesis. The Lee-Heinrich model (to recognize the contributions of R. Heinrich we will refer to the work proposed by Lee et al. [Lee, E., Salic, A., Krüger, R., Heinrich, R., Kirschner, M.W. (2003) The roles of APC and axin derived from experimental and theoretical analysis of the Wnt pathway. PloS Biol. 1, 116-132] as the Lee-Heinrich model) describes this pathway by use of coupled ordinary differential equations. Here, we extend this model by introducing negative feedback loops of the pathway using time-delay differential equations. Single- and multiple-parameter perturbations suggest a very robust behaviour of this pathway that can also demonstrate oscillatory behaviour. These findings are of biological significance as Wnt pathway components show oscillations during vertebrate somitogenesis.
Wawra
Christian
C
Internal Medicine I, Ulm University, Robert-Koch-Strasse, 8, D-89081 Ulm, Germany.
Kühl
Michael
M
Kestler
Hans A
HA
D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D008954:Models, Biological; D038081:Organogenesis / Q000502:physiology; D015398:Signal Transduction / Q000502:physiology*; D019170:Somites / Q000378:metabolism*; D014714:Vertebrates / Q000196:embryology; D051153:Wnt Proteins / Q000378:metabolism*; D051176:beta Catenin / Q000378:metabolism*
D051153:Wnt Proteins; D051176:beta Catenin