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.
Internal Medicine I, Ulm University, Robert-Koch-Strasse, 8, D-89081 Ulm, Germany.
Christian
C
Wawra
Michael
M
Kühl
Hans A
HA
Kestler
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