Dynamic Analysis of the Hedgehog Signalling Pathway

Abstract

In the machinery of any living organism, biological regulatory networks play an active

and crucial role, such that a commensurate understanding of their underlying dynam- ics across different clusters of genes becomes necessary, especially towards perfecting

drug therapies to combat cancer. This study focuses on the underlying dynamics, of the evolutionarily conserved Hedgehog (Hh) Pathway, which functions as a bi-stable genetic switch. The Hedgehog signaling pathway has the function of controlling the

growth, survival and fate of cells across the entire body structure and its transcrip- tion factor, Gli, has the dual function of regulating its own expression and taking

on the role of an antagonist. However, this pathway when deregulated or mutated contributes to the onset of tumorigenesis, accounting for one-third of all cancers. To

explore the different aspects of the Hedgehog Pathway, our study incorporates two dif- ferent methodologies, the Discrete and Hybrid Modelling Formalism of Ren ́e Thomas’

and the Petri Net based Formalism. These modeling formalisms are adapted to be fitted against many varieties of biological phenomena without losing internal integrity, and make it possible to simulate various aspects of the network under different posited situations and as a result, generate and validate different kinds of predictions, thereby unfolding the dynamic interplay between distinct cell fates. Our goal is to understand

the importance of the GLI auto regulatory loop and the role of its repressors, the con- ditions under which the system maintains bistability, and the configuration likely to

endow the system with homeostatic behavior. However, the results of these method- ologies correlate very well with prior studies, suggesting that the over-expression of

iv

the Gli transcription factor leads to an irreversible genetic switch and the system con- verges into a diseased state, whereas, the intermediate levels of Gli maintain oscillatory

behavior. In addition to correlating well with prior studies, this study makes some new predictions, suggesting that it is the co-expression of SMO and GLIA and the workings of its autoregulatory motif that are primarily responsible for the onset of advanced malignant stages. The GLI auto regulatory motif plays an extremely crucial role in defining system dynamics when subjected to varying threshold levels and is responsible for the irreversible genetic switch. However, by deterring its autonomous

regulatory influence on itself with the assistance of its repressors, the irreversible acti- vated GLI levels are allowed to recuperate. Moreover, Patched is primarily responsible

for inducing cyclic behavior. In addition, the results of the Petri Nets based Formal- ism set out to reveal insights about the nature and forte of crucial interactions which

are instrumental in the tight regulation and normal functioning of the pathway. Our study concludes that HIP is an ideal target that can refurbish the system with the necessary inhibition, to counter the effects of over active Hh autocrine loop and it is of great importance to understand the delicate balance between GLIR and GLIA that can prevent the system from entering into an intense self-replication perplexity. Moreover, we observe that every key protein in the pathway can be coupled with a specific repressor counterpart which has an inherent restorative scheme.