Mathematical Modeling and Non-linear Analysis of Synthetic and Endogeneous Gene Regulatory Networks

Gene regulatory networks are characterised by positive or negative regulatory interactions between transcription factors and their target genes: their composition allows the network to perform diff?erent functions in di?fferent contexts, thus conferring speci?fic dynamical properties to the expressed genes. Considering the single components it is possible to use mathematical models to evaluate the behaviour of the whole system, thus revealing its function and predicting its behaviour as a result of endogeneous and exogeneous stimuli. One way to characterize the single components in order to predict the function of the complete system is to describe the single parts using di?fferential equations and looking for a solution able to reproduce the measured response of the system. Here, a mathematical study on some gene regulatory network topologies is proposed, thus explaining the function of common regulatory motifs observed at molecular level, highligthing the appeareance of unexpected behaviours due to the intrinsic nonlinearities and also revealing the versatility of some of these networks in performing di?fferent actions, simply varying the behaviour of a single component. Ad-hoc constructed synthetic networks and endogeneous ones are analysed.