Biyolojik saat modellemesi

Circadian rhythms are endogenously driven periodic oscillations of physiological, biochemical and behavioral processes within approximately 24 hours periodicity in diverse species range of orgaisms. In this thesis, we developed a detailed, predictive mathematical model for mammalian circadian clock. The concentrations of proteins are represented by ordinary differential equations, and first order mass action kinetic is assumed for every biological rate. These differential equations are solved by GAMS solver.In the first part of this thesis, we try to optimize the equations by orthogonal collocation method, which is performed by GAMS, Those equations represent mRNA concentrations of oscilatting clock genes (Pers and Crys) and they are optimized to show a circadian behavior. After obtaining the results, the profiles are compared with real time data, and it is seen that the model is accordant with empirical results.In the second part of the thesis, the aim is to knock out the genes that play role in the circadian clock mechanism. Equations, which are related to the knocked out gene, are removed from the model. Then the kinetic data set, which is obtained from the optimization, is fixed, and finally, simulation is performed. This procedure is applied for all the genes in the circadian clock. After obtaining the concentration profiles, those profiles are compared with the RT-PCR results which are found from the literature. It is seen that the model is capable of simulating the knock-out procedure.In the last part, gene dosing is performed on core clock genes. Transcriptional rate that is obtained from the optimization part is multiplied by a certain number, and the rest of the system is left with the original kinetic data set. Per1, Per2, Cry1, Cry2 genes are subjected to gene dosing and it is seen that changing the transcription rates affects the circadian clock dramatically.We built a predictive, detailed circadian model which is capable of simulating the RT-PCR concentration profiles of clock mRNAs. The most important advantage of this model is that it uses real time data, which makes the simulation biologically meaningful. Also including the post-translational modifications makes the system more realistic. The most important contribution of this study is the usage of optimization in order to find the kinetic parameters.