| The survival of cells depends on the highly coordinated action of a great number and variety of proteins. The efficient execution of cellular processes requires that the protein synthesis machinery operate with great precision. Understanding the process of protein synthesis in the context of gene regulatory networks is essential for comprehending the operation of all living organisms. Mathematical models of gene regulatory networks must consider the essential mechanistic details of the molecular processes involved in order to make reliable predictions. However, even though the description of the processes becomes more accurate as more mechanistic details are incorporated into the mathematical model, the added mathematical complexity makes it difficult to parameterize and extract information from such models given the limited amount of experimental data.;As a first objective, we first develop a methodology to reduce a mechanistic model of protein synthesis that considers mRNA concentrations fixed in time into a time-delay model by performing systematic approximations, retaining the essential details of the process. Our reduction provides a systematic mapping between the original parameters of the mechanistic model and all of the parameters in our time-delay model. Hence, our time-delay model may be parametrized with no need of parameter fitting.;As a second objective, we extend the previously mentioned mechanistic model of protein translation and formulate three mechanistic models that include mRNA degradation, corresponding to the three main molecular mechanisms that have been proposed for message decay. We perform systematic comparisons of the three models, in order to identify the distinguishing features of each decay mode.;In our third and final objective, we apply the reduction methodology that we devised previously, and formulate a time-delay model of protein translation that includes mRNA degradation. Our model reduction provides an insightful conceptual picture of the translation process and opens up the possibility of using powerful mathematical techniques, such as bifurcation analysis, to understand the complex dynamics displayed by genetic networks. We then apply our time-delay model of translation and mRNA degradation to the analysis of a self-repressing gene and use bifurcation analysis to understand the complex dynamics displayed by this network. Our analysis provides new insight into the operation of this genetic circuit and supplies design guidelines to be used in synthetic biology. The studies that we carry out with our time-delay model would not be practical using large-scale mechanistic models. |
