Simulating cellular dynamics through a coupled transcription, translation, metabolic model

In order to predict the response of a cell to changes in its surroundings or to modifications of its genetic code, the dynamics of a cell are modeled using equations of metabolism, transport, transcription and translation implemented in the Karyote software. Our methodology accounts for the organelles of eukaryotes and the specialized zones in prokaryotes by dividing the volume of the cell into discrete compartments. Each compartment exchanges mass with others either through membrane transport or with a time delay effect associated with molecular migration. Metabolic and macromolecular reactions take place in user-specified compartments. The coupling among processes is accounted for and multiple scale techniques allow for the simulation of processes that occur on a wide range of time scales. Our model is implemented to simulate the evolution of concentrations for a user-specifiable set of molecules and reactions that underlie cellular activity. The equations integrate metabolic, transcription and translation reaction networks and provide a framework for simulating whole cells given a user-specified set of reactions. A rate equation formulation is used to simulate transcription from an input DNA sequence while the resulting mRNA is used via ribosome-mediated polymerization kinetics to accomplish translation. Feedback associated with the creation of species necessary for metabolism by the mRNA and protein synthesis modifies the rates of production of factors (e.g. nucleotides and amino acids) that, in turn, affect the dynamics of transcription and translation. The concentrations of predicted proteins can be compared with time series or steady state experiments. We present the mathematical model and solution techniques for capturing the coupling of transcription, translation and metabolism in Karyote and illustrate some of its unique characteristics.