This module will introduce the theory and methods for the analysis of genetic circuit models using ordinary differential equations (ODEs). In particular, it will describe the classical chemical kinetic model, numerical methods for ODE simulation of these models, and techniques to analyze these ODE models qualitatively.

This module will introduce stochastic analysis methods for genetic circuits. In particular, it will introduce the stochastic chemical kinetics model, Gillespie's Stochastic Simulation Algorithm (SSA) to analyze these models, and various alternative stochastic analysis methods. Finally, the module will conclude with some additional topics: the Chemical Langevin Equation, stochastic Petri nets, the phage lambda model, and spatial Gillespie methods.

This module presents several variations on the SSA algorithm to solve particular analysis problems. In particular, the hierarchical SSA (hSSA) methods enable the analysis of large models, the weighted SSA (wSSA) methods allow for the analysis of rare events, and the incremental SSA (iSSA) methods enable the determination of typical behaviors.

This module presents various ways that modeling can be utilized in genetic circuit design to select parts for optimal performance.