I'm doing my PhD in Systems Biology. Here we use a lot of software to model cell activities. If your system is small (which would mostly be the case with synthetic genes), you can use COPASI. For more complicated systems, software like MATLAB and Mathematica can be used.
MATLAB and Mathematica are not free but COPASI can be used for free (check the link) and COPASI is also user-friendly. I work mainly with Mathematica but I've some experience with COPASI. So, if you have issues I may be able to help you.
Hope that was helpful.