Computational/mathematical models for predicting phenotype from genotype
The Karr et al. paper attempts to capture most of the details in their model by combining features from the genome, transcriptome, proteome, and metabolome. This work heavily builds off of the coarse-grained models that you ask of especially on the work from Bernhard Palsson from which Markus Covert did his training. The answer to your question rests entirely on the type of question that you seek and what you want the model to do.

For the most part, most of your questions can be answered using COBRA, the COnstratins Based Reconstruction and Analysis Toolbox. You can get a good idea of what genotypes can be knocked out and see how it affects the phenotype as long as the phenotype is a known pathway that gets affected by that gene and you don't care about temporal and dynamic information.

There is also the E-Cell Project for E. coli. I personally don't know much about it but it has created some basic models for E. coli and that may be good enough.

If you want to build your own models, you should check out BiGG where all of the large-scale reconstructions exists. A good chunk of the code is stored at the Palsson lab website where you can attempt to use COBRA and start generating your own hypotheses.