traditional genome annotation involves the enumeration of open reading frames and their functional assignment. currently, there are on-going efforts to identify all the interactions between these components. the resulting map of interactions effectively represents a 2d annotation. it takes the form of a stoichiometric matrix, if the interactions are described with chemical equations. the formulation and properties of this matrix are detailed and how it can be used as the basis for computing allowable phenotypic functions. the issues associated with the packing of the bacterial genome and the function of the interaction map in 3d will also be discussed. finally, we will go over the issue of genomes changing in space and time (4d) through adaptive evolution and describe the full re- sequencing of bacterial genomes to map all genetic changes that occur during adaptation. all of these efforts represent mathematical challenges.