Genotypes and the sampling of genotype networks. a) Genotypes are subsets of reactions in a global reaction set. Since the global set has N reactions, a genotype having n reactions can be represented by a bit string of length N with n entries equal to 1 and all others equal to 0. b) At given n, the set of viable genotypes forms a "genotype network" that is a tiny fraction of the whole space. MCMC allows one to sample that tiny fraction by generating a random walk among viable genotypes, going from one viable to another by performing a reaction swap. If a swap leads to a non-viable genotype, the walk stays at the previous genotype for that step and then the process is repeated. The advantage of using reaction swaps in our approach is that it leaves the number of reactions constant over time.