Measuring gene similarity in two bacteria models

I'm currently working with some computational models of bacteria. The bacterium I am considering is an Ecoli K-12 which has 139 genes. I have several models of the same bacterium with different combinations of genes that are active. e.g. M1 - M3 are the models and G1 - G4 are the genes. 1 indicates the gene is active and 0 inactive.

M   G1 G2 G3 G4
M1  1  1   1  1
M2  1  0   1  0
M3  0  0   1  1


My assumption is that bacteria have a fixed number of chromosomes and randomly genes get activated. I intend to compute a similarity score between each pair of models (how similar two models are). I want to know what similarity means in terms of biology. Is a gene being active (1) considered a similarity or begin active and inactive (1 and 0)? For example if I compare M2 and M3 which similarity would be correct?

1. 1 similarity (only G3 is active)
2. 2 similarities (G3 is active and G2 is inactive)
• The word "bacteria" is the Latin plural of "bacterium". I have corrected this. However I find your question very difficult to understand. When you say the bacterium has 139 genes do you mean that you are considering 139 of the several thousand in E.coli? And as far as I can see, the genes are always present in the genome (which, incidentally, is a single circular chromosome), so if you modelling activity you cannot talk about present and absent, but need to use terms like "active" and "inactive". – David Apr 29 '18 at 17:52
• @David Thank you for the edit. Yes you are correct. I should have made it clearer. The model simulates only the metabolic activities in the E-coli. Therefore the genes are the ones that are related to the metabolic pathways. Also I think active and inactive should be the proper terms. – SriniShine Apr 29 '18 at 20:22
• I feel like you could look at this in terms of local and global features. In other words, sets of active/inactive genes that are part of their own module versus the overall set of active/inactive genes. You could also look at pairwise comparisons ({M1,M3} {M1,M2} {M2,M3}), or define a reference/wild-type to compare all other models against (as in differential expression, M1 vs. M2, M3... Mn). – CKM Apr 30 '18 at 14:37
• It may not be correct but if it were me, I'd look at M2 and M3 and say they are 50% similar because half the genes broadly "match". Something like "they have 2 similarities" seems odd to me. – CKM Apr 30 '18 at 14:49
• @CKM thank you for your comment. What I meant by 2 similarities is that they are 50% similar. Also I think computing the % activity is also a good idea. Thank you. – SriniShine May 1 '18 at 17:37