Constraint Based Flux Analysis is a mathematical way of representing biological system information and allows for easy manipulation of this data. It is based on a stoichiometric matrix of reactions which correspond to individual enzymatic or transport reactions which have been characterized inside of the organism. In other words, it computationally represents each reaction using a linear array of numbers (see Figure 1).

The flux can be defined as the amount of substrate moving to product for each individual reaction. The model assumes that the system is at steady state therefore, the overall flux is zero since each product becomes a substrate of another reaction. All substrates entering the system will have the same amount leaving the system. The products leaving the system can be removed by changing the boundary condition of the compound (that is making it unavailable to the system) or by using it to produce growth of the organism. A master growth equation determines which products are required for the cell to grow and this represented in units of DW/unit time. Systems Biology Markup Language (SBML) and the Cobra Toolbox (both produced from System’s Biology Research Group) allows for flux analysis to be performed in the MATLAB program.

We can perform single gene knockouts in the e. coli metabolic gene model and determine the resulting growth rate. Knockouts that result in a growth rate of approximately zero are put in a list for the researcher to study later. Deletion of any one of these genes will result in no growth. These genes are clearly essential.

FindEssentials.m

The Cobra Toolbox makes this single gene deletion analysis for every gene very easy. We found 187 of the model's genes to be essential with this code.

After enriching the in silico media with various substances (MediaChange.m), the code was run again, and a list of 112 genes resulted. Clearly, enriching the media relieves some genes of their function, perhaps by allowing the bypassing of a reaction catalyzed by a protein coded for by that gene. Comparing this list 112 genes to our previously complied list of researched literature essential genes, we found many differences which we found to be very helpful. Many of these missing genes were added to our master list of essential genes.

Obviously, since the code only analyses single gene deletions, the e. coli cell would not survive with just these 112 genes (these 112 genes are not the minimal genome). Multiple gene deletions were not taken into account. For instance, consider 2 genes that at first appear unessential. When one is knocked out, the cell lives. When the other is knocked out, the cell lives. But lets say that once both in the pair of genes is deleted, the cell dies. The single gene deletion analysis would not detect this.

Another code was written to find out how many pair of genes are essentially entangled in this way. We found that there are 81 of these pairs in the model (assuming glucose minimal media). To validate this model's claim of paired essentiality, we performed single and double gene knockouts in the lab for these essential pairs. See the Model Validation section for details.

It was our goal to find the model's minimal genome. It is clear that single gene knockout analysis would not suffice. Since performing every possible combination of multiple gene knockouts in the model would take most computers many years to accomplish, a different strategy was taken.

FindMinimalGenome.m

Start.m - this will set the solver to glpk (a way of solving the vast amounts of matrix equations), and load in the model that the researcher will be working with.

FindEssentials.m - Uses single gene deletion analysis to find a list of essential genes. A deletion of just one of these genes will cause cell death.

CheckForRepeats.m - Checks for repeats in a gene list (and can also remove the repeats if wanted). We use this to check our imported list (our researched literature essential gene list).

InvertList.m - "Inverts" the input List1 with respect to the input List2. The output is a list of genes in List2 that did not appear in List1. We use this to find the genes in our imported literature list that we would be deleting from the model. This helps us analyze the effects of deleting genes that we previously thought to be inessential.

FindMatches.m - Finds the matches between two lists of genes. We use this to compare our researched literature essential genes with our model's predicted essential genes. It outputs the number of matches and the list of matches.

MediaChange.m - We could reduce the amount of genes that were essential by changing the in silico media. We added to the glucose minimal media:

20 Standard Amino Acids Adenosine, Guanosine, Uridine, Thymidine, Cytidine Thiamine Pantothenic Acid Xylose Shikimate NMN Meso Diaminopimelic Acid Biotin

FindMinimalGenome.m - This is the code that finds the model's minimal genome(s) through iterative semi-random multiple gene deletions. Because of the fact that many genes code for the same reaction, many reactions perform the same function, and that one gene may control a few reactions, there are easily thousands of potential minimal genomes. This code finds many of them. We are not necessarily interested in the smallest minimal genome; we want to use the resulting lists to gain a better understanding of what genes should be included in an actual minimal genome that could be created in a real lab environment. You can specify the number of minimal genomes you want (the more you specify, the longer it will take). You can also specify the final growth rate wanted, and 2 other factors relating to how the algorithm is carried out which will affect the time it takes, and how small the minimal genomes will be. It outputs an array of minimal genome lists, and can also output the list of genes that are deleted for each minimal genome.

MaxMinAvg.m - This is a simple code which lets the user know the largest minimal genome, the smallest minimal genome, and the average size of the minimal genomes created in the FindMinimalGenome.m code. It can be used on other gene lists (for instance, on an array of gene lists that represent what genes are missing from the researched literature list with respect to each minimal genome found).

InvertListArray.m - "Inverts" input1 with respect to every gene list in input2. input2 may include any number of gene lists. This code is typically used when comparing your researched literature gene list with each of the model's minimal genome lists (produced by FindMinimalGenome).

FindMatchesArray.m - Typically only used with the array of minimal genomes and the researched literature essential genes. Outputs a list of matches for every minimal genome creating the output MatchListArray. The code also outputs the number of matches for each list and the position of the smallest difference between the model's minimal genome and your designed minimal genome (designed from research/literature). This is very helpful when trying to find what genes you are missing in your researched literature essential genes list when comparing them with the many minimal genomes produced by our code.

CellToMatrix.m - Code that makes it more convenient for you to copy and paste the array of lists into Excel. Without this step, you'd have to copy and paste the hundreds of unique minimal genome lists one at a time.