Model Level 1: Gene Network Model
July 11, 2007

We decided to put the work on the gene network model on hold because the model is very complex and difficult to accurately construct and its impact on the overall results is questionable. Thus we are focusing our attention on other more vital aspects of the project for now and will hopefully return to working on this model towards the end of the summer if time permits.

Model Level 2: Infection Model
July 11, 2007

Here is our model:

Reaction [rate constant]
Rxn_1: B + P --> I1 [200]
Rxn_2: I1 + P --> I2 [200]
Rxn_3: I2 + P --> I3 [200]
Rxn_4: I1 --> L [6.667000e-002]
Rxn_5: I1 --> K [6.000000e-001]
Rxn_6: I2 --> L [6.667000e-002]
Rxn_7: I2 --> K [1.555600e-001]
Rxn_8: I3 --> L [6.667000e-002]
Rxn_9: I3 --> K [6.667000e-002]
Rxn_10: K --> 100P [2.500000e-002]
Rxn_11: B + FA --> 2B [5.000000e-002]
Rxn_12: L + FA --> 2L [5.000000e-002]
Rxn_13: FT --> FA [5.000000e-002]

Initial Values
B=10000
P=100
FT=1.000000e+006

B represents uninfected bacteria, P represents phage virus, I is an intermediate stage, K represents lytic, L represents lysogenic, and FT and FA are food. The first reaction represents a phage virus infecting a bacterial cell. When the cell becomes infected, it can either turn lytic (a mass of phage viruses are replicated inside the cell and released by bursting the cell) or lysogenic (the phage stays dormant in the cell). This decision, to choose between lytic and lysogenic, is based on environmental factors surrounding the bacterial cell. If there are a surfeit of phage viruses in the environment, the infecting phage has a high probability of becoming lysogenic; however, if there is a scarcity of phage viruses surrounding the bacterial cell, there is a high probability that the phage will become lytic. The intermediate I is used as a reaction to set these probabilities. The growth of the bacteria and lysogenic cells are limited by available food. This is done so that the cells don't grow unhindered.

Observing the reactions in action:

As the phage (P) infects the uninfected bacteria (B) the amount of uninfected cells decline and number of lysogenic (L) and lytic (K) cells increase. As the lytic cells burst and release phage into the environment, the number of lytic gradually decline and the number of phage quickly increase.