We sought out to determine the optimal time to induce the E. coli in order to produce the largest quantity of antimicrobial peptides.  We created a theoretical model using MATLAB, using E. coli logistical growth combined with exponential decay (due to the antimicrobial peptide) at different induction times.  We simulated a 24 hour period and determined the optimal time to induce the cells is at mid-log (~8.5 hours) in order to maximize production of the peptide.  The graph to the right shows E. coli growth at with induction at different times.  They follow a logistic growth model until the inducer is added and then there is an exponential decay.  Overlayed with this graph is the total production of of the peptide with induction at every 3 minutes over the 24 hour period.  The MATLAB code for our model can be found <strong>Here</strong>.