Motivation
Evolutionary instability is an inherent flaw in any biological control using a lethal effect to control environmental growth. Microorganisms rapidly evolve to remove any genetic element that reduces fitness Knudsen and Karlstrom, 1991 Molin et al., 1993. Although we have designed a kill switch, most evolve to lose functionality within days, or have no data supporting their longevity Caliendo and Voigt, 2015. This begs the need for a multi-layered safety mechanism where, even with the mutational loss of the kill switch the chassis is still contained within the system.
In our case, the E. coli have to be contained within the sugarcane system. We chose auxotrophy as a preventative measure of biocontainment due to its ease of implementation and verification.
Twenty three amino acids have been detected in cane juice. When the supply of nitrogen is increased due to the application of fertilisers, it is observed that the neutral and acidic amino acids tend to increase and then decrease with increasing nitrogen supply. Consequently there is a less marked increase in basic amino acids, keeping their concentrations almost constant throughout Vinall et al., 2012
We attempted to create a double auxotroph of arginine and lysine, the rationale being that more stringent and tunable growth characteristics could be achieved with a double auxotroph over a single auxotroph system. Our model attempts to predict the growth kinetics of dual auxotrophic E. coli, auxotrophic to both Arginine and Lysine. Based on our literature review and inspiration from iGEM British Columbia’s 2012 auxotroph model, our mathematical model is based on Monod Kinetics.
The Monod equation is used to model the growth of microorganisms in aqueous environments. There is a major assumption made for this equation to be used, that is, the growth rates are dependent on the concentration of the limiting nutrient. The constants and variables in this equation are usually the specific growth rate \( \mu_g \), which is measured from experiments; the maximum growth rate \(\mu_m \), which is also measured from experiment; the saturation constant or the half-velocity constant, \( K_S \); and the concentration of the limiting substrate \(S \), which is the independent variable. The Monod equation is written as $$ \mu_g = \frac{\mu_m S}{K_S + S} $$
Therefore, the growth equation for the bacteria in would be $$ \frac{dOD}{dt} = \frac{\mu_m S}{K_S + S} OD $$
Bertels et al. 2012 have plotted the specific growth rate of different amino acids. From this graph we realised that the impact of lysine concentrations on specific growth rate far outweighs the impact of changes in arginine since the specific growth rate of lysine is greater than specific growth rate of arginine. The tunability of the growth of our chassis will depend on the concentration of lysine.
Figure 1: Time-dependent growth of the bacteria in the presence of the focal amino acid
Insights
This led us to rethinking our auxotroph approach. We decided to now use a single auxotrophic system which is auxotrophic to lysine. To reiterate, our main objective of this model was to show that auxotrophy can be used as a fail safe in our application. The graph above shows that any shock introduced to the system impacts its growth rate and hereby acts as a fail safe.
Note: We realise that the data that is formulated may have inaccuracies due to inaccessibility to labs. However, during Phase 2 we propose to refine our model with experimental data. This can be accomplished by running HPLC analysis to get accurate amino acid measurements. We would also like to conduct population dynamics studies that would give us information about the amount of inoculant required in our final product.