Calculating total DCM degraded

1) Obtaining theoretical growth curve

To start this calculation, we needed to know how many bacteria we could reasonably expect to have in our system. To do this, we used reasonable bead dimensions and reasonable bead numbers to calculate the volume of bacteria infused agarose that we were likely to have in the system. We then used the assumption that the bacteria would grow to an optimum density of 10^7 bacteria per ml of agarose (REFERENCE) and combined these to give us an approximation of how to scale the growth curve:

A = Gompertz vertical scaling constant

N = number of beads

V = volume of each bead in ml

ρ = number of bacteria per ml

Our theoretical growth curves were based on Gompertz functions for the reasons explained when you follow this link: (what are Gompertz functions?). An example output growth curve of the model is shown here.

The scaling of the growth rate of the Gompertz function comes directly from growth curves of the DM4 bacteria that we obtained in the lab. See more about our work with growth curves here.

2) Calculating the volume of DCM that these bacteria could degrade

Our next task was to model the rate of DCM degradation by the average bacteria. Using Michaelis-Menten kinetics[1], this was predicted to be:

d[Ndcm]/dt = rate of DCM molecule degradation (s-1)

Kcat = dcmA turnover rate (= 0.6 s-1 for DM4)

[DCM] = DCM concentration (= 0.02M for our system)

[DcmA] = Number of DcmA molecules per cell (87576) Where did this number come from?

Km = Michaelis constant ( = 9 x 10^-6 M for this reaction)

Through the use of diffusion-limiting beads, [DCM] is kept constant at 0.02M. This is significantly larger than our Michaelis constant so this equation can be simplified by using the following assumptions:

Multiplying this by our population function, the total rate of DCM molecule degradation is given as:

Turning this into a more recognisable value (a volume) gives the total rate of DCM degradation as:

Where:

When all of these calculations were modelled in Matlab with the input conditions shown above, the total volume of DCM that we would predict the native bacteria DM4 to degrade in 24 hours is shown by the red line on the right. This is before you account for the possible toxicity of the pH drop. This is taken into account in the sections below.

Reference:

  1. Michaelis L. and Menten M.L. Kinetik der Invertinwirkung Biochem. Z. 1913; 49:333–369 English translation Accessed 6 April 2007