Team:Groningen/Modelling/Characterization

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Revision as of 16:58, 21 October 2009

Optimization procedure

To fit our model to experimental data from different uptake experiments and/or papers we have implemented an optimization procedure that allows for experiments with different genotypes and circumstances by letting constants be overridden per experiment. It aims to optimize the sum of the RMS errors for each experiment using Simulated Annealing. By clicking the button "Fit" the optimization is started and its progress can be followed by looking at the table of constants and the graphs shown below the table (which are updated in real-time as the best solution is improved).

Relative Promotor Strength

We have four kinds of parts we would like to characterize (RPS stands for Relative Promoter Strength):

v5(RPS) = v5wt + Δv5*RPS

v5(0) = v5wt + Δv5*0
v5(S) = v5wt + Δv5*S

Δv5 = (v5(1) - v5(0))/S

Asbound(As(III)in)
 = S Bmax As(III)in^n
    / (K^n + As(III)in^n)

S(max) / S(0) = ars(max) / ars(0)
S(max) / S(0) = arsT / ars(0)
S(max) / S(0) = 1 + ArsR(0)²/KAd²
      ArsR(0) = KAd √(S(max)/S(0) - 1)

0 = βRN ars1(0) - (ln(2)/τR) ArsR(0)
0 = βRN ars1T S(0)/S(max)
     - (ln(2)/τR) KAd √(S(max)/S(0) - 1)
βRN ars1T S(0)/S(max)
 = (ln(2)/τR) KAd √(S(max)/S(0) - 1)
βRN τR = (ln(2)/ars1T) KAd
   (S(max)/S(0)) √(S(max)/S(0) - 1)

Uptake measurements

To gain measurements for the optimization procedure described above we conducted ICPMS measurements on our cells containing various devices. To optimize our findings we have conducted measurements both in time and in concentration. Details on ICPMS the experiments can be found on our Protocol Page. Measurments have been conducted at at times and concentrations as indicated in the table on the right. Results can be seen below.

First Uptake Measurement
In this case we looked at the arsenic uptake of our wildtype and of our wildtype with a lot of pArs promoters with RFP. The raw data can be found at our Download Section

Getting (Vc/Vs) and other conditions
To effectively determine our constants we need to give our model some extra information. For instance what kind of constructs are inside the cel for a given experiment. Also we need to give the model the volume of cells per liter of fluid. To optain this we use the optained dry weight and calculate how much wet weight it would have been and then use the density of E-coli to optain volume for our sample and eventyally the desired volume of cells per liter. Also our needs the absolute value of Arsenic taken up by the cell in the assumption that we have one liter of sample and we know (Vc/Vs). Once we know all these parameters the optimiztion procedure can start. Information

Fluorescence Measurements
Apart from giving our model all the conditions it needs to calculate all the constants By means of the optimization procedure we have also conducted some fluorescence measurements and grow curves of our construct with the pArs promotor with RFP. The cells where put into a solution with either not arsenic in it or at a concentration of 100 micromolair. On the left side one can see the graph of the luminance and on right side and on the right side one can see the coresponding grow curves. The raw data of these measurements can again be found under our Downloads

Using the formula below we where able to derive an RPU of 2.3. This means that on average the ars promotor 2,3 times more active at 100 micromolarity of arsenic than if there is no arsenic in the solution. For a detailed calculation I would like to refer to our Downloads section under the RPU sheet.

Second ICPMS measurement