Team:Groningen/Modelling/Characterization

We can measure how much v5 (v_max for As(III) import via GlpF) is in wild-type E.coli and when we over express GlpF at a certain promoter strength S (measured in RPUs). As v5 is a constant times the amount of (active) GlpF this leads to a simple equation for Δv5, if we assume the amount of (active) GlpF produced by our construct is linearly dependent on the promoter strength (v5(0) and v5(1) would be measured):

v5(RPS) = v5wt + Δv5*RPS

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

Δv5 = (v5(1) - v5(0))/S

Meng 2004 was able to knock out all efflux of arsenic. If there is no efflux of arsenic the dervative of the accumulation graph is the speed at wich arsenic is pumped inside the cell. The maximum speed would be v5. In such a senario two measurements would be enough to determine the relative promotor strength. One could even determine the reaction rate k6 and GlpF with a simple calculation, since v5 = k6 GlpFT (Vs/Vc). However we do have efflux, not only do we have efflux, but we have efflux that is dependent on the total amount of arsenic inside the cell. Also a portion arsenic gets bound to ArsR.

For both MBPArsR and fMT we assume the amount of bound As(III) for a given relative promoter strength S obeys (for MBPArsR n=1):

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

The ars promoter is part of a feedback loop, so it is not a simple matter of defining the (instantaneous) promoter strength. Instead we suggest using the relevant equations from our model. The necessary parameters can be determined by fitting uptake measurement data to our model. Specifically, if the RPS is measured without arsenic present and with enough arsenic present to keep the promoter fully active during the experiment we can determine βRN τR as follows (under the assumption that the RPS is linearly dependent on arsT/ars and using the fact that without any arsenic present the cells will be in equilibrium):

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)

RPS → GV The amount of gas vesicles can be expressed in terms of buoyant density, as volume fraction, using the total mass of the vesicles, etc. No matter how it is expressed, we assume a simple linear dependency between the RPS and the amount of gas vesicles. By taking (T)EM pictures of slices the amount of gas vesicles formed under influence of different RPSes can be determined and a straightforward fit made.

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