*Any modeling project should be tempered by the morality of laziness.*“ (Barnes

*et al.*, 2010)

Modeling

- toxicity modeling
- siRNA modeling
- ferritin structure modeling

The toxicity of copper ions on the cell is well characterized (Ning *et al.*, 2015) but for important parts of this project like the crossflow reactor we needed to know the exact point of time when our cells will die to achieve highest possible yields of copper.

The residence time should not exceed the rate of dying and cell lysis in the system. If cell lysis kicks in copper gets released back again into the substrate media and the yield minimizes. The modeling started with the copper uptake in our cells containing the BioBrick BBa_K2638204, which expresses *oprC* under pAraBAD (BBa_I0500)) control and induction at 1.0 % arabinose in. The toxicity is calculated for a single cell.

The first step was to calculate the rate of expression of *oprC*. Therefore the characterization of BBa_I0500) of Groningen was used to calculate the expression speed. At 1.0 % arabinose induction a raise of fluorescence of approx. *ΔF* = 82,000 within of t = 36,000 s was measurable.
The conversion from fluorescence units to concentration in mol/L was calculated as *k* = 2.5 * 10^{-6} mol*L^{-1} (Furtado and Henry, 2002) and the volume of the used capillaries was *V* = 3.14 * 10^{-9} L The rate of protein expression with 1.0 % arabinose is:

$$\frac{3.14 * 10^{-9} L * 2.5 * 10^{-6} mol L^{-1} * 87,500}{36,000 s} = 7.85 * 10^{-14} mol*s^{-1} (1)$$
can be described with (2) and (3):

kurve = []

for each in listCt[:end+1]:

for t in ts:

nOPRC = t*5*(10**(-29))

#print each

#print t

gleichung1 = vmax*t*nOPRC*6.022*(10**(23)) - C0 - math.log(C0)*KM

gleichung2 = -each - KM * math.log(each)

gleichung2small = gleichung2 - gleichung2*0.00001

gleichung2big = gleichung2 + gleichung2*0.00001

if gleichung2small <= gleichung1 and gleichung2big >= gleichung1:

kurve.append((each,t))

print each

print t

print kurve

with open ("Tupel_fuer_Kurve3.txt", "w") as out:

We assume that the rate of silencing by siRNAs depends in the first place on the promoter region in front of the RNAi gene. By gathering expression rates of the most popular promoters in the iGEM parts registry valuable information for modelling will be acquired. Furthermore additional factors like secondary structures, diffusion rates and degradation rates of RNA fragments. With that a model of the actual expression rate of proteins can be modeled with a given sequence that shall be silenced.
This modeling approach turned due to the high potential into our software project. The experimental part was shown on the silencing results site.

The crossflow reactor design was strongly influenced by the toxicity modeling. Another way to approach the high copper uptake were our anti toxicity measures the BioBricks BBa_K2638101, BBa_K2638100, BBa_K2638103, BBa_K2638105, BBa_K2638106, BBa_K2638120 and BBa_K2638121 enrich now the parts registry.