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Modeling

Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.

Inspiration

Here are a few examples from previous teams:

• ETH Zurich 2014
• Waterloo 2014

MATH!

blah, blah, blah

hey whoa popoluation inversely propotional to cells flou propotional to copper and populatio population depends on concentration of cu

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$$x = \begin{bmatrix}a & \dots & b\\ \vdots & \ddots & \vdots\\c & \dots & d\end{bmatrix}$$ The FRET efficiency ( {\displaystyle E} E) is the quantum yield of the energy transfer transition, i.e. the fraction of energy transfer event occurring per donor excitation event. It has been seen that the efficiency of this energy tranfer is inversely propotional to the sixth power of the distance between donor and acceptor. E depends on the donor-to-acceptor separation distance {\displaystyle r} r with an inverse 6th-power law due to the dipole-dipole coupling mechanism.

In our model, we have assumed the following decomposition of the {CFP-YFP} pair. CFP<-r->{YFP}^{}* = CFP<-r>YFP<-r>YFP<-r>YFP<-r>YFP<-r>YFP.... The energy tranfered from the acceptor fluorophore (CFP) to each YFP is given by: E(r) = 1/r\^{}6 + 1/(2r)\^{}6 + 1/(3r)\^{}6 + ... E(r) = 1/r\^{}6(1 + 1/2\^{}6 + 1/3\^{}6 + .... The above funnction is of the form: 1/r^6 $$\sum{n=1}^{\infty}1/n^6 Consider the function f(x) = 1/x\^{}p For p not equal to one, = $$\int{1}^{infty} 1/x^p dx$$ = $$\lim{M\to\infty} $$\int{1}^{infty} 1/x^p dx$$ $$ = $$\lim_{M\to\infty} (x\^{}(-p+1)/ (-1+p))/^M Note that this limits converges for -p + 1 < 0 We have p = 6 Therefore, the total energy tranfer is approximately equal to E(r) = 1/r\^{}6(1) This means that only the YFP adjacent to CFP recieves considerable amount of energy form the donor protien. The value the expression converges to is given by 1/1\^{}6 + 1/(2)\^{}6 + 1/(3)\^{}6 + ... = 1.0147