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From 2011.igem.org

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Modeling

Synthetic biologists engineer bacteria to carry out logical operations and functions that are not found in nature. In order model genetically engineered functions, synthetic biologists use computer aided design (CAD) applications to bridge the gap between computational modeling and biological data. In order to accomplish this, we have modeled our circuit in two ways:

1. Ordinary Differential Equations 2. Tinker Cell

Tinker Cell is a CAD software used by synthetic biologists to determine the rates of activity in bacteria.

Modeling the Etch-a-Sketch Circuit using MATLAB.

MATLAB is a programming language commonly used by engineers solve technical computing problems in a wide variety of applications. MATLAB provides an interactive workspace that allows programmers to work with image processing, control design, financial modeling and computational biology. With our project, we used MATLAB to graph Ordinary Differential Equations (ODEs).

mRNA protein 1 lovTAP 7 lovTAP 2 cI434 8 lovTAP* 3 T7P 9 CI434 4 trpR 10 T7P 5 cI 11 trpR 6 mRFP1 12 CI 13 mRFP1

parameters k transcription rate a translation rate u protein degradation y mRNA degradation K dissociation constant n hill coefficent b for all of x B sub x = .01 a sub x o 0 if light off, 1 if light on c rate of light induced lovTAP to lovTAP*

mRNA ODEs

lovTAPlovTAP mRNAdt= k1- y1 [lovTAP mRNA] [lovTAP mRNA]/dt = k1 - y1[lovTAP mRNA]

[cI434 mRNA]/dt = k2( K8 / [lovTAP*]^n8 + K8)( [trpR]^n11 / [trpR]^n11 + K11) - y2[cI434 mRNA]

[T7P mRNA]/dt = k3( K9 / [cI434]^n9 + K9 )( [cI]^n12 / [cI]^n12 + K12 ) - y3[T7P mRNA]

[trpR mRNA]/dt = k4( K9 / [cI434]^n9 + K9 )( [cI]^n12 / [cI]^n12 + K12 ) - y4[trpR mRNA]

[cI mRNA]/dt = k5( K9 / [cI434]^n9 + K9 )( [cI]^n12 / [cI]^n12 + K12 ) - y5[cI mRNA]

[mRFP1 mRNA]/dt = k6( [T7P]^n10 / [T7P]^n10 + K10 ) - y6[mRFP1 mRNA]

Protein ODEs

[lovTAP]/dt = a7[lovTAP mRNA] - oc[lovTAP] - u7[lovTAP]

[lovTAP*]/dt = oc[lovTAP] - u8[lovTAP*]

[cI434]/dt = a9[cI434 mRNA] - u9[cI434]

[T7P]/dt = a10[T7p mRNA] - u10[T7P]

[trpR]/dt = a11[trpR mRNA] - u11[trpR]

[cI]/dt = a12[cI mRNA] - u12[cI]

[mRFP1]/dt = a13[mRFP1 mRNA] - u13[mRFP1]