Background

This model aims to find out how much FRET protein should be added into our screening system.

Methods

Chemical equilibrium is used to determine the concentration of each protein, the fluorescence level, and the minimal FRET protein activity required to produce the fluorescence that can be detected. This model assumes the portion of active protein in all protein is constant. The equilibrium constants are from Victoria E. Ahn's study [1] and Zhihong Cheng's study [2]. The experiment budget for FRET proteins is considered in this model.

Results

The relationship between fluorescence and DKK1 expression level

The relationship between fluorescence and the activity of one of the FRET proteins

The plot of the optimal activity of a FRET protein vs. another

3D plot of the fluorescence, the objective function we want to maximize.

The x-axis is the concentration of one of the FRET protein and y-axis is that of the other

Contour plot of the fluorescence, the objective function we want to maximize.

The x-axis is the concentration of one of the FRET protein and y-axis is that of the other

Plot of the optimal “cheaper FRET protein” activity, vs. budget

Plot of the optimal “more expensive FRET protein” activity, vs. budget

Plot of the optimal ratio vs. budget

K_d values obtained from the references

Conclusion

The optimal ratio of the amount of one FRET protein to that of the other is as the following:

The figures in the table indicate the optimal ratio of the protein on the top over the protein on the left.

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Background

The efficiency of FRET is inversely proportional to the sixth power of the distance between donor and acceptor, making FRET extremely sensitive to small changes in distance. Therefore, simulating structure of protein-protein interactions is important. This model aims to predict the FRET efficiency in order to determine which molecules and which termini should be used.

Methods

pyDockWEB [3] is used for structural prediction of protein-protein interactions and the prediction of distances between donor and acceptor. Förster theory is used determine the FRET efficiency.

Results

The protein-protein interactions structural predictions are as follows:

Cyan: LRP6-BP1BP2 &nbsp&nbsp&nbsp&nbsp Green: LRP6-BP3BP4 &nbsp&nbsp&nbsp&nbsp Purple: DKK1

Cyan: LRP6-BP3BP4 &nbsp&nbsp&nbsp&nbsp Green: VHH G5 &nbsp&nbsp&nbsp&nbsp Purple: DKK1

Cyan: VHH H7 &nbsp&nbsp&nbsp&nbsp Green: VHH G5 &nbsp&nbsp&nbsp&nbsp Purple: DKK1

The predicted distances are (Ångström)

where N means YPet or CyPet is added to the N terminus and C means YPet or CyPet is added to the C terminus.

Conclusion

The FRET efficiency is given by the following table.

where N means YPet or CyPet is added to the N terminus and C means YPet or CyPet is added to the C terminus.

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Background

This project constructs a plasmid that connects DKK1 promoter to mCherry. The gene expression rate of DKK1 promoter is affected by testosterone activity and affects the expression level of mCherry. The expression level of mCherry should be greater than a threshold so that its fluorescence can be detected by devices. In order to achieve this threshold, sufficient amount of testosterone should be added into our screening system; this is the sensitivity of our screening system. This model aims to find out the sensitivity of our screening system.

Methods

This model simulates the kinetics of transcription signal the expression of DKK1 promoter. The process of protein synthesis is simulated with differential equations, assuming the synthesis of mCherry follows the central dogma of molecular biology. Signaling pathways of the androgen receptor is modeled based on chemical equilibrium of each transcription factor and intermediate.

Results

The increment of DKK1 gene expression rate caused by effective DHT activity

[DKK1] = 5 + 0.006 [DHT]^2

where [DKK1] indicates DKK1 activity in ng/ml and [DHT] indicates DHT activity in nM.

Note: This is accurate only when [DHT] is less than 50 nM.

Conclusion

[mCherry] = c_1 + c_2 [Testosterone]^2

where square brackets indicate activity in M, and c_1 and c_2 are constants to be determined.

Note: This model is accurate only when [DHT] is less than 50 nM.

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1. Victoria E. Ahn et al (2011). "Structural basis of Wnt signaling inhibition by Dickkopf binding to LRP5/6." Dev Cell . 2011 November 15; 21(5): 862–873. doi:10.1016/j.devcel.2011.09.003.
2. Zhihong Cheng (2011). "Crystal structures of the extracellular domain of LRP6 and its complex with DKK1." VOLUME 18 NUMBER 11 NOVEMBER 2011 nature structural & molecular biology.
3. Jiménez-García B, Pons C, Fernández-Recio J. (2013). "pyDockWEB: a web server for rigid-body protein-protein docking using electrostatics and desolvation scoring." Bioinformatics. 2013 Jul 1;29(13):1698-9. doi: 10.1093/bioinformatics/btt262. Epub 2013 May 9.
4. Meehan KL1, Sadar MD. (2003). "Androgens and androgen receptor in prostate and ovarian malignancies." Front Biosci. 2003 May 1;8:d780-800.