Team:USP-Brazil/Model:RFPVisibility
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<h2>RFP Visual Contrast Analysis</h2> | <h2>RFP Visual Contrast Analysis</h2> | ||
<h3>Stating the problem</h3> | <h3>Stating the problem</h3> | ||
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<div style="margin: 20px auto; width: 266px; height: 40px; background: url('https://static.igem.org/mediawiki/2013/9/9b/USPBrFormulasRFP.png') center -118px;"> </div> | <div style="margin: 20px auto; width: 266px; height: 40px; background: url('https://static.igem.org/mediawiki/2013/9/9b/USPBrFormulasRFP.png') center -118px;"> </div> | ||
- | <p>Where <i>A</i> is the Total | + | <p>Where <i>A</i> is the Total Absorptivity of the medium where the object |
is placed, <i>c<sub>i</sub></i> are the absorbing components and <i>ε<sub>i</sub></i> | is placed, <i>c<sub>i</sub></i> are the absorbing components and <i>ε<sub>i</sub></i> | ||
are their respective MECs.</p> | are their respective MECs.</p> | ||
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<p>In normal environment we don't need to be concerned about the frequency | <p>In normal environment we don't need to be concerned about the frequency | ||
- | of | + | of interaction of a RFP molecule and a foton because there are fotons |
in abundance. So we can come up with a simple formula to the intensity | in abundance. So we can come up with a simple formula to the intensity | ||
produced by concentration of RFP in a certain container of dimension | produced by concentration of RFP in a certain container of dimension | ||
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<p>Where <i>I<sub>B</sub></i> represents the background (locally homogeneous) light | <p>Where <i>I<sub>B</sub></i> represents the background (locally homogeneous) light | ||
intensity and <i>[RFP]</i> the RFP concentration. This formula states | intensity and <i>[RFP]</i> the RFP concentration. This formula states | ||
- | that all the | + | that all the background light inside the container with RFP is transformed |
in red light and the intensity is adjusted by the factor <i>Φε D[RFP]</i>.</p> | in red light and the intensity is adjusted by the factor <i>Φε D[RFP]</i>.</p> | ||
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<p>and extending the homogeneity of background light intensity we can | <p>and extending the homogeneity of background light intensity we can | ||
- | treat <i>I<sub>B</sub>(x)=I<sub>B</sub></i> for all | + | treat <i>I<sub>B</sub>(x)=I<sub>B</sub></i> for all possible values of <i>x</i>. This lead |
us to</p> | us to</p> | ||
<div style="margin: 20px auto; width: 266px; height: 22px; background: url('https://static.igem.org/mediawiki/2013/9/9b/USPBrFormulasRFP.png') center -286px;"> </div> | <div style="margin: 20px auto; width: 266px; height: 22px; background: url('https://static.igem.org/mediawiki/2013/9/9b/USPBrFormulasRFP.png') center -286px;"> </div> | ||
- | <p>Here <i>A</i> represents the atmospheric air | + | <p>Here <i>A</i> represents the atmospheric air absorptivity. And finally, |
the RFP concentration can be determined</p> | the RFP concentration can be determined</p> | ||
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<h3>Giving an estimate</h3> | <h3>Giving an estimate</h3> | ||
- | <p>Now, we can use our | + | <p>Now, we can use our knowledge about the human vision limits and about |
the RFP to estimate the RFP concentration necessary for it to be seen. | the RFP to estimate the RFP concentration necessary for it to be seen. | ||
- | To this end we do two | + | To this end we do two additional hypothesis and <i>A =0.5 m<sup>-1</sup></i> |
- | and <i>x=1 m</i>, i.e., the | + | and <i>x=1 m</i>, i.e., the atmospheric air absorbs half the light it |
interacts per meter and the observer will measure at 1 meter from | interacts per meter and the observer will measure at 1 meter from | ||
the RFP container. Our data is:</p> | the RFP container. Our data is:</p> | ||
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<li>→<i>[RFP] ∼ 8.9 × 10<sup>-5</sup>mol</i></li> | <li>→<i>[RFP] ∼ 8.9 × 10<sup>-5</sup>mol</i></li> | ||
</ul> | </ul> | ||
- | <p>The value for <i>D</i> was chosen to | + | <p>The value for <i>D</i> was chosen to represent a cylindrical flask with |
- | <i>2 cm</i> diameter. The values for <i>C</i> is a mean | + | <i>2 cm</i> diameter. The values for <i>C</i> is a mean calculated from |
data at [1].</p> | data at [1].</p> | ||
<h3>Conclusion</h3> | <h3>Conclusion</h3> | ||
- | <p>With this results we can compare the RFP production rate of Pichia | + | <p>With this results we can compare the RFP production rate of <i>Pichia |
- | pastoris with the photo-stability of our RFP to determine if we will | + | pastoris</i> with the photo-stability of our RFP to determine if we will |
- | be able to see the RFP produced in | + | be able to see the RFP produced in different conditions. However, more |
specific data will be required to proceed.</p> | specific data will be required to proceed.</p> | ||
- | <p>[1] Contrast Thresholds of the Human Eye - H. RICHARD BLACKWELL -JOURNAL OF THE OPTICAL | + | <h4 style="color:grey;">References</h4> |
+ | <p style="color:grey;">[1] Contrast Thresholds of the Human Eye - H. RICHARD BLACKWELL -JOURNAL OF THE OPTICAL | ||
SOCIETY OF AMERICA VOLUME 36, NUMBER 11 NOVEMBER, 1946</p> | SOCIETY OF AMERICA VOLUME 36, NUMBER 11 NOVEMBER, 1946</p> | ||
+ | |||
<p style="text-align:center;">RFP Visibility | <a href="#">Deterministic Model</a> | <a href="#">Stochastic Model</a></p> | <p style="text-align:center;">RFP Visibility | <a href="#">Deterministic Model</a> | <a href="#">Stochastic Model</a></p> |
Revision as of 20:24, 26 September 2013
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RFP Visual Contrast Analysis
Stating the problem
Here is the problem: we are trying to build a “machine” to detect methanol in alcoholic drinks using a yeast, genetically modified to produce RFP (Red Fluorescent Protein) through methanol consumption.
The chosen yeast was Pichia pastoris, especially because its natural ability to interact with methanol duo to the presence of an AOX promoter.
Among the questions we need to answer in order to accomplish this task, is the simple question about how do we “see” RFP signal that would be produced by methanol induction. To address this question we make use of some mathematical notions of visual contrast and bright.
Definitions
Let's define more precisely the meaning of visual contrast:
Visual Contrast: Consider some object placed at a distance x from an observer and emitting light with a certain intensity. This light is measured by the observer and called I(x). Suppose the background light intensity measured by the observer is IB(x).
We define the Visual Contrast (C) as:
Quantum Yield e Molar Extinction Coefficient: The brightness of a FP (Fluorescent Protein) is proportional to the product of its Quantum Yield and its Molar Extinction Coefficient (MEC).
The QY is defined by the rate of emitted fotons and absorbed fotons and we call it Φ?
The MEC, defined as the absorption force per mol per centimeter (M-1cm-1), is a property of the FP's chemical structure and we call it ε.
Beer-Lamber Law: Consider an object placed at x0=0 emitting light. Call I(x) the light intensity at a distance x. The Beer-Lambert law says the light intensity distant x from x0 suffers an exponential attenuation:
Where A is the Total Absorptivity of the medium where the object is placed, ci are the absorbing components and εi are their respective MECs.
Putting all together
Well, there is a natural link between the concepts described above. To see this we need to describe the intensity produced by the RFP through its QY and MEC, than we estimate the environment conditions and choose a desired contrast and determine the necessary concentration of RFP to achieve this.
Looking closely to the relevant quantity concerning the RFP, we can interpret the product Φε as the number of fotons absorbed and transformed in red light per mol of RFP per centimeter of distance.
In normal environment we don't need to be concerned about the frequency of interaction of a RFP molecule and a foton because there are fotons in abundance. So we can come up with a simple formula to the intensity produced by concentration of RFP in a certain container of dimension D.
Where IB represents the background (locally homogeneous) light intensity and [RFP] the RFP concentration. This formula states that all the background light inside the container with RFP is transformed in red light and the intensity is adjusted by the factor Φε D[RFP].
Inserting this in the definition of visual contrast
and extending the homogeneity of background light intensity we can treat IB(x)=IB for all possible values of x. This lead us to
Here A represents the atmospheric air absorptivity. And finally, the RFP concentration can be determined
Giving an estimate
Now, we can use our knowledge about the human vision limits and about the RFP to estimate the RFP concentration necessary for it to be seen. To this end we do two additional hypothesis and A =0.5 m-1 and x=1 m, i.e., the atmospheric air absorbs half the light it interacts per meter and the observer will measure at 1 meter from the RFP container. Our data is:
- RFP mCherry QY: Φ=0,22
- RFP mCherry MEC: ε=72000
- Visual contrast: C=0,10
- D∼2 cm
- →[RFP] ∼ 8.9 × 10-5mol
The value for D was chosen to represent a cylindrical flask with 2 cm diameter. The values for C is a mean calculated from data at [1].
Conclusion
With this results we can compare the RFP production rate of Pichia pastoris with the photo-stability of our RFP to determine if we will be able to see the RFP produced in different conditions. However, more specific data will be required to proceed.
References
[1] Contrast Thresholds of the Human Eye - H. RICHARD BLACKWELL -JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 36, NUMBER 11 NOVEMBER, 1946
RFP Visibility | Deterministic Model | Stochastic Model
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