Difference between revisions of "Team:ETH Zurich/Model/Environment Sensing/system specifications"

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<h1 class="headline">Definition of system specifications</h1>
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    <section class="toc">
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        <h1>TOC</h1>
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<section class="first goal">
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    </section>
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    <h1>Goal</h1>
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    <section class="main-content">
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    <p>Determine the target specifications of our bacterial system regarding the detection levels and azurin production levels</p>
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        <div class="headline">
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</section>
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            <h1>Definition of system specifications</h1>
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        </div>
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<section>
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        <section>
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    <h1>Overview</h1>
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            <details>
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    <p>In order to tune our bacteria so that it would behave correctly in vivo, we had to define precise, quantitative criteria that had to be met. This means that we first need to define the operating points that our system will encounter (in other words, the different environmental conditions our bacteria will meet: tumoral or healthy tissues for instance). We will then need to determine the relative level of toxin production in our bacteria that we are willing to tolerate in area where there is no need for treatment. As a result, we will get objective quantitative criteria, which will help us build upon it a strategy to optimize the performance of our system, thanks to further modeling.</p>
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                <summary>GOAL</summary>
+
</section>
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                <p>Determine the target specifications of our bacterial system regarding the detection levels and azurin production levels
+
 
−
                </p>
+
<section>
−
            </details>
+
    <h1>Determining operating points</h1>
−
        <p>In order to tune our bacteria so that it would behave correctly in vivo, we had to define precise, quantitative criteria that had to be met. This includes on the one hand the detection thresholds in term of bacterial cells density and lactate concentration for our AND gate, and on the other hand the azurin output level that could be reasonably obtained in the tumor from the lysis of our bacteria. As this later criterium is tightly related to the bacterial cells density that can be achieved in the tumor (the more bacterial, the more azurin is released), let us begin with focusing on bacterial cells density.
+
    <p>To know how to tune our system, we need to define the detection thresholds in term of bacterial cells density and lactate concentration for our AND gate. We will here establish for both variables a low value (in situations of healthy environment) and a high value(in situations of tumor environment).</p>
−
        </p>
+
 
−
        </section>
+
    <h2>Lactate concentration</h2>
−
        <section>
+
    <p>A high local lactate concentration is a fairly reliable indicator of a tumorous environment. Tumorous cell exhibit indeed an erratic metabolic behavior leading to a lactate production way over the levels of healthy cells (this is part of the so called "Warburg effect" <a href="#bib1" class="forward-ref">[1]</a>). Basal concentration of lactate in healthy tissues has been found to be below 1 mM, whereas it was found to be larger than 4 mM and up to 40 mM in tumors. <a href="#bib2" class="forward-ref">[2]</a></p>
−
        <div class="headline">
+
    <p>To build our model, we will take as reference value a lower lactate concentration of 1 mM for healthy tissues, and a higher one of 5 mM for tumors. As the activation of the synthesis of azurin is monotonous in regards to lactate concentration (the more lactate there is, the more it is activated), we believe that measuring the performance of our circuit with these two wisely chosen values will be suitable for a good assessment of its specificity.</p>
−
            <h2>Bacterial cells density</h1>
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</section>
−
        </div>
+
 
−
        <p>Estimating a precise distribution of cells into the tumor is not straightforward, and we had to apply assumptions that appeared reasonable to us to be able to estimate a plausible quantitative repartition of bacteria in solid tumors.
+
<section>
−
         </p>
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    <h2>Density of bacterial cells</h2>
−
                <ul>
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    <p>Estimating a precise distribution of cells into the tumor is not straightforward, and we had to apply assumptions that appeared reasonable to us to be able to estimate a plausible quantitative repartition of bacteria in solid tumors.</p>
−
                    <li>Volume of E. coli = 1 µm<sup>3</sup></li>
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−
                    <li>Diameter of the tumor = 20 mm</li>
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    <!-- TODO: Please make background transparent -->
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                    <li>Diameter of E. coli colonization shell area = 10 mm</li>
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    <!-- NOTE: Please make sure Helvetica is used -->
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                    <li>Width of E. coli colonization shell area = 0.5 mm</li>
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    <figure class="fig-nonfloat" style="max-width: 600px;">
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                </ul>
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         <img src="https://static.igem.org/mediawiki/2017/3/36/T--ETH_Zurich--tumor_geometry.png"
−
         </section>
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        alt="Geometry of tumor and bacterial colony"
−
     </section>
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        />    <figcaption>Geometry of the tumor and bacteria colony (green area: colonized by <span class="bacterium">E. coli</span> Nissle)</figcaption>
−
     </main>
+
    </figure>
−
</div>
+
 
 +
    <dl>
 +
        <dt>Volume of <span class="bacterium">E. coli</span> cell</dt>
 +
        <dd>1 µm<sup>3</sup> <a href="#bib3" class="forward-ref">[3]</a></dd>
 +
        <dt>Radius of tumor Tumor radius</dt>
 +
        <dd>20 mm</dd>
 +
        <dt>Radius of colony shell (concentric to tumor)</dt>
 +
        <dd>10 mm</dd>
 +
        <dt>Width of colony shell</dt>
 +
        <dd>0.5 mm</dd>
 +
    </dl>
 +
 
 +
    <p>The three last values where obtained from an estimation made from the microscopy images of mouse tumors presented in a paper studying <span class="bacterium">E. coli</span> Nissle colonization of tumors <a href="#bib4" class="forward-ref">[4]</a>. The proportions were kept and adapted to a model tumor of 4 cm in diameter, to be closer to a situation in the human body (the colonization was studied only in mice). In addition to this data, we took into account the measured overall concentration of <span class="bacterium">E. coli</span> in the tumor, 1e9
 +
CFU/g to deduce an estimated more precise distribution of the bacteria in the tumor. Considering that the bacteria colonize preferentially the "shell area" at the border between the necrotic area of the tumor and the alive tissue, the effective concentration of bacteria in this area can be inferred from a simple proportionality equation, as follows:</p>
 +
 
 +
    <p>We model the bacteria as inhabiting a layer inside a spherical tumor of radius <span class="math">\( r_2 = 20 \text{mm} \)</span>. According to <a href="#bib4" class="forward-ref">[4]</a>, the bacteria colonize the interface between live and necrotic tumor tissue, which we model occurring at radius <span class="math">\( r_1 = 10 \text{mm} \)</span>. The width of the colony is set to <span class="math">\( w = 0.5 \text{mm} \)</span>.</p>
 +
</section>
 +
<section class="latex">
 +
    <p>We expect that the concentration of bacteria in the tumor will be approximately 1e9 CFU/g (citation needed). The volume of a single bacterium is <span class="math">\( V_{\text{cell}} \approx 1 \mu m^3 \)</span>. We assume the density of the tumor to be the same as water: <span class="math">\( \rho_{\text{tumor}} = 1 \text{g/mL} \)</span>. We now calculate the effective volumetric occupancy of the cells (<span class="math">\( d_{\text{cell}} \)</span> —percentage) as follows:</p>
 +
    <p><span class="math">\[\begin{aligned}
 +
         V_{\text{bacteria}}
 +
        &amp;= d_{\text{cell}} V_{\text{layer}} &amp; \text{assuming homogeneity} \\
 +
        \frac{V_{\text{bacteria}}}{V_{\text{tumor}}}
 +
        &amp;= d_{\text{cell}} \frac{V_{\text{layer}}}{V_{\text{tumor}}} \\
 +
        \frac{V_{\text{cell}}\, N_{\text{cell}}}{m_{\text{tumor}}\, \rho_{\text{tumor}}}
 +
        &amp;\simeq d_{\text{cell}} \frac{4 \pi w r_{1}^{2}}{4/3 \pi r_{1}^{3}}
 +
        &amp; \text{assuming } w \ll r_{1} \\
 +
        \\
 +
        d_{\text{cell}}
 +
        &amp;\simeq \frac{N_{\text{cell}}}{m_{\text{tumor}}} V_{\text{cell}} \frac{1}{\rho_{\text{tumor}}} \frac{r_{1}}{3 w} \\
 +
        &amp;\simeq 1e9 \text{g}^{-1} \cdot 1 \mu m^3 \cdot 1 \text{mL.g}^{-1} \cdot \frac{10 \text{mm}}{1.5 \text{mm}} \\
 +
        &amp;\simeq 5\%\end{aligned}\]</span></p>
 +
 
 +
    <p>We could therefore infer the bacterial density present in the tumor: 5% of the volume is locally filled with bacteria, in a shell shape. As for other tissues, to be on the safe side, we take as a reference value a concentration of bacteria corresponding to the maximum observed in any healthy organ, for any bacterial strain that as been tested in the paper. This amounts to 1x10<sup>7</sup>CFU.g<sup>-1</sup>, and corresponds therefore to a bacterial density of around 0.05% </p>
 +
</section>
 +
 
 +
<section>
 +
     <h1>Criteria on the azurin production</h1>
 +
    <p>Now that we know at what points to evaluate our system, we can set criteria that have to be met to validate that the activation of the production of azurin is specific enough for our needs (priority 1), as well as the highest possible (priority 2) to be able to treat the biggest part of the tumor possible. </p>
 +
</section>
 +
 
 +
<section id="rel_criteria_sys_specs">
 +
     <h2>Relative criteria</h2>
 +
    <p>We only want azurin to be produced in the situation of a high lactate level (5 mM) and high bacterial cell density (5% density). This means that we want to maximize the ratio of azurin production in (high lactate, high density) state compared to the production in (low lactate, low density) state, or (low lactate, high density) and (high lactate, low density) states. To assess whether our system is good enough, we will set these quantified criteria:</p>
 +
 
 +
    <!-- TODO: Please make background transparent -->
 +
    <!-- NOTE: Please make sure Helvetica is used -->
 +
    <figure class="fig-nonfloat" style="max-width: 600px;">
 +
        <img src="https://static.igem.org/mediawiki/2017/9/9e/T--ETH_Zurich--azu_relative_expression_criteria.png"
 +
        alt="Criteria for a functional circuit: percentage of maximum Azurin expression allowed in each condition"
 +
        />
 +
    <figcaption>Criteria for a functional circuit: percentage of maximum Azurin expression allowed in each condition</figcaption>
 +
    </figure>
 +
 
 +
    <p>We have to keep in mind that these criteria are very arbitrary, and that their primary goal is to guide us in the engineering of our bacterial strain. They are not based on measured toxicity level of azurin, as azurin is already quite specific for tumor cells, therefore relying on such toxicity data could lead us to be allowed to express more azurin in healthy tissues, because it would not be less toxic there either way.</p>
 +
</section>
 +
 
 +
<section>
 +
    <h2>Absolute azurin expression</h2>
 +
    <p>As the colonizing bacterial population is concentrated in a small shell inside of the tumor (which represent only a fraction of the tumor volume) and is at most occupying 5% of the space there, we can already anticipate that it will have to synthetize the highest amount of azurin possible to be able to kill the most tumor cells possible. However, as we have no idea about the effective expression of azurin in <span class="bacterium">E. coli</span> cells, we can only relate it to the expression of another protein in our circuit. As the azurin will be expressed on the same operon than luxI, an enzyme taking part into the bacterial cell density sensing, we can try to get a sense of how stronger must be the expression of azurin in regards to luxI to reach a given arbitrary azurin concentration.</p>
 +
    <p>This way, we'll know whether our circuit leads intrinsically to high expressions of the luxI-azurin operon (the expression level of azurin compared to luxI will not be that high in this case), or on the contrary weak expressions of this operon (in this case the expression of azurin will have to be much higher than the one of luxI to reach the target concentration).</p>
 +
 
 +
    <p>We take as a reference value for azurin concentration 1 mM (absolute maximum of concentration of a given protein that can be achieved in <span class="bacterium">E.coli</span> <a href="#bib5" class="forward-ref">[5]</a>). This will be the goal to reach when our circuit is fully induced, in the (high lactate, high density) state.</p>
 +
</section>
 +
 
 +
<section class="references">
 +
    <h1>References</h1>
 +
    <ol>
 +
        <li id="bib1"><a href="#ref1">^ </a> <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2849637/">Vander Heiden, Matthew G., Lewis C. Cantley, and Craig B. Thompson. “Understanding the Warburg Effect: The Metabolic Requirements of Cell Proliferation.” <cite>Science</cite> (New York, N.Y.) 324.5930 (2009): 1029–1033. PMC. Web. 18 Oct. 2017.</a></li>
 +
        <li id="bib2"><a href="#ref2">^ </a> <a href="https://www.hindawi.com/journals/mi/2016/6456018/#B58">Yong Wu, Yunzhou Dong, Mohammad Atefi, Yanjun Liu, Yahya Elshimali, and Jaydutt V. Vadgama, “Lactate, a Neglected Factor for Diabetes and Cancer Interaction,” Mediators of Inflammation, vol. 2016, Article ID 6456018, 12 pages, 2016. doi:10.1155/2016/6456018</a></li>
 +
        <li id="bib3"><a href="#ref3">^ </a> <a href="http://book.bionumbers.org/how-big-is-an-e-coli-cell-and-what-is-its-mass/">Bionumbers.org</a></li>
 +
        <li id="bib4"><a href="#ref4">^ </a> <a href="http://www.sciencedirect.com/science/article/pii/S1438422107000197?via%3Dihub">Stritzker, Jochen, et al. "Tumor-specific colonization, tissue distribution, and gene induction by probiotic Escherichia coli Nissle 1917 in live mice." <cite>International journal of medical microbiology</cite> 297.3 (2007): 151-162.</a></li>
 +
        <li id="bib5"><a href="#ref5">^ </a> <a href="http://book.bionumbers.org/how-many-proteins-are-in-a-cell/">Bionumbers.org</a></li>
 +
    </ol>
 +
</section>
 +
</main>
 
</html>
 
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{{ETH_Zurich/Footer_N}}
 
{{ETH_Zurich/Footer_N}}

Latest revision as of 22:53, 1 November 2017

Definition of system specifications

Goal

Determine the target specifications of our bacterial system regarding the detection levels and azurin production levels

Overview

In order to tune our bacteria so that it would behave correctly in vivo, we had to define precise, quantitative criteria that had to be met. This means that we first need to define the operating points that our system will encounter (in other words, the different environmental conditions our bacteria will meet: tumoral or healthy tissues for instance). We will then need to determine the relative level of toxin production in our bacteria that we are willing to tolerate in area where there is no need for treatment. As a result, we will get objective quantitative criteria, which will help us build upon it a strategy to optimize the performance of our system, thanks to further modeling.

Determining operating points

To know how to tune our system, we need to define the detection thresholds in term of bacterial cells density and lactate concentration for our AND gate. We will here establish for both variables a low value (in situations of healthy environment) and a high value(in situations of tumor environment).

Lactate concentration

A high local lactate concentration is a fairly reliable indicator of a tumorous environment. Tumorous cell exhibit indeed an erratic metabolic behavior leading to a lactate production way over the levels of healthy cells (this is part of the so called "Warburg effect" [1]). Basal concentration of lactate in healthy tissues has been found to be below 1 mM, whereas it was found to be larger than 4 mM and up to 40 mM in tumors. [2]

To build our model, we will take as reference value a lower lactate concentration of 1 mM for healthy tissues, and a higher one of 5 mM for tumors. As the activation of the synthesis of azurin is monotonous in regards to lactate concentration (the more lactate there is, the more it is activated), we believe that measuring the performance of our circuit with these two wisely chosen values will be suitable for a good assessment of its specificity.

Density of bacterial cells

Estimating a precise distribution of cells into the tumor is not straightforward, and we had to apply assumptions that appeared reasonable to us to be able to estimate a plausible quantitative repartition of bacteria in solid tumors.

Geometry of tumor and bacterial colony
Geometry of the tumor and bacteria colony (green area: colonized by E. coli Nissle)
Volume of E. coli cell
1 µm3 [3]
Radius of tumor Tumor radius
20 mm
Radius of colony shell (concentric to tumor)
10 mm
Width of colony shell
0.5 mm

The three last values where obtained from an estimation made from the microscopy images of mouse tumors presented in a paper studying E. coli Nissle colonization of tumors [4]. The proportions were kept and adapted to a model tumor of 4 cm in diameter, to be closer to a situation in the human body (the colonization was studied only in mice). In addition to this data, we took into account the measured overall concentration of E. coli in the tumor, 1e9 CFU/g to deduce an estimated more precise distribution of the bacteria in the tumor. Considering that the bacteria colonize preferentially the "shell area" at the border between the necrotic area of the tumor and the alive tissue, the effective concentration of bacteria in this area can be inferred from a simple proportionality equation, as follows:

We model the bacteria as inhabiting a layer inside a spherical tumor of radius \( r_2 = 20 \text{mm} \). According to [4], the bacteria colonize the interface between live and necrotic tumor tissue, which we model occurring at radius \( r_1 = 10 \text{mm} \). The width of the colony is set to \( w = 0.5 \text{mm} \).

We expect that the concentration of bacteria in the tumor will be approximately 1e9 CFU/g (citation needed). The volume of a single bacterium is \( V_{\text{cell}} \approx 1 \mu m^3 \). We assume the density of the tumor to be the same as water: \( \rho_{\text{tumor}} = 1 \text{g/mL} \). We now calculate the effective volumetric occupancy of the cells (\( d_{\text{cell}} \) —percentage) as follows:

\[\begin{aligned} V_{\text{bacteria}} &= d_{\text{cell}} V_{\text{layer}} & \text{assuming homogeneity} \\ \frac{V_{\text{bacteria}}}{V_{\text{tumor}}} &= d_{\text{cell}} \frac{V_{\text{layer}}}{V_{\text{tumor}}} \\ \frac{V_{\text{cell}}\, N_{\text{cell}}}{m_{\text{tumor}}\, \rho_{\text{tumor}}} &\simeq d_{\text{cell}} \frac{4 \pi w r_{1}^{2}}{4/3 \pi r_{1}^{3}} & \text{assuming } w \ll r_{1} \\ \\ d_{\text{cell}} &\simeq \frac{N_{\text{cell}}}{m_{\text{tumor}}} V_{\text{cell}} \frac{1}{\rho_{\text{tumor}}} \frac{r_{1}}{3 w} \\ &\simeq 1e9 \text{g}^{-1} \cdot 1 \mu m^3 \cdot 1 \text{mL.g}^{-1} \cdot \frac{10 \text{mm}}{1.5 \text{mm}} \\ &\simeq 5\%\end{aligned}\]

We could therefore infer the bacterial density present in the tumor: 5% of the volume is locally filled with bacteria, in a shell shape. As for other tissues, to be on the safe side, we take as a reference value a concentration of bacteria corresponding to the maximum observed in any healthy organ, for any bacterial strain that as been tested in the paper. This amounts to 1x107CFU.g-1, and corresponds therefore to a bacterial density of around 0.05%

Criteria on the azurin production

Now that we know at what points to evaluate our system, we can set criteria that have to be met to validate that the activation of the production of azurin is specific enough for our needs (priority 1), as well as the highest possible (priority 2) to be able to treat the biggest part of the tumor possible.

Relative criteria

We only want azurin to be produced in the situation of a high lactate level (5 mM) and high bacterial cell density (5% density). This means that we want to maximize the ratio of azurin production in (high lactate, high density) state compared to the production in (low lactate, low density) state, or (low lactate, high density) and (high lactate, low density) states. To assess whether our system is good enough, we will set these quantified criteria:

Criteria for a functional circuit: percentage of maximum Azurin expression allowed in each condition
Criteria for a functional circuit: percentage of maximum Azurin expression allowed in each condition

We have to keep in mind that these criteria are very arbitrary, and that their primary goal is to guide us in the engineering of our bacterial strain. They are not based on measured toxicity level of azurin, as azurin is already quite specific for tumor cells, therefore relying on such toxicity data could lead us to be allowed to express more azurin in healthy tissues, because it would not be less toxic there either way.

Absolute azurin expression

As the colonizing bacterial population is concentrated in a small shell inside of the tumor (which represent only a fraction of the tumor volume) and is at most occupying 5% of the space there, we can already anticipate that it will have to synthetize the highest amount of azurin possible to be able to kill the most tumor cells possible. However, as we have no idea about the effective expression of azurin in E. coli cells, we can only relate it to the expression of another protein in our circuit. As the azurin will be expressed on the same operon than luxI, an enzyme taking part into the bacterial cell density sensing, we can try to get a sense of how stronger must be the expression of azurin in regards to luxI to reach a given arbitrary azurin concentration.

This way, we'll know whether our circuit leads intrinsically to high expressions of the luxI-azurin operon (the expression level of azurin compared to luxI will not be that high in this case), or on the contrary weak expressions of this operon (in this case the expression of azurin will have to be much higher than the one of luxI to reach the target concentration).

We take as a reference value for azurin concentration 1 mM (absolute maximum of concentration of a given protein that can be achieved in E.coli [5]). This will be the goal to reach when our circuit is fully induced, in the (high lactate, high density) state.

References

  1. ^ Vander Heiden, Matthew G., Lewis C. Cantley, and Craig B. Thompson. “Understanding the Warburg Effect: The Metabolic Requirements of Cell Proliferation.” Science (New York, N.Y.) 324.5930 (2009): 1029–1033. PMC. Web. 18 Oct. 2017.
  2. ^ Yong Wu, Yunzhou Dong, Mohammad Atefi, Yanjun Liu, Yahya Elshimali, and Jaydutt V. Vadgama, “Lactate, a Neglected Factor for Diabetes and Cancer Interaction,” Mediators of Inflammation, vol. 2016, Article ID 6456018, 12 pages, 2016. doi:10.1155/2016/6456018
  3. ^ Bionumbers.org
  4. ^ Stritzker, Jochen, et al. "Tumor-specific colonization, tissue distribution, and gene induction by probiotic Escherichia coli Nissle 1917 in live mice." International journal of medical microbiology 297.3 (2007): 151-162.
  5. ^ Bionumbers.org