Difference between revisions of "Team:NEU China A/Model"

In the affected area of patients with inflammatory bowel disease, the concentration of nitric oxide is significantly increased, so we chose it as the input signal of our anti-inflammatory device. However, the nitric oxide is very unstable, so we have introduced an amplifier which can converts unstable gas signals into stable intracellular signals for sustained high-level output. The amplifier is based on a positive feedback loop. Transcription activator B-A can self-drive in a manner independent of the input signal for a period of time after the signal is input, and the metabolic flow in this cycle can be transferred to the output circuit (Figure 1).

Figure 1. Schematic Design of the Synthetic amplifier After the signal is input, the transcriptional activator B-A is generated, which includes a DNA binding domain and a transcriptional activation domain. On the one hand, B-A can activate the expression of the reporter gene, and on the other hand can activate the expression of B-A itself. The constitutively expressed Binder will compete with B-A to suppress the leakage of the device.

In addition, when using an amplifier based on a positive feedback loop, we need to strictly limit its activation until the input signal is strong enough, which is beneficial to suppress leakage of the device. To this end, we introduce the concept of threshold, which is to achieve competition between B-A and B by constitutively expressing Binder with a certain intensity (Figure 1). In this way, the amplifier can only be effectively activated when the input signal is strong enough. We established a mathematical model to predict the performance of the amplifier under different restrictions.

Assumption

(1) The sequence that B-A and B bind is the same. So, it can be considered that both are combined with the same substrate.

(2) B-A and B have the same promotion or inhibition effect on the amplifier and output circuit.

Symbol Description

Table 1. The name and symbol of variable. Correction: X2 represents for the concentration of Binder-Activator and X3 represents for the concentration of Binder.

Fluorescence intensity of GFP with Constant Inflammatory Signal

1.Available when the bacterial resources are extremely rich

Firstly, the amplifier we described in Figure 1 can be simplified to the Figure 2.

Figure 2. Simple circuit of the amplifier

The concentration of the Binder-Activator expressed by the input circuit is $P_{2} (x_{1})$ when the inflammatory signal is at a concentration of $x_{1}$ per unit time. The amount of Binder-Activator or GFP expressed by the amplifier or output circuit is $P (x_{2}, x_{3})$ for the Binder-Activator and Binder at a concentration of $x_{2}$ and $x_{3}$ , respectively. When the amplifier is used, it can be seen from the Figure 2 that Binder-Activator ( $x_{2}$ ) has two synthetic pathways, one is that the inflammatory signal ( $x_{1}$ ) promotes the synthesis of the input circuit, and the other is that $x_{2}$ facilitates the synthesis of the amplifier by $x_{3}$ . So, we can get this equation:

......(1)

There is only one synthetic pathway of y , that is, $x_{2}$ and $x_{3}$ work together with the output circuit to release y, so it can be obtained by assumption 2:

......(2)

Ⅰ. $P_{1} (x_{1})$ expression solving

The gene (equivalent to the binding sequence of Binder-Activator) is abbreviated as G, various transcriptional activators are abbreviated as S, and various transcriptional repressors (e.g. Binder) are abbreviated as I. The binding of $x_{1}$ to the NorR (it means the NorR will bind NO to activate the promoter PnorV) of input circuit is a reversible reaction, so the binding reaction of $x_{1}$ to the input circuit can be expressed as:

......(3)

k1 and k2 are the reaction rate constants of the forward reaction and the reverse reaction, respectively. Refer to the Michaelis-Menten equation, we do the following analysis: when the reaction reaches equilibrium, the concentration of SG does not change, that is, the rate of SG generation and decomposition is equal, then we can get the following equation:

......(4)

......(5)

......(6)

In fact, the increased rate of transcription of a regulated gene depends on the proportion of transcriptional activators that bind to the gene, and the more transcriptional activators that bind to the gene, the more the rate of expression of the gene increases. The expression of conversion to mathematics is:

......(7)

Suppose that when the substrate concentration is large enough, $P_{1} (x_{1})$ will take the maximum value, set to $P_{1max}$ , and [S] will also be much larger than [G], so we can get this:

......(8)

Bring the formula (6), (8) into equation (7) to get the analytical expression of $P_{1} (x_{1})$ :

......(9)

Although the body's immune system can make timely adjustments to the inflammatory response, $x_{1}$ is considered to be a fixed value in a sufficiently short period of time, and $P_{1} (x_{1})$ can also be considered as a constant that varies with $x_{1}$ , abbreviated as A. The calculations that follow are handled this way.

Ⅱ. $P (x_{2}, x_{3})$ expression analysis

Since $x_{2}$ , $x_{3}$ binds to the same site in the gene, the gene will be activated when $x_{2}$ binds it while being inhibited when $x_{3}$ binds it. This can be regarded as the competition between $x_{2}$ and $x_{3}$ . Similar to the analysis we used to solve the expression of , we can get:

......(10)

......(11)

In the reaction, $x_{2}$ represents the concentration of S, and $x_{3}$ represents the concentration of I. The increase of the transcription rate of the gene depends on the concentration of SG, that is, the amount of the transcriptional activator that binds to the gene, and the gene that binds to $x_{3}$ can no longer bind to $x_{2}$ , resulting in inhibition of transcription. So,

Analogy to the analysis we used to solve the expression of $P_{1} (x_{1})$ , we list the following relationships: When it reaches equilibrium:

......(12)

......(13)

From this we can get the following equation:

......(14)

......(15)

Sort out the above two formulas to get:

......(16)

The same way we get:

......(17)

When [S] is large enough, $P (x_{2}, x_{3})$ will take the maximum value and set it to . $P_{2max}$ [S] will also be much larger than [G] and another in the denominator, so there are:

......(18)

Bringing Equations (16), (18) into Equation (17) yields:

......(19)

So, we get the expression of $P (x_{2}, x_{3})$ . Because the role of $x_{3}$ in the system is to set a threshold for the amplification of $x_{2}$ , and is set to a constitutive expression, $x_{3}$ can be regarded as a fixed value of the regulation, and $x_{3}$ becomes another variable constant.

III. Calculation of : $x_{2}$

From the analysis of Equation (1) and the above two steps, the relationship between $x_{2}$ and time after adding the amplifier can be obtained:

......(20)

The relationship between GFP fluorescence intensity and time:

......(21)

When the amplifier is not used, y is directly synthesized by the inflammatory signal ( $x_{1}$ ), from which we can get:

......(22)

2. Available when the bacterial resources are restricted

The resources in bacteria are actually limited. In addition to using resources to synthesize the GFP, bacteria also need resources to maintain their normal life activities. At this time, there is competition between the amplifier and the bacteria's own life activities. The eventual result is that after a limited amount of resources are exhausted, the bacteria die and the amplifier stops working. Therefore, the following bacterial resource attenuation model is established. Assuming that the total amount of resources in the bacteria is q, then when the resources decays, the following formula holds:

......(23)

......(24)

Among the above relationship, K is the total amount of initial resources before decay, and is the time constant of the decay process, we can get:

......(25)

Solution:

......(26)

Then, when there is no amplifier, the model is corrected to:

......(27)

When there is an amplifier, the model is corrected to:

......(28)

Fluorescence intensity of GFP with attenuated Inflammatory Signal

The above model consistently believes that the intensity of the inflammatory signal is constant. However, in the actual biological environment, the inflammatory signal will be attenuated to varying degrees with distance, time and drug release. Therefore, the attenuation model of the inflammatory signal intensity is first established as follows.

Figure 3. The effect of attenuated inflammatory signal intensity on GFP output when bacterial resources are limited with an amplifier

It is easy to get the inflammatory signal intensity decay rate as follows:

......(29)

Where $K_{s}$ is the intensity of the inflammatory signal at the initial moment and $T$ is the time constant of the decay process of the inflammatory signal. Solution:

......(30)

Then the amount $P_{1} (x_{1})$ of Binder-Activator expressed in the input circuit is as follows:

......(31)

Considering the attenuation of inflammatory signals and the limitation of bacterial resources, when there is no amplifier, the model is corrected to:

......(32)

Considering the attenuation of inflammatory signals and the limitation of bacterial resources, when adding an amplifier, the model is corrected to:

......(33)

Model solving

1. Parameter assignment table

By referring to some previous work, the parameters are as follows:

Table 2. Parameter assignment

2. Model solving without amplifier

Ⅰ. When the intensity of the inflammatory signal is constant and the bacterial resources are considered to be unlimited, record , then . So, the fluorescence intensity is:

......(34)

That is:

......(35)

Ⅱ. When the intensity of the inflammatory signal is constant but the bacterial resources are limited, record . So, the fluorescence intensity is:

......(36)

That is:

......(37)

Figure 4. The effect of bacterial resources on the GFP output without amplifier

III. When the inflammatory signal is attenuated, but the bacterial resources are considered to be unlimited, the output GFP is solved as:

......(38)

That is:

......(39)

IV. When the inflammatory signal is attenuated and the bacterial resources are considered to be limited, the GFP is solved as:

......(40)

That is:

......(41)

Figure 5. The effect of bacterial resources on the GFP output when inflammatory signal is attenuated without amplifier

3. Model solving with amplifier

Ⅰ. When the intensity of the inflammatory signal is constant and the bacterial resources are considered to be unlimited, record , then:

......(42)

Using MATLAB to solve for , it is:

......(43)

Let $x_{2} = g (t)$ , then we get:

......(44)

Then we get GFP as:

......(45)

Ⅱ. When the intensity of the inflammatory signal is constant but the bacterial resources are limited, record . So, the fluorescence intensity is:

......(46)

Figure 6. The effect of bacterial resources on the GFP output with amplifier

Figure 7. GFP output curve considering bacterial resources limitations with amplifier

III. When the inflammatory signal is attenuated and the bacterial resources are limited, the Runge-Kutta method is used to solve the differential equation and the GFP curve is obtained as follows. Compared with the GFP curve without amplifier, the addition of the amplifier has obvious effect.

Figure 8. GFP output curve considering inflammatory signal attenuation and bacterial resources limitation

4. Analysis of the regulatory role of Thresholder

When the intensity of the inflammatory signal is attenuated and the bacterial resources are limited, in order to avoid the leakage of the positive feedback loop, we set the threshold regulate component Binder, the concentration can be varied between 10 and 100 mM. The regulation curve is as follows.

Figure 9. Binder regulation curve considering inflammatory signal attenuation and bacterial resources limitation

In conclusion, the introduction of Thresholder does have a regulatory effect on the output of GFP and is very obvious, which has a positive effect on suppressing the leakage of the positive feedback loop.

Our established model is based on some assumptions and approximations and lacks the support of experimental data. But we believe that our work can provide a reference to other work that requires the use of a positive feedback loop and threshold. In addition, we will conduct experiments to test the validity of our model in the future.

[1] Smole,A., Lainsˇcek,D., Bezeljak,U., Horvat,S. and Jerala,R. (2017) A synthetic mammalian therapeutic gene circuit for sensing and suppressing inflammation. Mol. Ther., 25, 102–119.

[2] Michaelis L, Menten M L. Die kinetic der invertinwirkung. Biochem. Z. , 1913, 49: 334-336

[3] Runge, Carl David Tolmé (1895), "Über die numerische Auflösung von Differentialgleichungen", Mathematische Annalen, Springer, 46 (2): 167–178,

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+         <li><a href="https://2018.igem.org/Team:NEU_China_A/Improve">Improved Biobricks</a></li>
-        <li><a href="#!">Improved Biobricks</a></li>
      </ul>
      <ul id="hp" class="dropdown-content">
-         <li><a href="#!">Silver HP</a></li>
+         <li><a href="https://2018.igem.org/Team:NEU_China_A/HumanPractices">Human Practices</a></li>
-         <li><a href="#!">Integrated HP</a></li>
+         <li><a href="https://2018.igem.org/Team:NEU_China_A/Collaborations">Collaborations</a></li>
-         <li><a href="#!">Collaborations</a></li>
+         <li><a href="https://2018.igem.org/Team:NEU_China_A/Engagement">Engagement</a></li>
      </ul>
      <ul id="team" class="dropdown-content">
-         <li><a href="#!">Team member</a></li>
+         <li><a href="https://2018.igem.org/Team:NEU_China_A/TeamMember">Team member</a></li>
-         <li><a href="#!">Attributions</a></li>
+         <li><a href="https://2018.igem.org/Team:NEU_China_A/Attributions">Attributions</a></li>
-         <li><a href="#!">Gallery</a></li>
+         <li><a href="https://2018.igem.org/Team:NEU_China_A/Gallery">Gallery</a></li>
      </ul>
-    <ul id="medalCriteria" class="dropdown-content">
+</header>
-        <li><a href="#!">For judges</a></li>
-    </ul>
-</head>
 <body>
-<div class="container">
+<div class="section hold"></div>
-     <div class="col s10 offset-s1 m12">
-         <div class="card white" id="Introduction">
+<div style="position:absolute;top: 20;width:100%">
-            <div class="card-content">
+    <div class="row ">
-                <span class="card-title black-text" style="font-size:2.5em">Introduction</span>
+        <h2 style="padding-left:200px; padding-top:calc(100vh - 250px)">Model</h2>
-                <p class="gray-text" style="font-size:1.5em">In the affected area of patients with inflammatory bowel disease, the concentration of nitric oxide is significantly increased, so we chose it as the input signal of our anti-inflammatory device. However, the nitric oxide is very unstable, so we have introduced an amplifier which can converts unstable gas signals into stable intracellular signals for sustained high-level output. The amplifier is based on a positive feedback loop. Transcription activator B-A can self-drive in a manner independent of the input signal for a period of time after the signal is input, and the metabolic flow in this cycle can be transferred to the output circuit (Figure 1). </p>
+    </div>
-                <img class="image" src="https://static.igem.org/mediawiki/2018/6/6c/T--NEU_China_A--model_figure1.png"/>
+</div>
-                <h6 style="font-size:2em">Figure 1. Schematic Design of the Synthetic amplifier</h6>
-                <p class="gray-text" style="font-size:1.5em">
+<div class="homeheight" style="margin-top: 64px">
-                    After the signal is input, the transcriptional activator B-A is generated, which includes a DNA binding domain and a transcriptional activation domain. On the one hand, B-A can activate the expression of the reporter gene, and on the other hand can activate the expression of B-A itself. The constitutively expressed Binder will compete with B-A to suppress the leakage of the device.
+    <div class="parallax-container homeheight">
-                </p>
+        <div class="parallax">
-                <p style="margin-top: 8px;font-size:1.5em">
+            <img class="responsive-img" src="https://static.igem.org/mediawiki/2018/c/c8/T--NEU_China_A--model.jpg">
-                    In addition, when using an amplifier based on a positive feedback loop, we need to strictly limit its activation until the input signal is strong enough, which is beneficial to suppress leakage of the device. To this end, we introduce the concept of thresholds, which is to achieve competition between B-A and B by constitutively expressing Binder with a certain intensity (Figure 1). In this way, the amplifier can only be effectively activated when the input signal is strong enough. We established a mathematical model to predict the performance of the amplifier under different restrictions.
+        </div>
-                </p>
+     </div>
+</div>
+<div class="container" style="margin-top: 16vh; width: 100%;">
+    <div class="row">
+         <div class="col s12">
+            <div class="card white" id="Introduction">
+                <a name="Introduction-a" style="position: relative;top: -32vh;"></a>
+                <div class="card-content">
+                    <span class="card-title light-blue-text" style="font-size:2.5em">Introduction</span>
+                    <p class="gray-text" style="font-size:1.5em">In the affected area of patients with inflammatory bowel disease, the concentration of nitric oxide is significantly increased, so we chose it as the input signal of our anti-inflammatory device. However, the nitric oxide is very unstable, so we have introduced an amplifier which can converts unstable gas signals into stable intracellular signals for sustained high-level output. The amplifier is based on a positive feedback loop. Transcription activator B-A can self-drive in a manner independent of the input signal for a period of time after the signal is input, and the metabolic flow in this cycle can be transferred to the output circuit (Figure 1). </p>
+                    <img class="image" src="https://static.igem.org/mediawiki/2018/6/6c/T--NEU_China_A--model_figure1.png"/>
+                    <p class="gray-text" style="font-size:1.5em">
+                        <strong class="black-text">Figure 1. Schematic Design of the Synthetic amplifier</strong>
+                        After the signal is input, the transcriptional activator B-A is generated, which includes a DNA binding domain and a transcriptional activation domain. On the one hand, B-A can activate the expression of the reporter gene, and on the other hand can activate the expression of B-A itself. The constitutively expressed Binder will compete with B-A to suppress the leakage of the device.
+                    </p>
+                    <p style="margin-top: 8px;font-size:1.5em">
+                        In addition, when using an amplifier based on a positive feedback loop, we need to strictly limit its activation until the input signal is strong enough, which is beneficial to suppress leakage of the device. To this end, we introduce the concept of threshold, which is to achieve competition between B-A and B by constitutively expressing Binder with a certain intensity (Figure 1). In this way, the amplifier can only be effectively activated when the input signal is strong enough. We established a mathematical model to predict the performance of the amplifier under different restrictions.
+                    </p>
+                </div>
              </div>
          </div>
-         <div class="card white">
+    </div>
-            <div class="card-content" id="Assumption">
+    <div class="row">
-                <span class="card-title black-text" style="font-size:2.5em">Assumption</span>
+         <div class="col s12">
-                <p class="gray-text" style="font-size:1.5em">
+            <div class="card white">
-                    (1) The sequence that B-A and B bind is the same. So, it can be considered that both are combined with the same substrate.
+                <div class="card-content" id="Assumption">
-                </p>
+                    <a name="Assumption-a" style="position: relative;top: -32vh;"></a>
-                <p class="gray-text" style="font-size:1.5em">
+                    <span class="card-title light-blue-text" style="font-size:2.5em">Assumption</span>
-                    (2) B-A and B have the same promotion or inhibition effect on the amplifier and output circuit.
+                    <p class="gray-text" style="font-size:1.5em">
-                </p>
+                        (1) The sequence that B-A and B bind is the same. So, it can be considered that both are combined with the same substrate.
+                    </p>
+                    <p class="gray-text" style="font-size:1.5em">
+                        (2) B-A and B have the same promotion or inhibition effect on the amplifier and output circuit.
+                    </p>
+                </div>
              </div>
          </div>
-         <div class="card white" id="Symbol Description">
+    </div>
-            <div class="card-content">
+    <div class="row">
-                <span class="card-title black-text" style="font-size:2.5em">Symbol Description</span>
+         <div class="col s12">
-                <img class="image"
+            <div class="card white" id="Symbol Description">
-                     src="https://static.igem.org/mediawiki/2018/9/9c/T--NEU_China_A--model_table1.png"/>
+                <div class="card-content">
-                <h6 style="font-size:2em">Table 1. The name and symbol of variable</h6>
+                    <a name="Symbol Description-a" style="position: relative;top: -32vh;"></a>
+                    <span class="card-title light-blue-text" style="font-size:2.5em">Symbol Description</span>
+                    <img class="image"
+                         src="https://static.igem.org/mediawiki/2018/9/9c/T--NEU_China_A--model_table1.png"/>
+                    <p class="black-text"><strong>Table 1. The name and symbol of variable. Correction: X2 represents for the concentration of Binder-Activator and X3 represents for the concentration of Binder. </strong></p>
+                </div>
              </div>
          </div>
-         <div class="card white" id="Fluorescence of GFP with Constant Inflammatory Signal">
+    </div>
-            <div class="card-content">
+    <div class="row">
-                 <span class="card-title black-text" style="font-size:2.5em">
+         <div class="col s12">
-                     Fluorescence of GFP with Constant Inflammatory Signal
+            <div class="card white" id="Fluorescence of GFP with Constant Inflammatory Signal">
+                <a name="Fluorescence of GFP with Constant Inflammatory Signal-a" style="position: relative;top: -32vh;"></a>
+                <div class="card-content">
+                 <span class="card-title light-blue-text" style="font-size:2.5em">
+                     Fluorescence intensity of GFP with Constant Inflammatory Signal
                  </span>
-                <h5 class="black-text">1.Available when the bacterial resources are extremely rich</h5>
+                    <h5 class="black-text" style="font-size: 2em">1.Available when the bacterial resources are extremely rich</h5>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Firstly, the amplifier we described in Figure 1 can be simplified to the Figure 2.
+                        Firstly, the amplifier we described in Figure 1 can be simplified to the Figure 2.
-                </p>
+                    </p>
-                <img class="image"
+                    <img class="image"
-                     src="https://static.igem.org/mediawiki/2018/thumb/7/77/T--NEU_China_A--model_figure2.png/800px-T--NEU_China_A--model_figure2.png"/>
+                         src="https://static.igem.org/mediawiki/2018/thumb/7/77/T--NEU_China_A--model_figure2.png/800px-T--NEU_China_A--model_figure2.png"/>
-                <h6 style="font-size:2em">Figure 2. Simple circuit of the amplifier</h6>
+                    <p class="black-text"><strong>Figure 2. Simple circuit of the amplifier</strong></p>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    The concentration of the Binder-Activator expressed by the input circuit is
+                        The concentration of the Binder-Activator expressed by the input circuit is
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>P</mi><mn>2</mn></msub>
+                                <msub><mi>P</mi><mn>2</mn></msub>
-                            <mo>(</mo>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    when the inflammatory signal is at a concentration of
+                        when the inflammatory signal is at a concentration of
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    per unit time. The amount of Binder-Activator or GFP expressed by the amplifier or effector is
+                        per unit time. The amount of Binder-Activator or GFP expressed by the amplifier or output circuit is
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <mtext>P</mtext>
+                                <mtext>P</mtext>
-                            <mo>(</mo>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                            <mtext>,</mtext>
+                                <mtext>,</mtext>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    for the Binder-Activator and Binder at a concentration of
+                        for the Binder-Activator and Binder at a concentration of
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    and
+                        and
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    , respectively.
+                        , respectively.
-                    When the amplifier is used, it can be seen from the Figure 2 that Binder-Activator (
+                        When the amplifier is used, it can be seen from the Figure 2 that Binder-Activator (
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    ) has two synthetic pathways, one is that the inflammatory signal (
+                        ) has two synthetic pathways, one is that the inflammatory signal (
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    ) promotes the synthesis of the input circuit, and the other is that
+                        ) promotes the synthesis of the input circuit, and the other is that
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    facilitates the synthesis of the amplifier by
+                        facilitates the synthesis of the amplifier by
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    . So, we can get this equation:
+                        . So, we can get this equation:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/b/b1/T--NEU_China_A--model_formula1.png">
+                        <img src="https://static.igem.org/mediawiki/2018/b/b1/T--NEU_China_A--model_formula1.png">
-                    <p>......(1)</p>
+                        <p>......(1)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    There is only one synthetic pathway of y
+                        There is only one synthetic pathway of y
-                    , that is,
+                        , that is,
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    and
+                        and
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    work together with the output circuit to release y,
+                        work together with the output circuit to release y,
-                    so it can be obtained by assumption 2:
+                        so it can be obtained by assumption 2:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/b/b5/T--NEU_China_A--model_formula2.png">
+                        <img src="https://static.igem.org/mediawiki/2018/b/b5/T--NEU_China_A--model_formula2.png">
-                    <p>......(2)</p>
+                        <p>......(2)</p>
-                </div>
+                    </div>
-                <h6>
+                    <h6>
-                    Ⅰ.
+                        Ⅰ.
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>P</mi><mn>1</mn></msub>
+                                <msub><mi>P</mi><mn>1</mn></msub>
-                            <mo>(</mo>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    expression solving
+                        expression solving
-                </h6>
+                    </h6>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    The gene (equivalent to the binding sequence of binder) is abbreviated as G, various transcriptional activators are abbreviated as S, and various transcriptional repressors (e.g. Binder) are abbreviated as I. The binding of
+                        The gene (equivalent to the binding sequence of Binder-Activator) is abbreviated as G, various transcriptional activators are abbreviated as S, and various transcriptional repressors (e.g. Binder) are abbreviated as I. The binding of
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    to the transcription factor (it means the NorR will be activated to bind the promoter PnorV) of input circuit is a reversible reaction, so the binding reaction of
+                        to the NorR (it means the NorR will bind NO to activate the promoter PnorV) of input circuit is a reversible reaction, so the binding reaction of
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    to the input circuit can be expressed as:
+                        to the input circuit can be expressed as:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/4/41/T--NEU_China_A--model_formula3.png">
+                        <img src="https://static.igem.org/mediawiki/2018/4/41/T--NEU_China_A--model_formula3.png">
-                    <p>......(3)</p>
+                        <p>......(3)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    k1 and k2 are the reaction rate constants of the forward reaction and the reverse reaction, respectively.
+                        k1 and k2 are the reaction rate constants of the forward reaction and the reverse reaction, respectively.
-                    Refer to the Michaelis-Menten equation, we do the following analysis: when the reaction reaches equilibrium, the concentration of SG does not change, that is, the rate of SG generation and decomposition is equal, then we can get the following equation:
+                        Refer to the Michaelis-Menten equation, we do the following analysis: when the reaction reaches equilibrium, the concentration of SG does not change, that is, the rate of SG generation and decomposition is equal, then we can get the following equation:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/3/31/T--NEU_China_A--model_formula4.png">
+                        <img src="https://static.igem.org/mediawiki/2018/3/31/T--NEU_China_A--model_formula4.png">
-                    <p>......(4)</p>
+                        <p>......(4)</p>
-                </div>
+                    </div>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/1/19/T--NEU_China_A--model_formula5.png">
+                        <img src="https://static.igem.org/mediawiki/2018/1/19/T--NEU_China_A--model_formula5.png">
-                    <p>......(5)</p>
+                        <p>......(5)</p>
-                </div>
+                    </div>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/7/7f/T--NEU_China_A--model_formula6.png">
+                        <img src="https://static.igem.org/mediawiki/2018/7/7f/T--NEU_China_A--model_formula6.png">
-                    <p>......(6)</p>
+                        <p>......(6)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    In fact, the increased rate of transcription of a regulated gene depends on the proportion of genes that bind to a transcriptional activator, and the more genes that bind to a transcriptional activator, the more the rate of expression of the gene increases. The expression of conversion to mathematics is:
+In fact, the increased rate of transcription of a regulated gene depends on the proportion of transcriptional activators that bind to the gene, and the more transcriptional activators that bind to the gene, the more the rate of expression of the gene increases. The expression of conversion to mathematics is:
-                    In fact, the increased rate of transcription of a regulated gene depends on the proportion of genes that bind to a transcriptional activator, and the more transcriptional activators that bind to the gene, the more the rate of expression of the gene increases. The mathematical expression is:
+                    </p>
-                </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/7/7f/T--NEU_China_A--model_formula6.png">
+                        <img src="https://static.igem.org/mediawiki/2018/7/7f/T--NEU_China_A--model_formula6.png">
-                    <p>......(7)</p>
+                        <p>......(7)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Suppose that when the substrate concentration is large enough,
+                        Suppose that when the substrate concentration is large enough,
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>P</mi><mn>1</mn></msub>
+                                <msub><mi>P</mi><mn>1</mn></msub>
-                            <mo>(</mo>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    will take the maximum value, set to
+                        will take the maximum value, set to
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>P</mi><mn>1max</mn></msub>
+                                <msub><mi>P</mi><mn>1max</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    , and [S] will also be much larger than [G], so we can get this:
+                        , and [S] will also be much larger than [G], so we can get this:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/7/73/T--NEU_China_A--model_formula8.png">
+                        <img src="https://static.igem.org/mediawiki/2018/7/73/T--NEU_China_A--model_formula8.png">
-                    <p>......(8)</p>
+                        <p>......(8)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Bring the formula (6), (8) into equation (7) to get the analytical expression of
+                        Bring the formula (6), (8) into equation (7) to get the analytical expression of
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>P</mi><mn>1</mn></msub>
+                                <msub><mi>P</mi><mn>1</mn></msub>
-                            <mo>(</mo>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    :
+                        :
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/1/17/T--NEU_China_A--model_formula9.png">
+                        <img src="https://static.igem.org/mediawiki/2018/1/17/T--NEU_China_A--model_formula9.png">
-                    <p>......(9)</p>
+                        <p>......(9)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Although the body's immune system can make timely adjustments to the inflammatory response,
+                        Although the body's immune system can make timely adjustments to the inflammatory response,
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    is considered to be a fixed value in a sufficiently short period of time, and
+                        is considered to be a fixed value in a sufficiently short period of time, and
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>P</mi><mn>1</mn></msub>
+                                <msub><mi>P</mi><mn>1</mn></msub>
-                            <mo>(</mo>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    can also be considered as a constant that varies with
+                        can also be considered as a constant that varies with
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    , abbreviated as A. The calculations that follow are handled this way.
+                        , abbreviated as A. The calculations that follow are handled this way.
-                </p>
+                    </p>
-                <h6>Ⅱ.
+                    <h6>Ⅱ.
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <mtext>P</mtext>
+                                <mtext>P</mtext>
-                            <mo>(</mo>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                            <mtext>,</mtext>
+                                <mtext>,</mtext>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    expression analysis
+                        expression analysis
-                </h6>
+                    </h6>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Since
+                        Since
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    ,
+                        ,
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    binds to the same site in the gene, the gene is activated when
+                        binds to the same site in the gene, the gene will be activated when
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    binds it while being inhibited when
+                        binds it while being inhibited when
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    binds it. This can be regarded as the competition between
+                        binds it. This can be regarded as the competition between
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    and
+                        and
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    . Similar to the analysis we used to solve the expression of , we can get:
+                        . Similar to the analysis we used to solve the expression of , we can get:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/c/c0/T--NEU_China_A--model_formula10.png">
+                        <img src="https://static.igem.org/mediawiki/2018/c/c0/T--NEU_China_A--model_formula10.png">
-                    <p>......(10)</p>
+                        <p>......(10)</p>
-                </div>
+                    </div>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/c/ca/T--NEU_China_A--model_formula11.png">
+                        <img src="https://static.igem.org/mediawiki/2018/c/ca/T--NEU_China_A--model_formula11.png">
-                    <p>......(11)</p>
+                        <p>......(11)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    In the reaction,
+                        In the reaction,
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    represents the concentration of S, and
+                        represents the concentration of S, and
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    represents the concentration of I. The increase of the transcription rate of the gene depends on the concentration of SG, that is, the amount of the transcriptional activator that binds to the gene, and the gene that binds to
+                        represents the concentration of I. The increase of the transcription rate of the gene depends on the concentration of SG, that is, the amount of the transcriptional activator that binds to the gene, and the gene that binds to
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    can no longer bind to
+                        can no longer bind to
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    , resulting in inhibition of transcription. So,
+                        , resulting in inhibition of transcription. So,
-                    <img src="https://static.igem.org/mediawiki/2018/b/bf/T--NEU_China_A--model_%26%E3%80%90SG%E3%80%91.png">
+                        <img src="https://static.igem.org/mediawiki/2018/b/bf/T--NEU_China_A--model_%26%E3%80%90SG%E3%80%91.png">
-                </p>
+                    </p>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Analogy to the analysis we used to solve the expression of
+                        Analogy to the analysis we used to solve the expression of
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>P</mi><mn>1</mn></msub>
+                                <msub><mi>P</mi><mn>1</mn></msub>
-                            <mo>(</mo>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    , we list the following relationships:
+                        , we list the following relationships:
-                    When it reaches equilibrium:
+                        When it reaches equilibrium:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/3/3c/T--NEU_China_A--model_formula12.png">
+                        <img src="https://static.igem.org/mediawiki/2018/3/3c/T--NEU_China_A--model_formula12.png">
-                    <p>......(12)</p>
+                        <p>......(12)</p>
-                </div>
+                    </div>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/f/fe/T--NEU_China_A--model_formula13.png">
+                        <img src="https://static.igem.org/mediawiki/2018/f/fe/T--NEU_China_A--model_formula13.png">
-                    <p>......(13)</p>
+                        <p>......(13)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    From this we can get the following equation:
+                        From this we can get the following equation:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/d/de/T--NEU_China_A--model_formula14.png">
+                        <img src="https://static.igem.org/mediawiki/2018/d/de/T--NEU_China_A--model_formula14.png">
-                    <p>......(14)</p>
+                        <p>......(14)</p>
-                </div>
+                    </div>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/5/50/T--NEU_China_A--model_formula15.png">
+                        <img src="https://static.igem.org/mediawiki/2018/5/50/T--NEU_China_A--model_formula15.png">
-                    <p>......(15)</p>
+                        <p>......(15)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Sort out the above two formulas to get:
+                        Sort out the above two formulas to get:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/8/87/T--NEU_China_A--model_formula16.png">
+                        <img src="https://static.igem.org/mediawiki/2018/8/87/T--NEU_China_A--model_formula16.png">
-                    <p>......(16)</p>
+                        <p>......(16)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    The same way we get:
+                        The same way we get:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/1/1d/T--NEU_China_A--model_formula17.png">
+                        <img src="https://static.igem.org/mediawiki/2018/1/1d/T--NEU_China_A--model_formula17.png">
-                    <p>......(17)</p>
+                        <p>......(17)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    When [S] is large enough,
+                        When [S] is large enough,
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <mtext>P</mtext>
+                                <mtext>P</mtext>
-                            <mo>(</mo>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                            <mtext>,</mtext>
+                                <mtext>,</mtext>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    will take the maximum value and set it to .
+                        will take the maximum value and set it to .
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>P</mi><mn>2max</mn></msub>
+                                <msub><mi>P</mi><mn>2max</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    [S] will also be much larger than [G] and another in the denominator, so there are:
+                        [S] will also be much larger than [G] and another in the denominator, so there are:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/d/dd/T--NEU_China_A--model_formula18.png">
+                        <img src="https://static.igem.org/mediawiki/2018/d/dd/T--NEU_China_A--model_formula18.png">
-                    <p>......(18)</p>
+                        <p>......(18)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Bringing Equations (16), (18) into Equation (17) yields:
+                        Bringing Equations (16), (18) into Equation (17) yields:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/3/34/T--NEU_China_A--model_formula19.png">
+                        <img src="https://static.igem.org/mediawiki/2018/3/34/T--NEU_China_A--model_formula19.png">
-                    <p>......(19)</p>
+                        <p>......(19)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    So, we get the expression of
+                        So, we get the expression of
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <mtext>P</mtext>
+                                <mtext>P</mtext>
-                            <mo>(</mo>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                            <mtext>,</mtext>
+                                <mtext>,</mtext>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    .
+                        .
-                    Because the role of
+                        Because the role of
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    in the system is to set a threshold for the amplification of
+                        in the system is to set a threshold for the amplification of
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    , and is set to a constitutive expression,
+                        , and is set to a constitutive expression,
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    can be regarded as a fixed value of the regulation, and
+                        can be regarded as a fixed value of the regulation, and
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>3</mn></msub>
+                                <msub><mi>x</mi><mn>3</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    becomes another variable constant.
+                        becomes another variable constant.
-                </p>
+                    </p>
-                <h6>
+                    <h6>
-                    III. Calculation of :
+                        III. Calculation of :
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                </h6>
+                    </h6>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    From the analysis of Equation (1) and the above two steps, the relationship between
+                        From the analysis of Equation (1) and the above two steps, the relationship between
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
+                                <msub><mi>x</mi><mn>2</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    and time after adding the amplifier can be obtained:
+                        and time after adding the amplifier can be obtained:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/6/6c/T--NEU_China_A--model_formula20.png">
+                        <img src="https://static.igem.org/mediawiki/2018/6/6c/T--NEU_China_A--model_formula20.png">
-                    <p>......(20)</p>
+                        <p>......(20)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    The relationship between GFP fluorescence and time:
+                        The relationship between GFP fluorescence intensity and time:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/0/0f/T--NEU_China_A--model_formula21.png">
+                        <img src="https://static.igem.org/mediawiki/2018/0/0f/T--NEU_China_A--model_formula21.png">
-                    <p>......(21)</p>
+                        <p>......(21)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    When the amplifier is not used, y is directly synthesized by the inflammatory signal (
+                        When the amplifier is not used, y is directly synthesized by the inflammatory signal (
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
+                            <mrow>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    ), from which we can get:
+                        ), from which we can get:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/4/40/T--NEU_China_A--model_formula22.png">
+                        <img src="https://static.igem.org/mediawiki/2018/4/40/T--NEU_China_A--model_formula22.png">
-                    <p>......(22)</p>
+                        <p>......(22)</p>
-                </div>
+                    </div>
-                <h5 class="black-text">2. Available when the bacterial resources are restricted</h5>
+                    <h5 class="black-text" style="font-size: 2em">2. Available when the bacterial resources are restricted</h5>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    The resources in bacteria are actually limited. In addition to using resources to synthesize the GFP, bacteria also need resources to maintain their normal life activities. At this time, there is competition between the amplifier and the bacteria's own life activities. The eventual result is that after a limited amount of resources are exhausted, the bacteria die and the amplifier stops working. Therefore, the following bacterial resource attenuation model is established.
+                        The resources in bacteria are actually limited. In addition to using resources to synthesize the GFP, bacteria also need resources to maintain their normal life activities. At this time, there is competition between the amplifier and the bacteria's own life activities. The eventual result is that after a limited amount of resources are exhausted, the bacteria die and the amplifier stops working. Therefore, the following bacterial resource attenuation model is established.
-                    Assuming that the total amount of resources in the bacteria is q, then when the resource decays, the following formula holds:
+                        Assuming that the total amount of resources in the bacteria is q, then when the resources decays, the following formula holds:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/0/08/T--NEU_China_A--model_formula23.png">
+                        <img src="https://static.igem.org/mediawiki/2018/0/08/T--NEU_China_A--model_formula23.png">
-                    <p>......(23)</p>
+                        <p>......(23)</p>
-                </div>
+                    </div>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/4/43/T--NEU_China_A--model_formula24.png">
+                        <img src="https://static.igem.org/mediawiki/2018/4/43/T--NEU_China_A--model_formula24.png">
-                    <p>......(24)</p>
+                        <p>......(24)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Among the above relationship, K is the total amount of initial resources before decay, and
+                        Among the above relationship, K is the total amount of initial resources before decay, and
-                    <img src="https://static.igem.org/mediawiki/2018/6/60/T--NEU_China_A--model_formula_special1.png">
+                        <img src="https://static.igem.org/mediawiki/2018/6/60/T--NEU_China_A--model_formula_special1.png">
-                    is the time constant of the decay process, we can get:
+                        is the time constant of the decay process, we can get:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/5/57/T--NEU_China_A--model_formula25.png">
+                        <img src="https://static.igem.org/mediawiki/2018/5/57/T--NEU_China_A--model_formula25.png">
-                    <p>......(25)</p>
+                        <p>......(25)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Solution:
+                        Solution:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/5/51/T--NEU_China_A--model_formula26.png">
+                        <img src="https://static.igem.org/mediawiki/2018/5/51/T--NEU_China_A--model_formula26.png">
-                    <p>......(26)</p>
+                        <p>......(26)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Then, when there is no amplifier, the GFP model is corrected to:
+                        Then, when there is no amplifier, the model is corrected to:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/4/47/T--NEU_China_A--model_formula27.png">
+                        <img src="https://static.igem.org/mediawiki/2018/4/47/T--NEU_China_A--model_formula27.png">
-                    <p>......(27)</p>
+                        <p>......(27)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    When there is an amplifier, the GFP model is corrected to:
+                        When there is an amplifier, the model is corrected to:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img style="width: 70%" src="https://static.igem.org/mediawiki/2018/f/fc/T--NEU_China_A--model_formula28.png">
+                        <img style="width: 70%" src="https://static.igem.org/mediawiki/2018/f/fc/T--NEU_China_A--model_formula28.png">
-                    <p>......(28)</p>
+                        <p>......(28)</p>
-                </div>
+                    </div>
-                <span class="card-title black-text" style="font-size:2.5em">
+                    <span class="card-title light-blue-text" style="font-size:2.5em" id="Fluorescence of GFP with attenuated Inflammatory Signal">
-                     Fluorescence of GFP with attenuated Inflammatory Signal
+                     Fluorescence intensity of GFP with attenuated Inflammatory Signal
-                </span>
+                    </span>
-                <p class="gray-text" style="font-size:1.5em">
+                    <a name="Fluorescence of GFP with attenuated Inflammatory Signal-a" style="position: relative;top: -48vh;"></a>
-                    The above model consistently believes that the intensity of the inflammatory signal is constant. However, in the actual biological environment, the inflammatory signal will be attenuated to varying degrees with distance, time and drug release. Therefore, the attenuation model of the inflammatory signal intensity is first established as follows.
+                    <p class="gray-text" style="font-size:1.5em">
-                </p>
+                        The above model consistently believes that the intensity of the inflammatory signal is constant. However, in the actual biological environment, the inflammatory signal will be attenuated to varying degrees with distance, time and drug release. Therefore, the attenuation model of the inflammatory signal intensity is first established as follows.
-                <img class="image" src="https://static.igem.org/mediawiki/2018/e/ea/T--NEU_China_A--model_figure3.png">
+                    </p>
-                <h6 style="font-size:2em">Figure 3. The effect of attenuated inflammatory signal intensity on GFP output when bacterial resources are limited with an amplifier</h6>
+                    <img class="image" src="https://static.igem.org/mediawiki/2018/e/ea/T--NEU_China_A--model_figure3.png">
-                <p class="gray-text" style="font-size:1.5em">
+                    <p><strong>Figure 3. The effect of attenuated inflammatory signal intensity on GFP output when bacterial resources are limited with an amplifier</strong></p>
-                    It is easy to get the inflammatory signal intensity decay rate as follows:
+                    <br>
-                </p>
+                    <p class="gra1y-text" style="font-size:1.5em">
-                <div style="display: flex; justify-content: center ;align-items: center">
+                        It is easy to get the inflammatory signal intensity decay rate as follows:
-                    <img src="https://static.igem.org/mediawiki/2018/b/b1/T--NEU_China_A--model_formula29.png">
+                    </p>
-                    <p>......(29)</p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                </div>
+                        <img src="https://static.igem.org/mediawiki/2018/b/b1/T--NEU_China_A--model_formula29.png">
-                <p class="gray-text" style="font-size:1.5em">
+                        <p>......(29)</p>
-                    Where
+                    </div>
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                    <p class="gray-text" style="font-size:1.5em">
-                        <mrow>
+                        Where
-                            <msub><mi>K</mi><mn>s</mn></msub>
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        </mrow>
+                            <mrow>
-                    </math>
+                                <msub><mi>K</mi><mn>s</mn></msub>
-                    is the intensity of the inflammatory signal at the initial moment and
+                            </mrow>
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                        </math>
-                        <mrow>
+                        is the intensity of the inflammatory signal at the initial moment and
-                            <mtext>T</mtext>
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        </mrow>
+                            <mrow>
-                    </math>
+                                <mtext>T</mtext>
-                    is the time constant of the decay process of the inflammatory signal. Solution:
+                            </mrow>
-                </p>
+                        </math>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                        is the time constant of the decay process of the inflammatory signal. Solution:
-                    <img src="https://static.igem.org/mediawiki/2018/7/7c/T--NEU_China_A--model_formula30.png">
+                    </p>
-                    <p>......(30)</p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                </div>
+                        <img src="https://static.igem.org/mediawiki/2018/7/7c/T--NEU_China_A--model_formula30.png">
-                <p class="gray-text" style="font-size:1.5em">
+                        <p>......(30)</p>
-                    Then the amount
+                    </div>
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
+                    <p class="gray-text" style="font-size:1.5em">
-                        <mrow>
+                        Then the amount
-                            <msub><mi>P</mi><mn>1</mn></msub>
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
-                            <mo>(</mo>
+                            <mrow>
+                                <msub><mi>P</mi><mn>1</mn></msub>
+                                <mo>(</mo>
-                            <msub><mi>x</mi><mn>1</mn></msub>
+                                <msub><mi>x</mi><mn>1</mn></msub>
-                            <mo>)</mo>
+                                <mo>)</mo>
-                        </mrow>
+                            </mrow>
-                    </math>
+                        </math>
-                    of Binder-Activator expressed in the input circuit is as follows:
+                        of Binder-Activator expressed in the input circuit is as follows:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/a/ae/T--NEU_China_A--model_formula31.png">
+                        <img src="https://static.igem.org/mediawiki/2018/a/ae/T--NEU_China_A--model_formula31.png">
-                    <p>......(31)</p>
+                        <p>......(31)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Considering the attenuation of inflammatory signals and the limitation of bacterial resources, when there is no amplifier, the model is corrected to:
+                        Considering the attenuation of inflammatory signals and the limitation of bacterial resources, when there is no amplifier, the model is corrected to:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://2018.igem.org/File:T--NEU_China_A--model_formula32.png">
+                        <img src="https://static.igem.org/mediawiki/2018/a/ae/T--NEU_China_A--model_formula32.png">
-                    <p>......(32)</p>
+                        <p>......(32)</p>
-                </div>
+                    </div>
-                <p class="gray-text" style="font-size:1.5em">
+                    <p class="gray-text" style="font-size:1.5em">
-                    Considering the attenuation of inflammatory signals and the limitation of bacterial resources, when adding an amplifier, the model is corrected to:
+                        Considering the attenuation of inflammatory signals and the limitation of bacterial resources, when adding an amplifier, the model is corrected to:
-                </p>
+                    </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    <img style="width: 70%" src="https://2018.igem.org/File:T--NEU_China_A--model_formula33.png">
+                        <img style="width: 70%" src="https://static.igem.org/mediawiki/2018/a/a2/T--NEU_China_A--model_formula33.png">
-                    <p>......(33)</p>
+                        <p>......(33)</p>
+                    </div>
                  </div>
              </div>
          </div>
-         <div class="card white" id="Model solving">
+    </div>
-            <div class="card-content">
+    <div class="row">
-                <span class="card-title black-text" style="font-size:2.5em">Model solving</span>
+         <div class="col s12">
-                <h6 style="font-size:2em">1. Parameter assignment table</h6>
+            <div class="card white" id="Model solving">
-                <p class="gray-text" style="font-size:1.5em">
+                <a name="Model solving-a" style="position: relative;top: -36vh;"></a>
-                    By referring to some previous work, the parameters are as follows:
+                <div class="card-content">
-                </p>
+                    <span class="card-title light-blue-text" style="font-size:2.5em">Model solving</span>
-                <img class="image" src="https://static.igem.org/mediawiki/2018/5/5d/T--NEU_China_A--model_table2.png">
+                    <h6 style="font-size:2em">1. Parameter assignment table</h6>
-                <h6 style="font-size:2em">Table 2. Parameter assignment</h6>
+                    <p class="gray-text" style="font-size:1.5em">
-                <h6 style="font-size:2em">2. Model solving without amplifier</h6>
+                        By referring to some previous work, the parameters are as follows:
-                <p class="gray-text" style="font-size:1.5em">
+                    </p>
-                    Ⅰ. When the intensity of the inflammatory signal is constant and the bacterial resources are considered to be unlimited, record
+                    <img class="image" src="https://static.igem.org/mediawiki/2018/5/5d/T--NEU_China_A--model_table2.png">
-                    <img src="https://static.igem.org/mediawiki/2018/b/be/T--NEU_China_A--model_record...png">
+                    <p><strong>Table 2. Parameter assignment</strong></p>
-                    , then
+                    <h6 style="font-size:2em">2. Model solving without amplifier</h6>
-                    <img src="https://static.igem.org/mediawiki/2018/5/59/T--NEU_China_A--model_then...png">
+                    <p class="gray-text" style="font-size:1.5em">
-                    . So, the fluorescence is:
+                        Ⅰ. When the intensity of the inflammatory signal is constant and the bacterial resources are considered to be unlimited, record
-                </p>
+                        <img src="https://static.igem.org/mediawiki/2018/b/be/T--NEU_China_A--model_record...png">
-                <div style="display: flex; justify-content: center ;align-items: center">
+                        , then
-                    <img src="https://static.igem.org/mediawiki/2018/0/0e/T--NEU_China_A--model_formula34.png">
+                        <img src="https://static.igem.org/mediawiki/2018/5/59/T--NEU_China_A--model_then...png">
-                    <p>......(34)</p>
+                        . So, the fluorescence intensity is:
-                </div>
+                    </p>
-                <p class="gray-text" style="font-size:1.5em">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    That is:
+                        <img src="https://static.igem.org/mediawiki/2018/0/0e/T--NEU_China_A--model_formula34.png">
-                </p>
+                        <p>......(34)</p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    </div>
-                    <img src="https://static.igem.org/mediawiki/2018/b/bb/T--NEU_China_A--model_formula35.png">
+                    <p class="gray-text" style="font-size:1.5em">
-                    <p>......(35)</p>
+                        That is:
-                </div>
+                    </p>
-                <p class="gray-text" style="font-size:1.5em">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    Ⅱ. When the intensity of the inflammatory signal is constant but the bacterial resources are limited, record
+                        <img src="https://static.igem.org/mediawiki/2018/b/bb/T--NEU_China_A--model_formula35.png">
-                    <img src="https://static.igem.org/mediawiki/2018/b/be/T--NEU_China_A--model_record...png">
+                        <p>......(35)</p>
-                    . So, the fluorescence is:
+                    </div>
-                </p>
+                    <p class="gray-text" style="font-size:1.5em">
-                <div style="display: flex; justify-content: center ;align-items: center">
+                        Ⅱ. When the intensity of the inflammatory signal is constant but the bacterial resources are limited, record
-                    <img src="https://static.igem.org/mediawiki/2018/c/c9/T--NEU_China_A--model_formula36.png">
+                        <img src="https://static.igem.org/mediawiki/2018/b/be/T--NEU_China_A--model_record...png">
-                    <p>......(36)</p>
+                        . So, the fluorescence intensity is:
-                </div>
+                    </p>
-                <p class="gray-text" style="font-size:1.5em">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                    That is:
+                        <img src="https://static.igem.org/mediawiki/2018/c/c9/T--NEU_China_A--model_formula36.png">
-                </p>
+                        <p>......(36)</p>
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    </div>
-                    <img src="https://static.igem.org/mediawiki/2018/4/4e/T--NEU_China_A--model_formula37.png">
+                    <p class="gray-text" style="font-size:1.5em">
-                    <p>......(37)</p>
+                        That is:
-                </div>
+                    </p>
-                <img class="image" src="https://static.igem.org/mediawiki/2018/4/49/T--NEU_China_A--model_figure4.png">
+                    <div style="display: flex; justify-content: center ;align-items: center">
-                <h6 style="font-size:2em">Figure 4. The effect of bacterial resources on the GFP output without amplifier</h6>
+                        <img src="https://static.igem.org/mediawiki/2018/4/4e/T--NEU_China_A--model_formula37.png">
-                <p class="gray-text" style="font-size:1.5em">
+                        <p>......(37)</p>
-                    III. When the inflammatory signal is attenuated, but the bacterial resources are considered to be unlimited, the output GFP is solved as:
+                    </div>
-                </p>
+                    <img class="image" src="https://static.igem.org/mediawiki/2018/4/49/T--NEU_China_A--model_figure4.png">
-                <div style="display: flex; justify-content: center ;align-items: center">
+                    <p><strong>Figure 4. The effect of bacterial resources on the GFP output without amplifier</strong></p>
-                    <img src="https://static.igem.org/mediawiki/2018/8/8d/T--NEU_China_A--model_formula38.png">
+                    <p class="gray-text" style="font-size:1.5em">
-                    <p>......(38)</p>
+                        III. When the inflammatory signal is attenuated, but the bacterial resources are considered to be unlimited, the output GFP is solved as:
+                    </p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
+                        <img src="https://static.igem.org/mediawiki/2018/8/8d/T--NEU_China_A--model_formula38.png">
+                        <p>......(38)</p>
+                    </div>
+                    <p class="gray-text" style="font-size:1.5em">
+                        That is:
+                    </p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
+                        <img src="https://static.igem.org/mediawiki/2018/b/ba/T--NEU_China_A--model_formula39.png">
+                        <p>......(39)</p>
+                    </div>
+                    <p class="gray-text" style="font-size:1.5em">
+                        IV. When the inflammatory signal is attenuated and the bacterial resources are considered to be limited, the GFP is solved as:
+                    </p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
+                        <img src="https://static.igem.org/mediawiki/2018/6/6c/T--NEU_China_A--model_formula40.png">
+                        <p>......(40)</p>
+                    </div>
+                    <p class="gray-text" style="font-size:1.5em">
+                        That is:
+                    </p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
+                        <img src="https://static.igem.org/mediawiki/2018/3/3d/T--NEU_China_A--model_formula41.png">
+                        <p>......(41)</p>
+                    </div>
+                    <img class="image" src="https://static.igem.org/mediawiki/2018/4/44/T--NEU_China_A--model_figure5.png">
+                    <p><strong>Figure 5. The effect of bacterial resources on the GFP output when inflammatory signal is attenuated without amplifier</strong></p>
+                    <h6 style="font-size:2em">3. Model solving with amplifier</h6>
+                    <p class="gray-text" style="font-size:1.5em">
+                        Ⅰ. When the intensity of the inflammatory signal is constant and the bacterial resources are considered to be unlimited, record
+                        <img src="https://static.igem.org/mediawiki/2018/b/be/T--NEU_China_A--model_record...png">
+                        , then:
+                    </p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
+                        <img src="https://static.igem.org/mediawiki/2018/6/6c/T--NEU_China_A--model_formula20.png">
+                        <p>......(42)</p>
+                    </div>
+                    <p class="gray-text" style="font-size:1.5em">
+                        Using MATLAB to solve for
+                        <img style="width: 30%" src="https://static.igem.org/mediawiki/2018/0/04/T--NEU_China_A--model_solve_for...png">
+                        , it is:
+                    </p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
+                        <img src="https://static.igem.org/mediawiki/2018/5/5b/T--NEU_China_A--model_formula43.png">
+                        <p>......(43)</p>
+                    </div>
+                    <p class="gray-text" style="font-size:1.5em">
+                        Let
+                        <math xmlns="http://www.w3.org/1998/Math/MathML">
+                            <mrow>
+                                <msub><mi>x</mi><mn>2</mn></msub>
+                                <mo>=</mo>
+                                <mtext>g</mtext>
+                                <mo>(</mo>
+                                <mtext>t</mtext>
+                                <mo>)</mo>
+                            </mrow>
+                        </math>
+                        , then we get:
+                    </p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
+                        <img style="width: 45%" src="https://static.igem.org/mediawiki/2018/7/76/T--NEU_China_A--model_formula44.png">
+                        <p>......(44)</p>
+                    </div>
+                    <p class="gray-text" style="font-size:1.5em">
+                        Then we get GFP as:
+                    </p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
+                        <img style="width: 70%" src="https://static.igem.org/mediawiki/2018/d/de/T--NEU_China_A--model_formula45.png">
+                        <p>......(45)</p>
+                    </div>
+                    <p class="gray-text" style="font-size:1.5em">
+                        Ⅱ. When the intensity of the inflammatory signal is constant but the bacterial resources are limited, record
+                        <img src="https://static.igem.org/mediawiki/2018/b/be/T--NEU_China_A--model_record...png">
+                        . So, the fluorescence intensity is:
+                    </p>
+                    <div style="display: flex; justify-content: center ;align-items: center">
+                        <img style="width: 70%" src="https://static.igem.org/mediawiki/2018/6/61/T--NEU_China_A--model_formula46.png">
+                        <p>......(46)</p>
+                    </div>
+                    <img class="image" src="https://static.igem.org/mediawiki/2018/9/93/T--NEU_China_A--model_figure6.png">
+                    <p><strong>Figure 6. The effect of bacterial resources on the GFP output with amplifier</strong></p>
+                    <img class="image" src="https://static.igem.org/mediawiki/2018/a/a0/T--NEU_China_A--model_figure7.png">
+                    <p><strong>Figure 7. GFP output curve considering bacterial resources limitations with amplifier</strong></p>
+                    <p class="gray-text" style="font-size:1.5em">
+                        III. When the inflammatory signal is attenuated and the bacterial resources are limited, the Runge-Kutta method is used to solve the differential equation and the GFP curve is obtained as follows. Compared with the GFP curve without amplifier, the addition of the amplifier has obvious effect.
+                    </p>
+                    <img class="image" src="https://static.igem.org/mediawiki/2018/9/9d/T--NEU_China_A--model_figure8.png">
+                    <p><strong>Figure 8. GFP output curve considering inflammatory signal attenuation and bacterial resources limitation</strong></p>
+                    <h6 style="font-size:2em">4. Analysis of the regulatory role of Thresholder</h6>
+                    <p class="gray-text" style="font-size:1.5em">
+                        When the intensity of the inflammatory signal is attenuated and the bacterial resources are limited, in order to avoid the leakage of the positive feedback loop, we set the threshold regulate component Binder, the concentration can be varied between 10 and 100 mM. The regulation curve is as follows.
+                    </p>
+                    <img class="image" src="https://static.igem.org/mediawiki/2018/4/43/T--NEU_China_A--model_figure9_update.png">
+                    <p><strong>Figure 9. Binder regulation curve considering inflammatory signal attenuation and bacterial resources limitation</strong></p>
+                    <p class="gray-text" style="font-size:1.5em">
+                        In conclusion, the introduction of Thresholder does have a regulatory effect on the output of GFP and is very obvious, which has a positive effect on suppressing the leakage of the positive feedback loop.
+                    </p>
+                    <p class="gray-text" style="font-size:1.5em">
+Our established model is based on some assumptions and approximations and lacks the support of experimental data. But we believe that our work can provide a reference to other work that requires the use of a positive feedback loop and threshold. In addition, we will conduct experiments to test the validity of our model in the future.
+                    </p>
+                    <br>
+                    <p class="gray-text" style="font-size:1.5em">
+[1] Smole,A., Lainsˇcek,D., Bezeljak,U., Horvat,S. and Jerala,R. (2017) A synthetic mammalian therapeutic gene circuit for sensing and suppressing inflammation. Mol. Ther., 25, 102–119.
+                    </p>
+                    <p class="gray-text" style="font-size:1.5em">
+[2] Michaelis L, Menten M L. Die kinetic der invertinwirkung. Biochem. Z. , 1913, 49: 334-336
+                    </p>
+                    <p class="gray-text" style="font-size:1.5em">
+[3] Runge, Carl David Tolmé (1895), "Über die numerische Auflösung von Differentialgleichungen", Mathematische Annalen, Springer, 46 (2): 167–178,
+                    </p>
                  </div>
-                <p class="gray-text" style="font-size:1.5em">
-                    That is:
-                </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/b/ba/T--NEU_China_A--model_formula39.png">
-                    <p>......(39)</p>
-                </div>
-                <p class="gray-text" style="font-size:1.5em">
-                    IV. When the inflammatory signal is attenuated and the bacterial resources are considered to be limited, the GFP is solved as:
-                </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/6/6c/T--NEU_China_A--model_formula40.png">
-                    <p>......(40)</p>
-                </div>
-                <p class="gray-text" style="font-size:1.5em">
-                    That is:
-                </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/3/3d/T--NEU_China_A--model_formula41.png">
-                    <p>......(41)</p>
-                </div>
-                <img class="image" src="https://static.igem.org/mediawiki/2018/4/44/T--NEU_China_A--model_figure5.png">
-                <h6 style="font-size:2em">Figure 5. The effect of bacterial resources on the GFP output when inflammatory signal is attenuated without amplifier</h6>
-                <h6 style="font-size:2em">3. Model solving with amplifier</h6>
-                <p class="gray-text" style="font-size:1.5em">
-                    Ⅰ. When the intensity of the inflammatory signal is constant and the bacterial resources are considered to be unlimited, record
-                    <img src="https://static.igem.org/mediawiki/2018/b/be/T--NEU_China_A--model_record...png">
-                    , then:
-                </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/6/6c/T--NEU_China_A--model_formula20.png">
-                    <p>......(42)</p>
-                </div>
-                <p class="gray-text" style="font-size:1.5em">
-                    Using MATLAB to solve for
-                    <img style="width: 50%" src="https://static.igem.org/mediawiki/2018/0/04/T--NEU_China_A--model_solve_for...png">
-                    , it is:
-                </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
-                    <img src="https://static.igem.org/mediawiki/2018/5/5b/T--NEU_China_A--model_formula43.png">
-                    <p>......(43)</p>
-                </div>
-                <p class="gray-text" style="font-size:1.5em">
-                    Let
-                    <math xmlns="http://www.w3.org/1998/Math/MathML">
-                        <mrow>
-                            <msub><mi>x</mi><mn>2</mn></msub>
-                            <mo>=</mo>
-                            <mtext>g</mtext>
-                            <mo>(</mo>
-                            <mtext>t</mtext>
-                            <mo>)</mo>
-                        </mrow>
-                    </math>
-                    , then find:
-                </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
-                    <img style="width: 70%" src="https://static.igem.org/mediawiki/2018/7/76/T--NEU_China_A--model_formula44.png">
-                    <p>......(44)</p>
-                </div>
-                <p class="gray-text" style="font-size:1.5em">
-                    Then find GFP as:
-                </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
-                    <img style="width: 85%" src="https://static.igem.org/mediawiki/2018/d/de/T--NEU_China_A--model_formula45.png">
-                    <p>......(45)</p>
-                </div>
-                <p class="gray-text" style="font-size:1.5em">
-                    Ⅱ. When the intensity of the inflammatory signal is constant but the bacterial resources are limited, record
-                    <img src="https://static.igem.org/mediawiki/2018/b/be/T--NEU_China_A--model_record...png">
-                    . So, the fluorescence is:
-                </p>
-                <div style="display: flex; justify-content: center ;align-items: center">
-                    <img style="width: 85%" src="https://static.igem.org/mediawiki/2018/6/61/T--NEU_China_A--model_formula46.png">
-                    <p>......(46)</p>
-                </div>
-                <img class="image" src="https://static.igem.org/mediawiki/2018/9/93/T--NEU_China_A--model_figure6.png">
-                <h6 style="font-size:2em">Figure 6. The effect of bacterial resources on the GFP output with amplifier</h6>
-                <img class="image" src="https://static.igem.org/mediawiki/2018/a/a0/T--NEU_China_A--model_figure7.png">
-                <h6 style="font-size:2em">Figure 7. GFP output curve considering bacterial resources limitations with amplifier</h6>
-                <p class="gray-text" style="font-size:1.5em">
-                    III. When the inflammatory signal is attenuated and the bacterial resources are limited, the Runge-Kutta method is used to solve the differential equation and the GFP curve is obtained as follows. Compared with the GFP curve without amplifier, the addition of the amplifier has obvious effect.
-                </p>
-                <img class="image" src="https://static.igem.org/mediawiki/2018/9/9d/T--NEU_China_A--model_figure8.png">
-                <h6 style="font-size:2em">Figure 8. GFP output curve considering inflammatory signal attenuation and bacterial resources limitation</h6>
-                <h6 style="font-size:2em">Analysis of the regulatory role of Thresholder</h6>
-                <p class="gray-text" style="font-size:1.5em">
-                    When the intensity of the inflammatory signal is attenuated and the bacterial resources are limited, in order to avoid the leakage of the positive feedback loop, we set the threshold regulate component Binder, the concentration can be varied between 10 and 100 mM. The regulation curve is as follows.
-                </p>
-                <img class="image" src="https://static.igem.org/mediawiki/2018/d/d3/T--NEU_China_A--model_figure9.png">
-                <h6 style="font-size:2em">Figure 9. Binder regulation curve considering inflammatory signal attenuation and bacterial resources limitation</h6>
-                <p class="gray-text" style="font-size:1.5em">
-                    In conclusion, the introduction of Thresholder does have a regulatory effect on the output of GFP and is very obvious, which has a positive effect on suppressing the leakage of the positive feedback loop.
-                </p>
              </div>
          </div>
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Difference between revisions of "Team:NEU China A/Model"

Latest revision as of 01:52, 21 November 2018

Model

1.Available when the bacterial resources are extremely rich

Ⅰ. P1 ( x1 ) expression solving

Ⅱ. P ( x2 , x3 ) expression analysis

III. Calculation of : x2

2. Available when the bacterial resources are restricted

1. Parameter assignment table

2. Model solving without amplifier

3. Model solving with amplifier

4. Analysis of the regulatory role of Thresholder

Ⅰ. $P_{1} (x_{1})$ expression solving

Ⅱ. $P (x_{2}, x_{3})$ expression analysis

III. Calculation of : $x_{2}$