Difference between revisions of "Team:SEU/Contribution"

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                                           <h2>Contribution</h2>
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                                           <h2>Model</h2>
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                                           <p style="font-size=36px">Through the comprehensive use of life science and information science knowledge, we have obtained the results of this experiment. In the whole process, we encountered many difficulties and challenges, but after careful thinking and practice, we finally successfully overcome these. In addition, we have also summarized some information that may be helpful to other teams, hoping to make some contributions to the iGEM community. </p>
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                                          <h3>Computation method</h3>
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                                          <p >Addition: \(A_1 \xrightarrow{k_1} O,\quad A_2 \xrightarrow{k_2} O\)</p>
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                                           <p style="font-size=36px">1.We propose a computation model in molecular computing based on reaction kinetic analysis. </p>
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                                           <p style="font-size=24px">Proof: \(\dfrac{d [A_i](t)}{d t}=-k_i[A_i](t)\) \(\Rightarrow [A_i](t)=[A_i](0)e^{-k_it}, \) \(\dfrac{d [O](t)}{d t}=\sum_{i=1}^2 k_i[A_i](t)\) \(\Rightarrow [O](\infty)=\int_0^\infty \sum_{i=1}^2 k_i[A_i](t)dt = [A_1](0)/k_1+[A_2](0)/k_2.\) If \(k_1\approx k_2\), then addition is successfully implemented.</p>
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                                           <p style="font-size=24px">Subtraction: \(A+B \xrightarrow{k_1} \phi\)</p>
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                                           <p style="font-size=24px">Proof: It is identical with [1]. Apparently, \([A](t)=[B](t)+\Delta \). <br>If \(\Delta \neq 0\), \(\dfrac{d [A](t)}{d t}=-[A](t)([A](t)-\Delta)\) \(\Rightarrow [A](t)=\dfrac{[A](0)\Delta}{-[A](0)+[A](0)e^{\Delta t}+\Delta e^{\Delta t}} (\Delta \neq 0).\) If \(\Delta > 0\), \([A](\infty)=\Delta\). Otherwise \([A](\infty)=0\).
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                                           <p style="font-size=36px">2.Using such a model, we implement a neuron, the basic element of neural network.</p>
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                                          <br>If \(\Delta =0\), \([A](t)=\dfrac{[A](0)}{1+[A](0)t}\). \([A](\infty)=0\). Hence substraction is implemented.</p>
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                                           <center><a href="https://2019.igem.org/Team:SEU/Demonstrate" class="buttonContri">Demonstrate</a></center>
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                                           <p style="font-size=24px">Multiplication: \(\alpha \xrightarrow{k_1} \phi, A+B+\alpha \xrightarrow{k_2} A+B+\alpha+C\)</p>
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                                           <p style="font-size=24px">Proof: \(\dfrac{d [\alpha](t)}{d t}=-k_1[\alpha](t)\) \(\Rightarrow [\alpha](t)=[\alpha](0)e^{-k_1t},\) \(\dfrac{d [A](t)}{d t}=\dfrac{d [B](t)}{d t}=0, \dfrac{d [C](t)}{d t}=k_2[A](t)[B](t)[\alpha](t)\) \(\Rightarrow [C](\infty)=\int_0^\infty [A](0)[B](0)[\alpha](t)=k_2/k_1[\alpha](0)[A](0)[B](0)\). Hence multiplication is implemented.</p>
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                                           <p style="font-size=36px">3.To help with experiment, we develop a webpage tool which can generate DNA structures and sequences. Researchers can directly use such sequences to conduct experiments.</p>
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                                          <h3>References</h3>
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                                           <center><a href="https://2019.igem.org/Team:SEU/Software" class="buttonContri">Software</a></center>
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                                           <p>[1]C. Fang, Z. Shen, Z. Zhang, X. You and C. Zhang, "Synthesizing a Neuron Using Chemical Reactions," 2018 IEEE International Workshop on Signal Processing Systems (SiPS), Cape Town, 2018, pp. 187-192.</p>
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                                           <p>[2]M. Vasic, D. Soloveichik, S. Khurshid, "CRN++: Molecular Programming Language." arXiv preprint arXiv 1809.07430.</p>
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Revision as of 09:14, 2 October 2019





Model

Computation method

Addition: \(A_1 \xrightarrow{k_1} O,\quad A_2 \xrightarrow{k_2} O\)

Proof: \(\dfrac{d [A_i](t)}{d t}=-k_i[A_i](t)\) \(\Rightarrow [A_i](t)=[A_i](0)e^{-k_it}, \) \(\dfrac{d [O](t)}{d t}=\sum_{i=1}^2 k_i[A_i](t)\) \(\Rightarrow [O](\infty)=\int_0^\infty \sum_{i=1}^2 k_i[A_i](t)dt = [A_1](0)/k_1+[A_2](0)/k_2.\) If \(k_1\approx k_2\), then addition is successfully implemented.

Subtraction: \(A+B \xrightarrow{k_1} \phi\)

Proof: It is identical with [1]. Apparently, \([A](t)=[B](t)+\Delta \).
If \(\Delta \neq 0\), \(\dfrac{d [A](t)}{d t}=-[A](t)([A](t)-\Delta)\) \(\Rightarrow [A](t)=\dfrac{[A](0)\Delta}{-[A](0)+[A](0)e^{\Delta t}+\Delta e^{\Delta t}} (\Delta \neq 0).\) If \(\Delta > 0\), \([A](\infty)=\Delta\). Otherwise \([A](\infty)=0\).
If \(\Delta =0\), \([A](t)=\dfrac{[A](0)}{1+[A](0)t}\). \([A](\infty)=0\). Hence substraction is implemented.

Multiplication: \(\alpha \xrightarrow{k_1} \phi, A+B+\alpha \xrightarrow{k_2} A+B+\alpha+C\)

Proof: \(\dfrac{d [\alpha](t)}{d t}=-k_1[\alpha](t)\) \(\Rightarrow [\alpha](t)=[\alpha](0)e^{-k_1t},\) \(\dfrac{d [A](t)}{d t}=\dfrac{d [B](t)}{d t}=0, \dfrac{d [C](t)}{d t}=k_2[A](t)[B](t)[\alpha](t)\) \(\Rightarrow [C](\infty)=\int_0^\infty [A](0)[B](0)[\alpha](t)=k_2/k_1[\alpha](0)[A](0)[B](0)\). Hence multiplication is implemented.

References

[1]C. Fang, Z. Shen, Z. Zhang, X. You and C. Zhang, "Synthesizing a Neuron Using Chemical Reactions," 2018 IEEE International Workshop on Signal Processing Systems (SiPS), Cape Town, 2018, pp. 187-192.

[2]M. Vasic, D. Soloveichik, S. Khurshid, "CRN++: Molecular Programming Language." arXiv preprint arXiv 1809.07430.