Difference between revisions of "Team:SEU/Model"

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                                          <h2>Model</h2>
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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">Proof: \(\dfrac{d A_i}{d t}=-k_i[A_i](t) \Rightarrow [A_i](t)=[A_i](0)e^{-k_it} \Rightarrow \dfrac{d O}{d t}=\sum_{i=1}^2 k_i[A_i](t) \Rightarrow [O](\infty)= [A_1](0)/k_1+[A_2](0)/k_2.\) If \(k_1\approx k_2\), then addition is successfully implemented.</p>
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                                          <p style="font-size=36px">Subtraction: \(A+B \xrightarrow{k_1} \phi\)</p>
  <li class='has-sub'><a href='https://2019.igem.org/Team:SEU'><span>Home</span></a></li>
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                                          <p style="font-size=36px">Multiplication: \(\alpha \xrightarrow{k} \phi, A+B+\alpha \xrightarrow{k} A+B+\alpha+C\)</p>                                        
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              <h1 class="entry-title">Model</h1>
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Revision as of 07:40, 2 October 2019





Model

Computation method

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

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

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

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