From 7099430690388dfeacd0d480817fe8983fdc8f0a Mon Sep 17 00:00:00 2001
From: Kang Wang <888666wang4286@gmail.com>
Date: Tue, 1 Oct 2024 14:10:57 +0000
Subject: [PATCH] =?UTF-8?q?=E4=BF=AE=E6=94=B9model=E7=9A=84=E5=85=AC?=
=?UTF-8?q?=E5=BC=8F=E7=BC=96=E5=8F=B7=E5=8A=A0=E6=8B=AC=E5=8F=B7?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
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---
src/contents/model.tsx | 285 ++++++++++++++---------------------------
1 file changed, 96 insertions(+), 189 deletions(-)
diff --git a/src/contents/model.tsx b/src/contents/model.tsx
index b44c9c7..38ba602 100644
--- a/src/contents/model.tsx
+++ b/src/contents/model.tsx
@@ -143,21 +143,19 @@ export function Model() {
<MathJax.Provider>
<div className='indent formula_content' >
<span className='formula_line'><MathJax.Node formula={`{PEA_{gut}\\overset{k_{\\text{diff}}\\_{\\text{PEA}}}{\\underset{k_{\\text{diff}}\\_{\\text{PEA}}}{\\rightleftharpoons}} PEA_{peri}}`} /> </span>
- <span className='formula_number'>1</span>
+ <span className='formula_number'>(1)</span>
</div>
</MathJax.Provider>
<p>According to the law of mass action, this process can be represented by an ordinary differential equation (ODE) as follows</p>
<MathJax.Provider>
<div className='indent formula_content' >
<span className='formula_line'> <MathJax.Node formula={`\\frac{\\mathrm{d}[PEA_{peri}]}{\\mathrm{d}t} = \\frac{k_{diff\\_PEA}}{V_{peri}}([PEA_{gut}] - [PEA_{peri}])`} /> </span>
- <span className='formula_number'>2</span>
-
+ <span className='formula_number'>(2)</span>
</div>
<div className='indent formula_content'>
<span className='formula_line'> <MathJax.Node formula={`\\frac{\\mathrm{d}[PEA_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_PEA}}{V_{gut}}([PEA_{peri}] - [PEA_{gut}])`} /> </span>
- <span className='formula_number'>3</span>
- </div>
+ <span className='formula_number'>(3)</span> </div>
</MathJax.Provider>
<p>where <MathJax.Provider>
@@ -169,8 +167,7 @@ export function Model() {
<MathJax.Provider>
<div className='indent formula_content'>
<span className='formula_line'><MathJax.Node formula={` PEA\\xrightarrow[K_{M\\_TynA},k_{cat\\_TynA}]{TynA} PA_{peri} + NH_{3\\_peri}`} /> </span>
- <span className='formula_number'>4</span>
- </div>
+ <span className='formula_number'>(4)</span> </div>
</MathJax.Provider>
<p>The Michaelis-Menten mechanism describes the enzymatic conversion of a substrate <MathJax.Provider>
<span>
@@ -190,8 +187,7 @@ export function Model() {
<MathJax.Provider>
<div className='indent formula_content'>
<span className='formula_line'><MathJax.Node formula={`{{E+S}\\overset{k_{f1}}{\\underset{k_{r1}}{\\rightleftharpoons}} ES \\xrightarrow[]{k_{cat}}E + P}`} /> </span>
- <span className='formula_number'>5</span>
- </div>
+ <span className='formula_number'>(5)</span> </div>
</MathJax.Provider>
<p>where <MathJax.Provider>
<span>
@@ -221,13 +217,11 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`k_{f1}[E][S] = \\left( k_{r1} + k_{\\mathrm{cat}} \\right) [ES]`} /> </span>
- <span className='formula_number'>6</span>
- </div>
+ <span className='formula_number'>(6)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`[ES] = \\frac{ k_{f1}[E][S] }{ k_{r1} + k_{\\mathrm{cat}} }`} /> </span>
- <span className='formula_number'>7</span>
- </div>
+ <span className='formula_number'>(7)</span> </div>
</MathJax.Provider>
@@ -236,8 +230,7 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`[E_{\\text{total}}] = [E] + [ES]`} /> </span>
- <span className='formula_number'>8</span>
- </div>
+ <span className='formula_number'>(8)</span> </div>
</MathJax.Provider>
<p>Substitute <MathJax.Provider>
<span>
@@ -255,8 +248,7 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`[ES] = \\frac{[E_{\\text{total}}] [S]}{\\frac{k_{r1} + k_{\\text{cat}}}{k_{f1}} + [S]}`} /> </span>
- <span className='formula_number'>9</span>
- </div>
+ <span className='formula_number'>(9)</span> </div>
</MathJax.Provider>
<p>The Michaelis constant <MathJax.Provider>
<span>
@@ -268,8 +260,7 @@ export function Model() {
<span className='formula_line'>
<MathJax.Node formula={`K_M = \\frac{k_{r1} + k_{\\text{cat}}}{k_{f1}}
`} /> </span>
- <span className='formula_number'>10</span>
- </div>
+ <span className='formula_number'>(10)</span> </div>
</MathJax.Provider>
<p>This simplifies the expression for to</p>
@@ -278,7 +269,7 @@ export function Model() {
<span className='formula_line'>
<MathJax.Node formula={`ES = \\frac{ {[E\\_total][S]} }{K_M + [S]}`} /> </span>
- <span className='formula_number'>11</span> </div>
+ <span className='formula_number'>(11)</span> </div>
</MathJax.Provider>
<p>The rate of product formation is
@@ -287,8 +278,7 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`v_0 = k_{cat}[ES]`} /> </span>
- <span className='formula_number'>12</span>
- </div>
+ <span className='formula_number'>(12)</span> </div>
</MathJax.Provider>
<p>Substituting <MathJax.Provider>
<span>
@@ -300,8 +290,7 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`v_0 = \\frac{V_{max}[s]}{K_M+[S]}`} /> </span>
- <span className='formula_number'>13</span>
- </div>
+ <span className='formula_number'>(13)</span> </div>
</MathJax.Provider>
<p>where <MathJax.Provider>
@@ -331,20 +320,17 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PA_{peri}]}{\\mathrm{d}t} = \\frac{k_{cat\\_TynA}[TynA][PEA_{peri}]}{K_{M\\_TynA}+[PEA_{peri}]}`} /></span>
- <span className='formula_number'>14</span>
-
+ <span className='formula_number'>(14)</span>
</div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[NH_{3\\_peri}]}{\\mathrm{d}t} = \\frac{k_{cat\\_TynA}[TynA][PEA_{peri}]}{K_{M\\_TynA}+[PEA_{peri}]}`} /> </span>
- <span className='formula_number'>15</span>
-
+ <span className='formula_number'>(15)</span>
</div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PEA_{peri}]}{\\mathrm{d}t} = -\\frac{k_{cat\\_TynA}[TynA][PEA_{peri}]}{K_{M\\_TynA}+[PEA_{peri}]}`} /></span>
- <span className='formula_number'>16</span>
-
+ <span className='formula_number'>(16)</span>
</div>
</MathJax.Provider>
@@ -353,14 +339,12 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`PA_{peri}\\overset{}{\\underset{}{\\rightleftharpoons}}PA_{cyto}`} /></span>
- <span className='formula_number'>17</span>
-
+ <span className='formula_number'>(17)</span>
</div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`NH_{3\\_peri}\\overset{}{\\underset{}{\\rightleftharpoons}}NH_{3\\_cyto}`} /> </span>
- <span className='formula_number'>18</span>
-
+ <span className='formula_number'>(18)</span>
</div>
</MathJax.Provider>
<p>According to the law of mass action</p>
@@ -368,26 +352,22 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PA_{cyto}]}{\\mathrm{d}t} = \\frac{k_{diff\\_PA}}{V_{cyto}}([PA_{peri}]-[PA_{cyto}])`} /></span>
- <span className='formula_number'>19</span>
-
+ <span className='formula_number'>(19)</span>
</div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PA_{peri}]}{\\mathrm{d}t} = \\frac{k_{diff\\_PA}}{V_{peri}}([PA_{cyto}]-[PA_{peri}])`} /> </span>
- <span className='formula_number'>20</span>
-
+ <span className='formula_number'>(20)</span>
</div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[NH_{3\\_cyto}]}{\\mathrm{d}t} = \\frac{k_{diff\\_NH3}}{V_{cyto}}([NH_{3\\_peri}]-[NH_{3\\_cyto}])`} /></span>
- <span className='formula_number'>21</span>
-
+ <span className='formula_number'>(21)</span>
</div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[NH_{3\\_peri}]}{\\mathrm{d}t} = \\frac{k_{diff\\_NH3}}{V_{peri}}([NH_{3\\_cyto}]-[NH_{3\\_peri}])`} /> </span>
- <span className='formula_number'>22</span>
-
+ <span className='formula_number'>(22)</span>
</div>
</MathJax.Provider>
@@ -398,20 +378,17 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`FeaR+PA_{cyto}\\overset{}{\\underset{}{\\rightleftharpoons}}FearR-PA`} /></span>
- <span className='formula_number'>23</span>
-
+ <span className='formula_number'>(23)</span>
</div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`FeaR-PA\\xrightarrow{}FearR+PAA_{cyto}`} /> </span>
- <span className='formula_number'>24</span>
-
+ <span className='formula_number'>(24)</span>
</div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`PAA_{cyto}\\overset{}{\\underset{}{\\rightleftharpoons}}PAA_{gut}`} /></span>
- <span className='formula_number'>25</span>
-
+ <span className='formula_number'>(25)</span>
</div>
</MathJax.Provider>
<p>The FeaR-phenylacetaldehyde complex can bind and activate the PTynA promoter. In this case, the concentration of the enzyme-substrate complex <MathJax.Provider>
@@ -439,8 +416,7 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`K_M = \\frac{k_{r1}+k_{cat}}{k_{f1}}`} /></span>
- <span className='formula_number'>26</span>
-
+ <span className='formula_number'>(26)</span>
</div>
</MathJax.Provider>
@@ -484,8 +460,7 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`k_{f1} \\approx \\frac{k_{cat}}{K_m}`} /></span>
- <span className='formula_number'>27</span>
-
+ <span className='formula_number'>(27)</span>
</div>
</MathJax.Provider>
@@ -494,29 +469,24 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[FeaR\\mathrm{-}PA]}{\\mathrm{d}t} = \\frac{k_{cat\\_FeaR}[FeaR][PA_{cyto}]}{K_{M\\_FeaR}} - k_{cat\\_FeaR}[FeaR\\mathrm{-}PA]`} /></span>
- <span className='formula_number'>28</span>
- </div>
+ <span className='formula_number'>(28)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[FeaR]}{\\mathrm{d}t} = - \\frac{k_{cat\\_FeaR}[FeaR][PA_{cyto}]}{K_{M\\_FeaR}} + k_{cat\\_FeaR}[FeaR\\mathrm{-}PA]`} /> </span>
- <span className='formula_number'>29</span>
- </div>
+ <span className='formula_number'>(29)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PA_{cyto}]}{\\mathrm{d}t} = - \\frac{k_{cat\\_FeaR}[FeaR][PA_{cyto}]}{K_{M\\_FeaR}}`} /> </span>
- <span className='formula_number'>30</span>
- </div>
+ <span className='formula_number'>(30)</span> </div>
<div className='indent formula_content' id='long_formula'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PAA_{cyto}]}{\\mathrm{d}t} = k_{cat\\_FeaR}[FeaR\\mathrm{-}PA] + \\frac{k_{diff\\_PAA}}{V_{cyto}}([PAA_{gut}]-[PAA_{cyto}])`} /> </span>
- <span className='formula_number'>31</span>
- </div>
+ <span className='formula_number'>(31)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PAA_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_PAA}}{V_{gut}}([PAA_{cyto}]-[PAA_{gut}])`} /> </span>
- <span className='formula_number'>32</span>
- </div>
+ <span className='formula_number'>(32)</span> </div>
</MathJax.Provider>
@@ -530,42 +500,35 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`P_{TynA\\_GS}+FeaR-PA\\overset{}{\\underset{}{\\rightleftharpoons}}P_{TynA\\_GS\\_active}`} /></span>
- <span className='formula_number'>33</span>
- </div>
+ <span className='formula_number'>(33)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`P_{TynA\\_TPH1}+FeaR-PA\\overset{}{\\underset{}{\\rightleftharpoons}}P_{TynA\\_TPH1\\_active}`} /> </span>
- <span className='formula_number'>34</span>
- </div>
+ <span className='formula_number'>(34)</span> </div>
</MathJax.Provider>
<p>The corresponding set of ODEs is</p>
<MathJax.Provider>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[P_{TynA\\_GS\\_active}]}{\\mathrm{d}t} = k_{f\\_PtynA}[P_{TynA\\_GS}][FeaR\\mathrm{-}PA] - k_{r\\_PtynA}[P_{TynA\\_GS\\_active}]`} /></span>
- <span className='formula_number'>35</span>
- </div>
+ <span className='formula_number'>(35)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[P_{TynA\\_TPH1\\_active}]}{\\mathrm{d}t} = k_{f\\_PtynA}[P_{TynA\\_TPH1}][FeaR\\mathrm{-}PA] - k_{r\\_PtynA}[P_{TynA\\_TPH1\\_active}]`} /> </span>
- <span className='formula_number'>36</span>
- </div>
+ <span className='formula_number'>(36)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[P_{TynA\\_GS}]}{\\mathrm{d}t} = -k_{f\\_PtynA}[P_{TynA\\_GS}][FeaR\\mathrm{-}PA] + k_{r\\_PtynA}[P_{TynA\\_GS\\_active}]`} /></span>
- <span className='formula_number'>37</span>
- </div>
+ <span className='formula_number'>(37)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[P_{TynA\\_TPH1}]}{\\mathrm{d}t} = -k_{f\\_PtynA}[P_{TynA\\_TPH1}][FeaR\\mathrm{-}PA] + k_{r\\_PtynA}[P_{TynA\\_TPH1\\_active}]`} /></span>
- <span className='formula_number'>38</span>
- </div>
+ <span className='formula_number'>(38)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[FeaR\\mathrm{-}PA]}{\\mathrm{d}t} = -k_{f\\_PtynA}[P_{TynA\\_GS}][FeaR\\mathrm{-}PA] - k_{f\\_PtynA}[P_{TynA\\_TPH1}][FeaR\\mathrm{-}PA] + k_{r\\_PtynA}[P_{TynA\\_GS\\_active}] + k_{r\\_PtynA}[P_{TynA\\_TPH1\\_active}]`} /></span>
- <span className='formula_number'>39</span>
- </div>
+ <span className='formula_number'>(39)</span> </div>
</MathJax.Provider>
<p>where <MathJax.Provider>
@@ -587,71 +550,59 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`P_{TynA\\_GS\\_active} \\rightarrow P_{TynA\\_GS\\_active} + mRNA_{GS}`} /></span>
- <span className='formula_number'>40</span>
- </div>
+ <span className='formula_number'>(40)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`P_{TynA\\_TPH1\\_active} \\rightarrow P_{TynA\\_TPH1\\_active}+mRNA_{TPH1}`} /> </span>
- <span className='formula_number'>41</span>
- </div>
+ <span className='formula_number'>(41)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`mRNA_{GS}\\rightarrow \\varnothing`} /> </span>
- <span className='formula_number'>42</span>
- </div>
+ <span className='formula_number'>(42)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`mRNA_{TPH1}\\rightarrow \\varnothing`} /> </span>
- <span className='formula_number'>43</span>
- </div>
+ <span className='formula_number'>(43)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[mRNA_{GS}]}{\\mathrm{d}t} = k_{mRNA\\_GS}[P_{TynA\\_GS\\_active}] - d_{mRNA\\_GS}[mRNA_{GS}]`} /> </span>
- <span className='formula_number'>44</span>
- </div>
+ <span className='formula_number'>(44)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[mRNA_{TPH1}]}{\\mathrm{d}t} = k_{mRNA\\_TPH1}[P_{TynA\\_TPH1\\_active}] - d_{mRNA\\_TPH1}[mRNA_{TPH1}]`} /> </span>
- <span className='formula_number'>45</span>
- </div>
+ <span className='formula_number'>(45)</span> </div>
</MathJax.Provider>
<p>Next is the process of translation and degradation of the target protein.</p>
<MathJax.Provider>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`mRNA_{GS}\\rightarrow mRNA_{GS}+GS`} /></span>
- <span className='formula_number'>46</span>
-
+ <span className='formula_number'>(46)</span>
</div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`mRNA_{TPH1}\\rightarrow mRNA_{TPH1}+TPH1`} /> </span>
- <span className='formula_number'>48</span>
- </div>
+ <span className='formula_number'>(48)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`GS\\rightarrow \\varnothing`} /> </span>
- <span className='formula_number'>49</span>
- </div>
+ <span className='formula_number'>(49)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`TPH1\\rightarrow \\varnothing`} /> </span>
- <span className='formula_number'>50</span>
- </div>
+ <span className='formula_number'>(50)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[GS]}{\\mathrm{d}t} = p_{GS}[mRNA_{GS}] - d_{GS}[GS]`} /> </span>
- <span className='formula_number'>51</span>
- </div>
+ <span className='formula_number'>(51)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[TPH1]}{\\mathrm{d}t} = p_{TPH1}[mRNA_{TPH1}] - d_{TPH1}[TPH1]`} /> </span>
- <span className='formula_number'>52</span>
- </div>
+ <span className='formula_number'>(52)</span> </div>
</MathJax.Provider>
@@ -661,23 +612,19 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`Glu_{gut}\\overset{}{\\underset{}{\\rightleftharpoons}}Glu_{cyto}`} /></span>
- <span className='formula_number'>53</span>
- </div>
+ <span className='formula_number'>(53)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`NH_{3_{Peri}}\\overset{}{\\underset{}{\\rightleftharpoons}}NH_{3_{cyto}}`} /> </span>
- <span className='formula_number'>54</span>
- </div>
+ <span className='formula_number'>(54)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`Glu_{cyto}+ NH_{3\\_cyto}\\xrightarrow[] Gln_{cyto}`} /> </span>
- <span className='formula_number'>55</span>
- </div>
+ <span className='formula_number'>(55)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`Gln_{cyto}\\overset{}{\\underset{}{\\rightleftharpoons}} Gln_{gut}`} /> </span>
- <span className='formula_number'>56</span>
- </div>
+ <span className='formula_number'>(56)</span> </div>
</MathJax.Provider>
<p>For an enzyme-catalyzed reaction involving two substrates that form a single product, the Michaelis-Menten equation can be extended to account for the involvement of both substrates. The general reaction can be written as</p>
@@ -685,16 +632,14 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`E+A+B\\overset{k_{f1}}{\\underset{k_{r1}}{\\rightleftharpoons}}EAB \\xrightarrow{k_{cat}}E+P]`} /></span>
- <span className='formula_number'>57</span>
- </div>
+ <span className='formula_number'>(57)</span> </div>
</MathJax.Provider>
<p>The Michaelis-Menten equation is</p>
<MathJax.Provider>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`v_0 = \\frac{V_{max} [A] [B]}{K_{M\\_A}[B] + K_{M\\_B}[A] + [A][B]}`} /></span>
- <span className='formula_number'>58</span>
- </div>
+ <span className='formula_number'>(58)</span> </div>
</MathJax.Provider>
<p>where <MathJax.Provider>
<span>
@@ -727,28 +672,23 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Glu_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_Glu}}{V_{gut}}([Glu_{cyto}]-[Glu_{gut}])`} /></span>
- <span className='formula_number'>59</span>
- </div>
+ <span className='formula_number'>(59)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Glu_{cyto}]}{\\mathrm{d}t} = \\frac{k_{diff\\_Glu}}{V_{cyto}}([Glu_{gut}]-[Glu_{cyto}]) - \\frac{k_{cat\\_GS}[GS][Glu_{cyto}][NH_{3\\_cyto}]}{(K_{M\\_GS\\_Glu}+[Glu_{cyto}])(K_{M\\_GS\\_NH3}+[NH_{3\\_cyto}])}`} /></span>
- <span className='formula_number'>60</span>
- </div>
+ <span className='formula_number'>(60)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[NH_{3\\_cyto}]}{\\mathrm{d}t} = \\frac{k_{diff\\_NH3}}{V_{cyto}}([NH_{3\\_peri}]-[NH_{3\\_cyto}]) - \\frac{k_{cat\\_GS}[GS][Glu_{cyto}][NH_{3\\_cyto}]}{(K_{M\\_GS\\_Glu}+[Glu_{cyto}])(K_{M\\_GS\\_NH3}+[NH_{3\\_cyto}])}`} /> </span>
- <span className='formula_number'>61</span>
- </div>
+ <span className='formula_number'>(61)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Gln_{cyto}]}{\\mathrm{d}t} = \\frac{k_{cat\\_GS}[GS][Glu_{cyto}][NH_{3\\_cyto}]}{(K_{M\\_GS\\_Glu}+[Glu_{cyto}])(K_{M\\_GS\\_NH3}+[NH_{3\\_cyto}])} + \\frac{k_{diff\\_Gln}}{V_{cyto}}([Gln_{gut}]-[Gln_{cyto}])`} /></span>
- <span className='formula_number'>62</span>
- </div>
+ <span className='formula_number'>(62)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Gln_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_Gln}}{V_{gut}}([Gln_{cyto}]-[Gln_{gut}])`} /></span>
- <span className='formula_number'>63</span>
- </div>
+ <span className='formula_number'>(63)</span> </div>
</MathJax.Provider>
<p>TPH1 converts tryptophan that enters the cytoplasm into 5-hydroxytryptophan, which is then transported from the cytoplasm into the gut. The corresponding reaction equations and ODEs are as follows</p>
@@ -757,38 +697,31 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`Trp_{gut}\\overset{}{\\underset{}{\\rightleftharpoons}}Trp_{cyto}`} /></span>
- <span className='formula_number'>64</span>
- </div>
+ <span className='formula_number'>(64)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`Trp_{cyto}\\xrightarrow{TPH1}5-HTP_{cyto}`} /></span>
- <span className='formula_number'>65</span>
- </div>
+ <span className='formula_number'>(65)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`5-HTP_{cyto}\\overset{}{\\underset{}{\\rightleftharpoons}}5-HTP_{gut}`} /></span>
- <span className='formula_number'>66</span>
- </div>
+ <span className='formula_number'>(66)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Trp_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_Trp}}{V_{gut}}([Trp_{cyto}]-[Trp_{gut}])`} /> </span>
- <span className='formula_number'>67</span>
- </div>
+ <span className='formula_number'>(67)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Trp_{cyto}]}{\\mathrm{d}t} = \\frac{k_{diff\\_Trp}}{V_{cyto}}([Trp_{gut}]-[Trp_{cyto}]) - \\frac{k_{cat\\_TPH1}[TPH1][Trp_{cyto}]}{K_{M\\_TPH1}+[Trp_{cyto}]}`} /></span>
- <span className='formula_number'>68</span>
- </div>
+ <span className='formula_number'>(68)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[5\\mathrm{-}HTP_{cyto}]}{\\mathrm{d}t} = \\frac{k_{cat\\_TPH1}[TPH1][Trp_{cyto}]}{K_{M\\_TPH1}+[Trp_{cyto}]} - \\frac{k_{diff\\_5-HTP}}{V_{cyto}}([5\\mathrm{-}HTP_{gut}]-[5\\mathrm{-}HTP_{cyto}])`} /></span>
- <span className='formula_number'>69</span>
- </div>
+ <span className='formula_number'>(69)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[5\\mathrm{-}HTP_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_5-HTP}}{V_{gut}}([5\\mathrm{-}HTP_{cyto}]-[5\\mathrm{-}HTP_{gut}])`} /></span>
- <span className='formula_number'>70</span>
- </div>
+ <span className='formula_number'>(70)</span> </div>
</MathJax.Provider>
<h3>1.4 Full ODE Model</h3>
@@ -797,133 +730,107 @@ export function Model() {
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PEA_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_PEA}}{V_{gut}}([PEA_{peri}]-[PEA_{gut}])`} /></span>
- <span className='formula_number'>71</span>
- </div>
+ <span className='formula_number'>(71)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PEA_{peri}]}{\\mathrm{d}t} = \\frac{k_{diff\\_PEA}}{V_{peri}}([PEA_{gut}]-[PEA_{peri}]) -\\frac{k_{cat\\_TynA}[TynA][PEA_{peri}]}{K_{M\\_TynA}+[PEA_{peri}]}`} /> </span>
- <span className='formula_number'>72</span>
- </div>
+ <span className='formula_number'>(72)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PA_{peri}]}{\\mathrm{d}t} = \\frac{k_{cat\\_TynA}[TynA][PEA_{peri}]}{K_{M\\_TynA}+[PEA_{peri}]} + \\frac{k_{diff\\_PA}}{V_{peri}}([PA_{cyto}]-[PA_{peri}])`} /> </span>
- <span className='formula_number'>73</span>
- </div>
+ <span className='formula_number'>(73)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[NH_{3\\_peri}]}{\\mathrm{d}t} = \\frac{k_{cat\\_TynA}[TynA][PEA_{peri}]}{K_{M\\_TynA}+[PEA_{peri}]} + \\frac{k_{diff\\_NH3}}{V_{peri}}([NH_{3\\_cyto}]-[NH_{3\\_peri}])`} /> </span>
- <span className='formula_number'>74</span>
- </div>
+ <span className='formula_number'>(74)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PA_{cyto}]}{\\mathrm{d}t} = \\frac{k_{diff\\_PA}}{V_{cyto}}([PA_{peri}]-[PA_{cyto}]) - \\frac{k_{cat\\_FeaR}[FeaR][PA_{cyto}]}{K_{M\\_FeaR}}`} /> </span>
- <span className='formula_number'>75</span>
- </div>
+ <span className='formula_number'>(75)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[NH_{3\\_cyto}]}{\\mathrm{d}t} = \\frac{k_{diff\\_NH3}}{V_{cyto}}([NH_{3\\_peri}]-[NH_{3\\_cyto}]) - \\frac{k_{cat\\_GS}[GS][Glu_{cyto}][NH_{3\\_cyto}]}{(K_{M\\_GS\\_Glu}+[Glu_{cyto}])(K_{M\\_GS\\_NH3}+[NH_{3\\_cyto}])}`} /></span>
- <span className='formula_number'>76</span>
- </div>
+ <span className='formula_number'>(76)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PAA_{cyto}]}{\\mathrm{d}t} = k_{cat\\_FeaR}[FeaR\\mathrm{-}PA] + \\frac{k_{diff\\_PAA}}{V_{cyto}}([PAA_{gut}]-[PAA_{cyto}])`} /> </span>
- <span className='formula_number'>77</span>
- </div>
+ <span className='formula_number'>(77)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[PAA_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_PAA}}{V_{gut}}([PAA_{cyto}]-[PAA_{gut}])`} /></span>
- <span className='formula_number'>78</span>
- </div>
+ <span className='formula_number'>(78)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[P_{TynA\\_GS\\_active}]}{\\mathrm{d}t} = k_{f\\_PtynA}[P_{TynA\\_GS}][FeaR\\mathrm{-}PA] - k_{r\\_PtynA}[P_{TynA\\_GS\\_active}]`} /> </span>
- <span className='formula_number'>79</span>
- </div>
+ <span className='formula_number'>(79)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[P_{TynA\\_TPH1\\_active}]}{\\mathrm{d}t} = k_{f\\_PtynA}[P_{TynA\\_TPH1}][FeaR\\mathrm{-}PA] - k_{r\\_PtynA}[P_{TynA\\_TPH1\\_active}]`} /> </span>
- <span className='formula_number'>80</span>
- </div>
+ <span className='formula_number'>(80)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[P_{TynA\\_GS}]}{\\mathrm{d}t} = -k_{f\\_PtynA}[P_{TynA\\_GS}][FeaR\\mathrm{-}PA] + k_{r\\_PtynA}[P_{TynA\\_GS\\_active}]`} /> </span>
- <span className='formula_number'>81</span>
- </div>
+ <span className='formula_number'>(81)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[P_{TynA\\_TPH1}]}{\\mathrm{d}t} = -k_{f\\_PtynA}[P_{TynA\\_TPH1}][FeaR\\mathrm{-}PA] + k_{r\\_PtynA}[P_{TynA\\_TPH1\\_active}]`} /></span>
- <span className='formula_number'>82</span>
- </div>
+ <span className='formula_number'>(82)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[FeaR]}{\\mathrm{d}t} = - \\frac{k_{cat\\_FeaR}[FeaR][PA_{cyto}]}{K_{M\\_FeaR}} + k_{cat\\_FeaR}[FeaR\\mathrm{-}PA]`} /> </span>
- <span className='formula_number'>83</span>
- </div>
+ <span className='formula_number'>(83)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[FeaR\\mathrm{-}PA]}{\\mathrm{d}t} = \\frac{k_{cat\\_FeaR}[FeaR][PA_{cyto}]}{K_{M\\_FeaR}} - k_{cat\\_FeaR}[FeaR\\mathrm{-}PA] -k_{f\\_PtynA}[P_{TynA\\_GS}][FeaR\\mathrm{-}PA] - k_{f\\_PtynA}[P_{TynA\\_TPH1}][FeaR\\mathrm{-}PA] + k_{r\\_PtynA}[P_{TynA\\_GS\\_active}] + k_{r\\_PtynA}[P_{TynA\\_TPH1\\_active}]`} /> </span>
- <span className='formula_number'>84</span>
- </div>
+ <span className='formula_number'>(84)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[mRNA_{GS}]}{\\mathrm{d}t} = k_{mRNA\\_GS}[P_{TynA\\_GS\\_active}] - d_{mRNA\\_GS}[mRNA_{GS}]`} /></span>
- <span className='formula_number'>85</span>
- </div>
+ <span className='formula_number'>(85)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[mRNA_{TPH1}]}{\\mathrm{d}t} = k_{mRNA\\_TPH1}[P_{TynA\\_TPH1\\_active}] - d_{mRNA\\_TPH1}[mRNA_{TPH1}]`} /> </span>
- <span className='formula_number'>86</span>
- </div>
+ <span className='formula_number'>(86)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[GS]}{\\mathrm{d}t} = p_{GS}[mRNA_{GS}] - d_{GS}[GS]`} /> </span>
- <span className='formula_number'>87</span>
- </div>
+ <span className='formula_number'>(87)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[TPH1]}{\\mathrm{d}t} = p_{TPH1}[mRNA_{TPH1}] - d_{TPH1}[TPH1]`} /> </span>
- <span className='formula_number'>88</span>
- </div>
+ <span className='formula_number'>(88)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Glu_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_Glu}}{V_{gut}}([Glu_{cyto}]-[Glu_{gut}])`} /> </span>
- <span className='formula_number'>89</span>
- </div>
+ <span className='formula_number'>(89)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Glu_{cyto}]}{\\mathrm{d}t} = \\frac{k_{diff\\_Glu}}{V_{cyto}}([Glu_{gut}]-[Glu_{cyto}]) - \\frac{k_{cat\\_GS}[GS][Glu_{cyto}][NH_{3\\_cyto}]}{(K_{M\\_GS\\_Glu}+[Glu_{cyto}])(K_{M\\_GS\\_NH3}+[NH_{3\\_cyto}])}`} /> </span>
- <span className='formula_number'>90</span>
- </div>
+ <span className='formula_number'>(90)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Gln_{cyto}]}{\\mathrm{d}t} = \\frac{k_{cat\\_GS}[GS][Glu_{cyto}][NH_{3\\_cyto}]}{(K_{M\\_GS\\_Glu}+[Glu_{cyto}])(K_{M\\_GS\\_NH3}+[NH_{3\\_cyto}])} + \\frac{k_{diff\\_Gln}}{V_{cyto}}([Gln_{gut}]-[Gln_{cyto}])`} /> </span>
- <span className='formula_number'>91</span>
- </div>
+ <span className='formula_number'>(91)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Gln_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_Gln}}{V_{gut}}([Gln_{cyto}]-[Gln_{gut}])`} /></span>
- <span className='formula_number'>92</span>
- </div>
+ <span className='formula_number'>(92)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Trp_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_Trp}}{V_{gut}}([Trp_{cyto}]-[Trp_{gut}])`} /></span>
- <span className='formula_number'>93</span>
- </div>
+ <span className='formula_number'>(93)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[Trp_{cyto}]}{\\mathrm{d}t} = \\frac{k_{diff\\_Trp}}{V_{cyto}}([Trp_{gut}]-[Trp_{cyto}]) - \\frac{k_{cat\\_TPH1}[TPH1][Trp_{cyto}]}{K_{M\\_TPH1}+[Trp_{cyto}]}`} /></span>
- <span className='formula_number'>94</span>
- </div>
+ <span className='formula_number'>(94)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[5\\mathrm{-}HTP_{cyto}]}{\\mathrm{d}t} = \\frac{k_{cat\\_TPH1}[TPH1][Trp_{cyto}]}{K_{M\\_TPH1}+[Trp_{cyto}]} - \\frac{k_{diff\\_5-HTP}}{V_{cyto}}([5\\mathrm{-}HTP_{gut}]-[5\\mathrm{-}HTP_{cyto}])`} /> </span>
- <span className='formula_number'>95</span>
- </div>
+ <span className='formula_number'>(95)</span> </div>
<div className='indent formula_content'>
<span className='formula_line'>
<MathJax.Node formula={`\\frac{\\mathrm{d}[5\\mathrm{-}HTP_{gut}]}{\\mathrm{d}t} = \\frac{k_{diff\\_5-HTP}}{V_{gut}}([5\\mathrm{-}HTP_{cyto}]-[5\\mathrm{-}HTP_{gut}])`} /> </span>
- <span className='formula_number'>96</span>
- </div>
+ <span className='formula_number'>(96)</span> </div>
</MathJax.Provider>
<h3>Initial Conditions</h3>
<p>Except for the variables mentioned below, the initial values of all other variables are set to 0.</p>
@@ -948,7 +855,7 @@ export function Model() {
<MathJax.Provider>
<div className='indent formula_content' >
<span className='formula_line'><MathJax.Node formula={`\\begin{align*}&\\max \\quad \\mathbf{c}^T \\mathbf{v}\\\\&\\begin{array}{r@{\\quad}l@{}l@{\\quad}l}\\text{s.t.} \\quad & \\mathbf{S} \\mathbf{v} = \\mathbf{0}\\\\&\\mathbf{v}_{\\text{min}} \\leq \\mathbf{v} \\leq \\mathbf{v}_{\\text{max}}\\end{array} \\end{align*}`} /> </span>
- <span className='formula_number'>1</span>
+ <span className='formula_number'>(1)</span>
</div>
</MathJax.Provider>
<p>Where:</p>
--
GitLab