Team:NYMU-Taipei/Modeling/Ethanol/explanation

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==Explanation:==
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\frac{d[mRNAT7]}{dt}=\frac{ [ROSoxyR]^{nROSoxyR} }{ KdROSoxyR^{nROSoxyR}+[ROSoxyR]^{nROSoxyR} }\times{PoPStrxC}\times\frac{N}{V}\times{a}+\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7}\times\frac{N}{V}-KdegmRNA\times[mRNAPDC]</div></html>

PoPS represents the promoter strength which is measured by the rate of RNApolymerase binding to the starting site of DNA transcription; <html><span lang="latex">\frac{ [molecule]^{nmolecule} }{ Kdmolecule^{nmolecule}+[molecule]^{nmolecule} }</span></html> represents the hill effect of transcription factors (either activators or repressors) to the promoter.<br>
　　

In this equation, the production rate of mRNAT7 is composed of both synthesizing rate and degrading rate. <html><span lang="latex">\frac{ [ROSoxyR]^{nROSoxyR} }{ KdROSoxyR^{nROSoxyR}+[ROSoxyR]^{nROSoxyR} }\times{PoPStrxC}\times\frac{N}{V}\times{a}</span></html> represents how activator ROSoxyR influences promoter trxC on synthesizing mRNAT7 and how thresholds behind the promoter blocks the synthesis of mRNAT7 (the possibility of RNA polymerase to skip thresholds right after trxC promoter is shown in probability);<html><span lang="latex">\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7｝\times\frac{N}{V}</span></html>represents how T7 polymerase influences promoter T7 on synthesizing mRNAT7; <html><span lang="latex">-KdegmRNA\times[mRNAT7]</span></html> represents the natural degrading rate of mRNAT7.<br>


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\frac{d[protein of T7 polymerase ]}{dt}=RBS\times{PoPStrxC}\times\frac{N}{V}\times{a}\times{\frac{ [ROSoxyR]^{n1} }{ [Kd]^{n1}+[ROSoxyR]^{n1} }}}+PoPST7\times{T7 effect}\times\frac{N}{V}-{KdegT7}\times{T7}
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In this equation, the production rate of T7 polymerase is composed of both synthesizing rate and degrading rate. RBS represents ribosome binding site strength, which is the affinity of ribosome to the starting site of mRNA; PoPS represents the promoter strength and <html><span lang="latex">\frac{[molecule]^{nmolecule}}{ Kdmolecule^{nmolecule}+[molecule]^{nmolecule} }</span></html>, as mentioned above, represents the hill effect of transcription factors to the promoter.

For the section of the equation,<html><span lang="latex">\RBS\times{PoPStrxC}\times\frac{N}{V}\times{a}\times{\frac{ [ROSoxyR]^{n1} }{ [Kd]^{n1}+[ROSoxyR]^{n1} }}}</span></html> represents the synthesizing rate of T7 polymerase under the influence of activator ROSoxyR complex, promoter trxC and terminators downstream; <html><span lang="latex">\PoPST7\times{T7 effect}\times\frac{N}{V}</span></html>, similarly, represents the synthesizing rate of T7polymerase under the influence of T7promoter; <html><span lang="latex">\-{KdegT7}\times{T7}</span></html>represents the natural degrading rate of T7 polymerase.<br>

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<div lang="latex" class="equation">
\frac{d[mRNAPDC]}{dt}=\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7}\times\frac{N}{V}-KdegmRNA\times[mRNAPDC]
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<div lang="latex" class="equation">
\frac{d[mRNAADH]}{dt}=\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7}\times\frac{N}{V}-KdegmRNA\times[mRNAADH]
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In these two equations, the production rate of mRNAPDC and mRNAADH is composed of both synthesizing rate and degrading rate. <html><span lang="latex">\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7｝\times\frac{N}{V}</span></html> represents how T7 polymerase influences promoter T7 on synthesizing mRNAPDC and mRNAADH;<html><span lang="latex">\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }</span></html> and<html><span lang="latex">\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }</span></html> represents the natural degrading rate of mRNAPDC and [mRNAADH].






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<div lang="latex" class="equation">
\frac{d[PDC]}{dt}=RBS\times{PoPST7effect}\times\frac{N}{V}-{kdegPDC}\times[PDC}]
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<div lang="latex" class="equation">
\frac{d[ADH]}{dt}=RBS\times{PoPST7effect}\times\frac{N}{V}-{KdegADH}\times[ADH]}
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In these two equations, the production rate of PDC and ADH is composed of both synthesizing rate and degrading rate. RBS represents ribosome binding site strength, which is the affinity of ribosome to the starting site of mRNA; PoPST7 represents the promoter strength of T7 promoter.<br>

For the section of the equation, RBS ×PoPS"T7effect ×N/V"  represents the synthesizing rate of PDC and ADH under the influence of T7promoter; "- KdegPDC ×[PDC]"  and" - KdegADH ×[ADH]"  represents the natural degrading rate of PDC and ADH.<br>


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<div lang="latex" class="equation">
\frac{d[ethanol]}{dt}=Kpyruvateacetaldehyde\times{Kacetaldehydeethanol}\times\frac{[PDC]^{nPDC} }{ KdPDC^{nPDC}+[PDC]^{nPDC}}\times\frac{[ADH]^{nADH} }{ KdADH^{nADH}+[ADH]^{nADH}}-Km\times\frac{[ADH]^{nADH}}{ KdADH^{nADH}+[ADH]^{nADH}}\times[ethonal]</div></html>

In this equation, the production rate of ethanol is composed of both synthesizing rate and degrading rate. Kpyruvateacetaldehyde represents reaction rate constant of pyruvate→acetaldehyde, while Kacetaldehydeethanol  represents reaction rate constant of acetaldehyde→ethanol; <html><span lang="latex">\frac{ [PDC]^{nPDC} }{ KdPDC^{PDC}+[PDC]^{PDC} }</span></html>represents hill effect of PDC to pyruvate→acetaldehyde reaction, while <html><span lang="latex">\frac{ [ADH^{nADH} }{ KdADH^{ADH}+[ADH]^{ADH} }</span></html>represents hill effect of ADH to acetaldehyde→ethanol reaction; Km represents the rate constant of ethanol→acetaldehyde, a reverse reaction of the second process of ethanol synthesis. 
For the section of the equation, <html><span lang="latex">\times{ Kpyruvateacetaldehyde }{ Kacetaldehydeethanol }\frac{ [PDC]^{nPDC} }{ KdPDC^{PDC}+[PDC]^{PDC} }{ [ADH^{nADH} }{ KdADH^{ADH}+[ADH]^{ADH} }</span></html> represents the synthesizing rate of ethanol from pyruvate to acetaldehyde to ethanol under the influence of enzymes ADH and PDC; <html><span lang="latex">\times{ -Km }{ Kacetaldehydeethanol }{ [ADH^{nADH} }{ KdADH^{ADH}+[ADH]^{ADH} }{[ethanol]}</span></html> takes the reverse reaction of acetaldehyde to ethanol into consideration, which results in the decreasing of ethanol.



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