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<body data-spy="scroll" data-target=".navbar-example"> | <body data-spy="scroll" data-target=".navbar-example"> | ||
<div class="container content"> | <div class="container content"> | ||
− | + | <div class="headstyle"> | |
+ | <h1 class="head">Kinetic law</h1> | ||
+ | </div> | ||
+ | <div class="righttitle"> | ||
+ | <h6 class="subtitle">Calculation and Derivation</h6> | ||
+ | </div> | ||
<div class="navbar-example"> | <div class="navbar-example"> | ||
<div class="row"> | <div class="row"> | ||
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Michaelis and Menten considered a quasi equilibrium between E and the ES-Complex to simplify the system. | Michaelis and Menten considered a quasi equilibrium between E and the ES-Complex to simplify the system. | ||
</p> | </p> | ||
− | <p class="pcontent">$${{ | + | <p class="pcontent">$${{d[S] \over dt} = -k_1[E] \cdot [S]+ k_{-1}[ES]}$$</p> |
− | <p class="pcontent">$${{ | + | <p class="pcontent">$${{d[ES]\over dt} = k_1[E] \cdot [S] - (k_{-1} + k_2)[ES]}$$</p> |
− | <p class="pcontent">$${{ | + | <p class="pcontent">$${{d[E] \over dt} = k_1[E] \cdot [S] - (k_{-1} + k_2)[ES]}$$</p> |
− | <p class="pcontent">$${{ | + | <p class="pcontent">$${{d[P] \over dt} = k_2[ES]}$$</p> |
− | <p class="pcontent">After derivation $${v = {-ds \over dt} = { | + | <p class="pcontent">After derivation $${v = {-ds \over dt} = {d[P] \over dt}}$$</p> |
<p class="pcontent">where V<sub>m</sub> represents the maximum rate achieved by the system, | <p class="pcontent">where V<sub>m</sub> represents the maximum rate achieved by the system, | ||
and the Km is the substrate concentration at which the reaction rate is half of V<sub>m</sub>. | and the Km is the substrate concentration at which the reaction rate is half of V<sub>m</sub>. | ||
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it is thus called turnover number. | it is thus called turnover number. | ||
</p> | </p> | ||
− | <p class="pcontent">$${Vmax = k_2 \cdot E_{total} = k_{cat} \cdot E_{total}}$$</p> | + | <p class="pcontent">$${Vmax = k_2 \cdot [E_{total}] = k_{cat} \cdot [E_{total}]}$$</p> |
<p class="pcontent">B. A more realistic description of a enzymatic reactions than pure Michaelis Menten Kinetics | <p class="pcontent">B. A more realistic description of a enzymatic reactions than pure Michaelis Menten Kinetics | ||
is given by considering the product forming reaction step as reversible. | is given by considering the product forming reaction step as reversible. | ||
</p> | </p> | ||
<p class="pcontent">$${E + S \underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons}} ES \xrightarrow{k_2} E + P}$$</p> | <p class="pcontent">$${E + S \underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons}} ES \xrightarrow{k_2} E + P}$$</p> | ||
− | <p class="pcontent">The Enzyme(E) forms a Complex (ES) with the Substrate (S) and modifies it to the Product (P). | + | <p class="pcontent">The Enzyme (E) forms a Complex (ES) with the Substrate (S) and modifies it to the Product (P). |
In the reversible Michaelis-Menten reaction the Product can bind the enzyme again and react back to the substrate. | In the reversible Michaelis-Menten reaction the Product can bind the enzyme again and react back to the substrate. | ||
This process is described by the ODE system. | This process is described by the ODE system. | ||
</p> | </p> | ||
− | <p class="pcontent">$${{ | + | <p class="pcontent">$${{d[S] \over dt} = -k_1[E] \cdot [S] + k_{-1}[ES]}$$</p> |
− | <p class="pcontent">$${{ | + | <p class="pcontent">$${{d[ES] \over dt} = k_1[E] \cdot [S] + k_{-2}[E] \cdot [P] - (k_{-1} + k_2)[ES]}$$</p> |
− | <p class="pcontent">$${{ | + | <p class="pcontent">$${{d[E] \over dt} = k_1[E] \cdot [S] - k_{-2}[E] \cdot [P] - (k_{-1} + k_2)[ES]}$$</p> |
− | <p class="pcontent">$${v = { | + | <p class="pcontent">$${v = {d[P] \over dt} = k_2[ES] - k_{-2}[E]\cdot [P] = v_f - v_b}$$</p> |
− | <p class="pcontent">After derivation $${v = {-ds \over dt} = { | + | <p class="pcontent">After derivation $${v = {-ds \over dt} = {d[P] \over dt}}$$</p> |
− | <p class="pcontent">Finally we use V<sub>fmax</sub> = | + | <p class="pcontent">Finally we use V<sub>fmax</sub> = k<sub>2</sub>⋅E<sub>total</sub> and V<sub>bmax</sub> = k<sub>−1</sub>⋅E<sub>total</sub> to get the common form for the reversible Michaelis Menten equation</p> |
<p class="pcontent">$${v = {v^{max}_f S/K_{m,1} - v^{max}_b P/K_{m,2} \over (1 + S/K_{m,1} + P/K_{m,1})}}$$</p> | <p class="pcontent">$${v = {v^{max}_f S/K_{m,1} - v^{max}_b P/K_{m,2} \over (1 + S/K_{m,1} + P/K_{m,1})}}$$</p> | ||
<p class="pcontent">Where V<sub>f</sub> is the forward rate and the Vb is backwared rate while $${K_{m,1} = {K_{-1} + K_2 \over K_1}}$$ or represents as K<sub>S</sub>, | <p class="pcontent">Where V<sub>f</sub> is the forward rate and the Vb is backwared rate while $${K_{m,1} = {K_{-1} + K_2 \over K_1}}$$ or represents as K<sub>S</sub>, | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
− | <td colspan="1">$${RuBP + CO_2 \xrightarrow{ | + | <td colspan="1">$${RuBP + CO_2 \xrightarrow{Rubisco} + 3PG}$$</td> |
<td colspan="1">Ribulose-1,5-bisphosphate carboxylase/ oxygenase</td> | <td colspan="1">Ribulose-1,5-bisphosphate carboxylase/ oxygenase</td> | ||
<td colspan="1">Ping-Pong-Bi-Bi</td> | <td colspan="1">Ping-Pong-Bi-Bi</td> | ||
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<div id="centerimg"> | <div id="centerimg"> | ||
<img class="twoimg contentimg" src="https://static.igem.org/mediawiki/2018/e/e6/T--NCKU_Tainan--kinetic_law_fig6.png"> | <img class="twoimg contentimg" src="https://static.igem.org/mediawiki/2018/e/e6/T--NCKU_Tainan--kinetic_law_fig6.png"> | ||
− | <p class="pcenter">Fig 20. whole xylose | + | <p class="pcenter">Fig 20. whole xylose metabolism diagram of simbiology</p> |
</div> | </div> | ||
</div> | </div> | ||
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} | } | ||
} else { | } else { | ||
− | if ($(this).scrollTop() >= | + | if ($(this).scrollTop() >= 500) { |
var position = $("#sidelist").position(); | var position = $("#sidelist").position(); | ||
if(position == undefined){} | if(position == undefined){} |
Latest revision as of 01:46, 18 October 2018