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+ | <h1 class="head">Kinetic law</h1> | ||
+ | </div> | ||
+ | <div class="righttitle"> | ||
+ | <h6 class="subtitle">Calculation and Derivation</h6> | ||
+ | </div> | ||
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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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<li class="smallp">U. Sauer, J. E. Bernhard, The PEP—pyruvate—oxaloacetate node as the switch point for carbon flux distribution in bacteria. FEMS Microbiology Reviews, Volume 29, Issue 4, 1 September 2005, Pages 765–794.</li> | <li class="smallp">U. Sauer, J. E. Bernhard, The PEP—pyruvate—oxaloacetate node as the switch point for carbon flux distribution in bacteria. FEMS Microbiology Reviews, Volume 29, Issue 4, 1 September 2005, Pages 765–794.</li> | ||
<li class="smallp">O. Mugihito, S. Hideaki, T. Yukihiro , M Noriko, S. Tatsuya, O. Masahiro, I. Ayaaki, S. Kenji, Kinetic modeling and sensitivity analysis of xylose metabolism in Lactococcus lactis IO-1. Journal of Bioscience and Bioengineering VOL. 108 No. 5, 376–384, 2009.</li> | <li class="smallp">O. Mugihito, S. Hideaki, T. Yukihiro , M Noriko, S. Tatsuya, O. Masahiro, I. Ayaaki, S. Kenji, Kinetic modeling and sensitivity analysis of xylose metabolism in Lactococcus lactis IO-1. Journal of Bioscience and Bioengineering VOL. 108 No. 5, 376–384, 2009.</li> | ||
− | <li class="smallp"> | + | <li class="smallp"> W. Akira, N. Keisuke, H. Tomohiro, S. Ryohei, Reaction mechanism of phosphoribulokinase from a cyanobacterium, Synechococcus PCC7942. Photosynthesis Research 56: 27–33, 1998</li> |
− | <li class="smallp"> | + | <li class="smallp">G. B. Guillaume, D. F. Graham, T. J. Andrews, Despite slow catalysis and confused substrate specificity, all ribulose bisphosphate carboxylases may be nearly perfectly optimized Proc Natl Acad Sci U S A. 2006 May 9; 103(19): 7246–7251.</li> |
− | <li class="smallp"> | + | <li class="smallp"> L. Yun, A. M. Keith, Determination of Apparent Km Values for Ribulose 1,5- Bisphosphate Carboxylase/Oxygenase (Rubisco) Activase Using the Spectrophotometric Assay of Rubisco Activity. Plant Physiol. (1991) 95, 604-609</li> |
<li class="smallp">Rong-guang Z, C. Evalena A., Alexei S., Tatiana S., Elena E., Steven B., Cheryl H. A., Aled M. E., Andrzej J., and Sherry L. M. Structure of <i>Escherichia Coli</i> Ribose-5-Phosphate Isomerase: A Ubiquitous Enzyme of the Pentose Phosphate Pathway and the Calvin Cycle Structure, Vol. 11, 31–42, January, 200</li> | <li class="smallp">Rong-guang Z, C. Evalena A., Alexei S., Tatiana S., Elena E., Steven B., Cheryl H. A., Aled M. E., Andrzej J., and Sherry L. M. Structure of <i>Escherichia Coli</i> Ribose-5-Phosphate Isomerase: A Ubiquitous Enzyme of the Pentose Phosphate Pathway and the Calvin Cycle Structure, Vol. 11, 31–42, January, 200</li> | ||
<li class="smallp">Inês L., Joana F., Christine C., Sandra M., Nuno S., Nilanjan R., Anabela C., and Joana T. Ribose 5-Phosphate Isomerase B Knockdown Compromises Trypanosoma brucei Bloodstream Form Infectivity PLoS Negl Trop Dis. 2015 Jan; 9(1): e3430.</li> | <li class="smallp">Inês L., Joana F., Christine C., Sandra M., Nuno S., Nilanjan R., Anabela C., and Joana T. Ribose 5-Phosphate Isomerase B Knockdown Compromises Trypanosoma brucei Bloodstream Form Infectivity PLoS Negl Trop Dis. 2015 Jan; 9(1): e3430.</li> | ||
<li class="smallp">Singh2006 TCA mtu model1. SBML2LATEX. Web : http: //www.ra.cs.uni-tuebingen.de/software/SBML2LaTeX</li> | <li class="smallp">Singh2006 TCA mtu model1. SBML2LATEX. Web : http: //www.ra.cs.uni-tuebingen.de/software/SBML2LaTeX</li> | ||
− | <li class="smallp"> | + | <li class="smallp">J. Shen, Modeling the glutamate–glutamine neurotransmitter cycle, Front. Neuroenergetics, 28 January 2013</li> |
− | <li class="smallp"> | + | <li class="smallp">X. Feng, H. Zhao, Investigating xylose metabolism in recombinant Saccharomyces cerevisiae via 13C metabolic flux analysis, Microb Cell Fact. 2013; 12: 114.</li> |
− | <li class="smallp"> | + | <li class="smallp">D. Runquist, M. Bettiga, Increased expression of the oxidative pentose phosphate pathway and gluconeogenesis in anaerobically growing xylose-utilizing Saccharomyces cerevisiae, Microbial Cell Factories 2009, 8:49</li> |
<li class="smallp">Kalle Hult rev 2005, 2007 Linda Fransson Department of Biotechnology KTH, Stockholm, Enzyme kinetics, An investigation of the enzyme glucose-6- phosphate isomerase</li> | <li class="smallp">Kalle Hult rev 2005, 2007 Linda Fransson Department of Biotechnology KTH, Stockholm, Enzyme kinetics, An investigation of the enzyme glucose-6- phosphate isomerase</li> | ||
<li class="smallp">Model name: “Mosca2012 - Central Carbon Metabolism Regulated by AKT”, SBML2LATEX. Web : http: //www.ra.cs.uni-tuebingen.de/software/SBML2LaTeX</li> | <li class="smallp">Model name: “Mosca2012 - Central Carbon Metabolism Regulated by AKT”, SBML2LATEX. Web : http: //www.ra.cs.uni-tuebingen.de/software/SBML2LaTeX</li> | ||
− | <li class="smallp"> | + | <li class="smallp">M. Ettore, A. Roberta, M. Carlo, B. Annamaria, C. Gianfranco, M. Luciano, Computational modeling of the metabolic states regulated by the kinase Akt, Front. Physiol., 21 November 2012</li> |
− | <li class="smallp"> | + | <li class="smallp">E. G. Jacqueline, P. L. Christopher, R. A. Maciek, Comprehensive analysis of glucose and xylose metabolism in <i>Escherichia Coli</i> under aerobic and anaerobic conditions by 13C metabolic flux analysis, Metabolic Engineering Volume 39, January 2017, Pages 9-18</li> |
− | <li class="smallp">N. | + | <li class="smallp">N. N. Ulusu, C. Şengezer, Kinetic mechanism and some properties of glucose-6- phosphate dehydrogenase from sheep brain cortex, Türk Biyokimya Dergisi [Turkish Journal of Biochemistry–Turk J Biochem] 2012; 37 (4) ; 340–347</li> |
− | <li class="smallp"> | + | <li class="smallp">H. Stefania, M. Katy, C. Carlo, M. Morena, D. Franco, 6-Phosphogluconate Dehydrogenase Mechanism EVIDENCE FOR ALLOSTERIC MODULATION BY SUBSTRATE, J Biol Chem. 2010 Jul 9; 285(28): 21366–21371.</li> |
− | <li class="smallp">K. Nielsen, P.G. Sørensen, F. Hynne, H. | + | <li class="smallp">K. Nielsen, P.G. Sørensen, F. Hynne, H. G. Busse, Sustained oscillations in glycolysis: an experimental and theoretical study of chaotic and complex periodic behavior and of quenching of simple oscillations, Biophysical Chemistry 72 (1998) 49–62</li> |
<li class="smallp">UniProtKB - A0RV30 from web : https://www.uniprot.org/uniprot/A0RV30</li> | <li class="smallp">UniProtKB - A0RV30 from web : https://www.uniprot.org/uniprot/A0RV30</li> | ||
</ol> | </ol> | ||
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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