Difference between revisions of "Team:ULV-LC-CV/Model"

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<h2 style="float:left" id="tst1" <b> ♦Enzyme Kinetics with Lauric Acid♦</b></h2><br><br><br><br>
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<h2 style="float:left" id="tst1" <b> ♦Enzyme Kinetics of FAME Production with SAM as a Constant♦</b></h2><br><br><br><br>
 
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https://lh3.googleusercontent.com/vzFrmlnI1dBo-CBW84xZk-cTaXJt2pRQmnhXl28HxiWBSg30ApUrkU8lc6g1QepLFC3Zyb84BYg167s6BpnBNq6EoTvlYh0yU5ojs6dveGZCQ_aD_BSfcRbP_GjDg75K04AmTHWHKS2NgghXw0MBYMf4KWG94VVaARHAI6ookeAiXWQEMxL3nYfYGZSFM-GtgtXKCT9caEgnJKsMFEOHwxJKZiQqsfFApW4Om7a21RRqvpeWSxDmeEGgY0S2oEO14lbR_b9I2KiNYvGlyHhf-0KnSYAm7TPZjjix5tdXvD8N9YNdDKfJKelRja02CnX0W6ObXy7kwLYTogW4MotlPhJuUONFF0MIQhn1G2AI6rDdgwjmvyJCh4GlDKqYoLsbK5-Q5AsUzeQ8HBLjsKFLGMW2jDSta41QKTSIFoioz-XMFEKBWWTUiS4WU0Bm1kgiQGv-Zt0bB8BrnUTb6CWsyglqeDvjZoFJBgkAaDhHlJHXp9I4gaV8LF89tjWLvHFYCmjuWd0XZ-qVP_8uNPnMb8KhpGApP5Ks6cNZe9JxQNX6LRijHIOwExNT5z3LGceLBMRw058X=w1257-h741-k
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https://lh3.googleusercontent.com/CpkTADacohPdBPP0yUFHDmYMCZaqgLRMkT7nMKu-hTDOv0vO9I62Szzo5JQ8GWdqIPyRHRYGJbbfSt4tq7T2qmE-No6RUCrEDCq5N2MwqeGq-QPcDkD2OXgZ4BWN7llYr2X_Io3jsIPNwp1xCfDKy_l9W4_y9Xbrzfjn9c7NbyNzcTHK-RhvVZVVgn86Vh-oiNydeGqOC5Cd33FK4RGkg_gt1wLibXfmJvhqaN-vpl55iv0SIsuKmRMDNFE2FjwXgqQM41enazTWlpOA3X2-uxMEUx8uSqjD3-DEdzLK9pZu4Z0Ctz0WI_-px84-bJ2uDXAY8Mtkf1uvkcJkKNF4LhFY0N0xYJLnz7tgcSmRdyd27y_WD_kKd7wgbwYnVcZXSEeNcknopU8hXlrBczPO66H6_4o-3CoUEPUqUSqRujDRx-qudCn8Ag89ROxR4LdzIB2Sri8BA6OpFfLYl8RPQicdip3pg4o-w2gMoZGYHlk7GlrNuGrD0ASwDhGbO7fpk3Db7GGkhN4o35ePI41goqpvu47UEY2_WlqQFL6zimKj4ZqXAj9ccexgkXxNpNTkz8giYtZ1=w1165-h726
 
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<p class="align right" style="border:3px; border-style:dashed; border-color:green; padding: 1em;margin:100px;" >This figure was based off of the Michaelis-Menten enzyme reaction:
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<p class="align right" style="border:3px; border-style:dashed; border-color:green; padding: 1em;margin:100px;" >The theoretical output of the production of fatty acid methyl esters (FAME) was modeled by means of the Michaelis Menten equation using the starting concentrations of S-adenosylmethionine (SAM) , 0.2 mM, Drosophila melanogaster juvenile hormone acid O-methyltransferase (DmJHAMT), 6.14 mM and lauric acid (FFAs), 7.38 mM (Sherkhanov et al, 2016 ). SAM is fixed as a constant because it is assumed to be replenished within the cell. The Km and Vmax were also obtained from the Sherkhanov et al article.
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E + S1 + S2ES1+ES2E+P using the values from Sherkanov et. al paper and the following equations: <br>
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dx(1)=-k1*x(1)*x(2)+k2*x(3)-k5*x(1)*x(4)+k6*x(6)+k9*x(5); <br>
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dx(2)=-k1*x(1)*x(2)+k2*x(3)+k8*x(5)-k7*x(6)*x(2);<br>
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dx(3)=-k3*x(3)*x(4)+k4*x(5)-k2*x(3)+k1*x(1)*x(2); <br>
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dx(4)=-k5*x(1)*x(4)-k6*x(6)+k4*x(5)-k3*x(3)*x(4); <br>
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dx(5)=k3*x(3)*x(4)+k7*x(6)*x(2)-(k8+k4+k9)*x(5); <br>
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dx(6)=-k7*x(6)*x(2)+k8*x(5)-k6*x(6)+k5*x(1)*x(4); <br>
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dx(7)=k9*x(5); <br>
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Where k1=ka with a value of 7.7min-1; k2=ka2 with a value of 144 min-1;  k3=a*k5 with a value is 7.7min-1; k4=a*k6; k5=kb1 with a value is 7.7min-1; k6=kb2 with a value of 0.103min-1; k7=a*k1; k8=a*k2; k9=k7 with a value of 7.7min-1; x(1)=[DmJHAMT] with a value of 3.32μM; x(2)=[SAM] with a value of 0.05μM; x(3)=[DmJHAMT+SAM]; x(4)=[Lauric acid] with a value of 59μM; x(5)=[DmJHAMT+SAM+Lauric acid]; x(6)=[DmJHAMT+Lauric acid]; x(7)=[FAMEs]; ‘a’ is a constant of 1 since it just represents alpha.
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The starting concentration of lauric acid (59μM) slowly decreases as time progresses because it converts to FAMEs as it gets methylated by s-adenosyl methionine (SAM) with the help of Drosophila melanogaster juvenile hormone adenyl methyltransferase (DmJHAMT). Because of low intracellular concentrations of SAM (0.05μM) and DmJHAMT (3.32μM), FAME production is not seen on this graph. <br>
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<b>Figure 1: </b>The starting concentration of lauric acid (59μM) slowly decreases as time progresses because it converts to FAMEs as it gets methylated by s-adenosyl methionine (SAM) with the help of Drosophila melanogaster juvenile hormone adenyl methyltransferase (DmJHAMT). Because of low intracellular concentrations of SAM (0.05μM) and DmJHAMT (3.32μM), FAME production is not seen on this graph.
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<h2 style="float:left" id="tst1" <b> ♦Enzyme Kinetics with Oleic Acid♦</b></h2><br><br><br><br>
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<h2 style="float:left" id="tst1" <b> ♦Enzyme Kinetics of FAME Production with SAM♦</b></h2><br><br><br><br>
 
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https://lh3.googleusercontent.com/40r1d9P9o_wQ-PxWTfVQQZ2-zH9S_d0Rh_WPibdEke6PYwakjtgiiA81jE7kLMsAraPjucIk_GTgL4i8ZWGg3rFjq6tmmz2LLL51gnW5u8ebV4rQbWB99vSuVXmKTIuZ-sub7XieqiSM_ocCkgNeaX5jvng8FG6SAe2W5xn-9HZflHewQTpQLy84IAFvzG2_FGUGwYCzS-8ZzMPrU_o8KHM2of8I4afmDzm5CkEPlr6NYZuAnoARFFugmxpAYAUKn84D2L16y6_o2wCwyUJumH10naqNKX9F2C8DfnQ4soKtL1aBLKCLeNAvjEeBHuRDMurvJ9StfR28_-YP2oYYq20Y1Rmz3J13wAHFuAURwpQZosbXxmLIw0ONOzmbW72IqSFGt6oa21H-W8VAGsI0dEzqI9U2yMfWZyIx5WEgVGNzjAWmLXaMPtxqFtlb2bNe18Ym1SbU9bdnKWG33eV53xV6y6CZZ61NQ0Zha3uLpGGHnh4Jznoz3Z4Cs1K_Q-atX6yVZOm_DzqkR_uWNrHHz2g3E6r-vzZXbhnUjEt2mPm_KTQc5EzYeajE0Bt-ZvSxi2Wfq6Gf=w1257-h741-k
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https://lh3.googleusercontent.com/naYZDETLL-cvtD-ktF_xuHxYasLVWUxNB2GKkdTWIw014De4MP8L-o6h0kGRbR82e7h2R8EafEVZmKyau7feTfYTSofNNdB4XQqX9Nz6gDFAVtNvxFlIs-s1TThf4GByQWgZyQEdp8S-nVAdYI0h-NMr8nTu83nEbIPoaGl1NAnFQ4FfhGVKcqTVFXjfex81bNkpTZ0ma8BloTY9_q9RyOoVsHVWFA66I6Y7Z0cdMIUh7wb6eMy4E4c4RA3Ph087FZUa4e1w5eFl6sElKvkNNoQj9DoNb6yDu7haRmnUS1FIPMA7dCKbqf3AmVXhxxJMXRm5st9rY3sz9erUyRqWFf-izZ_rV89L1AXmVD1lu3zUKcqkNLF2QMuGG-VbIA7mjRynJvozQ2gEfiwLj_OjBWkHA1NSY4s5KxH0R8BKQWviAB5ppjkQ1OX02uydOzt5ZXZCWj3rT_5CbQ9bqVtu2oHB_ZSaTWOAtUeWX2Junfx4AMshJj3aJ1ZxBYa95cvAk5i37uGXuFMjOgnSOmQDazH_ktOMo62xrKlFHz1ITY_kVzrJio2UW9phr4C-_RB2NqyBm4uU=w1165-h726
 
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<p class="align right" style="border:3px; border-style:dashed; border-color:green; padding: 1em;margin:100px;" >This figure was based off of the Michaelis-Menten enzyme reaction:
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<p class="align right" style="border:3px; border-style:dashed; border-color:green; padding: 1em;margin:100px;" >The theoretical output of the production of fatty acid methyl esters (FAME) was modeled by means of the Michaelis Menten equation using the starting concentrations of S-adenosylmethionine (SAM) , 0.2 mM, Drosophila melanogaster juvenile hormone acid O-methyltransferase (DmJHAMT), 6.14 mM and lauric acid (FFAs), 7.38 mM (Sherkhanov et al, 2016 ). The Km and Vmax were also obtained from the Sherkhanov et al article.
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E + S1 + S2 ES1 +ES2E+P using the values from Sherkanov et. al paper and the following equations: <br>
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−
dx(1)=-k1*x(1)*x(2)+k2*x(3)-k5*x(1)*x(4)+k6*x(6)+k9*x(5); dx(2)=-k1*x(1)*x(2)+k2*x(3)+k8*x(5)-k7*x(6)*x(2); <br>
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dx(3)=-k3*x(3)*x(4)+k4*x(5)-k2*x(3)+k1*x(1)*x(2); <br>
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−
dx(4)=-k5*x(1)*x(4)-k6*x(6)+k4*x(5)-k3*x(3)*x(4); <br>
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−
dx(5)=k3*x(3)*x(4)+k7*x(6)*x(2)-(k8+k4+k9)*x(5); <br>
+
−
dx(6)=-k7*x(6)*x(2)+k8*x(5)-k6*x(6)+k5*x(1)*x(4); <br>
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dx(7)=k9*x(5); <br>
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Where k1=ka and its value is 7.7min-1; k2=ka2 and its value is 144min-1;  k3=a*k5 and its value is 7.7min-1; k4=a*k6; k5=kb1 and its value is 7.7min-1 k6=kb2 and its value is 0.103min-1; k7=a*k1; k8=a*k2; k9=k7 and its value is 7.7min-1; x(1)=[DmJHAMT]; x(2)=[SAM]; x(3)=[DmJHAMT+SAM]; x(4)=[FFAs]; x(5)=[DmJHAMT+SAM+FFA]; x(6)=[DmJHAMT+FFA]; x(7)=[FAMEs]; ‘a’ is a constant of 1. <br>
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<b>Figure 2:</b> Oleic acid has a starting concentration of 78μM and the graph shows that as time increases, oleic acid decreases due to methylation from the interaction with S-adenosyl methionine (SAM) and drosophila melanogaster juvenile hormone adenomethyl transferase (DmJHAMT). Together, the oleic acid, SAM, and DmJHAMT produce fatty acid methyl esters (FAMEs) which has a small yield due to the low concentrations of DmJHAMT (3.32uM) and SAM (0.05uM). The Michaelis-Menten enzymatic reaction equation shows that the enzyme, DmJHAMT, is consistent throughout the reaction and is present in both the reactants and products.  
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  </p></div><br><br><br><br><br>
  

Revision as of 19:12, 2 December 2016


Team:ULV-LC-CV-2016.igem.org iGEM Main Page

♦Enzyme Kinetics of FAME Production with SAM as a Constant♦





The theoretical output of the production of fatty acid methyl esters (FAME) was modeled by means of the Michaelis Menten equation using the starting concentrations of S-adenosylmethionine (SAM) , 0.2 mM, Drosophila melanogaster juvenile hormone acid O-methyltransferase (DmJHAMT), 6.14 mM and lauric acid (FFAs), 7.38 mM (Sherkhanov et al, 2016 ). SAM is fixed as a constant because it is assumed to be replenished within the cell. The Km and Vmax were also obtained from the Sherkhanov et al article.

♦Enzyme Kinetics of FAME Production with SAM♦





The theoretical output of the production of fatty acid methyl esters (FAME) was modeled by means of the Michaelis Menten equation using the starting concentrations of S-adenosylmethionine (SAM) , 0.2 mM, Drosophila melanogaster juvenile hormone acid O-methyltransferase (DmJHAMT), 6.14 mM and lauric acid (FFAs), 7.38 mM (Sherkhanov et al, 2016 ). The Km and Vmax were also obtained from the Sherkhanov et al article.