Team:LCG-UNAM-Mexico/Notebook/2008-August

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LCG-UNAM-MexicoTeam

LCG-UNAM-Mexico

iGEM 2008 TEAM

August

2008-08-04

Hill's cooperativity
5th Reaction
Reminder:

A + B <--> AB
Ka=Keq=[AB]/[A][B]=1/Kd
θ=[AB]/([AB]+[A])=[B]/([B]+Kd)

MWC Model (Cooperativity)
A + nB <--> ABn
Ka=Keq=[ABn]/[A][B]n=1/Kd
θ=[B]n/([B]n+Kd)
log(θ/(1- θ))=nlog(B)-log(kd)                        …Hill's equation

Suppression mediated by cI:
ρ + nCI <--> ρ:CIn     (k+, k-)
Keq=Ka=[ρ:CIn]/[ρ][CI]n
Si ρ0=[ρ]+[ρ:CIn]
… ρ0=[ρ]+Keq[ρ][CI]n
=> ρ= (ρ0/Keq)/((1/keq)+[CI]n)

Flow= k+[ρ][CI]n = K+((ρ0/Keq)/((1/Keq)+[CI]n))[CI]n

Flow= k+([ρ0]/Keq) [CI]n / ((1/Keq)+[CI]n)

=> Vm= k+([ρ0]/Keq) & Kp=1/Keq=Kd

So:
Keq = exp( -ΔG / R T )
k+ = (KB/h) T exp( -ΔG / R T ) = (KB/h) T Keq

Keq=	2.89517E+17		KB=	1.38E-23	J/K
k+=	1.79764E+30	/s	h=	6.63E-34	J s
			R=	1.9872	cal/(K mol)
ΔG=	-23810	cal/mol	T=	298	K

2008-08-05

August 5th(summary)- -- -- -- -- -- -- -- - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ---- --- --- -- - ------ -- ---- --- --- --- -- -- ----- ---, --- - - --- -- -- -- -- -- -- -- - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ----.

2008-08-07

August 7th(summary)- -- -- -- -- -- -- -- - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ---- --- --- -- - ------ -- ---- --- --- --- -- -- ----- ---, --- - - --- -- -- -- -- -- -- -- - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ----.

2008-08-11

August 11th(summary)- -- -- -- -- -- -- -- - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ---- --- --- -- - ------ -- ---- --- --- --- -- -- ----- ---, --- - - --- -- -- -- -- -- -- -- - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ----.

2008-08-20

August 20th(summary)- -- -- -- -- -- -- -- - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ---- --- --- -- - ------ -- ---- --- --- --- -- -- ----- ---, --- - - --- -- -- -- -- -- -- -- - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ----.

2008-08-21

August 21st(summary)- -- -- -- -- -- -- -- - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ---- --- --- -- - ------ -- ---- --- --- --- -- -- ----- ---, --- - - --- -- -- -- -- -- -- -- - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ----.

@@ Line 93: / Line 93: @@
          </tr>
          <tr>
-<td class="bodyText"><p>August 4th(summary)- -- -- -- -- -- -- --   - ------ -----. --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ---- --- --- -- - ------ -- ---- ---  ---  --- -- -- ----- ---, --- - -  --- -- -- -- -- -- -- --   - ------ -----.
+<td class="bodyText"><p><strong>Hill's cooperativity</strong><br />
- --- ------ --- ---- -- --- ----- -- -- -- ------ ---- ---- - -- - ---- - ----- ---- ---, - ----- --- ----- ---- ---- ---- -- --- --- --- --- -- ---- ---------- - ------ ---- --- ---- ----- --- --- ----- ---- ----- ------ ---- -- -- --- ------- - ----- --- ----. </p>
+    <strong>5th Reaction </strong> <br />
+    <strong>Reminder:</strong> </p>
+<p>A  + B &lt;--&gt; AB&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br />
+    <strong>Ka=Keq=[AB]/[A][B]=1/Kd</strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br />
+   θ=[AB]/([AB]+[A])=[B]/([B]+Kd) </p>
+<p><strong><u>MWC  Model</u></strong> (Cooperativity)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br />
+A + nB &lt;--&gt; ABn&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br />
+<strong>Ka=Keq=[ABn]/[A][B]n=1/Kd</strong>&nbsp;&nbsp; <br />
+θ=[B]n/([B]n+Kd)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br />
+log(θ/(1- θ))=nlog(B)-log(kd)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  …Hill's equation</p>
+<p>&nbsp;</p>
+<p><strong>Suppression mediated by cI:</strong> <br />
+  ρ  + nCI &lt;--&gt; ρ:CIn&nbsp;&nbsp;&nbsp;&nbsp; (k+,  k-)&nbsp; <br />
+  <strong>Keq=Ka=[ρ:CIn]/[ρ][CI]n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br />
+  </strong>Si ρ0=[ρ]+[ρ:CIn]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br />
+  &nbsp;… ρ0=[ρ]+Keq[ρ][CI]n <br />
+  &nbsp; =&gt;  ρ= (ρ0/Keq)/((1/keq)+[CI]n) </p>
+<p>Flow=  k+[ρ][CI]n = K+((ρ0/Keq)/((1/Keq)+[CI]n))[CI]n </p>
+<p><strong>Flow= k+</strong><strong>([ρ</strong><strong>0</strong><strong>]/K</strong><strong>eq</strong><strong>)</strong> <strong>[CI]n / ((1/Keq)+[CI]n)</strong></p>
+<p><strong>=&gt; </strong><strong>Vm=  k</strong><strong>+</strong>([ρ0]/Keq)<strong>&nbsp;&nbsp; &amp;&nbsp;&nbsp; Kp=1/Keq=K</strong>d </p>
+<p><strong>So:</strong> <br />
+  Keq = exp(  -ΔG / R T )&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <br />
+  k+ = (KB/h) T exp( -ΔG / R T ) = (KB/h) T Keq </p>
+<table border="0" cellspacing="0" cellpadding="0" width="436">
+  <tr>
+    <td width="68" nowrap="nowrap"><p>Keq= </p></td>
+    <td width="84" nowrap="nowrap"><p>2.89517E+17 </p></td>
+    <td width="55" nowrap="nowrap"><p>&nbsp; </p></td>
+    <td width="24" nowrap="nowrap"></td>
+    <td width="32" nowrap="nowrap"><p><strong>K</strong><strong>B</strong><strong>=</strong> </p></td>
+    <td width="77" nowrap="nowrap"><p>1.38E-23 </p></td>
+    <td width="95" nowrap="nowrap"><p>J/K </p></td>
+  </tr>
+  <tr>
+    <td width="68" nowrap="nowrap"><p>k+= </p></td>
+    <td width="84" nowrap="nowrap"><p>1.79764E+30 </p></td>
+    <td width="55" nowrap="nowrap"><p>/s </p></td>
+    <td width="24" nowrap="nowrap"></td>
+    <td width="32" nowrap="nowrap"><p><strong>h=</strong> </p></td>
+    <td width="77" nowrap="nowrap"><p>6.63E-34 </p></td>
+    <td width="95" nowrap="nowrap"><p>J s </p></td>
+   </tr>
+  <tr>
+    <td width="68" nowrap="nowrap"></td>
+    <td width="84" nowrap="nowrap"></td>
+    <td width="55" nowrap="nowrap"></td>
+    <td width="24" nowrap="nowrap"></td>
+    <td width="32" nowrap="nowrap"><p><strong>R=</strong> </p></td>
+    <td width="77" nowrap="nowrap"><p>1.9872 </p></td>
+    <td width="95" nowrap="nowrap"><p>cal/(K mol) </p></td>
+  </tr>
+  <tr>
+    <td width="68" nowrap="nowrap"><p><strong>ΔG=</strong> </p></td>
+    <td width="84" nowrap="nowrap"><p><strong>-23810</strong> </p></td>
+    <td width="55" nowrap="nowrap"><p><strong>cal/mol</strong> </p></td>
+    <td width="24" nowrap="nowrap"></td>
+    <td width="32" nowrap="nowrap"><p><strong>T=</strong> </p></td>
+    <td width="77" nowrap="nowrap"><p>298 </p></td>
+    <td width="95" nowrap="nowrap"><p>K </p></td>
+  </tr>
+</table> </p>
           </td>
         </tr>