Biomod/2011/TUM/TNT/LabbookA/Calculation of intercalator concentrations: Difference between revisions
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{{ | {{TUMNanUHeaderLabbookA}} | ||
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=Calculation of DNA binder concentrations= | =Calculation of DNA binder concentrations= | ||
==Intention== | ==Intention== | ||
| Line 6: | Line 6: | ||
<math>K_{D} = \frac{c_{B}c_{bp}}{c_{B bp}}</math> | <math>K_{D} = \frac{c_{B}c_{bp}}{c_{B bp}}</math> | ||
with <math>K_{D}</math> the dissociation constant of the DNA binder, <math>c_{B}</math> the concentration of DNA binder, <math>c_{bp}</math> the concentration of base pairs and <math>c_{B bp}</math> the concentration of the occupied basepairs | with <math>K_{D}</math> the dissociation constant of the DNA binder, <math>c_{B}</math> the concentration of DNA binder, <math>c_{bp}</math> the concentration of base pairs and <math>c_{B bp}</math> the concentration of the occupied basepairs<br> | ||
<br> | |||
However, this formula is not suited for such small concentrations, therefore we derived a more exact one. | |||
==Derivation== | ==Derivation== | ||
* Take the dissociation constant K<sub>D</sub> and replace the concentrations with the total concentrations of the DNA binders and base pairs: | * Take the dissociation constant K<sub>D</sub> and replace the concentrations with the total concentrations of the DNA binders and base pairs: | ||
<math>{c_{B}}^{T} = c_{B bp} + c_{B}</math> → <math>c_{B}= | <math>{c_{B}}^{T} = c_{B bp} + c_{B}</math> → <math>c_{B}= {c_{B}}^{T} - c_{B bp} </math> | ||
and | and | ||
<math>{c_{bp}}^{T} = c_{B bp} + c_{bp}</math> → <math>c_{bp} = | <math>{c_{bp}}^{T} = c_{B bp} + c_{bp}</math> → <math>c_{bp} = {c_{bp}}^{T} - c_{B bp} </math> | ||
* Now assume that every n-th base a DNA binder should have bound in equilibrium | * Now assume that every n-th base a DNA binder should have bound in equilibrium | ||
<math>{c_{B bp}} = \frac{c_{bp}}{n}</math> | <math>{c_{B bp}} = \frac{{c_{bp}}^T}{n}</math> | ||
* With this, we get to a K<sub>D</sub> which is only dependent on the total concentrations of base pairs (c.f. structure) and DNA binders | * With this, we get to a K<sub>D</sub> which is only dependent on the total concentrations of base pairs (c.f. structure) and DNA binders | ||
| Line 30: | Line 32: | ||
<math>{c_{B}}^{T} = \frac{K_{D}}{n -1} + \frac{{c_{bp}}^{T}}{n}</math> | <math>{c_{B}}^{T} = \frac{K_{D}}{n -1} + \frac{{c_{bp}}^{T}}{n}</math> | ||
</div> | |||
Latest revision as of 19:24, 2 November 2011
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Calculation of DNA binder concentrations
Intention
- First approach was to determine the appropriate concentrations of DNA binders with a simple approximation:
[math]\displaystyle{ K_{D} = \frac{c_{B}c_{bp}}{c_{B bp}} }[/math]
with [math]\displaystyle{ K_{D} }[/math] the dissociation constant of the DNA binder, [math]\displaystyle{ c_{B} }[/math] the concentration of DNA binder, [math]\displaystyle{ c_{bp} }[/math] the concentration of base pairs and [math]\displaystyle{ c_{B bp} }[/math] the concentration of the occupied basepairs
However, this formula is not suited for such small concentrations, therefore we derived a more exact one.
Derivation
- Take the dissociation constant KD and replace the concentrations with the total concentrations of the DNA binders and base pairs:
[math]\displaystyle{ {c_{B}}^{T} = c_{B bp} + c_{B} }[/math] → [math]\displaystyle{ c_{B}= {c_{B}}^{T} - c_{B bp} }[/math]
and
[math]\displaystyle{ {c_{bp}}^{T} = c_{B bp} + c_{bp} }[/math] → [math]\displaystyle{ c_{bp} = {c_{bp}}^{T} - c_{B bp} }[/math]
- Now assume that every n-th base a DNA binder should have bound in equilibrium
[math]\displaystyle{ {c_{B bp}} = \frac{{c_{bp}}^T}{n} }[/math]
- With this, we get to a KD which is only dependent on the total concentrations of base pairs (c.f. structure) and DNA binders
[math]\displaystyle{ K_{D} = ({c_{B}}^{T} - \frac{{c_{bp}}^{T}}{n}) (n -1) }[/math]
Result
- Now we are able to calculate the right concentration of the DNA binders in the sample to get an occupancy of n (i.e. one DNA binder each n-th base pair)
[math]\displaystyle{ {c_{B}}^{T} = \frac{K_{D}}{n -1} + \frac{{c_{bp}}^{T}}{n} }[/math]
