Difference between revisions of "Biomod/2011/TUM/TNT/LabbookA/Calculation of intercalator concentrations"

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(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==

Latest revision as of 18:24, 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle K_{D} = \frac{c_{B}c_{bp}}{c_{B bp}}}

with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle K_{D}} the dissociation constant of the DNA binder, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle c_{B}} the concentration of DNA binder, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle c_{bp}} the concentration of base pairs and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle c_{B bp}} 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle {c_{B}}^{T} = c_{B bp} + c_{B}}Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle c_{B}= {c_{B}}^{T} - c_{B bp} }

and

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle {c_{bp}}^{T} = c_{B bp} + c_{bp}}Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle c_{bp} = {c_{bp}}^{T} - c_{B bp} }

  • Now assume that every n-th base a DNA binder should have bound in equilibrium

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle {c_{B bp}} = \frac{{c_{bp}}^T}{n}}

  • With this, we get to a KD which is only dependent on the total concentrations of base pairs (c.f. structure) and DNA binders

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle K_{D} = ({c_{B}}^{T} - \frac{{c_{bp}}^{T}}{n}) (n -1)}

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)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle {c_{B}}^{T} = \frac{K_{D}}{n -1} + \frac{{c_{bp}}^{T}}{n}}