Biomod/2011/TUM/TNT/LabbookA/Calculation of intercalator concentrations

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Calculation of DNA binder concentrations


  • First approach was to determine the appropriate concentrations of DNA binders with a simple approximation:

[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

However, this formula is not suited for such small concentrations, therefore we derived a more exact one.


  • Take the dissociation constant KD 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}= {c_{B}}^{T} - c_{B bp} [/math]


[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

[math]{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]K_{D} = ({c_{B}}^{T} - \frac{{c_{bp}}^{T}}{n}) (n -1)[/math]


  • 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]{c_{B}}^{T} = \frac{K_{D}}{n -1} + \frac{{c_{bp}}^{T}}{n}[/math]