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

Calculation of intercalator concentrations

Intention

• First approach was to determine the right concentration of intercalators with a simple approximation:

[math]\displaystyle{ K_{D} = \frac{c_{I}c_{Bp}}{c_{I Bp}} }[/math]

with [math]\displaystyle{ K_{D} }[/math] the dissociation constant of the intercalator, [math]\displaystyle{ c_{I} }[/math] the concentration of intercalator, [math]\displaystyle{ c_{Bp} }[/math] the concentration of base pairs and [math]\displaystyle{ c_{I Bp} }[/math] the concentration of the occupied basepairs

Derivation

• Take the dissociation constant K_D and replace the concentrations with the total concentrations of the intercalators and base pairs:

[math]\displaystyle{ {c_{I}}^{T} = c_{I Bp} + c_{I} }[/math] → [math]\displaystyle{ c_{I}= c_{I Bp} - {c_{I}}^{T} }[/math]

and

[math]\displaystyle{ {c_{Bp}}^{T} = c_{I Bp} + c_{Bp} }[/math] → [math]\displaystyle{ c_{Bp} = c_{I Bp} - {c_{Bp}}^{T} }[/math]

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

[math]\displaystyle{ {c_{I Bp}} = \frac{c_{Bp}}{n} }[/math]

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

[math]\displaystyle{ K_{D} = ({c_{I}}^{T} - \frac{{c_{Bp}}^{T}}{n}) (n -1) }[/math]

Result

• Now we are able to calculate the right concentration of the intercalator in the sample to get an occupancy of n (i.e. one intercalator each n-th base pair)

[math]\displaystyle{ {c_{I}}^{T} = \frac{K_{D}}{n -1} + \frac{{c_{Bp}}^{T}}{n} }[/math]