Equations for BMB400

Binding equilibria

The equilibrium constant for the binding of a protein (P) to a DNA fragment (D) is KB.

The fraction of DNA in a complex with the protein is a function of KB and [P]:

The specificity of binding of a protein (P) to DNA is described by the following equation. KS is the equilibrium binding constant to specific DNA sites, or DS. KNS is the equilibrium binding constant to nonspecific DNA sites, or DNS. Concentrations are moles/L, i.e. molar.

Relationship between DG and Keq, where Keq is an equilibrium constant:

DG = -RT ln Keq

R = 1.98 ¥ 10-3 kcal deg-1 mol-1

T = 298° K

RT = 0.59 kcal/mol

In an abortive transcription assay, the lag time between the mixing of reagents and the optimal rate of abortive transcript production is related to the concentration of RNA polymerase (or [RNAP]) by the following equation. KB is the equilibrium constant for binding of RNAP to the promoter, and kf is the forward rate constant for the closed to open transition.

 

Cot analysis

 

Supercoiling:

T = Twisting Number

For B form DNA, it is + (# bp/10 bp per twist)

For A form DNA, it is + (# bp/11 bp per twist)

For Z form DNA, it is - (# bp/12 bp per twist)

DL = DW + DT

Superhelical density = s = W/T = -0.05 for natural bacterial DNA

Recombinant DNA:

N = ln(1-P)

ln(1-f)

N is the number of recombinants required to obtain a given probability (P) of having a particular sequence in the library. f = the fraction of the genome in a single recombinant molecule, i.e. f = insert size / genome size.