In a DNA renaturation experiment the concentration of single strands remaining as a function of time is found to be 2nd order in single-strand concentration C.
Integration between t = 0 and t yields:
which can be expressed as:
Here C/Co is the fraction of the single strands remaining. Note that when
kCot = 1, t → t1/2 = 1/kCo and k = 1/Cot1/2
At that point, C/Co = 0.5, or one half of the DNA is in the single-stranded form. The equation above could be expressed as:
In terms of the fraction of the DNA renatured, fren, we have:
A DNA is allowed to renature for a time t, and the fraction that has renatured (fren) during that time is measured. Knowing the initial [DNA], Co, the product Cot, referred to as the “Cot” can now be used to obtain k. From above, k can then be related to the “Cot1/2”:
Cot1/2 = 1/ k
The “Cot1/2” which is a constant (1/k) for a particular DNA could be obtained directly from the midpoint of the renturation curve, i.e. if you find the time precisely for 50% renaturaton. It can be calculated, however, from the time required for any value of fren along the curve. Equation 6. can be expressed as:
From the data below for T4 DNA, fren = 0.436 (43.6% renatured) at Cot = 0.325 Ms. This Cot value was obtained from the product of t = 65 s and a Co = 5x10-3 M.
You should be able to calculate a Cot1/2 value...