I want to calculate how many DNA molecules in theory were created during a PCR reaction with a known number of cycles and known amount of starting material.
For simplicity, lets say we initially have one double stranded template and therefore, we start with 2 copies of our gene. After one round we theoretically have 4, then 8 and so on.
That would be calculated like this: y=x * 2^(n)
with x the number of starting molecules and n the number of cycles and y the number of final molecules.
However, in reality, each elongation in the PCR is not 100% effective, rather 65-90%.
Now comes my question: How can I calculate y when each round has a certain efficiency below 100%?
Maybe like this? --> y=x* 2^(n) * z^(n)
with z being the efficiency, for example for 65% -->0.65
Thank you
Oh dear, I am not a mathematician... but having worked with real-time PCR (which allows you to obtain the efficiency directly from the process, because you measure DNA with a fluorescent dye in every cycle (-> have a look there, by the way)), I can add something:
Efficiency is between 0 (no duplications at all) and 1 (everything duplicated). To add that to the formula, you work with efficiency+1 (which gives you a factor between 1 and 2.
copies at cycle t = copies at start * (1+efficiency)^cycles
happy with that?
hopefully below paper help your regarding your enquiry
Article Counting individual DNA molecules by the stochastic attachme...
Why not just use 1.65 as the base instead of 2? If each cycle is resulting in only 65% of the molecules being copied, then it's not a doubling, it's an increase of 1.65x, which you can easily reflect in the exponential growth function. This is just like calculating compound interest on a principal amount of money - you would just do y = Principal * (1 + interest rate) ^ number of compounding periods.
Incidentally, where are you getting this 65% number from? Seems really low to me. I'd be curious to see some data validating that.
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