# PCR rate of amplification

by nobahar
Tags: amplification, rate
 P: 501 Hello! I was wondering if anyone is familiar with the theoretical rate of amplification in a Polymerase Chain Reaction. I tried to find a source that provided an equation which would give the number of target copies (i.e. double stranded DNA that includes only the region of interest, the target region, bounded by the primers) present at any given cycle, but this was to no avail. I put togeather a sequence that I thought, based on my understanding of the technique (always questionable!), expressed the number of target copies present at each cycle. Members of this forum then helped me to put togeather an algebraic equation for this sequence. The thread is here: http://www.physicsforums.com/showthread.php?t=347731 (note that there is an error in the attempt of the first post: I suck at Latex and there shouldn't be an (n-(n-2)) in there). It should have read: $$2^n + 2^{n-2} * (n-(n-4))+2^{n-3} * (n-(n-6))+...+2^2 * (2n-2) + 2^0 * 2n$$ (eq. 1)) Although this is not the correct way of expressing it. So Mark44 then helped me to understand the sequence, and the final equation is (this is altered to take account of the first two cycles, which do not produce target copies): $$2^{n-2}+2\sum_{a=2}^{n-2} a2^{n-2-a}$$ (eq.2) N denotes the number of cycles that have taken place. This equation is supported by the graph on this site (you may have to skip through the short demonstration, it’s a matter of seconds): http://www.dnalc.org/resources/animations/pcr.html I did eventually find a source, a book, that stated the ideal, or theoretical, rate of amplification is that it doubles each cycle, this would be the equation: $$2^{n-2}$$ (eq. 3) ($$2^n$$ is the overall number of copies, including the initial DNA copy - although they will not be associated with one another, as they will be generating 'intermediate strands', and these intermediate strands, which will be assoicated with target strands (i.e. DNA containing only the target sequence, which will form future target copies when associated with another target strand).) I cannot see equation 3 being correct. It neglects the contribution made by the initial two strands and the additional ‘intermediate strands’ (which increase each cycle as they are added by the two initial strands). Unfortunately I cannot cite the book as I do not have it to hand. Is equation 2 correct for the rate of amplification?