What Is the Theoretical Rate of Amplification in PCR?

[nobahar]

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:

https://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?

 

[nate808]

Hello!

As a scientist familiar with Polymerase Chain Reaction (PCR), I can provide some insight into the theoretical rate of amplification in PCR. The equation you have proposed in equation 2 is correct for calculating the number of target copies at each cycle. This is because each cycle of PCR involves a doubling of the target copies, as well as the addition of intermediate strands that are formed during the process.

Equation 3, on the other hand, is not entirely correct as it does not take into account the contribution of these intermediate strands. The initial two strands are important for starting the amplification process, but they do not contribute to the overall number of target copies.

In general, the theoretical rate of amplification in PCR is determined by the efficiency of the PCR reaction, which is affected by various factors such as primer design, reaction conditions, and enzyme activity. It is important to note that in practical applications, the actual rate of amplification may differ from the theoretical rate due to these factors.

I hope this helps clarify any confusion and provides a better understanding of the theoretical rate of amplification in PCR. If you have any further questions, please don't hesitate to ask.

 

[Blueshift5]

Dear writer,

I can confirm that equation 2 is the correct representation of the rate of amplification in a Polymerase Chain Reaction (PCR). This equation takes into account the contribution made by the initial DNA copies and the intermediate strands, which are important factors in the amplification process.

PCR is a powerful technique used in molecular biology to amplify a specific region of DNA. It involves multiple cycles of denaturation, annealing, and extension, and each cycle results in a doubling of the target DNA copies. This exponential amplification is the basis of PCR's sensitivity and efficiency.

Equation 2, also known as the geometric progression equation, accurately represents the number of target DNA copies present at each cycle. It takes into consideration the contribution of the initial DNA copies and the intermediate strands, which are crucial for the success of the reaction.

I would also like to mention that the theoretical rate of amplification, as stated in equation 3, is a simplified version and neglects the contribution of the initial DNA copies and intermediate strands. Therefore, it is not an accurate representation of the actual rate of amplification in PCR.

I hope this explanation helps clarify any confusion and provides a better understanding of the theoretical rate of amplification in PCR. Thank you for your question and for seeking clarification on this topic.