The volume of the reaction mix is 0.1 ml, the number of component molecults are listed in decreasing order [1]:

All of the consumable components, the four deoxynucleotide triphosphates and two primers, are present in considerable excess of the final number of product molecules, and thus concentrations do not change appreciably during the amplification.

The number of cycles was 25, and thus there would be a 2²⁵ = 34 x 10⁶ fold amplification of the template sequence if there was a doubling each cycle. Instead, the target sequence was actually amplified by a factor of 1.8/0.000018 = 10⁵. Note that the polymerase/product ratio is only about 1/ 20 at the end of the reaction. It takes an appreciable amount of time for polymerase to copy the DNA sequence, one estimate is 1-2 minutes per 1000 bases [2]. Thus there will not be sufficient polymerase to copy all the template molecules in later cycles, since the sequence copied here is 500 bases long, and only 15-60 seconds were allowed for extension. It is observed that accumulation of product is exponential in early cycles, but then becomes linear. The explanation is that in early cycles amplification is template limited, so when products doubles in one cycle, it doubles again in the next. However, in later cycles, amplification is polymerase limited, and since there is a constant amount of polymerase in the mix, product increases each cycle by a constant amount, i.e. linearly.

Thus, we would expect exponential amplification until there were about 0.08 x 10¹² product molecules, which is a 4000 fold increase, occurring at cycle 12, and then linear accumulation for the remaining 13 cycles of about 0.08 x 10¹² molecules per cycle. If each ploymerase could make only one copy per cycle, one would expect 1.1 x 10¹² molecules, close to what is observed.

[1] Composition of the "Positive Control" that is included with PCR kits sold by Perkin-Elmer. See their catalog "PCR Systems, Reagents & Consumables", 1997, pg 85

[2] Nielson, K.B., Costa, G.L., and Braman, J. (1996) Strategies 9:24-25