Efficiency of the Polymerase Chain Reaction

Abstract

The polymerase chain reaction (PCR) has found wide application in biochemistry and molecular biology such as gene expression studies, mutation detection, forensic analysis and pathogen detection. Increasingly quantitative real time PCR is used to assess copy numbers from overall yield. In this study the yield is analyzed as a function of several processes: (1) thermal damage of the template and polymerase occurs during the denaturing step, (2) competition exists between primers and templates to either anneal or form dsDNA, (3) polymerase binding to annealed products (primer/ssDNA) to form ternary complexes and (4) extension of ternary complexes. Explicit expressions are provided for the efficiency of each process, therefore reaction conditions can be directly linked to the overall yield. Examples are provided where different processes play the yield-limiting role. The analysis will give researchers a unique understanding of the factors that control the reaction and will aid in the interpretation of experimental results.

Figure A1

Three separate bands are seen above, corresponding to γ = 0.1, 0.3 and 0.5. In each band, the value of R(τ, γ, β) increases with β, the top curve in each band corresponding to β = 1 + 10⁻⁶. The maximum ratio achieved is less than 1.1, with β = 1 + 10⁻⁶ and γ = 0.5.

Figure 1

Schematic diagram of annealing phase reactions showing the formation of double-stranded DNA as well as binary- and ternary-complexes.

Figure 2

The analytical approximation (solid line) as well as numerical solutions (markers) for different parameter values. The top row shows the first two seconds of the reaction, while the bottom row shows the first ten seconds. (A1&A2): α = 0.03, β = 1 + 10⁻⁶ and γ = 10⁻³. These are the expected values for most PCR experiments. (B1&B2): α = 0.03, β = 1 + 10⁻⁶ and γ = 0.5. The higher value of γ is characteristic of the last and second to last PCR cycles. (C1&C2): α = 1, β = 5 and γ = 10⁻³. This simulation shows that the approximations hold for different values of α and β.

Figure 3

The annealing efficiency (η_a) as a function of the template:primer ratio (γ).

Figure 4

Efficiencies as a function of cycle number. D_i = 10⁵ copies, E_i = 12.6×10¹¹ copies, elongation period is 20 s (A), 10s (B) and 5s (C). (D): Normalized DNA product as a function of cycle number. D_i = 10⁵ copies, E_i = 12.6×10¹¹ copies, at elongation periods 20 s, 10 s and 5 s. The curves had the same maximum before normalization.

Figure 5

Efficiencies as functions of cycle number. D_i = 10⁵ copies, E_i = 6.3×10¹¹ copies, elongation period is 20 s (A), 10s (B) and 5s (C). (D) Normalized DNA product as a function of cycle number. D_i = 10⁵ copies, E_i = 6.3×10¹¹ copies, at elongation periods 20 s, 10 s and 5 s.

Figure 6

Efficiencies as functions of cycle number. D_i = 10⁵ copies, E_i = 2.1×10¹¹ copies, elongation period is 20 s (A), 10s (B) and 5s (C). (D) Serial dilution study - normalized DNA product as a function of cycle number. D_i = 10², 10³, 10⁴ and 10⁵ (as indicated in the legend), E_i = 12.6×10¹¹ copies, t_E = 20 s.