PCR & sequencing formulas for GATE Recombinant DNA Technology

PCR, sequencing, blotting and DNA fingerprinting. 7 formulas for GATE BT Recombinant DNA Technology and Tools, each with the condition it needs. Every one is taken from the topic notes, where it is explained and used.

All 7 PCR & sequencing formulas

IDEAL PCR AMPLIFICATION

N = N_{0} \times 2^{n}

$N_{0}$ = starting number of double-stranded template molecules, $n$ = number of cycles, $N$ = double-stranded molecules containing the target after $n$ cycles. Valid ONLY for 100% efficiency in every cycle (no reagent limitation, no plateau).

PCR AMPLIFICATION WITH EFFICIENCY E

N = N_{0} (1 + E)^{n}

$E$ = fraction of molecules copied per cycle ( $0 \leq E \leq 1$ ); $E = 1$ gives the ideal $2^{n}$ doubling.

DOUBLE-STRANDED PRODUCTS OF EXACTLY THE TARGET LENGTH

N_{exact} = N_{0} (2^{n} - 2 n)

Starting from $N_{0}$ double-stranded templates much longer than the target, at 100% efficiency, for $n \geq 1$ . Of the $2^{n}$ molecules per template, 2 still contain an original strand and $2 (n - 1)$ pair an exact-length strand with a 'long' strand bounded by a primer at one end only; the rest have both ends defined by the primers. Exact-length duplexes first appear in cycle 3.

WALLACE (2 + 4) RULE

T_{m} = 4 (G + C) + 2 (A + T)

$(G + C)$ and $(A + T)$ are COUNTS of bases in the primer, not percentages; $T_{m}$ in °C. A quick approximation for short oligonucleotides (conventionally applied below about 14 nt) at standard salt. When a question states a rule, use that rule.

LENGTH-CORRECTED RULE (PRIMERS OF ABOUT 14 NT OR LONGER)

T_{m} \approx 64.9 + 41 \times \frac{( G + C ) - 16.4}{N}

$N$ = primer length in nucleotides; $(G + C)$ = COUNT of G and C bases; $T_{m}$ in °C. Used where the 2 + 4 rule becomes inaccurate for longer primers.

RELATIVE QUANTIFICATION IN QPCR (ΔΔCT METHOD)

Δ C_{t} ΔΔ C_{t} Fold change = C_{t, target} - C_{t, reference} = Δ C_{t, sample} - Δ C_{t, control} = 2^{- ΔΔ C_{t}}

Valid when target and reference (housekeeping) genes both amplify with close to 100% and equal efficiency. Fold change is expression in the sample relative to the control, normalised to the reference gene.

PCR EFFICIENCY FROM A QPCR STANDARD CURVE

E = 1 0^{- 1/ slope} - 1

Slope of $C_{t}$ plotted against $lo g_{10}$ (starting quantity). $E = 1$ (100%) corresponds to a slope of about $- 3.32$ : a 10-fold dilution raises $C_{t}$ by about 3.32 cycles.

Where this was asked: 2019 (1), 2020 (1), 2022 (1), 2023 (2), 2024 (3). See the 8 previous-year questions on PCR & sequencing. A count of what was asked, not a forecast.

KEEP GOING

PCR & sequencing: the notes and 8 solved previous-year questions