GATE Recombinant DNA Technology formula sheet

L is the length in bp, and all four bases have probability 1/4, independently. The expected average spacing between sites is 4^n bp: 256 bp for a 4-cutter, 4096 bp for a 6-cutter, 65,536 bp for an 8-cutter such as NotI (GC^GGCCGC). A palindromic site reads the same on both strands, so each position is counted once. A non-palindromic site can occur on either strand of dsDNA, which doubles the expected count. Real genomes differ from these values because base composition is biased and sequence is not random.

g is the GC fraction, so each of G and C has probability g/2 and each of A and T has probability (1−g)/2. n_GC and n_AT count the G/C and A/T bases in the site. The expected average spacing is 1/P_site bp (palindromic site).

$N$ = number of independent clones required; $P$ = desired probability that a given sequence is present at least once. Genomic library: $f$ = average insert size / genome size, in the same units (bp). cDNA library: $f$ = the fraction of all mRNA molecules made up by the transcript of interest (its abundance). Assumes fragments are cloned at random and independently, with every fragment equally clonable. Always round $N$ up.

The same relation solved for $P$. For small $f$, $\ln (1-f)\approx -f$, so $N\approx \frac{-\ln (1-P)}{f}$, which slightly overestimates $N$.

$N_0$ = 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).

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

$d$ = minimum resolvable distance (same unit as $\lambda$); $\lambda$ = wavelength of the illumination; $\mathrm{NA}=n\sin \theta$ = numerical aperture of the objective, where $n$ is the refractive index of the medium between specimen and objective (air $\approx 1.00$, immersion oil $\approx 1.52$) and $\theta$ is the half-angle of the cone of light the objective accepts. Smaller $d$ = better resolution. Shorter wavelength and/or higher NA improve resolution; oil immersion raises NA (to about 1.4–1.5).

Abbe's form gives a slightly smaller $d$ than the Rayleigh form for the same $\lambda$ and NA. The two are different criteria, not different conventions for the same number — use the form the question specifies.

$\mu$ is the velocity $v$ per unit field strength $E$. $q$ is the net charge, $\eta$ the viscosity of the medium and $r$ the hydrodynamic radius. The second equality is an idealisation: it assumes a rigid sphere in free solution and ignores screening by the surrounding counter-ions. Mobility increases with net charge and decreases with size.

$R_f$ = (distance moved by the protein) ÷ (distance moved by the tracking-dye front). Plot ${\log }_{10}$(MW) of standard proteins against $R_f$. The plot is approximately a straight line over the gel's resolving range, with $b>0$ because larger proteins have smaller $R_f$. Read the unknown's MW from this line.

Under reducing conditions the result is the mass of each individual polypeptide chain (subunit), not of a native multi-subunit protein. Heavily glycosylated, unusually highly charged or incompletely denatured proteins can fall off the line.

$P_{\text{error}}$ is the probability that the base call is wrong. Q = 20 means $P=10^{-2}$ (1 error in 100, 99% accuracy); Q = 30 means $P=10^{-3}$ (1 in 1000, 99.9%). In the common Phred+33 encoding, the quality character's ASCII code equals Q + 33.

$q_{ab}$ = observed frequency of residues a and b aligned in related sequences; $p_a$, $p_b$ = background frequencies of each residue; $\lambda$ = scaling constant (values are then rounded to integers). A positive score means the pair occurs more often than chance (a conservative or likely substitution), zero means as often as chance, and a negative score means less often than chance.