The whole Recombinant DNA Technology and Tools formula sheet, to print

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.

Starting from $N_0$ double-stranded templates much longer than the target, at 100% efficiency, for $n\ge 1$. 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.

$(G+C)$ 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.

$N$ = 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.

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.

Slope of $C_t$ plotted against ${\log }_{10}$(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.

$d$ = 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.

$h$ = Planck's constant; $\nu$ = frequency; $c$ = speed of light; $\lambda$ = wavelength; $\tilde{\nu }=1/\lambda$ = wavenumber (usually in $\mathrm{c}{\mathrm{m}}^{-1}$). Shorter wavelength = higher energy.

$I_0$ = intensity of light entering the sample; $I$ = intensity transmitted; $T$ = transmittance. Absorbance is dimensionless. Example: $T=10\%$ gives $A=1$; $T=1\%$ gives $A=2$.

$A$ = absorbance (dimensionless); $ϵ$ = molar absorption (extinction) coefficient in ${\mathrm{M}}^{-1}\mathrm{c}{\mathrm{m}}^{-1}$, specific to the molecule, wavelength and solvent; $c$ = molar concentration (M = mol ${\mathrm{L}}^{-1}$); $l$ = path length (cm; a standard cuvette is 1 cm). Holds for monochromatic light in dilute, non-scattering solutions, within the linear range of the instrument — at high absorbance (often above about 1) the response deviates from linearity and the sample should be diluted. For a mixture of non-interacting absorbers, absorbances at a given wavelength add.

Conventional factors $F$: an $A_{260}$ of 1.0 in a 1 cm path corresponds to about 50 µg/mL double-stranded DNA, about 40 µg/mL RNA, and about 33 µg/mL single-stranded DNA.

A rough purity indicator only. A ratio well below these values suggests protein (or phenol) contamination; a DNA preparation reading near 2.0 may contain RNA. The ratio is affected by the pH of the solution. A companion check, $A_{260}/A_{230}$, is about 2.0–2.2 for clean nucleic acid; lower values indicate carry-over of contaminants that absorb near 230 nm (e.g. guanidine salts, phenol, carbohydrates).

$E$ = efficiency of energy transfer from donor to acceptor; $r$ = donor–acceptor distance; $R_0$ = Förster distance, the distance at which $E=0.5$ (typically a few nanometres). Requires overlap of the donor emission spectrum with the acceptor excitation spectrum. The sixth-power dependence makes FRET a sensitive 'molecular ruler' over roughly 1–10 nm.

$A_{\mathrm{L}}$, $A_{\mathrm{R}}$ = absorbance of left- and right-circularly polarised light. $\Delta A$ is non-zero only for chiral chromophores, or chromophores in a chiral environment (e.g. peptide bonds in a folded protein, bases in a nucleic-acid helix). CD is often reported as ellipticity.

$z$ = charge number; $e$ = elementary charge; $V$ = accelerating potential; $m$ = ion mass; $v$ = velocity in the field-free flight tube; $L$ = flight-tube length; $t$ = flight time. Every ion leaves the source with kinetic energy $zeV$, so for the same $V$ and $L$: at a fixed charge a heavier ion arrives later; at a fixed mass a more highly charged ion arrives sooner.

$M$ = neutral molecular mass (Da); $n$ = number of protons added (charge); $m_{{\mathrm{H}}^{+}}$ = mass of a proton $\approx 1.007$ Da (often rounded to 1). For two ADJACENT peaks $p_1<p_2$ in the charge-state series, $p_2$ carries charge $n$ (given by the second formula) and $p_1$ carries $n+1$; then $M=n(p_2-m_{{\mathrm{H}}^{+}})$.

$\nu$ = resonance (Larmor) frequency; $\gamma$ = gyromagnetic ratio of the nucleus; $B_0$ = applied magnetic field. The chemical shift $\delta$ is measured relative to a reference (tetramethylsilane, TMS, set at $\delta =0$) and is independent of field strength. A stronger field spreads the signals further apart (better resolution and sensitivity).

$\mu$ 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.

By convention, one unit (U) converts 1 µmol of substrate per minute under stated assay conditions. The SI unit is the katal, where 1 kat = 1 mol s⁻¹. Hence 1 U = $10^{-6}/60$ kat ≈ 16.67 nkat.

Units: U mg⁻¹. Specific activity measures enzyme purity. It rises through a purification as contaminating protein is removed, even though the total units recovered fall.

Both are calculated against the starting crude extract, not against the previous step.

$A={\log }_{10}(I_0/I)$ is the absorbance (dimensionless). $\epsilon$ is the molar absorption (extinction) coefficient of the absorbing species in M⁻¹cm⁻¹, $c$ its concentration in M (mol L⁻¹), and $l$ the path length in cm (commonly 1 cm). The law holds for dilute solutions at low absorbance.

This gives the rate in M per unit time when only the monitored species changes absorbance. Multiply by the reaction volume (in L) to get mol per unit time. Then use the stoichiometry to convert to substrate converted, and compare with the unit definition.

$N$ is the number of reads, $L$ the read length in bp, $G$ the genome size in bp, and $C$ the mean coverage (depth, '×'). The $e^{-C}$ estimate assumes reads land at random and uniformly (Poisson sampling). Real data are less uniform, so gaps are more common than this predicts.

$P_{\text{error}}$ 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.

g = gap length; α = gap-opening penalty (the cost of the first gap position); β = gap-extension penalty (the cost of each further position), with α > β. Convention: some programs write the same idea as $W=o+eg$, where the opening cost is charged on top of a per-position cost for every position. Always check which form a question uses.

F(i,j) = best score for aligning the first i residues of X with the first j residues of Y; $s(x_i,y_j)$ = match/mismatch or matrix score; d = linear gap penalty, written as a positive number and subtracted. Initialisation: F(0,0) = 0, F(i,0) = −i·d, F(0,j) = −j·d. For sequences of lengths m and n this takes O(mn) time and memory.

The same as global alignment except for the 0 option and an initialisation of F(i,0) = F(0,j) = 0. The local alignment score is the largest F(i,j) anywhere in the matrix, and traceback stops at a cell with value 0.

E = the number of alignments with score ≥ S expected by chance alone in a search of this size; m = query length; n = total length of the database (in residues); S = the RAW alignment score; K and λ = statistical parameters of the scoring system. E rises in proportion to the search space (m·n) and falls exponentially as S rises. A smaller E-value means a more significant hit.

The bit score S′ normalises the raw score so that scores from different scoring systems can be compared. Each extra bit halves E. P is the probability of at least one chance hit scoring ≥ S; when E is small (below about 0.01), P ≈ E.

The distance from the merged cluster (i,j) to cluster k is the average of the two distances, weighted by the numbers of sequences $n_i$ and $n_j$ in each cluster. This equals the plain average over all member pairs. Using the simple average $(d_{i,k}+d_{j,k})/2$ without weights is a different method, WPGMA.

Valid for n ≥ 3 (unrooted) and n ≥ 2 (rooted); !! is the double factorial (the product of odd numbers). Check: n = 4 gives 3 unrooted and 15 rooted trees; n = 5 gives 15 unrooted and 105 rooted trees. The number of rooted trees for n taxa equals the number of unrooted trees for n + 1 taxa.

S = stoichiometric matrix (rows = metabolites, columns = reactions); v = vector of reaction fluxes. At steady state the net rate of change of every internal metabolite is zero, giving one linear equation per metabolite. The bounds encode irreversibility and uptake limits. c selects the objective (e.g. biomass or product flux). The problem is solved by linear programming, not by simulating dynamics. Before the bounds are applied, the steady-state solutions form a space of dimension (number of reactions) − rank(S).