Assays & electrophoresis formulas

$\mu$ 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.