Microbiology formulas

$N_0$ is the initial count and $N_t$ the survivors after time $t$ at one fixed temperature; $D$ is in the same unit as $t$. Valid while the death curve is a straight line on a log scale.

$D_{T_1}$ and $D_{T_2}$ are the D-values at temperatures $T_1$ and $T_2$ ($T_2>T_1$); $z$ is in the same temperature unit.

$d$ is the smallest resolvable distance, $\lambda$ the wavelength, $n$ the refractive index between specimen and objective and $\theta$ half the angle of the cone of light entering the objective. This is the Rayleigh form; some texts use $d=0.5\lambda /\text{NA}$. A smaller $d$ means better resolution.

Here the dilution factor is the fraction left after all dilutions, for example $10^{-6}$ after six tenfold steps. Equivalently, CFU/mL = colonies × reciprocal of the dilution ÷ volume plated.

Use only for the exponential phase. $N_0$ and $N$ are the cell counts at the start and end of the interval.

$t$ is the elapsed exponential time; $k$ is generations per unit time.

Per unit time (for example per hour). It uses the natural log, so $\mu =0.693k$.

$S$ is the limiting nutrient concentration; $K_s$ is the value of $S$ at which $\mu ={\mu }_{\max }/2$ (units of concentration). It applies when one nutrient is limiting.

$\bar{S}$ and $\bar{X}$ are the steady-state substrate and biomass concentrations, and $Y_{X/S}$ is the biomass yield (mass of cells formed per mass of substrate used). This assumes Monod kinetics with no cell death and no maintenance consumption.