Plant, Animal and Microbial Biotechnology formula sheet

$V_1$ is the volume of stock at concentration $C_1$ needed to make volume $V_2$ of medium at concentration $C_2$. Put both concentrations in one unit and both volumes in one unit before substituting (1 mg/mL = 1000 mg/L).

Biomass concentration $X$ at time $t$ during the exponential phase; $X_0$ is the biomass at the start of that phase and $\mu$ the specific growth rate.

Applies when one protoplast of each parent fuses, the nuclei fuse and no chromosomes are lost. The hybrid of two diploid parents is an amphidiploid (allotetraploid). Chromosome loss or elimination makes the number lower, and a hybrid made with irradiated donor protoplasts keeps fewer chromosomes.

For a primary transformant that is hemizygous at n independent, unlinked single-copy loci, with each locus carrying a dominant, fully expressed marker and no loss in transmission or viability, selfed. At one locus the selfed progeny are 1/4 homozygous, 1/2 hemizygous and 1/4 without the transgene, so 3 with the transgene to 1 without and P = 3/4. Two loci give 15:1. Does not apply to linked loci or to plastid genes, which are maternally inherited.

X is the viable cell concentration (cells/mL), X_0 its value at the start of the exponential phase, and μ the specific growth rate (per hour); valid only in the exponential phase.

X in cells/mL and t in hours, so μ is in per hour; both points must lie in the exponential phase.

For one autosomal locus with Mendelian segregation and equal viability of all genotypes. The fraction of homozygous null (knock-out) pups is 1/4. To be homozygous null at two unlinked loci the chance is 1/4 x 1/4 = 1/16. If the null homozygote dies as an embryo, live pups are +/+ : +/- = 1 : 2, so 2/3 of them are heterozygous.

X is biomass concentration (g/L). In exponential growth with constant $\mu$, $X=X_0{e}^{\mu t}$.

Valid only in the exponential phase, where $\mu$ is constant. $\mu$ is in h${}^{-1}$, so $t_d$ is in hours.