#### Enrichment of different generation times as function of label strength and incubation time

### About

## Isotope labeling calculator

###
This app is intended for use in
*estimating*
expected enrichments from stable isotope labeling in microbial populations. It is based on isotopic enrichment resulting from unbiased clonal growth in the presence of an isotopic label: $$F{\left(t\right)}=F_{N}\left(1-e^{-{\mu}\cdot{t}}\right)+F_{t_0}\cdot{e^{-{\mu}\cdot{t}}}
\left(\mu{}=\ln(2)/T\right)$$ with \({F_{N}}\) the isotopic composition of new biomass generated in the presence of the isotope label (using fractional abundances \(F\) is important for correct mass balance!). Substituting the growth rate for the generation time \(\left(ยต = \ln(2) / T\right)\), one can readily calculate the required labeling time to reach a target isotopic composition \({F_{f}}\): $$t_{label}=\frac{T}{ln(2)}\cdot{\ln\left(\frac{F_N-F_{t_0}}{F_N-F_f}\right)}$$ This app is intended to make it easy to explore this space for different isotope systems and takes care of all the isotope conversions and mixing calculations between existing and isotopically labelled pools.

## Source code

### This app was written by Sebastian Kopf and is powered by RStudio 's Shiny engine . The source code for this application is released under GPL-3 and is available on GitHub . Please use the repository's Issue Tracker for any feedback, suggestions and bug reports.

### Plot Options

### Isotope system

**Target enrichment:**