# [R] Equation of a curve

Boris Steipe boris.steipe at utoronto.ca
Thu Apr 3 20:09:50 CEST 2014

```You may have a different use in mind, but I think integration does not make sense for growth curves. And there is no simple, general equation that I'm aware of:

When you determine the area under the curve (integration), you are essentially multiplying bacterial mass by time. Imagine that you would kill your bacteria and continue observing. Then the integral would just grow, and grow ... that's possibly not what you want. Bacterial growth parameters are often characterized by *doubling times*, or *growth rate* and these are essentially derived from *differentiating* the observed concentration (or absorbance) with respect to time - relative mass-increase per time unit.

That said, you will usually observe non ideal behaviour at the start of growth (lag phase), a phase of rapid growth (exponential phase) and slowing of growth as the culture conditions become nutrient limited (stationary phase) - possibly followed by a drop of absorbance when your bacteria die off. Modelling this with equations is not trivial, and the parameters you are fitting are usually not of interest anyway.

Probably the best approach is to focus on that part of your growth curve that actually shows the expected exponential growth. This part should be linear if you plot the log of your measurement.

1: Take the log of your measurement;
2: plot it and determine the time interval you should analyze;
3: perform a simple linear regression on the data points in that interval. See: ?lm in R.
4: Calculate your doubling time (or whatever number you need) from the slope.

Hope this helps,
B.

On 2014-04-03, at 11:26 AM, Frances Cheesman wrote:

> Hi all,
>
> I have a number of bacterial growth curves I would like to find the
> equations for these and then integrate them to find the area under the
> curves for me to do stats on later.
>
> Is there any way I can do this in R?
>
> Thanks,
>
> Frances
>
> 	[[alternative HTML version deleted]]
>
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```

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