# Population Dynamics: Bacterial Growth Curves Provide Data to Calculate Growth Rates and Carrying Capacity

## Summary

Bacterial growth rates are monitored by OD and OD converted to cell population density from a standard curve derived from plate counts. The resulting data are used to fit a logistic model solved at discrete time steps. The derived model parameters r, intrinsic growth rate, and K, carrying capacity are used to test the goodness of fit to the data. Initial variables are starting population density. Students use the results to make hypotheses and design experiments of their choice--most alter nutrient density or composition--and test these again determining r and K.

## Learning Goals

This is the first in a series of labs to link data collection to modeling and interesting parameter estimation. The goals are:

- Gain an understanding of population behavior and dependence on density conditions

- Practice our lab skills including planning a multipart experiment and using micropipetters, absorbance spectrophotometry, dilutions, plating bacteria.

- Plot raw data to see actual growth curve and test assumptions regarding OD and population density.

- Work through the modeling process: mathematical formulation, parameter estimation, model validation

- Use the mathematical model to predict population size at any given time & compare the prediction with the actual experimental results

- Finally, use the outcomes (experimental and calculated) to refine questions, experimental and mathematical design.

MATLAB could replace "R" easily -- as the tool essential for manipulating large data sets, graphing, simple calculations and conversions as well as calculating least squares linear fits and iterative solutions to a model.

Students present their work orally to the class and in a formal notebook with the experimental and computational steps documented, conclusions drawn and next steps proposed.

- Gain an understanding of population behavior and dependence on density conditions

- Practice our lab skills including planning a multipart experiment and using micropipetters, absorbance spectrophotometry, dilutions, plating bacteria.

- Plot raw data to see actual growth curve and test assumptions regarding OD and population density.

- Work through the modeling process: mathematical formulation, parameter estimation, model validation

- Use the mathematical model to predict population size at any given time & compare the prediction with the actual experimental results

- Finally, use the outcomes (experimental and calculated) to refine questions, experimental and mathematical design.

MATLAB could replace "R" easily -- as the tool essential for manipulating large data sets, graphing, simple calculations and conversions as well as calculating least squares linear fits and iterative solutions to a model.

Students present their work orally to the class and in a formal notebook with the experimental and computational steps documented, conclusions drawn and next steps proposed.

## Context for Use

This wet lab takes place over two or three lab periods as part of a Mathematical Biology course designed for mathematics, computer science and biology college undergraduates. As written, the instructions assume "R" and that the students have worked through basic exercises on inputting data, entering commands and using the graphing function: however, the actual code is given in the lab write-up. The course requires linear algebra but this is not required for this lab. We do teach basic pipetting and spectrophotometry skills with an exercise on dilution (with dye) prior to this lab exercise: they learn how to think about exponential and linear relationships. We think this activity would be easy to adapt (yeast instead of bacteria or data sets instead of actual measurements).

## Description and Teaching Materials

The full description of this activity is uploaded as a WORD file as the first "supporting materials" item.

student handout for Population Dynamics—Bacterial Growth Curves Provide Data to Calculate Growth Rates and Carrying Capacity (Microsoft Word 2007 (.docx) 573kB Oct17 16)

student handout for Population Dynamics—Bacterial Growth Curves Provide Data to Calculate Growth Rates and Carrying Capacity (Microsoft Word 2007 (.docx) 573kB Oct17 16)

## Teaching Notes and Tips

(NOTE to Instructors: The steps of this experiment may completed by different lab groups and the data combined or each lab group may do all steps required for complete data collection. The plate counts are messy and should be done by as many hands as possible for accurate data: alternatively, the literature reports that an OD600 = 1 (pathlength 1 cm) is about 8 x 108 cells/ml (Agilent Technologies) and our data suggest that OD600 = 0.1 represents 5.2 x 107 cells/ml and an OD600 = 1 is 5 x 108 cells/ml. )

## Assessment

Assessment --

--Formal lab manual writeup with completed annotated calculations and graphs.

--Take-home exam questions include related material.

--Formal lab manual writeup with completed annotated calculations and graphs.

--Take-home exam questions include related material.