Experiment 2:  Growth Rate of Dictyostelium discoideum


You will set up cultures at about 1x104 to 1x105 cells/ml in petri dishes to follow the increase in titer of the cells over the rest of the week and calculate the growth rate (doubling time) of your cells. 



Setting up Cell Cultures

(**Recall everything you do from here is done using sterile technique**)


Starting with the right number of cells, the key is to start off with enough cells to allow them to grow in log phase for several days since it will be those data points needed for the generation time (time it takes the population to double).


First, triturate the cells in your growth plate and then pipette the cells and media into a 15 ml sterile tube.  Vortex the tube and then titer the cells using the hemocytometer.


Counting Cells Using a Haemocytometer


Now you want to determine the cell titer using a haemocytometer.  The bottom glass part of the unit has two counting chambers.  When you put the coverslip onto the supports, it creates a chamber of a precisely known volume.  You then count the number of cells using a grid ruled onto the glass surface and since the counting area is a known size, and the volume is a known size, you can derive the titer of the cells you added.


This simple looking device is very expensive because of the precision necessary to create the chamber.  BE VERY CAREFUL HANDLING IT!  It should never move farther than your benchtop and the drawer it is stored in!!!  DO NOT CARRY IT TO THE SINK TO CLEAN IT.  SIMPLY WIPE OFF THE COVERSLIP AND CHAMBER AREA WITH A KIMWIPE!  If you never hold it over the floor, you will never drop it on the floor.



Procedure:


1.Assemble the chamber by putting the special heavy glass coverslip onto the chamber.

2.Make sure you have a homogeneous suspension of cells (vortex the tube or pipette the cells in the dish up and down). Using 20-200 ul micropipette, take up 10-15 ul of culture.

3.Gently expel the liquid into the space between the coverslip and the heavy glass slide. (this should move across the measuring field via capillary action). 

4.There are two identical chambers so you could count two samples at one time.  Use both and count both to check your reproducibility.

5.Carefully lift the hemocytometer to the microscope and focus on the gridded area shown in Figure 1.

6.The central area (marked #5 in Figure 1) is a 5x5 grid of squares. In the corners are 4 areas gridded as 4x4 (marked #1-4 in Figure 1) that are exactly the same size.

7.Start by counting the central area. If the titer is low, begin counting the outer 4 areas. Your goal is to count about 100 cells. If the titer is too low, you will not get to that number so your titer will be less accurate.  If the titer is too high, it can become difficult to count all the cells. 

8.You can use a mechanical counter or count in your head.

7.  To calculate the titer, multiply the number of cells per counting area (1-5) by 1x104.


For example,


If you count 45 cells in the central 5x5 area, you have 45 x 104 cells/ml or 4.5 x 105 cells/ml

If you count 100 cells by counting all 5 areas, you have 2x105 cells/ml


If the volume of culture you used to take the sample is 10 mL, then you have

4.5 x 105 cells/mL x 10mL =  4.5 x 106 total cells



You may count one square of the 5x5 grid and multiply by 25, but this is a very rough estimate and should not be used to determine an accurate titer.



Calculations


Be careful to use units in your calculations and to show your calculations in your lab notebook.  Sometimes you will work with numbers of cells and sometimes with density of cells (cells/ml) and it can be confusing at first if you don’t use units!


To calculate the number of cells to add to your new culture, you can use the equation

C1 x V1 = C2 x V2

Where C1= the density of cells (cells/ml) you determined with the hemocytometer

V1= the volume of your initial culture to put into your final volume

C2= the cell titer you want in the new dish

V2= the volume of HL-5 you will start your growth curve culture in


Your calculations may look something like this if you have a culture that is at 6x107 cells/ml and you want to start a new culture that is at 5x104 cells/ml in a total of 10ml:


C1 = 6 x 107 cells/ml

V1 = unknown (need to calculate)

C2 = 5 x 104 cells/ml

V2 = 10 mL of HL-

Now calculate your unknown (how much of your starter culture to add to the new culture using this algebraic equation: (6x107)(V1)=( 1x105)(10mL)


V1 = .0166mL Convert to uL (.017 mL)(1000µl/mL) =  17µL


Alternative Method: You want a culture of 1x105 cells/ml in 10ml which means you need 1x106 cells.  So how much volume of your 6x107 culture do you need for 1x106 cells?

(6x107 cells/ml) X = (1x106 cells)  X=(1x106)/(6x107)ml



Determining Growth rate (generation time)


You will do a trial run of measuring the growth rate over the next few days. This will give you practice at triturating, sterile technique, using the hemocytometer and microscope, and the start of your notebook and web site. 


Start a dish of cells at a density between 1x104 and 5x104 cells/ml.  You could use a lower density, but remember that a density of 1x104 cells/ml means 1 cell per counting area, so it will not be very accurate count. 

You can each do your own dish or share one, but we suggest more than one in case you spill or contaminate as you learn these techniques. 


Once cultures are set up, take an immediate sample to check your starting cell density to make sure you calculated and pipetted correctly.  For the Petri dish, if you do this immediately after adding the cells, you can simply swirl and take a sample.  If you wait, you will need to detach them again from the surface by triturating. 


Titer the cells in your petri dish at least twice per day using the hemocytometer. More data will give you a more accurate growth curve and more practice.  Each time you titer the cells, you will need to triturate the dish and then take out 10-15µl to add to the hemocytometer.


Record the concentration and time when you took the titer in your notebook.  You can add the data directly to an Excel spreadsheet on the lab computers as you collect the data so you can watch the growth curve evolve.


Growth curves are usually done over the course of five to seven days. This will allow you many data points which when plotted on a log scale should give you a pattern of log growth then a plateau.  For the growth curve, you will be most interested in the data points which are part of the logarithmic part of the growth curve.  It is from this data that you will be able to calculate generation time.     


Presentation of Data


1.For your result, you will be graphing the data as total time vs. titer. This could be done using Excel or other spreadsheet programs.

2.Make sure you use a XY scatter so that the X values represent numbers and are correctly spaced.  Bar graphs plot the data equally separated regardless of the numerical values.

3.Plot both a linear graph and a semilog graph (double click on the Y axis and you will be given choices including log scale) of the data and note the difference. In the semilog graph, the linear portion of the data represents exponential growth.  Therefore if your cells were not in log phase (exponential growth) throughout the experiment, you will need to replot the portion that is exponential, so that your trend line is only for that portion of the data.  Cells will eventually go into stationary phase, and you don’t want that affecting your calculation of the growth rate. So in your writeup, note the difference between the log plot and the linear and what portion you chose for your calculation.

4. Number your graphs (Figure 1 etc.) and refer to them by number in the web site writeup. 



Biologically, you are starting with a certain number of cells and over time the cell number will increase as an exponential function (2, 4, 8, 16, 32 or 2x).  Mathematically it looks like Nt = N0 2tf


So the cell number at time t (Nt) is equal to the starting cell number increased by a factor of 2 each cell generation.  t= time (hr) and f=generation frequency (generations/hr). 


What you want to figure out is the generation time (hr/generation) which is 1/f.  So basically when one generation is passed you have 21 times as many cells etc.  


The simplest way to estimate the generation time is from the raw data.  Look for the period when the cells are growing exponentially (so-called mid log phase).  Then figure out how long it took to get twice as many cells simply by looking at the numbers.  If the cells increased 2 fold over two days then they are dividing once per day (or about a 24 hour generation time).  If they increase 6 fold then you calculate from 2x=6 telling you how many generations they did in that amount of time.




Plotting in Excel [Office 2008]


Here is a detailed protocol how to make your graph in Excel 2008.


1.First enter all your data into the spreadsheet. It does not matter if it is in rows or in columns.

2.Highlight all your data then click the gallery icon. This icon will open a huge gallery divided into four sections. Click the Chart gallery, and select XY scatter. This will open different types of XY scatter charts and you can select the one you want by clicking on the chart. Once you click a chart, the chart you selected with you data on it will appear in a separate box.   

3.To label Axes, click on the toolbox icon and a box will appear. Now, select your graph by highlighting it and go to chart options in the toolbox. You can choose any category from the dropdown menu, and below that, there is a box where you can type the Chart title, vertical axis and horizontal axis of your chart. Once you are done typing, you can immediately see it in your chart.

4.Chart legends. Legends are important in some cases but not in others. If you want to include the growth of two different cell types in a graph, then legend should be shown to distinguish between the two populations. The legend box is by default shown everytime you make a graph. If you don’t want to show the legend, right-click the legend box and choose delete. If you want to edit the legend, double click the legend box and a box labeled format legend will appear. You can play around how your legend would look like using this box.  To change the title in the legend from “series” to something more meaningful, right click on the legend and choose “select data”.  A box opens up where you will see a “name” section and here you may enter whatever title you wish.

5.Formatting  Axes. In case you want to change the scale (i.e., minimum and maximum number) in the X or Y axes, double click on the values of the axis you want to change then a box named format axis will appear. Now you can enter values you want for your minimum and maximum numbers. Not only that, you can also change major and minor units that separate the values you indicated and will appear as lines in your graph. You can also play around with graph and line color,weight, etc... using the format axis box.

6.To create a semilog chart, double click the values in the Y axis. In the format axis box, click “scale” on the left hand side. Check the logarithmic scale box and  now, your Y axis  is in logarithmic scale while your axis is still in linear scale.  

7.Assuming that your semilog chart only contains the log phase data extracted from the growth profiles of your cells, you want to determine the doubling time or generation time of these cells. To get the generation time, right click the data in the graph and from the chart dropdown menu, click add trendline.  A box for format trendline will appear and on the side menu, click type. This will open different types of trendlines. Click on exponential then go back to the side menu and click options and then check the box for display equation on chart and then click OK.

8.The equation given in the trendline can be used to calculate for generation time indicated in method 1 below.



Method1. On the linear plot in Excel, you will get a curve that starts low and then steeply curves upward.  This is the essence of exponential growth.  You have few cells for a long time and then all of a sudden the population explodes as doubling gives you a greater increase with each generation.  If you apply an exponential curve fit to the data:


(Chart/Apply Trendline (exponential) and then in options check the show equation box)

You should see a nice fit to your data.  (To check yourself, you can create an imaginary dataset with perfect numbers doubling at some arbitrary rate of your choosing. )



Excel fits an exponential with the function


Nt = N0 etf


Where N= number of cells at time t

N0= number of cells at initial time

t=time in hr    and f=generation/hr


In order to find the generation time, you need to solve the equation for the case you want: that is when Nt =2 N0 or what is t when you have twice the number of cells you started with (doubling time). 


   So:  2= etf

Ln2=tf x Ln(e)

          .693=tf


Excel will give you f from its curve fit and you solve for t, which is the hours for one generation. 



Discussion: This data should be added to your Web site along with any relevant information about the experiment.


If your plates became contaminated describe some of the causes and what you would do to prevent future contaminations in new cultures. Did you get enough data for a conclusion even if you didn’t get all you wanted?

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