Biology 332 - Protistology Term 2 - 2002-2003

Grazing Rate and Clearance Rate in Paramecium.

Background. Phagotrophic protists fall into two general categories, raptorial feeders and filter feeders. Raptorial feeders capture relatively large prey on a one-to-one basis, while filter feeders remove small prey from the water by pumping water through a filter usually composed of comb-like rows of flagella. In this experiment we are going to examine the rate of feeding in Paramecium, a filter-feeder, and how it changes over time as the concentration of prey changes. Before starting some definitions are helpful.

Clearance rate = the volume of water from which prey are removed per unit time by a single predator.

Feeding rate = the number of prey eaten per unit time per predator.

Start by thinking about the process of filter feeding. Consider as the first hypothesis that an ideal filter feeder passively removes prey from the medium with a constant efficiency. Think what would happen as the concentration of prey changes (start by considering a decrease in prey concentration). What do you expect would be the effect on clearance rate? On feeding rate? Hint: What does feeding rate depend on? Can you write a simple mathematical expression that describes how you would expect feeding rate to change as prey concentration changes. It is a good idea to try to do this before you start. It will make everything a lot easier to figure out later. Big hint: review 1^st order reaction kinetics.  Consider an as an alternative hypothesis that Parmaecium feeds at a constant rate over a wide range of prey concentrations. How would this change the expectations? How would the relationships of feeding rate and clearance rate to prey density differ from those in the first hypothesis?

Objective. Determine whether Paramecium behaves as an ideal filter feeder by observing the feeding rate as a function of prey concentration over the course of time.

Plan of Experiment.

1. Count the number of Paramecium per ml. The cell cycle length of Paramecium cells is about 7 h. Do you think that you can safely ignore the change in number of paramecium per ml over the course of your experiment?

2. Determine how many bacteria are present at time 0, and at 10 minute intervals for 40 minutes.

3. Determine feeding rate and clearance rate.

4. Analyze data.

Procedure:

Counting Paramecium. Remove 3 samples of 50 ul of well mixed culture. Count the number of Paramecium cells in each sample by catching them one by one with a micropipette and counting them as they disappear.

Counting bacteria. There are 3 possible approaches: a) plate count, b) haemocytometer count and c) turbidity measurements. We will try the second. We have tried plate count several times and the class data are to inconsistent for accurate analysis. The haemocytometer counts are accurate but tedious. While conceptually easier, turbidity measurements have not worked well as the range of turbidities that we are working with are quite small. That is, the bacterial cultures are not all that dense at the start..

Haemocytometer counts. Samples are prepared as described above. Transfer a small drop to the table of the haemocytometer. Carefully add a cover slip. Count the number of bacteria in a series of the smallest squares (with 40x objective) until at least 120 cells have been counted. Record the count and the number of squares counted. The smallest squares in the haemocytometer are 1/20 (0,05) mm on each side. The counting chamber is 0.1 mm deep.

Analysis.

Link to data

1. Data work-up. Convert bacteria counts to an estimate of the number of bacteria per ml. Do the same with the Paramecium counts. Plot the bacteria counts as a function of time.

2. Estimate the rate at which bacteria are eaten at each point. There are several approaches that could be used. The best would be to make a general model for the relationship between rate of feeding and prey density for a filter feeder, and to then examine the fit of the expected function to the data. Alternatively, you can try to estimate the feeding rate at each data point. This is substantially less accurate and the nature of the inaccuracies need to be discussed. . What are the units of the feeding rate? Would you expect the feeding rate to change with time? If so, how? and why? How many bacteria are eaten per paramecium per minute?

3. Calculate the clearance rate at each sample point.

Modeling filter feeding: How is the rate of feeding determined? Is it affected by the concentration of prey, or is it independent of the prey concentration? Make a set of alternative mathematical models for the feeding process. Test the fit of each of these models to the data. Which has the better fit?

Model I. Feeding is not dependent on prey density. Assume that the rate of feeding is constant. Write an equation that describes the rate of feeding. Integrate it with respect to time to determine how the concentration of bacteria changes over time. Let the concentration of Bacteria be B, time t, and the rate of feeding -v. The rate is negative because bacteria are being lost. 

e.g.  dB/dt = -v

Integrate this over time. When you do the integration, do not forget the integration constant. Call it B₀

Model II. Feeding is dependent on the concentration of prey. Write an equation to describe how the rate of feeding is related to the concentration of prey.  Key idea:  If filter feeders are non selective, and if their rate of feeding is not limited by internal processes (assume here that it is not, unless your data indicate otherwise) the rate of feeding should be proportional to prey density. Let B= the concentration of bacteria, t= time and -v the rate of feeding. The rate is negative because bacteria are being lost.  Integrate this over time. (This is a very easy integral). Reminder: the first step to perform integration is to get all of the terms with the independent variable (B) on the left side of the equation This is pretty easy. Don't let it throw you. Do not forget the constant of integration (call it lnB₀). Development of this simple conceptual model will make it very easy to analyse and interpret the class data.

Fitting the models to the data. How do the results expected from the two models differ? Which provides a better fit to the data?

Those of you who have had a statistics course (STAT 200 or BIOL 300) will know that you need to test the goodness of fit of the models to the data. I suggest that you use regression analysis. The key statistic is the coefficient of determination (r²). The higher the value of r² the better the fit of the line to the data. This fitting of the two models to the data is very easy if you use MS Excel or some other spreadsheet program. This program is available on the computers in Zoolab (room 2434). The program gives you the rate constant and the value for r^2. It is very handy.   Which model fits the data better?

3. Analysis and discussion.

How well do the models fit the data? How would the feeding rate and the clearance rate be expected to change with each of the models? You can estimate the feeding rate at any particular time by determining the value for B_t and subtracting from it the value for one minute later ( B_t+1).  The clearance rate is the volume of medium from which bacteria are removed per unit time. This is the feeding rate for time t divided by B_t. Check out the units they should always be what you expect, and what makes sense.

Calculate the clearance rates corresponding to the feeding rate for each model. Does clearance rate change as a function of prey concentration? Key idea: You calculated the number of bacteria per ml at each point, think about ml/ bacterium. The number of bacteria removed per minute represents removal of bacteria from a certain volume of medium per medium. This is the clearance rate.  How do the models differ with regard to the expected relation between feeding rate and clearance rate as a function of time?  How do you think that clearance rate relates to work?

Using the model that gives the best fit to the data, calculate how long it takes a Paramecium to clear a volume of medium equal to its own cell volume. Paramecium cell length = 120 um, width = 40 um. Assume that the cell is a prolate spheroid. Volume = pi (Lw²/6), where L is length, w is width.

Conclude with some comments on the biological significance of your finding.