Title: Counting the Number of Yeast Cells in a Suspension using Haemocytometer
Objective: To estimate the number of cells of yeast per mm3 in five different dilutions of yeast suspension.
Introduction: Biologists often need to count the density of cells in a liquid. “Density of cells” means “the number of cells per unit volume of liquid”. For example, they might want to find out the density of red blood cells in blood plasma, the density of bacteria in milk, or the population of Paramecium sp. (a protozoan) in water from a pond.
The simplest, most convenient and cheapest means of accurately determining the number of cells in a sample is to use a haemocytometer and a microscope. A haemocytometer is a specialised slide that has a counting chamber with a known volume of liquid. The haemocytometer is a device originally designed for the counting of blood cells. It is now also used to count other types of cells as well as other microscopic particles.
The haemocytometer was invented by Louis-Charles Malassez and consists of a thick glass microscope slide with a rectangular indentation that creates a chamber. This chamber is engraved with a laser-etched grid of perpendicular lines. The device is carefully crafted so that the area bounded by the lines is known, and the depth of the chamber is also known. It is therefore possible to count the number of cells or particles in a specific volume of fluid, and thereby calculate the concentration of cells in the fluid overall.
The haemocytometer consists of a heavy glass slide with two counting chambers, which is 0.1mm deep, each of which is divided into nine large 1mm squares, on an etched and silvered surface separated by a trough. A cover slip sits on top of the raised supports of the ‘H’ shaped troughs enclosing both chambers. There is a ‘V’ notch at either end where the cell suspension is loaded into the haemocytometer. When loaded with the cell suspension it contains a defined volume of liquid. The engraved grid on the surface of the counting chamber ensures that the number of particles in a defined volume of liquid is counted. The haemocytometer is placed on a microscope stage and the cell suspension is counted.
When a liquid sample containing immobilized cells is placed on the chamber, it is covered with a cover glass, and capillary action completely fills the chamber with the sample. Looking at the chamber through a microscope, the number of cells in the chamber can be determined by counting. Different kinds of cells can be counted separately as long as they are visually distinguishable. The number of cells in the chamber is used to calculate the concentration or density of the cells in the mixture from which the sample was taken: it is the number of cells in the chamber divided by the chamber's volume (the chamber's volume is known from the start), taking account of any dilutions and counting shortcuts.
Research Question: How do the different dilutions of yeast suspension affect the density of yeast cells?
Hypothesis: As the yeast suspension gets more diluted, the density of yeast cells will decrease. This is because as more distilled water is added to the yeast suspension, the number of yeast cells per mm3 of the yeast suspension decreases. The yeast cells are now more widely distributed because the volume of liquid (water) has increased. In diluted suspension, the number of yeast cells per unit volume ( in this case per mm3) of water is less than in a more concentrated solution, where the density of yeast cells is higher, due to the smaller ratio of yeast suspension to water. In a concentrated solution, the yeast cells are more tightly clustered together, because there is less water for the yeast cells to be distributed in, and the ratio of yeast suspension to water is greater. So for every mm3 of water, there are more yeast cell in a concentrated solution.
Variables:
Variables Unit Range Possible effect on results Ways of manipulating/ measuring/ controlling variable
Independent Dilution of yeast suspension - 1/10,000-1 - Different dilutions are prepared by dilution method.
Dependent Density of yeast cells Cells per mm3 - - The number of yeast cells is estimated using a haemocytometer observed through a microscope.

Controlled Standard yeast suspension - - Different yeast suspension used will affect the density of yeast cells All five dilutions are prepared using the same standard yeast suspension. Volume of yeast suspension used for each serial dilution cm3 1 cm3 Different volume of yeast suspension used will change the dilution of the yeast suspension The volume of yeast suspension used for each serial dilution is fixed at 1cm3 to ensure the dilution increases in fixed graduations of 1/10 for each dilution. Volume of distilled water added in each serial dilution cm3 9cm3 Different volume of distilled water added will change the dilution of the yeast suspension The volume of distilled water added for each serial dilution is fixed at 9cm3 to ensure the dilution increases in fixed graduations of 1/10 for each dilution.
Materials and apparatus:
Materials Quantity Volume/Size
Yeast suspension - 5cm3
Distilled water - 50cm3
Alcohol 1 reagent bottle -

Apparatus Quantity (per group) Volume/Size
Test tubes 5 Standard size
Dropper 1 Standard size
Haemocytometer slide 1 -
Microscope 1 -
Cover slip 1 -
Lens paper 1 -
Soft tissue paper 1 roll -
Spatula 1 -
Measuring cylinder 1 5 ml
Labelling paper 5 Standard size
Stop watch 1 -

Method: Refer to laboratory manual attached.
Data collection and processing:
Number of yeast cells estimated in yeast suspensions of different dilutions
Test tube Dilution Number of yeast cells / cells Trial I Trial II Trial III Square 1 Square 2 Square 3 Square 1 Square 2 Square 3 Square 1 Square 2 Square 3
A 1 192 165 156 132 110 100 120 110 108
B 1/10 10 16 12 11 18 21 12 6 20
C 1/100 7 15 6 12 13 15 10 11 11
D 1/1000 4 4 9 6 5 7 5 5 7
E 1/10,000 1 2 3 2 3 1 2 2 3

Qualitative data:
Test tube Observation
A The suspension is very dense and yellowish, and very opaque.
B The suspension is pale yellow in colour, and slightly opaque.
C The suspension is slightly yellowish, and slightly transparent.
D The suspension is very pale yellow, and transparent.
E The suspension is almost completely colourless and transparent; individual cell clumps can be seen in the suspension.

Average number of yeast cells
= (sum of Trial 1 + sum of Trial 2 + sum of Trial 3)/(total number of squares counted) e.g test tube A = ((192+165+156)+(132+110+100)+(120+110+108))/9 = 132.56 cells Volume of each square (tiny square is used for all trials)
= 0.05mm x 0.05mm x 0.1mm = 0.00025 mm3 Density of yeast cells = (Average number of cells)/(Volume of square)
e.g. Test tube A = (132.56 cells)/((0.00025) 〖mm〗^3 ) = cells per mm3

Density of yeast cells estimated in yeast suspensions of different dilutions
Test tube Dilution Average number of yeast cells/ cells Density of yeast cells / cells per mm3
A 1 132.56 530240.00
B 1/10 14.00 56000.00
C 1/100 11.11 44440.00
D 1/1000 5.78 23120.00
E 1/10,000 2.11 8440.00

Uncertainty of average number of yeast cells, ∆N
= Standard deviation of N
= √((∑〖(x)〗^2)/n-(x ̅^2))
Where x = number of cells in a square n = number of squares ¯x = average number of cells
e.g test tube A = √((〖192〗^2+〖165〗^2+〖156〗^2+〖132〗^2+〖110〗^2+〖100〗^2+〖120〗^2+〖110〗^2+〖108〗^2)/9-(〖132.56〗^2))
=√(166113/9-("17572.1536" )) = ±29.75 cells Uncertainty of density of yeast cells, ∆D
∆D/D=∆N/N , therefore ∆D = ∆N/N×D
e.g test tube A: ∆D = 29.75/(132.56 )× 530240.00 = ±119000 cells per mm3

Uncertainties of number of yeast cells and density of yeast cells
Test tube Dilution Uncertainty of number of yeast cells, ∆N (cells) Uncertainty of density of yeast cells, ∆D (cells per mm3)
A 1 ±29.75 ±119000
B 1/10 ±4.74 ±18960
C 1/100 ±2.96 ±11840
D 1/1000 ±1.54 ±6160
E 1/10,000 ±0.74 ±2960

Assumptions made: For the standard yeast suspension with dilution of 1 (test tube A) the number of yeast cells per mm3 is so great than it is difficult to count individual cells. Therefore, we estimate the number of cells per square by calculating the number of cells on two different border lines (top and left border) and multiplying it to get an estimate of the number of cells in each square.

Discussion:
Analysis of graph
In the graph, as the yeast suspension becomes more concentrated (i.e. value of dilution gets closer to 1), the density of yeast cells per mm3 increases. Inversely, as the yeast suspension becomes more diluted (i.e. value of dilution gets closer to 0), the density of yeast cells per mm3 decreases. There is a positive correlation between the dilution of yeast suspension and the density of yeast cells.
Conclusion: As the yeast suspension becomes more diluted (i.e. value of dilution gets closer to 0), the density of yeast cells per mm3 decreases.
This is because as the yeast suspension gets more diluted, the density of yeast cells decreases, as the yeast cells are now more widely distributed because the ratio of yeast suspension to water decreases. This means that there is a larger proportion of water compared to yeast suspension, which explains why there are less yeast cells per mm3 in a diluted suspension.
This is proven by the results:
Test tube Dilution Density of yeast cells (cells per mm3)
A 1 530240.00
B 1/10 56000.00
C 1/100 44440.00
D 1/1000 23120.00
E 1/10,000 8440.00
Thus, the hypothesis is accepted.
Test tube Dilution Uncertainty of density of yeast cells, ∆D (cells per mm3) Percentage uncertainty of density of yeast cells, ∆D (%)
A 1 ±119000 ±22.44
B 1/10 ±18960 ±33.86
C 1/100 ±11840 ±26.64
D 1/1000 ±6160 ±26.64
E 1/10,000 ±2960 ±35.07
There is quite a large standard deviation of around 22% to 35% for the data which indicate that the data is inaccurate. To calculate percentage uncertainty of density of yeast cells, ∆D:
% ∆D = ∆D/D×100%
e.g = 119000/530240 x 100% = ±22.44%
This can be explained by the following errors associated with using a haemocytometer and random errors, and suggestions on how to improve the experiment:
Limitations
Non-uniform suspensions It is assumed that the volume of cell suspension placed into the chamber represents a truly random sample. This will not be a valid assumption unless the suspension is well dispersed and free of cell clumps. Distribution in the haemocytometer chamber depends on the number of particles, therefore cell clumps will distribute in the same way as single cells, affecting the accuracy of the final result.

Improper filling of chamber In order to fill properly by capillary action, a chamber must be scrupulously clean. If not, the suspension will not be distributed evenly in the chamber and an accurate estimation of the number of cells per unit volume cannot be obtained.
Failure to adopt a convention for counting cells in contact with boundary lines or each other Some cells settle on the border gridlines and so it becomes difficult to decide whether or not to count such cells.
Statistical errors This error occurs due to errors in counting.

Parallax errors This error occurs when the taking measurements. If the eye is not parallel to the level of the meniscus of the solution, the reading will be inaccurate.
Impurities in the suspension Impurities transferred from the apparatus or from the surroundings might be mistaken as yeast cells and counted in the data collection. This will affect the accuracy of the results for density of yeast cells.
Movement of yeast cells The yeast cells are alive and move in the liquid, making it difficult to get an accurate calculation. The flow of liquid also causes this error to occur.
Assumptions made to estimate density of yeast cells in standard yeast suspension For the standard yeast suspension with dilution of 1 (test tube A) the number of yeast cells per mm3 is so great than it is difficult to count individual cells. Therefore, we estimate the number of cells per square by calculating the number of cells on two different border lines (top and left border) and multiplying it to get an estimate of the number of cells in each square. This is not an accurate result.
Suggestions
Non-uniform suspensions The suspension should be mixed thoroughly before placing it in the haemocytometer to estimate the accurate density of yeast cells in the suspension. If less than 90% of the cells are free from contact with other cells, the count should be repeated with a fresh sample.
Improper filling of chamber The chamber and cover slip should be cleaned first with distilled water, then by ethanol and wiped dry with a Kimwipe.
Failure to adopt a convention for counting cells in contact with boundary lines or each other Develop a convention on which you do not count half of the cells that touch a border. For example, you only count the cells that touch the top border and left border, but do not count the cells that touch the bottom and right border. You should be consistent to increase the accuracy of your results.
Statistical errors With careful attention to detail and by counting systematically and clearly, the overall error in counting can be reduced to between 10% and 15%.
Parallax errors Make sure your eye is parallel with the level of the meniscus.
Impurities in the suspension Clean all the apparatus thoroughly before beginning the experiment. Use a higher power of objective lens on the microscope to ascertain whether it is a yeast cell or not before counting a certain particle if you are unsure.
Movement of yeast cells Wait a few second till the liquid suspension has stopped flowing and the yeast cells have stabilised before counting.
Assumptions made to estimate density of yeast cells in standard yeast suspension For the standard yeast suspension with dilution of 1 (test tube A) we can use a higher power of objective lens on the microscope to focus on individual cells and count them one by one.