Lab: Cell Size

AP Biology

Background Sources

Text:

Science Encyclopedia: Why are Cells Small?

CUNY Brooklyn: Exploring Life

UCSB: ScienceLine

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Video:

TedEd: What is the biggest single-celled organism?

Bozeman Science: Why are cells small?

Diffusion is the movement of solutes down a concentration gradient, from high to low concentration. Diffusion occurs because atoms are always in motion, bouncing off one another. More densely packed molecules collide more, spreading out

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Diffusion can occur across cell membranes, provided the membrane is permeable to the molecule.

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high low conc.

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down

Diffusion is a very slow process. A large diameter cell would have to wait too long for nutrients to be dispersed, and for wastes to be removed, resulting in cell death.

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The efficiency of diffusion as a means of moving molecules into and throughout a cell is governed by the ratio between surface area and volume.

Example

Determine the volume and surface area of a set of blocks.

• Use the block dimensions, or quantify in terms of x (SA) and y (V)
• Refer to the formula sheet as needed

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Yellow block V = y

3cm

6cm

6cm

Side SA = 2x

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Describe each block as a ratio, surface area : volume.

• Reduce each SA:V ratio, so that all volumes = 1.

Rank the blocks, from highest to lowest SA:V ratio

• The blocks are physical models for larger and smaller cells.
• Which block ‘cell’ will most quickly diffuse molecules in and out ?

time 1 time 2

Lab: Agar ‘Cell’ Model

Agar is a seaweed product used in biological laboratories as a medium for culturing bacteria, and in kitchens as a thickening agent. Here, prepared with the pH indicator bromothymol blue, we can ‘see’ the diffusion of H⁺ ions into the agar as a change in color. The source of the H⁺ ions is an acetic acid ‘bath’.

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agar with BTB …

…and soaking in

acetic acid

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Methods

1. Cut the agar into 3 samples of small, medium, and large diameters using the cork borers. Cut all to a uniform length.

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• Determine core diameters from the internal diameter of each borer. Record. Measure core length. Record.

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• Put the cores into dishes; flood with 1.5% acetic acid

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• Begin timing immediately; do not disturb the dishes/cores during the trials.

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• Record the time needed for each core to be cleared of BTB.

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nested cork

borer set

Pre-Lab

• Identify the lab IV and DV
• write an investigation question that incorporates both variables

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• Use the blocks example to predict the relative time needed for each agar sample to be fully diffused by the H⁺ ions in the acetic acid.
• justify the prediction with a hypothesis

Data

• Calculate the surface area and volume of each of the agar samples (use a Sheet!)
• use your formula sheet
• write each as a ratio of SA:V, reduced so volume = 1

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• Record the total time per trial for the agar to be cleared of the BTB

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• Find the mean average time for the trials of equal size

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Results

• Graph the effect of SA:V ratio on the average time required to clear each cylinder.

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• For each core size, calculate H⁺ diffusion rate per minute
• rate is on the formula sheet

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Clean Up

• Return for reuse any unused agar; dispose of used agar
• Rinse glassware and cutting tools thoroughly
• Wipe up the table

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Extension

Design an agar ‘cell’ with maximized volume (measured as mass) but minimal diffusion time. Winner has the highest ratio of mass to time, calculated as (g/sec)

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RULES:

• ‘Cell’ mass < 16g • no holes through the agar
• No stirring, poking, or moving the agar or beaker
• Completely diffused through in < 30 minutes.

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Discussion

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1. Are the blocks a structural or functional analogy for a cell? What about the agar cubes? Make the distinction.
2. Beyond cells, a large surface area is key to the success of many organs in the human body. Infer why, specifically, humans have enough lung surface to cover half of a tennis court, and more than 20 feet of small intestine.
3. Explain why the candy bitten by a child does not last as long as the same candy that their sibling sucks on.
4. Determine the volume and surface area of cubes 1cm x 1cm, 2cm x 2cm, and 4cm x 4cm. Find & describe the mathematical pattern.

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5. To dilute 3% acetic acid to make a 1.5% solution

• Determine the volume needed per sample
• Use C1V1=C2V2 to determine how much 3% acid to use; for the remainder use tap water

CAUTION: Always add acid to water, not the reverse.

• Measure water with the graduated cylinder; add to the flask.
• Measure acetic acid; add to flask.
• Pour between flasks to mix.

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