Investigation: Why Are Cells So Small?
- Page ID
- 26445
This page is a draft and is under active development.
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Essential Question: How does the size and shape of a cell influence the speed at which materials can move into and out of the the cell?
Process: Create cell models using agar molds to compare rates of diffusion.
Materials:
- Agar Mold with BTB (made in advance)
- Tweezers, Scalpel (or plastic knife)
- Ruler, Beaker with white vinegar
Procedure
1. You will receive a small tray filled with an agar mold. *See below for directions* Avoid handling the agar with your bare hands and use a scalpel and tweezers to cut three agar cubes with the following approximate dimensions. Save your agar, you will need it later!
- 1 cm x 1 cm x 1 cm (small)
- 2 cm x 2 cm x 2 cm (medium)
- 1 cm x 1 cm x 6 cm (large)
2. Measure your cubes (the actual dimensions may not be perfect, depending on how you cut it) and determine the surface area, the volume, and the SA:V ratio. Record on data table.
3. Drop each block into a separate beaker (or container) of vinegar. The agar has been infused with a chemical called bromothymol blue, the blue will turn to a yellow in the presence of acid. You will be able to observe this change with your cubes. Record the time it takes for the blue to completely disappear.
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Actual Dimensions |
Surface Area |
Volume |
SA / V |
Time (Blue to Orange) |
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Small Cube |
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Medium Cube |
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Large Cube |
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Part 2: How Does Shape Influence Rates of Diffusion?
With what remains of your agar, design a cell that maximizes volume and mass, but minimizes diffusion time. Your "cell" will compete with other cells in the class to see which one has the fastest diffusion time.
Rules:
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No donut-like holes through the agar cell - cell membranes cannot sustain this shape
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No poking or agitating the beaker when the cell is submerged
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Instructor determines when 100% diffusion has occurred
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Agar cell will be massed at the end of the race
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Winner = highest ratio of mass divided by time
Sketch your design.
Analysis
- Which of the initial cubes had the fastest diffusion time? Which had the slowest?
- Which of the three variables you tested seemed to have the biggest impact on the rate of diffusion? Explain how you know this.
- How does the agar cube model the cell and the cell membrane?
- What designs (Part 2) seemed to have the fastest diffusion rate?
- How do these experiments model the cell and the cell membrane?