Surface Area & Cell Size - AP BIOLOGY



Cell Size

AP Biology

Cells are small - between 2 and 200 micrometers - too small to be seen with naked eye. Why so small? In order for cells to survive, they must constantly exchange ions, gases, nutrients, and wastes with their environment. These exchanges take place at the cell’s surface—across the cell membrane. The movement of these materials is accomplished mostly by diffusion (flow of solutes down a concentration gradient) across the cell membrane.

One of the core principles that governs the efficiency of diffusion is the ratio of surface area to volume. (Surface area is the amount of cell membrane available for diffusion, whereas volume is the amount of cytoplasm contained within the cell membrane.) Diffusion is a very slow process. If a cell were 20 cm (~8 inches), it would take days for nutrients to reach its center or for wastes to reach the cell membrane. The cell would quickly starve to death or poison itself with its own wastes. To perform diffusion efficiently, there must be an adequate ratio between the cell’s surface area and its volume.

However, as objects increase in size, volume increases at a greater rate than surface area. This is quantified as the cube-square law, first described in 1638 by Galileo Galilei. This law helps explain phenomena including why large mammals like elephants have a harder time cooling themselves than small ones like mice, and of interest to us here, why cells are small.

A. Block Model

1. Pick up a set of blocks of a variety of

sizes and shapes. Determine the volume,

surface area, and ratio between the two,

for each block. You can use metric

measurements, or assign them values

in terms of x and multiples thereof.

Record. 6 feet

or

X

2. Reduce the ratios so that volume =1. (divide each side of the ratio by the volume). Record. Rank the blocks from least to greatet SA:V ratio.

3. From the results, make a claim and explain via reasoning.

B. Agar ‘Cell’ Models

Agar containing bromthymol blue can be used to measure the effect of SA:V ratios on cell size, via diffusion. Recall that bromothymol turns from blue to green and yellow with inreasing acidity.

4. From the agar cut a set of three cylinders, variable in either length or diameter. (if you’ve enough agar, make a set of both)

5. Place the agar into a small dish and cover with a 50% solution of household vinegar (acetic acid). Start a timer.

6. While you wait:

• calculate the surface area and volume of each of the cylinders. Write each as a

ratio, reduced so volume = 1.

• use the SA:V ratio calculations to form a hypothesis about the relative time needed for the complete diffusion of acetic acid into the different cylinders.

7. Record the time it takes for each cylinder to be completely diffused through with acetic acid.

8. Graph surface area ratio (when volume = 1) against time of total diffusion.

Extension: Design a agar ‘cell’ with maximized volume & mass, but minimized diffusion time.

RULES:

• ‘Cells’ must be under 15g and be completely yellow in under 30 minutes.

• No holes through the agar (cell membranes cannot sustain that)

• No poking the ‘cells’, or moving the beaker during the trial

• Winner = highest ratio of (mass in grams/ time in seconds) x 100

Cell Size Model

Discussion

1. Are the blocks a structural or functional analogy for a cell? What about the agar cubes? Make the distinction.

2. Which is the most effective design for an organism? 2 small cells, or 1 cell, twice as large? Justify.

3. 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.

4. Explain why the candy bitten by a child does not last as long as the same candy that their sibling sucks on.

5. Determine the volume and surface area of cubes 1cm x 1cm, 2cm x 2cm, and 4cm x 4cm. Find/describe the mathematical pattern. Note that each cube size is a factor of two larger than the previous. Remember that surface area is two dimensional, and volume is three dimensional.

Agar cubes

Teacher notes:

|Mix 12g non-nutrient agar in .75 liter water. 
 | |

|Boil slowly in microwave or hot water bath until agar is melted. | |

|Remove from heat. Add a very small amount of powdered bromothymol blue and mix. If the mixture is green or yellow, you will need to stir in drops of NaOH (or another | |

|base) until it turns blue. | |

|Pour the agar into the rectangular blue hospital trays, at least 2cm deep -- and slice chunks for the students to cut from. | |

|Let agar harden at room temperature or in refrigerator. Can be made a couple of days in advance. Cover with plastic wrap to keep from drying out and store in | |

|refrigerator. | |

| | |

| | |
 |

|You will be testing the rate at which different size "cells" can diffuse materials into them. The goal - to create a cell with the best rate of diffusion. Baseline | | |

|test: an agar (jell-o) cube that is 1 cm on each side Design a "cell" that has a volume of 27 cm3 (this is based on a 3 cm x 3 cm x 3 cm cube), but has a better | | |

|surface area-to-volume ratio than the cube indicated (hint: FIND the ratio first so you know what to beat!) Include: Calculations for both the given cube and your new | | |

|design Drawing of your new cell with the dimensions indicated How will you measure if this cell is faster than the 1 cm x 1 cm x 1 cm cell? In other words - what data | | |

|are you going to collect? I had them work out their shapes/ideas on the whiteboards | | |

|I had one group try a star, but they couldn't figure out how to do the volume and surface area for a 3D pentagon. I let them use their smart phones or my laptops to | | |

|look up formulas for their shapes. One student found a site where you put the dimensions in and it spits out the surface area | | |

|at bare minimum, they had to beat the ratio for the 3x3x3 cube - bonus if they could beat the 6:1 ratio of the 1x1x1 cube :) Jennifer | | |

|We sometimes run a second race after a trial run, so students can improve designs. I make a lot of agar just in case. It's a fun learning day! | | |

| | | |

| | | |

A cube with a side length of 1 meter has a surface area of 6 m2 and a volume of 1 m3. If the dimensions of the cube were multiplied by 2, its surface area would be multiplied by the square of 2 and become 24 m2. Its volume would be multiplied by the cube of 2 and become 8 m3. Thus the Square-cube law. This principle applies to all solids.[3]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download