The Sensational Single Cell

Initiate a class discussion prior to beginning the activity.

Cancer happens when the body’s own cells—as the result of DNA damage— start reproducing in an unhealthy, uncontrolled way. Cancer cells keep dividing and spreading, crowding out healthy body cells and consuming too many resources.

Yeast and cancer cells both grow exponentially. Yeast has also been an important species in studying cancer, because the genes involved in cell division are very similar between yeast and humans, and errors in these genes are often the source of out-of-control cell growth, which leads to cancerous tumors.

Exponential growth in cancer means that tumors caught early on are much smaller and easier to treat than those caught later. The longer that cancer cells are allowed to divide the faster the tumor grows and spreads.

You can demonstrate the exponential growth in a population with a simple spreadsheet. We've created a template for your interactive use in a Google Sheets spreadsheet.

This file is intended to be used in a front-of-class demo, not as a student-led activity. Note that the Google Sheets has two tabs accessible in the lower left-hand corner of the interface.

(1) The first sheet's tab is labeled "chart start" — you can use this one to show your students how to use a spreadsheet to model exponential growth. The generation column adds "1" per row. Column B adds 2 hours per row. Column C doubles the line before it. To fill the cells of the first tab, copy Row 3, select as many rows as you'd like to fill, and paste to put all three formulas into all the selected cells at once.

(2) The second sheet's tab is labeled "complete and annotated"—this one has been filled out and annotated with rough equivalents, such as "more than the population of the entire world" for generation 34 (in Row 35).

You can add more math practice to this writing exercise by skipping the class introduction and asking your students to create an exponential growth chart by hand in their notebooks, either by doubling the values using pencil and paper or a calculator. Some calculators will display an error message if the result is too high.

This activity uses a pre-made Google spreadsheet. Copy it to your drive to make changes. If you prefer not to use it online, it can be downloaded from that site to use in any spreadsheet program (such as Numbers or Microsoft Word).

Exponential Growth in Numbers
(steps to filling the spreadsheet)

Step 1: Select all of Row 3 and copy to the clipboard.

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Step 2: Select multiple rows to fill.

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Step 3: Paste contents of the clipboard into the selected rows.

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Step 4: Ta-da! The rows are filled to model exponential growth.

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Step 5: You can keep going to fill in more rows.

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Initiate a class discussion prior to beginning the activity.

Paraphrase:

Cancer happens when the body’s own cells have their DNA damaged in such a way that they start reproducing in an unhealthy, uncontrolled way. Cancer cells keep dividing and spreading, crowding out healthy body cells and consuming too many resources.

Yeast and cancer cells both grow exponentially. Yeast has also been an important species in studying cancer, because the genes involved in cell division are very similar between yeast and humans, and errors in these genes are often the source of out-of-control cell growth, which leads to cancerous tumors.

Exponential growth in cancer means that tumors caught early on are much smaller and easier to treat than those caught later. The longer that cancer cells are allowed to divide the faster the tumor grows and spreads.

Looking at the differences in the graphs, what felt like major growth spurts early on look very minor once the population is in its 20th generation or beyond. Then, those early high numbers approximate zero.

The exponential growth charts are in a Google Slides presentation or available by clicking on the PDF below.

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Exponential Growth in Graphs

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Cancer is not just one illness, but dozens of different diseases with similar profiles. One reason that yeast cells are used to study cancer is because of their rapid multiplication, something that happens in the early stages of tumors.

Organism populations of any kind grow exponentially for a very short while. Soon, they run out of food and space, and the population plateaus. Cancer cells are like a population. Below a certain size threshold, cancer cell populations don't grow much. But as they reach a certain size, they grow exponentially. Then they grow more slowly. Medical mathematicians have been modeling this growth, and current science considers the growth an s-curve.

A single cancer cell is too small to be seen, but after doubling 30 times the tumor would be the size of a pea with about one billion cells. This animated illustration gets to about 500 "cells." After 40 doublings from the first single cancer cell, the patient would be close to dying. The tumor would have a trillion cells and weigh about a kilogram.

Video courtesy of Bissell Lab, Lawrence Berkeley National Laboratory.

Extension tip: To add more focus on cancer after this part of the activity, see Curing Cancer, a Teach Engineering activity made by the Integrated Teaching and Learning Program of the College of Engineering at the University of Colorado Boulder. While the lesson plan says the lesson is aimed at fifth grade, middle school students would benefit from the activity.

A visualization of cancer growth

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Time-lapse videos showing normal cells and cancer growth

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This introduction assumes that other lessons within L5 The Sensational Single Cell have been done by the class. Reword appropriately if you are doing this lesson in isolation.

Paraphrase:

In this unit, robots have come up a few times as analogies to cells. In the Science Scene, Tim compared real-life yeast cells to self-reproducing robots. Dr. Otto built a fleet of bakerbots.

Let's explore what limits the growth of a population of self-reproducing robots, if anything.

Share the reading and give students about 5 minutes to read through it. Then read it aloud to them as a class, stopping at some of the words they may have had a hard time understanding.

Read and define:

Imagine such a replicator (something that copies itself) floating in a bottle of chemicals, making copies of itself…the first replicator assembles (builds) a copy in one thousand seconds, the two replicators then build two more in the next thousand seconds, the four build another four, and the eight build another eight. At the end of ten hours, there are not thirty-six new replicators, but over 68 billion. In less than a day, they would weigh a ton; in less than two days, they would outweigh the Earth; in another four hours, they would exceed (be more than) the mass of the Sun and all the planets combined — if the bottle of chemicals hadn't run dry long before.

Grey goo could be considered a science-fictional metaphor for cancer. Robots go rogue, and these disobedient bots consume all the resources of the earth in their compulsion to replicate. In cancer, a few "misbehaving" cells with bad instructions crowd out healthy cells and consume the resources the whole body needs to function.

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Grey Goo?

Eric Drexler first used the term "grey goo" in his 1986 book Engines of Creation:

Imagine such a replicator floating in a bottle of chemicals, making copies of itself…the first replicator assembles a copy in one thousand seconds, the two replicators then build two more in the next thousand seconds, the four build another four, and the eight build another eight. At the end of ten hours, there are not thirty-six new replicators, but over 68 billion. In less than a day, they would weigh a ton; in less than two days, they would outweigh the Earth; in another four hours, they would exceed the mass of the Sun and all the planets combined — if the bottle of chemicals hadn't run dry long before.

When finished with the activity, ask students to discuss the question with a neighbor before writing creatively.

While wrapping up this session, make a connection between any suggestions the students had about how a fast-growing population can be stopped and next week's focus on multicellular organisms and immune response. Cancerous cells are often identified and removed by the body's immune system.

The suggested prompts assume that other lessons within L5 The Sensational Single Cell have been done by the class. Reword appropriately if you are doing this lesson in isolation.