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Passing Gas: Exploring Gas Exchange in Biological Systems

This teachable unit, "Passing Gas," focuses on the concept of gas exchange in biological systems and is suitable for introductory-level students in both math and biology. The unit includes examples that cover cellular, organismal, and ecological biology, assuming basic competency in algebra, geometry, and high school-level biology. The learning goals include enhancing students' comfort with using math in biological applications, developing quantitative skills, and analyzing biological phenomena at different scales.

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Passing Gas: Exploring Gas Exchange in Biological Systems

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  1. Group 3: MATH & BIOLOGY Teachable Unit: PASSING GAS Gas Exchange is a Unifying Concept in Biological Systems • This teachable unit, Passing Gas, will be presented to a student body consisting of majors and non-majors at the introductory level. • Passing Gas will have examples that can be utilized in sequences dealing with cellular, organismal and ecological biology. • The Passing Gas unit assumes that the students will have basic competency in algebra, geometry and high-school level biology.

  2. Unit Learning Goals • Biology students will become more comfortable using math in biological applications. • Students will develop quantitative skills. • Students will use math to analyze biological phenomena at multiple scales. • Students will understand that gas exchange is a unifying concept in biology.

  3. Learning Outcomes of Tidbit 1 • Students will use quantitative skills in novel situations involving gas exchange. • Students will determine the mathematical relationship between parameters that influence levels of gas exchange in an animal system.

  4. WHY COULD INSECTS THIS LARGE NEVER EXIST?

  5. Exoskeleton too weak • When shed exoskeleton when molting, collapse under weight • Can’t get enough oxygen • Limits on ant hill size • Lung capacity

  6. Clicker Question review from last semester • As the radius of a cell increases, the surface area to volume ratio • of the cell • Increases • Decreases • Stays the same • Insufficient data to answer this question

  7. A Review: Surface Area/Volume and Maximum Cell Size nutrients wastes Volume of a sphere = 4/3πr3 Surface area of a sphere = 4πr2

  8. flatworm Mini Lecture on Respiratory System of Insects Tracheal tube system • Exoskeleton with waxy cuticle prohibits • simple diffusion through epidermis • No blood vessels, so no lungs • Tube system that carries O2 from surface • to cells and takes up CO2

  9. Tracheal volume data Length of Beetles Tracheal volume (as % of body volume) 17mm 1.9% 18mm 2.1% 27mm 3.3% 47mm 5.7% 60mm 7.4% 62mm 7.6% 80mm 9.9% 129mm 15.8% Graph the data and determine the relationship between tracheal volume and beetle body length.

  10. Let’s do some math! • What is the mathematical formula describing the relationship • between these two variables? • A) x2 + y2 = 0 • B) y = mx + b • C) y = log x • D) y = 1/x • What does this information tell us about insect • size and tracheal system size?

  11. SUMMARY OF THE PROBLEM SMALL INSECT LARGE INSECT Large Insect Oxygen depleted if tube diameter stays the same Tracheole volume larger to accommodate needs

  12. Based on your data, what is the theoretical maximum length • of a beetle? • The largest living beetle today actually is 170 mm. • What do you think limits the body volume that an insect can • devote to the tracheal system?

  13. Entrance Ticket for Next Class • During the Carboniferous (350 mya) there were insects much larger than any found on Earth today. • Develop a hypothesis from this observation. • How would you test your hypothesis?

  14. Individual take-home question • The relationship between body length and the % of the body • volume taken up by tracheal tubes in beetles is defined by a line • with a slope of 0.123. Even today there are insects much longer • than the beetles we examined in this exercise. • If you assume that a maximum volume of tracheal tubes is 20% • of total insect volume, and the slope of the relationship between • length and tracheal volume is 0.056, what is the length of this • insect? • What does this insect look like? • Explain your answer.

  15. A Walking Stick • http://www.insectchat.com/showthread.php?p=2856

  16. SCIENTIFIC TEACHING • Active Learning Clicker Brainstorming Group problem solving Entrance ticket • Assessment-all of above formative Individual take-home question is summative • Diversity Auditory/visual/kinesthetic Spatial/mathematical Social learning

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