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Transcript
D.N.A. Solution (numbers rounded for ease of explanation/calculation) A) 3 x 109 base pairs x 0.34 x 10-9 meters/base pair = 1 x 100 meter = 1 meter Diploidy, thus 1 meter x 2 = 2 meters total DNA length/cell B) 2 meters/cell x (10 x 1012 cells) = 20 x 1012 meters = 2 x 1013 meters Notice that 10 trillion cells is probably an underestimate of cell population of an adult C) distance to sun (1 astronomical unit) = 1.5 x 108 kilometers = 1.5 x 1011 meters. Dividing B by C--- 2 x 1013 meters/1.5 x 1011 meters = 1.3 x 102 A.U.âs (130 trips to sun) or about 65 round trips. D) Comparing DNA distance to other astronomical objects: Average distance to Pluto = 63 A.U. (DNA could make a round trip to Pluto) Average distance to Neptune = 29 A.U. = 2 round trips to this planet Compaction Ratio Comparisons: Length:length 20 meters thread into .02 meter capsule length = about a 1,000/1 length:length compaction ratio. 2 meters DNA into a nucleus (assume large 1 micrometer long nucleus) = 2,000,000/1 length: length ratio. Notice that cells accomplish over a 1,000 greater length compaction ratio. Length:volume If considering length/volume compaction (a better analysis): 20 meters thread into a capsule volume of .02 x .01 x .01 meter or (2 x 10-6 m3). Cell manages to fit 2 meters of DNA into approximately (1 x 10-6m)3 or 1 x 10-18 m3. The difference in compaction ratios is on the order of 1013, or thirteen orders of magnitude. This incredible difference appears impossible, considering how difficult it was to get 20 meters of string into the capsule. There must be a flaw in the simulation. Students should be challenged to discover the weakness (flaw) in the simulation exercise. It might help top remind them of the Watson/Crick/Franklin dimensions for DNA (a labeled drawing or overhead should suffice). Notice that the width of DNA is about 2 nm (2 x 10-9 meter). The string is on the order of 0.1 mm or 10-4 meter (teachers can direct students to examine this under a microscope to obtain the best estimate for the string that they used). That great difference partially explains the discrepancy.
