Download How many Codons?

 BIGGEST EVER MATHS & SCIENCE LESSON GUINNESS WORLD RECORD DAY NOVEMBER 2015 Title: How many Codons? Learning Objective, Mathematics: Investigation of the number of different arrangements (permutations) that can be made of 3 objects chosen from a set containing 4 objects. Learning Objective, Science: DNA (DeoxyriboNucleic Acid) stores genetic information and RNA (RiboNucleic Acid) is used to transfer the genetic code from the nucleus to the ribosomes to make proteins. The elements of the encoding system, the nucleotides, have four different bases, known in DNA as adenine (A), thymine (T), guanine (G) and cytosine (C) but in RNA uracil (U) replaces thymine, so the bases in RNA are adenine (A), uracil (U), guanine (G) and cytosine (C). Information is transferred by the RNA in combinations of three of the bases called codons, for example AGU, AGC, UAA. Proteins found in nature consist of 20 naturally occurring amino acids. How can four nucleotides code for 20 amino acids? Every amino acid is coded by at least one nucleotide triplet or codon, and some triplet combinations give instructions for starting or stopping translation. The combinations UAA, UGA and UAG, are termination codons, while AUG is a translation starting codon. The Question: How many different codons are there in RNA? List them and explain your answer. Suggested Teaching Method We have to find out how many different 3 letter arrangements (codons) formed by choosing 3 letters from the letters A, U, G and C. We are looking for codons like AGU, GUA, AGC, UAA etc. Start the lesson by asking learners how many different arrangements (permutations) they can make from just the letters A, G and U. (They should find 6, that is AGU, AUG, GAU, GUA, UAG, UGA). Then ask how many different arrangements if one letter is repeated, for example GUU. (They should find 3 permutations GUU, UGU and UUG). Tell the class that there are many 3-­‐letter ‘codes’ using the letters A, U, G and C like the ones they have just found, that these are called codons, that they are used to transfer genetic information and that you want them to find out how many codons there are altogether. Ask them to write down some more codons and give them a few minutes to do so. You can explain some of the scientific facts given above, choosing your own emphasis according to whether your learning objective is more focussed on the mathematics or more on the science. Then ask the class how they will know when they have found all of them and they can stop looking for more. The class may come up with some very good ideas of their own and realise that it is important to have a way of recording the different codons systematically. It is possible that some learners may even have looked up the information and discovered that the answer is 4 x 4 x 4 = 64. Ideally you want the learners to find this out for themselves, and to be able to understand and explain why this is the answer. The class could try the common problem solving strategy of first working on simple cases. Can they list all the 2 letter permutations with 2 letters chosen from A, U, G and C? You could use the One, Two, Four, More strategy. Ask the learners to work individually to list as many 2-­‐letter permutations as they can find, then ask them to work in pairs and compare results, and to decide how they will know when they have found them all. U G C A AA A AU AG AC U UA UU UG UC G GA GU GG GC C CA CU CG CC If it does not happen that many learners find the answer 4 x 4 = 16 then you may want to ask each pair to consult another pair. Finally have a class discussion. You might at this stage introduce the grid on the right. Another way of explaining this is to use a tree diagram with 4 branches for the first letter and each of these branches leading to 4 branches for the second letter giving 4 x 4 = 16 outcomes. Then ask the question again: “What about 3 letter codons?” The tree diagram approach leads naturally to an explanation that each of the 16 branches leads to 4 more branches giving 4 x 4 x 4 outcomes but you would not want to draw this tree diagram and the class still have to list the results. As listed in the table below, there are 4 choices for the third letter to follow each of the 16 2-­‐letter permutations. rd
3 letter -­‐> The 64 codons A AAA
UAA
GAA
CAA
AUA
UUA
GUA
CUA
U AGA
UGA
GGA
CGA
ACA
UCA
GCA
CCA
AAU
UAU
GAU
CAU
AUU
UUU
GUU
CUU
G AGU
UGU
GGU
CGU
ACU
UCU
GCU
CCU
AAG
UAG
GAG
CAG
AUG
UUG
GUG
CUG
C AGG
UGG
GGG
CGG
ACG
UCG
GCG
CCG
AAC
UAC
GAC
CAC
AUC
UUC
GUC
CUC
AGC
UGC
GGC
CGC
ACC
UCC
GCC
CCC
Read more: http://biology.about.com/od/molecularbiology/ss/rna.htm http://faqs.org/espionage/Fo-­‐Gs/Genetic-­‐Code.html Teaching Channel Video: https://teachingchannel.org/videos/dna-­‐lesson-­‐plan (28 Minutes) Follow-­‐up or Extension Tackle the question “How many permutations are there of the sequence of bases on the DNA ladder?” by starting with a simpler problem: “How many different sequences for a ladder with 3 rungs?” With 3 rungs the reasoning is the same as for the number of codons because you are looking for the number of permutations of 3 bases chosen from 4 (A, T, C and G). The answer is 43. Can you extend this reasoning to answer the question for a DNA ladder with 4 rungs? What about 5 rungs? Or 6 rungs? Human DNA is made up of 3.2 billion rungs. How many permutations are there of the sequence of bases on the DNA ladder?