Chapter 1. Chapter 15 Online Worked Problem: Translation

1.1 Problem Statement

If there were five different types of bases in mRNA instead of four, what would be the minimum codon size (number of nucleotides) required to specify the following numbers of different amino acid types: (a) 4, (b) 20, (c) 30?

For help with this problem:

  1. Review Section 15.2 on The Genetic Code Determines How the Nucleotide Sequence Specifies the Amino Acid Sequence of a Protein.
  2. Review the section on Degeneracy of the Code, including Figure 15.10.
  3. Review End-Of-Chapter Problems 20 and 21.

Question

Begin by thinking about the steps to take to do this problem. Use the dropdown menu to put the steps in the order in which they should be performed.

Identify the relevant information provided that will enable you to answer the question. rBBC6ww4fdpL2n1SfriINw==
Use the formula and relevant information to solve the specific question asked. iQrv5b+I5xMOyJWWX4Ow9A==
Identify the mathematical relationship between the parts of the question. ERtoTFIKsuAK6xNnbvJriQ==
Identify the question being asked. AtTzzErpwCspTRZjRVC4AA==
2
Check with the “Instant TA” and try again.
Correct. A general problem-solving approach is to go from general to specific, where you gather more general knowledge and then apply it to your specific question. Now let’s proceed through those steps.
Incorrect. A general problem-solving approach is to go from general to specific, where you gather more general knowledge and then apply it to your specific question. Now let’s proceed through those steps.

Instant TA

Think about the steps listed and how they logically flow from one to another, from very general, information-gathering steps to more specific steps related directly to the question.

1.2 Step 1: Identify the question being asked.

Question

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
2
Correct.
Incorrect.
Check with the “Instant TA” and try again.

Instant TA

Focus on the “variables” for which you need to solve.

1.3 Step 2: Identify the relevant information provided that will enable you to answer the question.

Question

If there were five different types of bases in mRNA instead of four, what would be the minimum codon size (number of nucleotides) required to specify the following numbers of different amino acid types: (a) 4, (b) 20, (c) 30?

a. There is/are p7luMvsfRXBdHbqVMv01QBAk14HudK9cj7pM4p6DA45U67d9hojR7HbhyH9PNhQ7 base(s) in this question, instead of the normal I7uGW8GrAsdHg9eL17Bnhixn/0fsjXE+RmLOCQ== base(s).

b. Codon length, which is normally three bases, is now /LtHuNB/r6u0GxJ47z1rDMQg9a1guvLcolgtt+/ZH8fTWxZl bases.

2
Correct.
Check with the “Instant TA” and try again.
Incorrect.

Instant TA

Use the notepad to highlight or take note of relevant information as you read the question. This will help you keep it in mind while considering the ultimate questions being asked.

1.4 Step 3: Identify the mathematical relationship between the parts of the question.

Question

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
2
Correct.
Incorrect.
Check with the “Instant TA” and try again.

Instant TA

Visualize a card table with a space marker for laying down only one card. The space represents a single codon. If you have 5 different cards (bases), how many different codons will you be able to make?

Question

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
2
Correct.
Incorrect.
Check with the “Instant TA” and try again.

Instant TA

Visualize a card table with a space marker for laying down two cards. The two spaces together represent a single codon (amino acid). If you have 5 different cards (bases) for each of the two spaces, how many different codons (amino acids) will you be able to make?

Question

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
2
Correct.
Incorrect.
Check with the “Instant TA” and try again.

Instant TA

What mathematical formula can you use to arrive at these answers?

5 bases with 1 codon length = 5 codons/amino acids, can be viewed as 5 ____ 1 = 5.
5 bases with 2 codon length = 25 codons/amino acids, can be viewed as 5 ____ 2 = 25.

What mathematical symbol could you put into the empty space to make both answers correct? Addition, subtraction, division, multiplication, power, square root, log?

1.5 Step 4: Use the formula and relevant information to solve the specific question asked.

Question

Y4MBrPaUqx5gZMdqxAMsh8moZp9o8DJ0z53VUhCqn7u8uh9s5bU2JTElpnnKrGXqZg4Gv4gue8f+7iMNsacZQ2PIDTlZa58EqS9JL9bWEOiimxctpOILj7eYxZqWHNzP82pqPhfP6h8zE6nDFKcQGsVICVKZ4tn8u5752B4li2veTJ9dOeNXcv0J8T+mcdehL1G1jPDGFc2avsIMd/tJ+9+BPMQRizUkbSFsMGQVV1MR0hUJIM4tD1rW3Rr4xHpEAO6gxaJwZqFyZHclCGLzd4yCyM5k36UfzvlKdfnsP+dekzYIO1+5apeQmhNgi0B8M3pDAbrvhLhhGz7f9l3YaIi+zbs+9e84huqUBM/+q+tpE6yHuxRLva9qrmjpMlmb1J3kekI5dpnE9uhAZOn5AMsryJfRXJwD7ywXH5Mm2lqRfn274AW+3TBOcIGIsxV04ya6N6UBMgFlciID2AvAJxOMTQkuf0qId5mu0oKwiYvxWVTndtWKdvSELa/Agu4uYCGoR4gEhYCnNk2cJ1YitfUIEHj/o5Dnw+kP3rfOuOsd+37fvAaBV9BADHmqNTxZ2bm2uMz7Wf3io2vOtFd8T4oHiorlJIvSvEmq+O4vpVfEDrJHAql/P0tz78R9gSOv0WTq+XdZHh6mbKJMWr86j6Mr2ITl/tEvrYZs4w407TkTttIrzgSvAm2QjHe2oMtd+720jFdM0/P8l/IP9rq9DJ54pUML5Gvti0x1XFQ6ZV7CitfBznv4OqM5LkaflYpIUPDXH3QYnU+yAe79tC3t7VXUtjYt7hXpZfIUr8jpXfC69MS1ExgjFW9n+WTNZY/ieVoECF2wNaskabooSMDlsxqGaWs9kOe/wwP50ydywPbp6Rq/it4sNX0DMsKF522Asnk+D6fyuu+SkKUuPLDvLf+VBrsE+tcJGoEWpGpXTxfTLbNEdwrq4p0AagT8csDFBEk4hccckYtUYgcqfxoZN4FMdC77Se97PL3H0nMqoIDOs0uISk6F3G7NcEI=
2
Correct.
Check with the “Instant TA” and try again.
Incorrect.

Instant TA

Use the formula from the previous step. Remember, in reality more than one codon can usually specify a particular amino acid. You just need at least four codons/amino acids, but there can be more.

Question

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
2
Correct.
Incorrect.
Check with the “Instant TA” and try again.

Instant TA

Use the formula from the previous step. Remember, in reality more than one codon can usually specify a particular amino acid. You just need at least 20.

Question

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
2

Correct.

Further Exploration

This type of question is one where you can use a known scenario to build a model and then modify it to see how the model has to change to accommodate the new hypothetical information. Your background knowledge is that in real life, three nucleotides/bases make a codon and there are four bases (adenine, guanine, cytosine, and uracil). You can draw out or find manipulatives like the cards to generate this scenario. Three nucleotides per codon and four bases like this:

So, for 4 bases and 3 base “spots” per codon, we could have AAA or ACA or AGA or AUA and so on. You can simply list out all the possibilities to get the count and then find the mathematical equation that will give you that answer. So, more generally,

possible codons/amino acids = (number of bases)codon length .

If you look at the actual codon table, there are 64 different codons, but one amino acid can specify more than one codon (eg glycine is encoded by GGA, GGC, GGG, and GGT.) Here, x = 43 = 64 possible codons or amino acids using the formula.

So, now all you would need to do is change your model to accommodate 5 bases and an unknown codon length. Notice this requires that you work your problem backwards. But you are familiar with it now.

Incorrect.

Final Feedback

This type of question is one where you can use a known scenario to build a model and then modify it to see how the model has to change to accommodate the new hypothetical information. Your background knowledge is that in real life, three nucleotides/bases make a codon and there are four bases (adenine, guanine, cytosine, and uracil). You can draw out or find manipulatives like the cards to generate this scenario. Three nucleotides per codon and four bases like this:

So, for 4 bases and 3 base “spots” per codon, we could have AAA or ACA or AGA or AUA and so on. You can simply list out all the possibilities to get the count and then find the mathematical equation that will give you that answer. So, more generally,

possible codons/amino acids = (number of bases)codon length .

If you look at the actual codon table, there are 64 different codons, but one amino acid can specify more than one codon (eg glycine is encoded by GGA, GGC, GGG, and GGT.) Here, x = 43 = 64 possible codons or amino acids using the formula.

So, now all you would need to do is change your model to accommodate 5 bases and an unknown codon length. Notice this requires that you work your problem backwards. But you are familiar with it now.

Check with the “Instant TA” and try again.

Instant TA

Use the formula from the previous step replacing all variables with the values you know. For example, if there were 5 bases and the codon length was 8, the formula would be 58 codons/amino acids or 390625 codons/amino acids. Remember, in reality more than one codon can usually specify a particular amino acid. You just need at least 30.