Question

Sequences of numbers are a useful mathematical tool for exploring transitions and trends. Sequences of symbols create words, and sequences of words create languages, both Human and Computer. While sequences of nucleotides create DNA, which in turn create new sequences of nucleotides called RNA, which in turn creates sequences of amino acids called proteins, which in turn create, among other things, humans that create, among other things, computers. The quest to identify this “Source Code of Life” quickly became the focus of a great deal of science over the years, not to mention computing power. One method involves the use of certain enzymes that break the nucleotide chains at a specific chemical bond, and then analyzing the resulting fragments to determine the original structure. (The actual methods involved are in some ways harder than the problem in the Project, since you do not always know the sequence of the fragments, only their length. And in some ways much easier, since you have some idea of the count of each fragment contained in the original.)

For this Project you will use the given information and a bit of logic to find an RNA sequence. You should not have to do any outside research, but feel free to explore the topic in greater depth. If you do any external research be sure to properly cite your sources. If you work with another student(s), please include their name(s) in the write-up as well. If you use any electronic resources to help you track the possible sequences or perform calculations, name them in the report, and include sample calculations (in the case of something like a spreadsheet) or sample code (in the case of a programming language). You do not need to include the actual, executable program in the report.

Suppose that when an enzyme that breaks RNA chains after each G link is applied to a 12-link chain, the fragments obtained are AC, UG, and ACG. And when an enzyme that breaks RNA chains after a C or U link is applied, the fragments obtained are U, GU, and GAC. Can you determine the entire RNA sequence from these two sets of fragments? If not, why not? Would it help to know exactly how many of each fragment you have?

Answer 1

Total chain length =12

Enzymes used =2

Fragments obtained = 3 +3 =6

Enzyme treatment 1, Breaking after G =AC, UG, ACG  

The entire sequence contains only 2 G's and AC must be the last fragment of the sequence after being cut after a G.

Confirm sequence : _ _ _ _ _ _ _ _ _ GAC.

This sequence GAC should follow either U or AC.

Assumption sequence 1: _ _ _ _ _ _ _ _ UGAC (or)

Assimption sequence 2:  _ _ _ _ _ _ _ACGAC

The fragment UG and ACG can be anywhere within the first 10 bases.

Enzyme treatment 2, Breaking after U/C=U, GU, GAC

The fragment U must be the first fragment of the sequence after being after a U. We also have a fragment UG from enzyme treatment 1.so the first base U should be followed by a G. And from the fragment GU from enzyme treatment 2, the third base should be U.

  UGU _ _ _ _ _ _ GAC

After this we can neglect the assumption sequence 1, and confirm the assumption sequence 2

UGU _ _ _ _ ACGAC

this is the maximum interpretation we can obtain from the given data. The entire RNA sequence cannot be determined. Knowing how many of each fragment is obtained may help to some extent but the basic requirement that should be satisfied is that after treating with an enzyme, all the fragments must account to 12 bases. Only then we can align the sequence of bases.