Question

The \([(\mathrm{A}+\mathrm{G}) /(\mathrm{T}+\mathrm{C})]\) ratio in one strand of duplex DNA is \(0.3 .\) (a) What is the ratio in the complementary strand? (b) What is the ratio for the entire molecule? (c) If the \([(\mathrm{A}+\mathrm{T}) /(\mathrm{C}+\mathrm{G})]\) ratio is \(0.3\), what is the ratio in the complementary strand and in the entire molecule?

Short answer

The ratio in the complementary strand is 3.33, and the ratio for the entire molecule is 1.815. If the \((A+T)/(C+G)\) ratio is 0.3, the ratio in the complementary strand is still 3.33, and the ratio for the entire molecule remains 1.815.

Step-by-step solution

(a) Finding the ratio in the complementary strand

The given ratio for one strand is: \[(A+G)/(T+C) = 0.3\] Since adenine (A) pairs with thymine (T) and guanine (G) pairs with cytosine (C), in the complementary strand, the number of T's will equal the original number of A's, and the number of C's will equal the original number of G's. Thus, in the complementary strand we can write: \[(T+C)/(A+G) = 1 / 0.3\] Calculate the reciprocal of 0.3: \[(T+C)/(A+G) = 1 / 0.3 = 3.33\] So, the ratio in the complementary strand is 3.33.

(b) Finding the ratio for the entire molecule

In the entire DNA molecule, we have the sum of both strands, which means we have the sum of all four bases: A, T, C, and G. Instead of calculating the ratio for the entire molecule directly, we can simply average the ratios from both strands: \[((A+G)/(T+C) + (T+C)/(A+G)) / 2\] Insert the previously found ratios: \[((0.3 + 3.33) / 2)\] Calculate the average: \[((0.3 + 3.33) / 2) = 1.815\] Thus, the ratio for the entire molecule is 1.815.

(c) New Ratio for the complementary strand and entire molecule

Given that the ratio in one strand is now: \[(A+T)/(C+G) = 0.3\] The complementary strand has the same base pairing rules (A with T, C with G), so the ratio for the complementary strand is: \[(C+G)/(A+T) = 1 / 0.3 = 3.33\] To find the ratio for the entire molecule, take the average of the two ratios: \[((A+T)/(C+G) + (C+G)/(A+T)) / 2 = (0.3 + 3.33) / 2 = 1.815\] Therefore, the ratio in the complementary strand is 3.33, and the ratio for the entire molecule is 1.815.

Key concepts

Complementary DNA Strands

Understanding complementary DNA strands is fundamental to grasping not only the structure but also the function of DNA in all living organisms.

In the double helix model of DNA, two strands twist around each other with specific base pairing that determines the 'complementary' nature of these strands. This means that for every adenine (A) in one strand, there is a thymine (T) directly across from it on the complementary strand, and for every cytosine (C), there is a guanine (G).

This complementary base pairing is driven by the formation of hydrogen bonds, which are strong enough to hold the strands together but weak enough to allow them to separate during processes such as DNA replication and protein synthesis.

In the given exercise, we work out the ratio of the sum of adenine and guanine to the sum of thymine and cytosine in one strand. The bases on the complementary strand are determined directly by those on the first strand—dictated by these specific pairing rules.

Adenine (A) and Thymine (T) Pairing

One of the key pairings in DNA is between adenine (A) and thymine (T).

The Role of Hydrogen Bonds

These bases are able to pair because of the correct arrangement of hydrogen bond acceptors and donors. Adenine and thymine form two hydrogen bonds with each other, ensuring a stable but reversible connection.

This pairing rule is crucial when addressing exercises such as the one provided, where understanding the ratios involves knowing which bases will pair up across the double helix.

• If one strand has a high proportion of A, the complementary strand will have a correspondingly high proportion of T.
• If we are given a ratio of A to other bases, we can assume the same ratio will apply inverted for T in the complementary strand, because of the one-to-one pairing.

The ratio of other bases on one strand gives direct insights into the proportional presence of their partners on the other strand, hence solving which parts of the puzzle belong where.

Guanine (G) and Cytosine (C) Pairing

The guanine (G) and cytosine (C) pairing is another perfect example of DNA’s specificity. These two bases bond with each other through three hydrogen bonds, slightly stronger than the A–T pairing due to the additional bond.

As with A and T, the G and C pairing implies that the amounts of guanine will be equal to the amounts of cytosine in the complementary strand. This one-to-one ratio significantly eases the calculation of base ratios in exercises involving DNA nucleotides.

• Knowing the ratio of G to other bases on one strand directly defines the ratio of C on the complementary strand.
• Conversely, if more C bases are present on one strand, correspondingly more G bases must be present on the other strand to complement it.

Through the insight provided by these pairing rules, we can accurately deduce and calculate ratios in the complementary strand and in the entire DNA molecule, as showcased in the step-by-step solution of the exercise.