Problem 78 - Chemistry: The Central Science in SI Units, Global Edition

Question

You are working in a biotechnology lab and are analyzing DNA. You obtain a sample of a short dodecamer of DNA that contains 12 base pairs. (a) What must the ratio of adenine to thymine be in your sample? (b) What must the ratio of cytosine to guanine be in your sample? (c) Assume the counterions present in your DNA solution are sodium ions. How many sodium ions must there be per dodecamer? Assume the \(5^{\prime}\) end phosphates each bear a-1 charge.

Step-by-Step Solution

Answer

(a) The ratio of adenine to thymine in the DNA dodecamer is 1 : 1. (b) The ratio of cytosine to guanine in the DNA dodecamer is 1 : 1. (c) There are 2 sodium ions per dodecamer in the DNA solution.

Step 1: Find the ratio of adenine to thymine

In a DNA molecule, adenine always pairs with thymine. Since there are 12 base pairs in the dodecamer, the amount of adenine must be equal to the amount of thymine. So, Ratio of A to T = A : T = 1 : 1

Step 2: Find the ratio of cytosine to guanine

Similarly, cytosine always pairs with guanine in a DNA molecule. Since there are 12 base pairs in the dodecamer, the amount of cytosine must be equal to the amount of guanine. So, Ratio of C to G = C : G = 1 : 1

Step 3: Determine the total negative charges of the dodecamer

The total negative charge of the dodecamer will come from the \(5^{\prime}\) end phosphates. As stated in the exercise, each \(5^{\prime}\) end phosphate bears a -1 charge. Since there are two strands in the DNA molecule, we have two \(5^{\prime}\) end phosphates: Total negative charges = -1 charge/phosphate × 2 phosphates = -2 charges

Step 4: Determine the number of sodium ions in the dodecamer

To neutralize the negative charges on the dodecamer, there must be an equal number of positive charges coming from the sodium ions. Since each sodium ion has a +1 charge, we need the same number of sodium ions (+2 charges) to neutralize the -2 charges of the dodecamer. Therefore: Number of sodium ions = +2 charges / +1 charge/sodium ion = 2 sodium ions per dodecamer. The answers to the exercise are: (a) The ratio of adenine to thymine in the DNA dodecamer is 1 : 1. (b) The ratio of cytosine to guanine in the DNA dodecamer is 1 : 1. (c) There are 2 sodium ions per dodecamer in the DNA solution.

Key Concepts

Adenine-Thymine Ratio

In DNA, adenine (A) pairs with thymine (T) through two hydrogen bonds, a fundamental aspect of the DNA double helix structure. This specific pairing is known as complementary base pairing. When structuring a DNA strand, the logical inference is that if there are 'x' adenine, there must be 'x' thymine. This results in a 1:1 adenine to thymine ratio.

This balance is crucial for the DNA's structural integrity and function. Disruption in this precise ratio can lead to structural anomalies or mutations. Hence, in any standard DNA sample, checking for a balance between adenine and thymine is essential for ensuring genetic accuracy.

Equally spaced, these base pairs lend stability to the DNA through their uniform width, maintaining a consistent helical geometry.

Cytosine-Guanine Ratio

Cytosine (C) and guanine (G) form another vital pair within the DNA structure, linked by three hydrogen bonds. Similar to adenine and thymine, cytosine and guanine must also exhibit a complementary and balanced relationship, resulting in a 1:1 ratio.

This specific pairing provides additional stability to the DNA double helix due to the stronger bond established by three hydrogen bonds - one more than the A-T pairs. Variations in this ratio could potentially lead to harsh ramifications such as mutations or improper protein encoding.

• Balance ensures proper DNA replication.
• Aids in accurate genetic information transfer.

In any DNA sample analysis, verifying the integrity of cytosine and guanine balance is essential. These precise ratios contribute to the preservation of the genetic code during cell division and replication sequences.

Sodium Ion Balance

In a DNA solution, sodium ions play a significant role in balancing the molecule's charge, supporting structural stability. This becomes relevant especially because DNA molecules inherently possess negative charges due to their phosphate backbones.

Each phosphate group contributes a negative charge at the ends of the DNA strands. The sodium ions, carrying positive charges, help to offset these negative charges. This interaction is crucial to maintain the DNA in a stable, minimal-energy conformation.

In our specific example, where the DNA dodecamer exhibits two negative charges from its phosphate ends, two sodium ions will neutralize this charge.
Therefore, understanding sodium ion balance is key to assessing the chemical stability of DNA strands in various environments or experimental conditions.

DNA Charge Neutrality

Charge neutrality in DNA is achieved when the negative and positive charges within the molecule and its surroundings are balanced. This balance ensures the molecule remains stable and properly functional in physiological and experimental contexts.

DNA's phosphate backbone inherently carries a negative charge, which requires balancing through the presence of positively charged ions, like sodium in our example. This balance not only supports the structural integrity but also prevents unwarranted chemical reactions that could damage the DNA.

• Necessary for maintaining double helix structure.
• Prevents electrostatic repulsion between phosphate groups.

Ensuring charge neutrality is crucial, particularly during processes like DNA replication or transcription, where structural disintegration could lead to errors. Therefore, evaluating ion balance is an integral part of DNA research and practical biotechnology applications.