Problem 78 - Chemistry The Central Science

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

The ratio of adenine to thymine in the dodecamer DNA sample is 1:1, and the ratio of cytosine to guanine is also 1:1 due to complementary base pairing in the DNA double helix. There are 22 sodium ions per dodecamer, with 2 sodium ions neutralizing the negative charges in the 5' ends and 20 sodium ions for the remaining phosphate groups.

Step 1: Part (a): Ratio of Adenine to Thymine

Since adenine pairs with thymine in a DNA double helix, the ratio of adenine to thymine in the dodecamer DNA sequence must be 1:1. In other words, there is one adenine molecule for every thymine molecule in the DNA sample.

Step 2: Part (b): Ratio of Cytosine to Guanine

Similar to part (a), since cytosine pairs with guanine in a DNA double helix, the ratio of cytosine to guanine in the dodecamer DNA sequence must also be 1:1. In other words, there is one cytosine molecule for every guanine molecule in the DNA sample.

Step 3: Part (c): Sodium Ions per Dodecamer

To calculate the number of sodium ions per dodecamer, we first need to understand that the negatively charged phosphate groups in DNA are neutralized by the positively charged sodium ions. In a dodecamer, there are 11 phosphate groups per strand, bringing a total of 22 phosphate groups for both the strands. At the 5' ends of the DNA, the phosphates each bear a negative charge. Since there are 2 strands, there will be 2 phosphates with \((a - 1)\) charge. Let's assume \((a - 1)\) charge is -1. Therefore, there will be 2 sodium ions neutralizing the negative charges in the 5' ends. Now, there are 20 remaining phosphate groups in the dodecamer with 1 negative charge each. These phosphate groups will be neutralized by 20 sodium ions. Hence, the total number of sodium ions required per dodecamer is the sum of sodium ions neutralizing the 5' end phosphates and the remaining phosphate groups, which is 2 + 20 = 22.

Key Concepts

Base Pairing

DNA is often referred to as the blueprint of life because it contains the instructions needed to build and maintain an organism. One of the fundamental principles underlying DNA's structure is base pairing. This concept explains how the two strands of DNA are held together through interactions between specific nitrogenous bases.

In DNA, there are four types of nitrogenous bases: adenine (A), thymine (T), cytosine (C), and guanine (G). Base pairing is highly specific: adenine always pairs with thymine, and cytosine always pairs with guanine. This is known as complementary base pairing, and it is crucial for the structure and function of DNA. Complementary pairing enables the DNA strands to form a stable double helix structure.

• Adenine and Thymine: In a DNA double helix, each adenine base pairs with a thymine base through two hydrogen bonds. This gives the adenine-thymine pair stability.
• Cytosine and Guanine: Each cytosine base pairs with a guanine base through three hydrogen bonds, which provides even greater stability compared to the adenine-thymine bond.

These pairings ensure that the DNA strands are complementary to each other, meaning if you know the sequence of one strand, you can predict the sequence of the other. This principle is essential for DNA replication and transcription.

Phosphate Groups

DNA's backbone provides structural support and is composed of sugar molecules and phosphate groups. These components form a long chain, sometimes refered to as "sugar-phosphate backbone", running along the length of the DNA strand.

• Role: Phosphate groups are crucial because they link neighboring deoxyribose sugars together, forming a strong backbone for the DNA double helix. Each phosphate group connects to the 3' carbon of one sugar and the 5' carbon of the next.
• Charge: The phosphate groups give the DNA molecule an overall negative charge, due to the presence of negatively charged oxygen atoms. This characteristic plays a significant role in DNA's interactions with other molecules, such as proteins and ions.

Phosphate groups are not just structural; their negative charge is important for the stability of the DNA molecule. This is because they help maintain the double helix's shape by repelling each other, which keeps the strands evenly spaced apart.

Sodium Ions

Sodium ions play a crucial role in maintaining the stability and integrity of DNA in solution. This is particularly important because DNA itself is highly charged, primarily due to the negatively charged phosphate groups in its backbone.

• Neutralization: Since the DNA backbone carries a negative charge, it requires positive counterions to neutralize these charges and maintain structural stability. In many laboratory solutions, sodium ions serve as these counterions.
• Interaction in DNA Solutions: When in solution, sodium ions surround the DNA molecule, effectively reducing the repulsion between negatively charged phosphate groups. This enables the DNA to maintain its compact structure.

In the context of a dodecamer, which is a short DNA sequence of twelve base pairs, each phosphate group needs to be neutralized by a sodium ion. This shows how sodium ions are indispensable in preventing DNA strands from repelling each other, which would destabilize their structure. Understanding these interactions is key to manipulating and studying DNA in lab settings.