Question

Compositional constraint. The composition (in mole-fraction units) of one of the strands of a double-helical DNA molecule is \([\mathrm{A}]=0.30\) and \([\mathrm{G}]=0.24 .\) (a) What can you say about [T] and \([\mathrm{C}]\) for the same strand? (b) What can you say about [A], [G], \([\mathrm{T}],\) and \([\mathrm{C}]\) of the complementary strand?

Short answer

(a) [T] = 0.46, [C] = 0.24 (b) [A] = 0.46, [T] = 0.30, [G] = 0.24, [C] = 0.24

Step-by-step solution

Understand DNA Base Pairing

In a DNA molecule, adenine (A) pairs with thymine (T), and guanine (G) pairs with cytosine (C). This means the mole fractions of A in one strand will equal the mole fraction of T in the complementary strand, and the mole fraction of G in one strand will equal the mole fraction of C in the complementary strand.

Calculate Remaining Base Fractions for the Same Strand

For any DNA strand, the sum of the mole fractions of all bases must equal 1. We are given that \([\mathrm{A}]=0.30\) and \([\mathrm{G}]=0.24\). Therefore, we can calculate \([\mathrm{T}]=1 - ( [\mathrm{A}] + [\mathrm{G}] ) = 1 - (0.30 + 0.24) = 0.46\). Similarly, since \([\mathrm{C}] = [\mathrm{G}]\), we find \([\mathrm{C}]=1 - ( [\mathrm{A}] + [\mathrm{T}] ) = 1 - (0.30 + 0.46) = 0.24\).

Determine Base Fractions for the Complementary Strand

Based on complementary pairing (A with T, G with C): - The mole fraction of [A] in the complementary strand equals the mole fraction of [T] in the given strand: [A] in the complementary strand is 0.46. - The mole fraction of [T] in the complementary strand equals the mole fraction of [A] in the given strand: [T] in the complementary strand is 0.30. - The mole fraction of [G] in the complementary strand equals the mole fraction of [C] in the given strand: [G] in the complementary strand is 0.24. - The mole fraction of [C] in the complementary strand equals the mole fraction of [G] in the given strand: [C] in the complementary strand is 0.24.

Key concepts

Nucleotide Composition

DNA is composed of four main types of nucleotides, each represented by a specific base: adenine (A), thymine (T), guanine (G), and cytosine (C). These nucleotides are the building blocks of DNA. In any single DNA strand, these bases must sum to a mole fraction of 1, meaning their combined proportion accounts for the entire composition of the strand.
A typical process in understanding nucleotide composition involves knowing the fraction or percentage of one or more bases and using these values to calculate the others.

• A and T are complementary bases, meaning they always pair with each other.
• G pairs with C, which is crucial for the stability and replication of DNA.

When given [A] = 0.30 and [G] = 0.24, determine the remaining bases by ensuring the total adds up to 1 for the strand being analyzed.

Molecular Biology

Molecular biology explores the molecular underpinnings of the fundamental processes in living organisms, especially in terms of genetic information encoding and expression. DNA is central to these processes, as it carries the genetic blueprint of life.
The study of molecular biology includes understanding how genes are transcribed into RNA and translated into proteins. However, at the core of these processes is the structure and function of DNA itself.
In solving problems associated with DNA composition, molecular biology principles help explain the natural laws governing the arrangement and replication of DNA where the concept of complementary base pairing is a key component.
Understanding these principles allows scientists to decipher genetic codes and conduct genetic engineering, sequencing, and more.

Double Helix Structure

The double helix structure of DNA is one of the most iconic images in science. Described by Watson and Crick, this twisted ladder structure underpins the physical and functional properties of DNA.
This structure is formed by two intertwined strands of DNA, held together by hydrogen bonds between paired bases.

• A pairs with T via two hydrogen bonds.
• G pairs with C via three hydrogen bonds, providing a stronger connection.

The double helix allows for DNA replication, where each strand serves as a template for a new complementary strand. Thus, knowing the base pairs on one strand determines those in the complementary strand.
This feature is critical in genetic duplication and inheritance, ensuring the accurate transmission of genetic information from one generation to the next.