The two sides of the DNA double nine). Because of the...

The two sides of the DNA double nine). Because of the geometric shape of these molecules, adenine bonds with thymine and cytosine bonds with guanine. Figure $\mathbf{E} 21.18$ shows the bonding of thymine and adenine. Each charge shown is $\pm e,$ and the $\mathrm{H}-\mathrm{N}$ distance is $0.110 \mathrm{nm}$. (a) Calculate the net force that thymine exerts on adenine. Is it attractive or repulsive? To keep the calculations fairly simple, yet reasonable, consider only the forces due to the $\mathrm{O}-\mathrm{H}-\mathrm{N}$ and the $\mathrm{N}-\mathrm{H}-\mathrm{N}$ combinations, assuming that these two combinations are parallel to each other. Remember, however, that in the $\mathrm{O}-\mathrm{H}-\mathrm{N}$ set, the $\mathrm{O}^{-}$ exerts a force on both the $\mathrm{H}^{+}$ and the $\mathrm{N}^{-}$, and likewise along the $\mathrm{N}-\mathrm{H}-\mathrm{N}$ set. (b) Calculate the force on the electron in the hydrogen atom, which is $0.0529 \mathrm{nm}$ from the proton. Then compare the strength of the bonding force of the electron in hydrogen with the bonding force of the adenine- -thymine molecules.

The two sides of the DNA double
nine). Because of the geometric shape of these molecules, adenine bonds with thymine and cytosine bonds with guanine. Figure $\mathbf{E} 21.18$ shows the bonding of thymine and adenine. Each charge shown is $\pm e,$ and the $\mathrm{H}-\mathrm{N}$ distance is $0.110 \mathrm{nm}$. (a) Calculate the net force that thymine exerts on adenine. Is it attractive or repulsive? To keep the calculations fairly simple, yet reasonable, consider only the forces due to the $\mathrm{O}-\mathrm{H}-\mathrm{N}$ and the $\mathrm{N}-\mathrm{H}-\mathrm{N}$ combinations, assuming that these two combinations are parallel to each other. Remember, however, that in the $\mathrm{O}-\mathrm{H}-\mathrm{N}$ set, the $\mathrm{O}^{-}$ exerts a force on both the $\mathrm{H}^{+}$ and the $\mathrm{N}^{-}$, and likewise along the $\mathrm{N}-\mathrm{H}-\mathrm{N}$ set. (b) Calculate the force on the electron in the hydrogen atom, which is $0.0529 \mathrm{nm}$ from the proton. Then compare the strength of the bonding force of the electron in hydrogen with the bonding force of the adenine- -thymine molecules.

Key Concepts

Comparison of Interatomic Force Scales

Comparing the force that holds a hydrogen bond in a DNA base pair with that between an electron and a proton in a hydrogen atom provides insight into the relative strengths of different bonding interactions. Such a comparison highlights that while hydrogen bonds are crucial for biological structure and function, they are significantly weaker than the electrostatic forces within atoms, influencing how molecules behave under different conditions.

Superposition Principle of Forces

In many molecular problems, the total net force on a particle is determined by summing all individual forces vectorially. This principle allows one to compute the overall effect of multiple interactions—such as those in complex biomolecules—by considering each contribution separately and then combining them to find the resultant force.

Hydrogen Bonding

Hydrogen bonding is a type of noncovalent interaction that occurs when a hydrogen atom covalently bonded to an electronegative atom (such as oxygen or nitrogen) interacts with another electronegative atom nearby. This interaction, though weaker than covalent bonds, is critical for the stabilization of structures like the DNA double helix through specific base pairing between nucleotides.

Coulomb's Law

Coulomb's law describes the force between two point charges, stating that the magnitude of the force is proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle is essential for calculating the forces between charged atoms or groups in molecules, such as in the interactions between the charged parts of the molecular groups in DNA.

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