BIO Base Pairing in DNA, I. The two sides of the DNA double...

BIO Base Pairing in DNA, I. The two sides of the DNA double helix are connected by pairs of bases (adenine, thymine, cytosine, and guanine). Because of the geometric shape of these molecules, adenine bonds with thymine and cytosine bonds with guanine. Figure E21.23 shows the thymine-adenine bond. 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 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

DNA Base Pairing

DNA base pairing refers to the specific hydrogen bonding interactions that occur between the nucleobases in the double helix, where adenine pairs with thymine and cytosine pairs with guanine. This complementary pairing is fundamental to the structure of DNA and ensures the precise replication and transcription of genetic information. It relies on the spatial arrangement and electrical properties of the atoms within the bases, which allow for selective hydrogen bonding between the pairs.

Hydrogen Bonding

Hydrogen bonds are comparatively weak electrostatic attractions that occur when a hydrogen atom covalently bonded to an electronegative atom, such as oxygen or nitrogen, interacts with another electronegative atom. In biological molecules like DNA, these bonds are crucial for maintaining the double helical structure. Although each individual hydrogen bond is weak, collectively, they provide substantial stability to the overall structure.

Electrostatic Interactions and Coulomb's Law

Electrostatic interactions, described by Coulomb's law, are the forces between charged particles. In molecular systems, these forces govern how ions and partially charged groups interact. The principles of Coulomb's law are used to calculate the attractive or repulsive forces between charged components in molecules, such as the interactions involving the charged groups in hydrogen bonds in DNA, enabling quantitative assessments of molecular stability.

Force Comparisons Between Molecular and Atomic Interactions

Comparing forces at different scales, such as the bonding forces in DNA and the electrostatic force acting on an electron in a hydrogen atom, helps demonstrate the range of interaction strengths in nature. While both scenarios involve electrostatic forces, the relative magnitudes differ dramatically due to differences in distance scales and the magnitudes of charges involved, offering insight into the varying energy landscapes that govern atomic versus molecular bonding.

Transcript

00:01 In this problem, we'll be applying this force law to all the different combinations of interactions.

00:07 But throughout this problem, q1 times q2 and the absolute value around it will always be equal to e squared, since the charges of all the interactions will involve an excess charge of e.

00:19 And so first we're going to look at the oh interaction.

00:22 And as part of this interaction, i'm first going to look at the o and the h.

00:26 And so the force between these will be equal to k, which is 8.

00:32 0 .99 times 10 to the 9 times e squared, which is 1 .6 times 10 to the negative 19, and that's squared over r squared.

00:45 And the r value is given in the problem.

00:47 It's just the distance between this o and the h.

00:50 And it's 0 .17 times 10 to the minus 9.

00:55 And that's squared.

00:57 And so when you do this out, you get 7 .96 times 10 to the minus 9 newtons.

01:03 And because, because they are opposite sign, this is attractive.

01:09 This is an attractive force.

01:12 Now we're going to do the o minus with the n minus.

01:17 So first we did this interaction, and now we're going to do this interaction.

01:24 So i'm not going to repeat all the number crunching here because it's very similar.

01:28 The only thing that really changes is the r distance, since the distance between the o and n is different than the distance between the o and h.

01:34 What you'll get is 2 .94 times 10 to the minus 9 newtons and this is repulsive since they have light charges and so let's move on to the other interaction the n hn interaction so first we're going to do that and then we're going to do that so the n h interaction and just to be technical it's n minus h plus the force is going to be 638 times 10 to the negative 9 nons.

02:14 If you crunch that in, again, the only difference is the distance is changing.

02:19 The distance between n and h is different than the rest of the distances.

02:22 That's the only thing that's separating these numbers from each other.

02:26 And this force is attractive because they're opposite signs...

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