The two strands of the DNA molecule are held together by...

Name: Problem 91, Chapter 17: Physics
Uploaded: 2021-05-28T15:02:33-08:00
Duration: 7 min 11 s
Channel: Linda Winkler
Description: The two strands of the DNA molecule are held together by hydrogen bonds between base pairs (Sec. 16.1). When an enzyme unzips the molecule to separate the two strands, it has to break these hydrogen bonds. A simplified model represents a hydrogen bond as the electrostatic interaction of four point charges arranged along a straight line.

The two strands of the DNA molecule are held together by hydrogen bonds between base pairs (Sec. 16.1). When an enzyme unzips the molecule to separate the two strands, it has to break these hydrogen bonds. A simplified model represents a hydrogen bond as the electrostatic interaction of four point charges arranged along a straight line.

Key Concepts

Hydrogen Bonding

Hydrogen bonding refers to a type of weak intermolecular attraction where a hydrogen atom, covalently bonded to a highly electronegative element, interacts with another electronegative atom having a lone electron pair. This interaction is essential in stabilizing the three-dimensional structures of various biomolecules, influencing properties like the double helix formation in nucleic acids and the folding of proteins.

Electrostatic Interactions

Electrostatic interactions represent the forces between charged particles, governed by Coulomb’s law. These interactions are fundamental in understanding how molecular components attract or repel each other. They provide insight into the behavior of atoms and molecules, especially when modeling the interaction of charges, such as in approximations of hydrogen bonds.

Molecular Modeling

Molecular modeling involves the use of simplified representations or mathematical models to simulate and study complex molecular structures and interactions. By approximating bonds or interactions—like modeling a hydrogen bond as a system of point charges—researchers can predict behaviors, estimate energies, and gain a deeper understanding of how molecular structures are stabilized.

Transcript

00:01 Here we're asked to find the energy it takes to break a hydrogen bond that is holding together two strands of dna.

00:09 So there is a model for this that involves a co, a carbon oxygen dipole, if you will, and a nitrogen dipole.

00:24 So there are four point charges, two of the charges make a new, system and they are held together by their own internal bond, same with the other carbon oxygen system.

00:41 But our hydrogen bond is linking those two dipoles together and we want to know how much energy to break the hydrogen.

00:54 And what we'll be using is the potential energy relationship for point charges.

01:02 And what we're basically going to have to do is pick one side.

01:07 So i'm going to pick the nitrogen part.

01:12 And i'm going to say how much energy is holding that to the carbon oxygen.

01:21 So we want to think about each molecule, part of the molecule being bound to each part of the other molecule.

01:30 So let's think about what's holding the.

01:32 Hydrogen in place.

01:35 And so the potential energy is going to evolve the electrical constant, which i'll use 9 times 10 to the 9th, newton's meter squared over coolum squared.

01:48 It involves the hydrogen with the oxygen as q1 and q2, and then i'm going to have to add the hydrogen bound to the carbon as q1 and q2.

02:02 With a slightly different separation r.

02:06 So there's going to be two terms to this, and they will both involve the k and the positive 0 .3e, but what will differ is the, so that comes from the hydrogen, but what will differ is what's coming from the oxygen and the carbon.

02:29 So there's a minus 0 .4e over d.

02:36 Is the separation there plus 0 .4e, and the separation there is d plus l.

02:46 So i'm just using symbols for those distances, but we do know what they are in nanometers.

02:57 And i'll leave a little space, but we're then going to have to do the same with the nitrogen bound to the carbon oxygen link, if you will.

03:09 So the nitrogen is minus .3e.

03:16 And again, we have minus .4e, but the separation is d plus l and plus .4e, and the separation is d plus 2l.

03:36 Okay, and so evaluating this is not too difficult...