BIO Energy of DNA Base Pairing. (See Exercise 21.18 .) (a) Calculate the electric potential ener

BIO Energy of DNA Base Pairing. (See Exercise 21.18 .) (a)...

Key Concepts

Quantum Energy of the Hydrogen Atom

This concept refers to the discrete energy levels in the hydrogen atom, notably the potential energy associated with the interaction between the proton and electron. Comparing the energy of the DNA base pairing interactions with the energy of the ground state in hydrogen atoms helps contextualize the magnitude of biological bond energies within a framework familiar from atomic physics.

Coulomb's Law

Coulomb's Law is a fundamental principle used to quantify the force and potential energy between two charged particles. In bio-molecular systems, it underpins the calculation of electric potential energy in interactions such as hydrogen bonds within DNA base pairing, and serves as a basis for understanding the energy scale of these forces.

DNA Base Pairing

DNA base pairing involves the specific hydrogen bonding interactions between nucleotide pairs, such as adenine with thymine. These pairings are essential for the formation and stability of the DNA double helix, ensuring the fidelity of genetic information transfer during replication and transcription.

Electric Potential Energy

This concept pertains to the energy associated with charged particles due to their electrostatic interactions. In molecular contexts, it is calculated using Coulomb’s law, where the energy depends on the magnitudes of the charges and the distance between them, providing insight into the forces that hold molecules together.

Hydrogen Bonding

Hydrogen bonding is a specific type of dipole-dipole attraction between molecules, crucial in biological systems. It occurs when a hydrogen atom covalently bonded to an electronegative atom (such as oxygen or nitrogen) interacts with another electronegative atom, significantly influencing the structure and stability of molecules like DNA.

Transcript

00:01 So in this problem, what we're first asked to do is to calculate the electrical potential energy of the adenine -thamine bond, which is found in dna.

00:10 So if we see here, basically we want to look at this problem as if we're calculating the potential energy of individual pairs of charges.

00:22 So when we look at this, we might get a little bit overwhelmed.

00:25 We're seeing chemistry.

00:26 But essentially what this is is we're just looking at these bonds.

00:29 So oxygen to hydrogen and oxygen to nitrogen as well as nitrogen to nitrogen and nitrogen to hydrogen.

00:38 And we're just going to look at them like they're individual pairs of point charges.

00:44 So if we remember the way that we calculate the total electric potential energy is we just have to sum the individual potential energies of each pair of charges.

00:54 So if we go ahead and write that equation for just one pair of charges, we have this equation where we have k or constant, which we have the value down here.

01:07 And it's going to be times q times q prime, so the two charges, the two point charges that we're looking at, divided by the separation between them, that distance from one point charge to another.

01:20 So we have this equation that we can use to determine the potential energy of one pair.

01:26 But here, why don't we go ahead and list all the pairs that we actually have? so if we look at this first, we can see on this side where we have the bond of, we have this oxygen here.

01:41 So we're looking at two different bonds.

01:42 We have oxygen to the hydrogen.

01:47 And we also have hydrogen, excuse me, oxygen to the nitrogen.

01:59 So these are the two point charges that we're going to consider when we're looking at this bond between these two different.

02:06 Compounds.

02:07 So the next two pairs that we're going to be looking at is nitrogen to hydrogen, and then nitrogen to nitrogen.

02:25 So now that we have our four pairs listed, these are the electric potential energies that we're going to solve for.

02:32 What we need is we need the charge of each of these, and we need the distance between them.

02:39 So for the charge, we're simply going to use the charge of an electron, which is 1 .6 times 10 to the negative 19th couloms.

02:47 Since in a bond, we're just looking at valence electrons.

02:51 So we can consider this to be one valence electron per element here.

02:58 So what we have to do is we're given the distance between oxygen and nitrogen on this side and nitrogen to nitrogen on this side.

03:09 And we're also told that the distance from hydrogen to nitrogen in this bond here, and on this side over here, that distance is 0 .11 nanometers.

03:22 So we can solve for the distance from this hydrogen to this nitrogen, as well as this oxygen to this hydrogen, by simply subtracting this number from each of these two numbers listed on the graph here.

03:36 So we're going to go ahead and label these just so that we keep our numbers check.

03:45 So we'll call this bond one, bond two, bond three, and bond four.

03:53 So if we first calculate u1, we're looking at the oxygen to hydrogen, we go ahead and set up our equation.

04:06 So we're going to have a negative potential energy here because we're looking at unlike charges.

04:12 We're looking at opposite charges...

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