Biophysics problem - amino acid dipoles

[wfu113]

1. The dipole moment of a peptide bond is 3.7 Debye in water. Assuming that a hydrogen bond is essentially a dipole-dipole interaction, estimate the energy of a hydrogen bond between two peptides in water and in the interior of a protein (neglect the competing interactions with the solvent).

Homework Equations

$$_{}V_d_d = -2\left|\mu\right|^{}^2/D\left|r\right|^{}^3$$



3. The Debye part really confuses me. I tried plugging in 0.5 for the r value and using 1.23*10^-29 for the mu value. The D values are given as $$78.5\kappa\epsilon_{}_0$$ for water and $$3.5\kappa\epsilon_{}_0$$ for the interior of the protein. I feel like I'm almost there, but I don't quite have it. Please help! Thanks!

 

[Nate810]

Answer: The energy of a hydrogen bond between two peptides in water is calculated as follows: E_{}H_B = -2\left|\mu\right|^{}^2/D\left|r\right|^{}^3 = -2(1.23*10^{-29})^2/(78.5 * 8.85 * 10^{-12} * 0.5^3) = -9.32 * 10^{-21} J The energy of a hydrogen bond between two peptides in the interior of a protein is calculated as follows: E_{}H_B = -2\left|\mu\right|^{}^2/D\left|r\right|^{}^3 = -2(1.23*10^{-29})^2/(3.5 * 8.85 * 10^{-12} * 0.5^3) = -3.96 * 10^{-20} J

 

[Moetasim]

Dear student,

Thank you for your inquiry regarding the estimation of energy of a hydrogen bond between two peptides in water and in the interior of a protein based on the dipole moment of a peptide bond.

First, let's review the equation you have provided for the energy of a dipole-dipole interaction:

_{}V_d_d = -2\left|\mu\right|^{}^2/D\left|r\right|^{}^3

where V_d_d is the energy of the dipole-dipole interaction, \mu is the dipole moment, D is the dielectric constant, and r is the distance between the dipoles.

In order to use this equation to estimate the energy of a hydrogen bond, we need to make some assumptions. First, we can assume that the two peptide bonds are oriented in a way that maximizes the dipole-dipole interaction, which would be a head-to-tail orientation. We can also assume that the distance between the two peptide bonds is approximately equal to the length of a peptide bond, which is about 1.3 Å.

Now, let's plug in the given values for the dipole moment and the dielectric constant for water and the interior of the protein:

For water:
V_d_d = -2*(3.7 Debye)^2/(78.5*kappa*epsilon_0)*(1.3 Å)^3
= -0.0772 kcal/mol

For the interior of the protein:
V_d_d = -2*(3.7 Debye)^2/(3.5*kappa*epsilon_0)*(1.3 Å)^3
= -0.339 kcal/mol

Therefore, the estimated energy of a hydrogen bond between two peptides in water is approximately 0.0772 kcal/mol, while in the interior of a protein it is approximately 0.339 kcal/mol. Keep in mind that these are rough estimates and other factors such as the specific amino acid residues involved and the surrounding environment can affect the strength of the hydrogen bond.

I hope this helps clarify the confusion and provides a better understanding of the energy of hydrogen bonds in biophysics. Good luck with your studies!