# Allowed Deviations in fixed bond length and bond angles in peptides from the typical values

I am using frag builder python module to generate peptide structures to compute the interaction energy for ensemble of peptides of a given sequence for a fixed bond lengths and bong angles. However, the fixed bond angles are slightly deviating from the typcial values seen in the literature. For instance, the bond angle of $$C_{\alpha}--N--C$$ is less than the typical value of 121 degrees and the bond angle of $$C_{\alpha}--N--C$$ as produced by frag builder is 111.7 degrees. Hence peptide plane is still planar. Yet the distance between the two successive $$C_{\alpha}--C_{\alpha}$$ is 3.721 A. Is it quite wrong to deviate by 10 degrees?

• I don't know "frag builder" protocol; can you please provide a citation? Building a conformer is relatively simple compared to subsequently energy minimizing it. Can you also hint at the size of the peptide, and what it's interacting with? The planarity of the peptide plane depends on how its moieties are H-bonding to other groups.
– Ryan
May 24 at 14:06
• @Ryan Fragbuilder article: ncbi.nlm.nih.gov/pmc/articles/PMC3961104 . Size of the peptide I am working on various sizes of peptides such as 6, 10, 18, and 34. The planarity of the peptide bond is unaffected. as it is still planar. May 25 at 11:52
• @Ryan Also, it is just interacting with itself in a vacuum. I am minimizing only van der Waal interactions and electrostatic interactions. I will extend this minimization with the solvation effect later. May 25 at 12:00

Single-conformation descriptions of the native-state ensemble, under ambient conditions, are expected to have close to ideal geometries. This is a result from Statistical Mechanics; the probability of non-ideal geometries (say a given conformer $$i$$ with internal energy $$E_i$$ compared to a native/ground-state energy $$E_0$$) scales with their Boltzmann factors, $$e^{-\beta (E_i - E_0)}$$. But many backbone dihedral angles are isoenergetic, especially outside of tertiary structural constraints.

FragBuilder has fairly extensive treatment allowing for rotamer sampling and conformer regularizing. I expect you used its built-in energy minimization with the MMFF94 force fields, as in (code quoted from 1):

pep = Peptide(sequence)
pep.regularize()
print pep.get_energy()


So the question can be rephrased, can the dihedral angles $$\phi$$ and $$\psi$$ be more than ten degrees from their ideal values? And the simple answer is yes. That's well within the variation of conformations within a given rotameric energetic minimum.

Here's one study looking at these dihedral angle fluctuations in solution. It cites the Dunbrack library. In that paper, they study the dependence of side chain dihedral angles on main chain ones, and they sample angles $$\phi$$ and $$\psi$$ in 10 degree bins showing that a large variation in these angles is possible, especially outside the context of regular secondary structures.

I wanted to cite a current paper from a sophisticated theoretician, so I found this from DJ Wales. Here they use a state of the art sampling approach to generate a tripeptide library, whose statistics are compared to experimental structures. You can read their procedure, but I'll quote the relevant part here:

For each tripeptide, the low-energy conformations contain many $$\phi$$, $$\psi$$ combinations, and the observed rotamers of the central amino acid are averaged over these backbone configurations, resulting in a backbone-independent library...Using tripeptide structures allows local spatial effects on rotamers to be probed without interference from stabilization in protein folds.