Helices can be described by the notation nm, where n is the...

Helices can be described by the notation $n_{m}$, where $n$ is the number of residues per helical turn and $m$ is the number of atoms, including $\mathrm{H}$ in the ring that is closed by the hydrogen bond. (a) What is this notation for the $\alpha$ helix? (b) Is the $3_{10}$ helix steeper or shallower than the $\alpha$ helix?

Helices can be described by the notation $n_{m}$, where $n$ is the number of residues per helical turn and $m$ is the number of atoms, including $\mathrm{H}$ in the ring that is closed by the hydrogen bond.
(a) What is this notation for the $\alpha$ helix?
(b) Is the $3_{10}$ helix steeper or shallower than the $\alpha$ helix?

Key Concepts

Helical Notation

Helical notation is a systematic way to describe the conformation of a helical structure in polymers such as proteins. It is represented as n_m, where n indicates the number of residues per turn of the helix and m indicates the number of atoms (including hydrogen) that form the closed loop of atoms in the hydrogen-bonded ring. This notation helps in summarizing the geometric features of different helical conformations and their hydrogen bonding patterns.

Alpha Helix

The alpha helix is a common secondary structure in proteins characterized by a right-handed coil, in which the backbone N-H group of an amino acid forms a hydrogen bond with the C=O group of an amino acid that is four residues earlier. In the helical notation, the alpha helix has an average of about 3.6 residues per turn and forms a ring involving 13 atoms (including the hydrogen atom), making its notation 3.6_13.

3_10 Helix

The 3_10 helix is another type of helical secondary structure found in proteins, distinguished by a tighter hydrogen bonding pattern. In this helix, every residue has its N-H group hydrogen bonded to the C=O group three residues earlier, resulting in exactly 3 residues per turn and a 10-atom ring closure. This structural difference gives the 3_10 helix unique physical properties compared to the alpha helix.

Helical Steepness

Helical steepness refers to the longitudinal rise of the helix per residue and the overall 'vertical' progression of the helical structure. Because the 3_10 helix has fewer residues per turn compared to the alpha helix, it has a larger rise per residue, which results in a steeper helix. This means that for each residue, the 3_10 helix advances more along its central axis than the alpha helix, affecting its overall geometry and compactness.

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