Final answer:
The length of a 45-kDa single-stranded alpha-helical protein segment, assuming a mean residue mass of 110 Da, is approximately 613.66 Å or 61.4 nanometers, calculated by estimating the number of amino acid residues and the pitch of the helix.
Step-by-step explanation:
The alpha-helix structure is a type of secondary structure in proteins where the polypeptide chain coils into a helix, stabilized by hydrogen bonds. Given the information that our target protein has a mass of 45 kDa and the average residue mass is 110 Da, we can calculate the number of amino acid residues in the protein segment.
Firstly, the molecular mass of the protein (45 kDa) must be converted to daltons (45000 Da). Dividing this by the mean residue mass of 110 Da gives us:
45000 Da / 110 Da/residue = 409.09 residues
Since an alpha helix makes one turn for every 3.6 amino acids, we can estimate the number of turns in our protein segment:
409.09 residues / 3.6 residues/turn ≈ 113.64 turns
Lastly, assuming a pitch of 5.4 Å per turn (which is standard for an alpha helix), we can estimate the length of the helix:
113.64 turns * 5.4 Å/turn = 613.66 Å
Therefore, the length of a 45-kDa single-stranded α-helical protein segment is approximately 613.66 Å or 61.4 nanometers.