Alpha Helix Pitch and Rise: Videos & Practice Problems

The alpha helix structure features a pitch of 5.4 angstroms, indicating the distance per turn along its axis, with 3.6 amino acid residues per turn. The rise, calculated as the pitch divided by the number of residues, is 1.5 angstroms per residue. To find the length of an alpha helix, multiply the total number of amino acids by the rise. For example, with 52 residues, the length is $521.5=78$ angstroms.

Alpha Helix Pitch and Rise

In this video, we're going to talk about the alpha helix pitch and rise. So both the alpha helix pitch and rise are referring to a specific length or distance along the alpha helix axis. And so the alpha helix pitch is literally just the length or distance per turn along the alpha helix axis between adjacent corresponding points. And because the pitch is literally just the length or distance, it's measured in units of distance. And the pitch is literally equal to 5.4 angstroms, and angstroms is a unit of distance symbolized with the symbol shown here. And so down below in our example, you can see that 1 angstrom is equivalent to 10-10 meters. And because the pitch is literally the length or distance per turn, the pitch literally indicates one single turn of the alpha helix backbone. And in one single turn of the alpha helix backbone, there are 3.6 amino acid residues. And so taking a look down below at our example, you'll see we have a backbone and an alpha helix conformation. And you can tell because the backbone is coiling up and making these spiral like conformation where it's making these 360 degree rotations of the backbone. And so notice that the R groups of the backbone are completely excluded in this image, so that we can only focus on the backbone. And notice that this white pole that's going through the center here is the alpha helix axis. And so, literally, the pitch is a specific distance along the alpha helix axis that corresponds to one turn of the backbone. So you can see that the pitch is literally referring to the distance between these two adjacent corresponding points. And that's, essentially indicating one single turn of the backbone, which is 360 degrees of rotation of the backbone. And then in one turn, we know that there are 3.6 amino acid residues, as we indicated helix rise is also a specific length or distance along the alpha helix axis. But it's not the length or distance per turn. It's the length or distance covered per amino acid residue. And so in order to get the rise, which is the distance per amino acid residue, we take the pitch, which is the length along the axis per turn, divided by the number of residues and that will give us the rise. So essentially, if you take 5.4 and divide it by 3.6, you'll get the rise, which is 1.5. And so down below in our image, we can indicate that the rise is 1.5. And again, that's the distance between, or the distance covered along the axis for 1 amino acid residue. And because in one turn there are 360 degrees of rotation, and also in one turn there are 3.6 amino acid residues, so 3.6 residues. Essentially, if you take 360 and divide it by 3.6, you'll get an answer of 100 degrees, which says that there's 100 degrees of rotation of the backbone per residue. And that's exactly what this next point down here is saying, essentially that the alpha helix backbone turns 100 degrees per residue. And that's why we see that the rise is associated with 100 degrees of rotation of the backbone. And so, in our next lesson video, we'll talk about how we can use the alpha helix pitch and rise to calculate the length of an alpha helix. And so that concludes our lesson on the alpha helix pitch and rise, and I'll see you guys in our next video.

How many amino acid residues are needed for the α-helix backbone to obtain exactly one full periodic repeat?

• A. 1.5
• B. 3.6
• C. 5.4
• D. 18

Answer: (D)

Alpha Helix Pitch and Rise

So now that we know about the alpha helix pitch and the rise, we can talk about how to calculate the length of an alpha helix. The length of an alpha helix can actually be pretty easily calculated. All you really need to know is the total number of amino acid residues, and you need to be able to remember the alpha helix rise, which remember, is the length per residue and that's that small distance of just 1.5 angstroms.

Below, we have the equation for calculating the length of an alpha helix, and it's just going to be the total number of amino acid residues multiplied by the alpha helix rise, which again, is just 1.5 angstroms. In our example, it's asking us what the length of an alpha helix is. Let's say this is our alpha helix; basically, it's saying that from this point to this point over here, there are 52 amino acids. For the length, if we're calculating the length, all we need to know is the total number of amino acid residues in the alpha helix, which is 52. So, 52 amino acids, and we need to multiply this by our rise, and our rise is just 1.5 angstroms.

So if we type this into our calculator, 52×1.5, what comes out is 78 angstroms. This matches up with answer option D. We can go ahead, give D a check mark to indicate D is correct, and all our other ones here are incorrect, and we can cross them off. It's a pretty simple formula; take the number of residues, multiply it by the rise. So, we'll get some practice calculating the length of an alpha helix in our practice problems. So I'll see you in those videos.

Suppose a cell membrane is 45 Å thick & an embedded protein has 7 parallel transmembrane α-helical segments. Calculate the minimum # of aa-residues required for all 7 α-helical segments to traverse the membrane.

• A. 125 residues.
• B. 39 residues.
• C. 71 residues.
• D. 210 residues.

Answer: (D)

Hair is predominantly made of α-helix structures. Suppose hair grows at a rate of 20 cm/year. What is the rate at which amino acid residues are synthesized to account for the indicated growth of hair?

• A. 42 residues/sec
• B. 21 residues/sec
• C. 57 residues/sec
• D. 34 residues/sec

Answer: (A)

Here’s what students ask on this topic:

What is the pitch of an alpha helix and how is it measured?

The pitch of an alpha helix is the length or distance per turn along the alpha helix axis between adjacent corresponding points. It is measured in units of distance, specifically angstroms (Å). The pitch of an alpha helix is 5.4 Å, which means that for every complete 360-degree turn of the helix, the backbone advances 5.4 Å along the axis. This measurement helps in understanding the helical structure and spacing of amino acid residues within the helix.

How do you calculate the rise of an alpha helix?

The rise of an alpha helix is the distance covered along the helix axis per amino acid residue. It is calculated by dividing the pitch by the number of residues per turn. Given that the pitch is 5.4 Å and there are 3.6 residues per turn, the rise can be calculated as follows:

$\frac{5.4}{3.6}=1.5$ Å per residue.

This means that each amino acid residue advances the helix by 1.5 Å along its axis.

How can you calculate the length of an alpha helix?

To calculate the length of an alpha helix, you need to know the total number of amino acid residues and the rise per residue. The formula is:

$\mathrm{Length}=\mathrm{Number} \mathrm{of} \mathrm{residues} \times \mathrm{Rise}$

For example, if an alpha helix has 52 residues and the rise is 1.5 Å per residue, the length is:

$52 \times 1.5=78$ Å.

This simple multiplication gives you the total length of the alpha helix.

What is the significance of the 100 degrees of rotation per residue in an alpha helix?

The 100 degrees of rotation per residue in an alpha helix is significant because it describes the helical twist of the backbone. Since there are 360 degrees in a full turn and 3.6 residues per turn, each residue contributes:

$\frac{360}{3.6}=100$ degrees of rotation.

This rotational angle ensures the helical structure is maintained, allowing for the proper spatial arrangement of amino acids and the formation of hydrogen bonds that stabilize the helix.

How many amino acid residues are there per turn in an alpha helix?

In an alpha helix, there are 3.6 amino acid residues per turn. This means that for every complete 360-degree rotation of the helix, the backbone includes 3.6 residues. This specific number of residues per turn is crucial for the stability and geometry of the alpha helix, allowing for optimal hydrogen bonding and structural integrity.