Assuming that 145 base pairs of DNA wrap around the histone...

Assuming that 145 base pairs of DNA wrap around the histone octamer 1.75 times, estimate the radius of the histone octamer. Assume $3.4 \AA$ per base pair and simplify the calculation by assuming that the wrapping is in two rather than three dimensions and neglecting the thickness of the DNA.

Key Concepts

DNA Wrapping Around Protein Complexes

In the context of nucleosomes, DNA wraps around a histone octamer a specific number of times, which can be used to estimate the geometric properties of the core particle. By knowing how many times the DNA wraps and its length, one can derive the effective circumference—and thus the radius—of the histone core.

Circular Geometry and the Circumference-Radius Relationship

In geometry, the relationship between the circumference of a circle and its radius is given by the formula C = 2?r. This principle is critical when modeling biological structures as circles or arcs, such as approximating how DNA wraps around a histone octamer.

DNA Structural Properties

DNA has a well-defined structural property where each base pair contributes a specific length (approximately 3.4 Å) along the DNA strand. This property allows for converting the number of base pairs into a physical length, which is essential when estimating dimensions in molecular biology.

Transcript

00:01 So our question is talking about histones.

00:04 So before we kind of dive into how to solve this problem, let's just take a look at the purpose of histones.

00:12 So we know that histones are used and they're used to package chromosomal dna inside the nucleus of a cell.

00:27 And one important thing about the histones is they're positively charged proteins, and they help to strongly attach negatively charged dna.

00:39 We know our dna is negatively charged to attach it to this negatively charged dna.

00:46 And we form things called nucleosomes.

00:50 So now let's kind of take a look at it to what we're talking about.

00:57 We've got this structure, so this is actually dna, and then we have our histone octamer, which i'm just going to kind of draw a pie shape, and it actually is two -dimensional, well, three, but i'm just going to kind of give you an idea of what it looks like.

01:24 So this is supposed to be kind of 2d, not necessarily 3d, but 2d picture of our histone octamer.

01:35 And so once these combine, it actually looks like beads on a string.

01:53 So our octamer, histone octamer attached to our dna.

01:58 Remember, the dna has the negative charge and our histone has a positive charge.

02:03 It's going to look like beads on a string.

02:05 And so from our question, we can now look at our question.

02:09 Our question is telling us we have 145 base pairs.

02:14 And it says that the dna will wrap around the histone 1 .75 times.

02:28 Excuse me, 1 .75 times.

02:31 And we know that, so i'm just going to put the 1 .75 times up here so we remember...