If you take a strand of DNA, it will tightly wrap around what are known as nucleosomes which consists of proteins that bind to DNA called histones. You need an octamer of histones to make a nucleosome that the DNA wraps around and is about 10 nanometers in diameter. This is where the analogy beads on a string comes into play because if you continue to wrap the DNA along nucleosomes, you form a solenoid structure of approximately 6 nucleosomes per turn, the DNA is now compacted into a chromere which is 30 nanometers in diameter and multiple chromeres stacked on each other form a chromatid fiber. The chromatid fiber is further coiled into loops of approximately 300 diameters which further compress by folding tightly to form chromatin that is approximately 700 diameters and is the result of the DNA being tightly packaged as mentioned above to form two sister chromatids that are bound together at the centromere and form a chromosome that is approximately 1400 nanometers in diameter. Keep in mind that the DNA can go back and forth from being tightly condensed or unpacked that occurs through various modifications of various lysine and arginine residues on histones which in a sense allows the DNA to unwind or condense. (Note: I think of the DNA as breathing in the unpacked state and exhaling in the condensed state as a metaphor to help me remember how it works. It doesn’t actually breathe, it’s just a helpful metaphor for me for clarity’s sake).
Here’s a diagram for reference. It helps to draw it out on paper.
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