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        <title>DNA topology with string</title>
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        <description>==Origin of the major and minor grooves== Hold strings parallel, look at grooves on both sides. Twist strings, the grooves are still there and still separate, just harder to follow. ==Linking number (Lk)== Hold your strings parallel with both hands and then with your right hand rotate the top of the string towards you, you are increasing the linking number. Rotate it away from you, you are decreasing the linking number. If you twist in the middle without letting the ends rotate, the linking number in the regions on either side of where you twist go in opposite directions, but the total linking number remains the same. ==Linking number in relaxed double stranded DNA== If you hang two pieces of string next to each other they don't wrap around each other. If you hang two complementary strands of DNA next to each other (under normal cellular conditions), they form a right handed helix with 10.5 bp per turn. From that point, if you twist the strands you are creating tension. Twist in a right handed manner and you are "overwinding" Twist in a left handed manner and you are "underwinding" ==Supercoiling== Twist your string together move ends closer together. The easiest thing for string to do is just unwind at the end. DNA can't do that because of friction with water against the extremely long tail keeps that from happening in Eukaryotes. It doesn't happen in prokaryotes because the chromosome is circular. For string, you're holding the ends, so it can't return to its relaxed state. Instead, it twists around itself (in the opposite directions to how you wound it). A positive super coil is left handed because it is caused by over-twisting in the right hand direction. A negative super coil is right handed because it is caused by over twisting in the left hand direction. If you just let one end hang, the free end twists to relieve tension. If the slack is in the middle rather than at the end it will twist in exactly the same way, but when it rotates in the middle it wraps around itself rather than rotating freely. ==Supercoiled DNA is compact== More supercoiling = more compact. Same for prokaryotes (circle) and eukaryotes (linear). Most cellular DNA has negative supercoiling. Decreasing Lk makes it more supercoiled (Lk gets further away from the relaxed state). Increasing Lk makes it less supercoiled (Lk gets closer to the relaxed state). Sometimes when you run a gel with DNA isolated from cells (for example plasmids from bacteria) you see multiple bands when you expect to see only one.  This is due to supercoiling. Remember, gels don't always separate DNA by strand length.  Only (short) linear DNA. ==Twist and Writhe== When you twist the free ends of string you are changing linking number by changing twist. When the coils of string wrap around each other positive (or negative) twist is being converted into writhe of the same sign (positive to positive, negative to negative) so that linking number is preserved. When you let the strings supercoil, the individual strands become less tightly wound around each other. Twist is being converted into writhe. Until you let the end rotate, Lk remains the same. When you let the end unwind, you are decreasing linking number. ==Type I Topoisomerase== It's not too difficult to see how this would work with string. If you cut one strand in the middle, you can increase Lk by wrapping it around the other strand in a right handed direction, and decrease Lk by wrapping it in a left handed direction. ==Type II Topoisomerase== We can't really simulate double strand breaks with string too easily. But we still see how this works. Make a loop in the string, then pass one end of the string under the other one. Make another loop (with the same handedness) and repeat. By making a loop with the other handedness you can change linking number in the opposite direction. When the strand that starts on top is pointing to the right, pulling it through will decrease linking number, when the strand that starts on top is pointing to the left, pulling it through will increase linking number. Try it with supercoils as well and notice how based on the natural writhe of the supercoil a type II topo would relieve it. ==Nucleosomes== Take two strings of different colors (easier to follow). Wrap the strings around a finger or a pen such that the colors alternate along the pen. Wrap without letting go of either end of the string. (Wrap in a 'left handed' manner, that is, make a left handed spiral on the pen). Notice that tension builds up on the non-wrapped parts of the string. Pull it off, Lk is the same (still zero) Wrap again, this time let the tension at the end be relieved.  Then take it off. ==Helicase== stick finger through string, push in one direction.  The string winds tighter in front, and less tight behind. Most Images from Lehninger Principles of Biochemistry 5th edition. Helicase from Wikipedia.</description>
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