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DNA Supercoiling, The linear double stranded DNAs that we have discussed so far in this class exists in a topologically relaxed, state. The active DNA inside a cell is not relaxed DNA, but instead is supercoiled. This topological state of, supercoiling is the next highest order level of DNA organization after the linear relaxed state., In order for a DNA molecule to be supercoiled, its must be in a closed loop, with the ends fixed. Closure is, achieved most often by joining the ends of an each DNA strand to form a circle. This, however is not the, only way to close a loop; in a eukaryotic chromosome, for example loops are formed by holding the ends on, a protein scaffold or by simply restricting the freedom of rotation of the ends of a long DNA molecule., What is super coiling., Picture a 420 bp piece of DNA duplex in the B-form., The number of helical turns in this linear DNA is 42, (42/10). Now we shall join the ends of this helix., This circular DNA is said to be relaxed (FIGURE, 44). Suppose now instead, we unwind the duplex by, six turns before we join the ends. The resulting DNA, can now fold into one of two different structures; one, that contains 36 turns of B-helix and an unwound, loop or alternatively, it can adopt a structure with 36, turns of B-helix and six turns of superhelix. The, unwinding is taken up by allowing the previously, unwound region to adopt the B-form and twisting the, circle into a superhelical form., This is the, supercoiled form. This structure is energetically, favored over the one containing the unwound loop, (WHY??)., Notice that the superhelical form, produced from unwinding the DNA is right-handed., This unwind produced, right-handed superhelix is, called negatively supercoiled. On the other hand,, superhelices formed by overwinding are left-handed, and are said to be positively supercoiled. MOST, DNA IN ORGANISMS IS FOUND TO BE, NEGATIVELY SUPERCOILED., Figure 44, , Supercoiling play an important role on many life, processes. For example, both the transcription of, genes and replication of DNA require it to be unwound. Thus, negatively supercoiled molecules (right, handed superhelices that result from joining underwound strands) are poised for these processes. In fact, several antibiotics have been developed that kill by inhibiting the enzymes that modulate the degree of, supercoiling in infectious organisms. We will briefly discuss these enzymes later., DNA Topology, In order to better understand the relationship between the degree of supercoiling, and twist, we turn again to, the mathematicians. An equation has been worked out to describe supercoiled DNA ribbons. The key, , 26

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topolgical property of a circular DNA is its LINKING NUMBER Lk . This quantity is defined as the, number of times one strand of DNA winds around the other in the right-handed direction (since we are, taking as our reference B-DNA). For the relaxed DNA shown in FIGURE 44), the linking number is 42,, for the one in C, the linking number is 36. The circles corresponding to the joining the ends of these two, molecules is 42 and 36 respectively. NOTICE, THE SIZE OF THE DNA DID NOT CHANGE,, HOWEVER THE LINKING NUMBER DID-CIRCLES OF THE SAME SIZE CAN HAVE DIFFERENT, Lk. Molecules which are identical in length, and differ only in linking number are topological isomers or, topoisomers. Moreover, since the end of a circle are fixed-THE LINKING NUMBER OF A CIRCULAR, DNA CANNOT BE CHANGED-IT IS A TOPOLOGICAL QUANTITY-A PROPERTY OF THE, CIRCULAR STATE. Since we are dealing with closed circles, the only way to form a circle is to match up, the ends. THEREFORE, THE LINKING NUMBER OF A CIRCLE MUST BE AN INTEGER. Moreover,, the only way to change the linking number of a circle (convert one topoisomer into another) is to CUT the, strands. The linking number of a topoisomer is constant., In a relaxed unstrained circle shown in FIGURE 44b, the linking number equals the twist (Tw). The twist is, defined as the number of 360 degree turns the ribbon makes as it goes around the circle. The twist of a, given topoisomer can differ, and can be non-integral, however, the linking number as we have said is, constant for a particular topoisomer and, moreover IT MUST BE AN INTERGER. Twist is a metrical, property and for DNA is limited within narrow bounds because B-form DNA does not stray very far from, having 10 bp/turn. Thus for DNA, Tw is usually very close the the # of bp/10. Since topoisomers can have, linking #'s that vary at least by two integers, as we have seen, these linking differences can be taken up by, the unwinding DNA or, superhelix formation. Because of the structural demands of DNA, the various, values of Lk a circle can have results not in changes in twist, but formation of superhelix. This super helix, formation is decribed by the term writhe (Wr). These three terms are obviously physically related as we, have described, and are related mathematically by the equation:, Lk = Tw + Wr, As we mentioned before, L must be and integer once the DNA is closed and thus Tw and Wr can adopt any, value, dependent upon the three dimensional shape of the DNA. For DNA, right handed twisting is positive, as is righthanded rotations for Lk, but for right handed superhelices, the sign of Wr is negative., Let's demonstrate how the concept of writhing (or superhelix formation) prevents the changes in DNA twist, from causing alterations in the structure of the double helix. If circular DNA is confined to a planar, arrangement, the changes in linking #, ∆Lk = ∆Tw + ∆Wr, can only be compensated for by equivalent changes in twist, because Wr is held at zero. In this case, ∆Tw, can be compensated for by smoothly modifying all helical turns, or since B-DNA likes to remain that way,, by disrupting a few base pairs. If, on the other hand Tw is unchanged, then ∆Tw is zero and thus, ∆Lk = ∆Wr, that is the change in linking number is transformed almost entirely into writhe. Thus in the example given, in FIGURE 44c & d, the DNA is twisted in a right handed sense (UNWINDING), i.e. REDUCTION of, Lk, and therefore the change in ∆Lk is compensated by righthanded motion superhelix formation, or negative, writhe., , 27

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As we said before, most DNA in vivo is negatively supercoiled. The degree to which a molecule is, supercoiled can be expressed as the specific linking difference or superhelical density. This quantity, gives a length independent measure of the number of supercoils per 10 base pairs. The formula:, σ = (L - Lo)/Lo, Lo is the linking number of the relaxed circular molecule and L linking number of the supercoiled molecule., For the DNA that is in the Figure, Lo is 25, L=23, thus σ= -.08. The superhelix density of DNA in cells is, between -.05 to -.09. That means, the DNA is negatively supercoiled (i.e. right handed superhelices, resulting from Unwinding)., Supercoiling and Hydrodynamics, The effect of circularizing a molecule, effectively halves the effective mean square, radius. Thus, the molecule appears smaller by, a number of experimental techniques, among, them gel electrophoresis and density gradient, centrifugation., Supercoiling a molecule, further compacts its shape. This compaction, is another reason why the DNA is a cell is, supercoiled-it compacts it., Intercalation means the insertion of a, planar molecule (e.g. other bases, drugs) base, between two others. This requires the spacing, between the two bases to increase. Several, dye molecules and antibiotic drugs insert, themselves between base pairs., These, Figure 45, intercalators are planar, aromatic molecules, which bind to the DNA by essentially becoming part of the base pair stack (FIGURE 45). Intercalative, binding is, therefore, characterized by high binding affinities., Intercalation changes the physical properties of the double helix. As the intercalator slides between the, bases, their normal stacking interactions are disrupted as they now stack with the drug. This separation of, the base pairs forces a severe distortion of the regular helical structure of the sugar phosphate backbone., Since the intercalation behaves nearly as an extra base pair, as the more intercalator is added, the greater is, the apparent length of the molecule. The separation of the base pairs causes them to UNWIND, in order to, accommodate the insertion., If we start out with negatively supercoiled DNA and add intercalator, we, further unwind the helix. In the case of ethidium bromide, the degree of, unwinding is -26o/molecule bound. Since we are not changing the linking, number of the plasmid, the changes in Tw are solely compensated for by, an increase in writhe. Recall that negatively s.c. DNA has negative writhe, so that an increase in Wr indicates that Wr-->0 as more intercalator is, added. As the Wr-->0, the DNA loses its compact shape and thus appears, "bigger" in gel or centrifugation experiments (FIGURE 47). At even, higher concentrations of intercalator, the Tw<Lk and thus, the Wr becomes, positive, with the opposite screw sense (Positive supercoils [+Wr], left, , 28, , Figure 47

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handed screw. This exercise illustrates the interrelation of these three quantities and the constraints imposed, on circle-i.e., the Lk never changes., For a change and much to your relief, the intercalation process does not cause a simple change in the back, bone configuration. The sugars of B-DNA appear to remain in the C2'endo family. The major changes in, the angles of the backbone occur at the phosphodiester linkages and at the χ-angle which now cause the, bases to become strictly perpendicular to the sugar., The enzymology of supercoiling, Inside of all cells there is a class of enzymes first discovered by Gellert and Wang in the early 1970's. These, enzymes called topoisomerases regulate the supercoiling of DNA in a cell. They are called this because, they can isomerize, one topoisomer (RECALL DEFINITION OF TOPOISOMER-DIFFERENT Lk) into, another. There are at least two kinds of topoisomerases, Topo I and Topo II., Topo I type topoisomerases relieve supercoiling, i.e., they relax supercoiled DNA. These enzymes do so, without the input of energy. They act by cutting one strand of the supercoiled double helix, rotating one, strand about the other and then reseal the strands. This reaction proceeds fueled only by the energy inherent, in supercoiled DNA. More about the inherent energy later, but there is an interesting enzyme mechanisms, question here, and that is how is the energy of the cleaved phosphodiester bond saved. Well it turns out that, the cleaved strand of the DNA forms a covalent bond to a tyrosine-the same type of high energy linkage, found in the phosphodiester backbone of DNA., Topo II type topoisomerases function to put supercoils into DNA. The enzyme gyrase required for DNA, replication is a type II topoisomerase. The introduction of supercoils into DNA requires the hydrolysis of, ATP. Topo II enzymes function by making double stranded breaks in the DNA and rotating one strand past, the other and rejoining them. SInce supercoiling is an active process, requiring energy in put, this indicates, that supercoiled DNA is a high energy form of DNA. In fact the ---- increases with the square of the, superhelix density., , 29