PHYSICS AND DNA Advances in manipulating single DNA molecules are opening up new ways to study the micromachines that read, replicate and repair the double helix The micromechanics of DNA John F Marko and Simona Cocco ALL LIVING cells contain long DNA ab c d molecules that carry genetic informa- TRASBOURG tion in their base sequences. These mo- , S lecules must be read so that proteins NIVERSITY can be made, and they must also be U ASTEUR duplicated and separated from one P another so that cells can divide. Fur- ef g h OUIS thermore, if a cell’s DNA suffers dam- , L OIRIER age, it must be repaired. These essential P ICHAEL processes are carried out by enzymes – M proteins that catalyse biochemical re- 20 µm actions – that “walk” along the DNA The mechanics of life – the remarkable process of cell division is the result of the mechanical work done by double helix. So where does physics nano-scale proteins on gigantic DNA molecules. Parts (a) to (h) illustrate how the organization of a cell’s DNA come in? changes drastically as the cell grows and divides. Paired, replicated chromosomes that contain about 1 m of DNA gradually become visible as short strings (b) and (c), before the copies are segregated to the daughter This cellular machinery must be con- cells (e) and (f ). A large number of enzymes play a critical role in this process, exerting forces of about 1 nN on sidered from a biomechanical as well the chromosomes. These images are phase-contrast light micrographs of cells from a species of newt with as a biochemical point of view, and particularly large chromosomes. this requires us to understand the micromechanical properties of DNA 1 Single-molecule DNA experiment itself. Furthermore, since these DNA- processing machines operate at the chemical label receptor nanometre scale with energies that are receptor 16.3 µm λ–DNA molecule comparable to single thermal fluctu- ations, statistical mechanics is a key tool in analysing their behaviour. The com- chemical label single-stranded 3 µm bead bination of biochemistry with physical glass slide synthetic DNA concepts and instrumentation is lead- A large single molecule of double-stranded DNA can be manipulated by attaching short, single-stranded ing to new insights into how DNA is DNA molecules to each of its ends. Chemical labels on the ends of these single-stranded molecules are organized and processed inside cells. used to attach one end to a glass surface and the other to a microscopic “handle” such as a bead. Forces can then be applied to the DNA molecule by moving the bead. The resulting extension of the DNA Double-helix mechanics molecule can be measured by monitoring the position of the bead with a microscope. The double helix is just that: two nucleic-acid polymer chains that are wound around one missing, or damaged nucleotide, and they can therefore be another to form a regular, right-handed helix. Each indi- reconstructed from only one strand. This is the simple but vidual chain is a series of chemical units called nucleotides remarkable principle behind DNA replication and certain that are joined together by single covalent bonds. The four types of DNA repair. types of nucleotides, which contain the “bases” adenine (A), The two oppositely directed chains are bound together thymine (T), guanine (G) and cytosine (C), can be chained by hydrogen bonds and other physical interactions, which together in any order.The sugar–phosphate backbone of the generate a binding free energy of roughly kBT per base pair structure has a directed chemical structure, which means that under cellular conditions, where kB is Boltzmann’s constant the base sequence along a single chain has a defined direction and T is temperature. Double helices that are more than 30 (see figure 2 on page 32). base pairs long are therefore immune to separation by ther- However, the double helix is only stable if the two chains mal fluctuations, since fluctuations of more than 30kBT do carry complementary base sequences because the bases only not occur over reasonable timescales. However, because the bind together in two combinations: A–T and G–C. The dou- work that must be done to begin to separate the two strands is ble helices that are found in cells (called B-DNA) obey this only a few kBT, two strands can be taken apart gradually by constraint, apart from the occasional erroneously synthesized, enzymes without breaking the covalently bonded backbones. P HYSICS W ORLD M ARCH 2003 physicsweb.org 37 PHYSICS AND DNA At physiological temperatures, ther- 2 Applying forces to DNA ble helix (r = 1 nm) and B/kBT=50nm, mal motion deforms the base pairs and we find a Young’s modulus for DNA the backbones, causing successive bases of about 300 MPa – a value similar to to rock back and forth by a few degrees. 2 that of plexiglass. Later we will describe The highly soluble and charged sugar– 10 experimental confirmation that this ex- phosphate backbones tend to keep the E trapolation of elasticity down to the 1 double helix from sticking to itself in 10 D nanometre scale is reasonable. its aqueous environment, which makes long, linear DNA double helices behave C Experiments on single DNA molecules 100 B like flexible polymers. In the biochemist’s force (pN) In the early 1990s Steve Smith and test tube, long double helices have no A Carlos Bustamante of the University fixed shape but instead fluctuate between 10–1 of California at Berkeley and Laura different random-walk conformations. Finzi at the University of Milan made 10–2 a direct measurement of the elastic The persistence length 0 0.5 1.0 1.5 2.0 properties of single molecules of DNA. A lot can be learned about DNA by DNA extension/B-form length Their pioneering technique is based starting with simple physical ideas. The The mechanics of DNA can be studied by on powerful DNA “cut and paste” bending flexibility of the double helix, measuring the extent to which a single DNA methods from molecular biology, and molecule stretches relative to its normal B-form for example, can be thought of in terms length when a force is applied. Double-stranded is now being used in different ways by of the bending elasticity of a thin rod. DNA (green line) requires only about 0.1 pN to be many other groups. Classical elasticity tells us that a thin, stretched to half its B-form length (A), but by Smith and co-workers used λ-DNA, straight rod that is bent into an arc has a applying large forces it can be stretched by more which is the genome of a virus that 2 than 170 % (E). The plateau at about 60 pN (D) is bending energy E = Bl/2R , where B is due to over-stretching of the DNA. When both infects the bacterium E. coli. This 48 502 the bending elastic constant of the rod, strands of double-stranded DNA are anchored at base pair DNA molecule, which has a l is the length of the rod and R is the both ends (red line) this plateau is pushed up to contour length of 16.3µm, can be found about 100 pN because untwisting of the double radius of the arc. Setting R = l gives us helix is blocked. For single-stranded DNA (blue in an infected cell in both circular and the energy of a 1 radian bend along the line), a force is required to extend the strand linear form. The latter is simply the initially because it sticks to itself. The shorter rod, and solving for when E ~ kBT gives circular form after it has been cut at a persistence length of single-stranded DNA also us the length of rod along which a ther- means that it takes greater force to extend it to particular position along the molecule, mally excited bend of 1 radian typically half its B-form length than for double-stranded leaving single-stranded overhangs that occurs: l ~ B/kBT. This is called the per- DNA. Above 70 pN both double- and single- are 12 base pairs long (figure 1). It is sistence length, since over shorter con- stranded DNA are extended to roughly the same thought that chromosomes – the DNA– length, corresponding to almost full extension of tour lengths – lengths measured along the sugar–phosphate backbones. protein complexes in cell nuclei that the double helix – the double helix is carry the genes and transmit hereditary essentially straight. information – are organized into DNA The persistence length of the double helix is about 50 nm segments of about this length. This makes λ-DNA a good or 150 base pairs. However, quoting a single persistence starting point for analysing genetic machinery. length is a simplification because the flexibility of DNA de- Smith and co-workers attached a synthetic, 12 base pair pends on its base sequence: G–C base-paired regions are single-stranded molecule to each single-stranded overhang expected to be stiffer than A–T regions because they are more of the λ-DNA molecule. The base sequences of these addi- strongly bound. A further complication is that some se- tional strands were complementary to those of the λ-DNA quences are known to generate severe permanent bends overhangs, allowing the two to link together or “hybridize”. along the double helix, even in the absence of thermally Chemical labels were attached to the free ends of the two syn- excited bending. Despite this, the use of a single persistence thetic molecules, which were able to stick to receptor mole- length to represent the flexibility of the double helix is a cules (proteins) that could be attached to arbitrary surfaces.