ABSTRACT
The resulting polymer is highly negatively charged as a result of the negatively charged phosphate groups between sugars. This large negative charge gives DNA its length-dependent charged character, which is not only useful for laboratory electrophoretic separation, but which also causes self-repulsion and provides unique electrostatic conditions within the nucleus. However, the structure of the DNA polymer is more complex than a self-repulsive negative polymer. For example, consider the deoxyribose sugar group has a five-carbon ring. Much like the boat-chair transition of six-ring molecules, four carbons are in plane and one carbon resides out of the plane of the molecule (Foloppe et al., 2001). This sugar “pucker” results in transitional states of the DNA in which the phosphate groups on either side of the pucker can be located at either 5.9 Å or 7.0 Å of one another at different equilibrium states (Chary et al., 1987). The 7 Å state is typically entropically and electrostatically preferred. High salt concentration and structural limitations imposed by the nitrogenous base pairing can alter the orientation of the sugar and overall DNA macromolecule as well as the higher-ordered structures of DNA, which we describe in more detail below. Additionally, the unique molecular structures of the four nitrogenous bases, adenine, guanine, cytosine, and thymine, are responsible for the overall DNA structure. The bases of course contain the genetic code for all organisms, as well as structural information for DNA conformation and stability. Pyrimidines (C and T) link via hydrogen bonding with purines (A and G) and pairs create steps within the DNA. AT-connections have two hydrogen bonds, whereas three hydrogen bonds bind the GC pairs. While it is nearly impossible to quantify the change in bonding energy of an individual base pair within a chain, the cooperative effect of several high-energy GC-pairs in a row significantly changes melting temperatures of the two strands. This greater melting temperature corresponds to the greater energy required for the double helix “unzipping,” which is performed by the helicase enzyme. Overall DNA shape and histone binding mechanics are also affected by GC content. For example, GC-rich regions force base pairs to stack into a planar structure within the DNA double helix (Dickerson, 1989). To compensate for this stacking, the entire backbone is slightly distorted. Additionally, GC-rich DNA is more likely to form the “A-DNA” structure, which is thicker and has a center hole, compared with “B-DNA,” which is
the “standard” double helix shape (Wahl and Sundaralingam, 1997). This structural alteration can further affect DNA doublestrand flexibility, especially under long-range curvature states.DNA can be structured as A-DNA, B-DNA, or Z-DNA. Z-DNA is a rare, left-handed form found at high salt concentrations, which alter the electrostatic repulsion (Leng, 1985). A-and B-DNA, the predominant forms, are right-handed helices that are 2.5 nm in diameter with 11 bp/turn. Major and minor grooves are formed from the double strands of DNA and allow for structural heterogeneity for protein binding along the genome. The double helix also provides for redundancy in the genetic code, allowing for proofreading during replication and repair against DNA damage since point mutations have incorrect pairing which leads to DNA destabilization (Kunkel and Erie, 2005). Unlike proteins, which rely on DNA to be properly made, in order for an organism to remain robust, it is critical that the genetic code remain unaltered despite insult from chemicals, radiation, etc. As such, having multiple mechanisms to maintain DNA’s fidelity is important for host survival and propagation. 3.1.2 DNA MechanicsThe one-dimensional mechanical measurements of DNA fall into different regimes based on the level of extensibility. For longer length scales, a majority of the DNA mechanical properties are defined by removal of entropic bends or undulations (i.e., pulling the DNA straight when it wants to explore a bent (more entropic) conformation). The length scale over which a molecule such as DNA is rigid before it bends is called the “persistence length,” B ,= EIk Tl (3.1)where E is the elastic modulus, I is the area moment of inertia and kBT is thermal energy (kB is Boltzmann’s constant and T is temperature). The expression of equation (3.1) may be viewed as the ratio between the product of a molecular structure’s capacity to sustain strain energy, E and its girth, I normalized by its natural propensity to explore a multitude of states, kBT. Note that the product of E and I is also commonly referred to as the bending
modulus, k = ΕΙ. For DNA, l = 53 ± 2 nm, which has been measured with many imaging modalities and physical manipulation (Hegner and Grange, 2002). Two biological factors related to the nucleosome fall out of the biophysics of DNA’s persistence length. While 50 nm is a short persistence length compared to other biological filaments, it is large compared to the length scales upon which DNA interacts within the nucleus. For example, DNA winds around histones, which are 10 nm in diameter. It is energetically unfavorable for DNA to mechanically bend around this 10 nm contour. However, the histone’s significant positive charge attracts the negatively charged DNA, thereby overcoming DNA’s resistance to bending. This interplay of mechanics and charge allows for unwrapping of DNA from histones when charges are locally screened, such as by complexes which remove DNA from histones during transcription (Montecino et al., 2007).At high strains or short length scales, DNA can also undergo other deformations such as extension, torsion, and torsion-stretch coupled extension. These deformation modalities are only significant after the DNA has been pre-strained to remove any entropic bends. However, these deformations are extremely important in calculating forces required for functional DNA processing which require molecular motors to produce extension and twist on DNA at the length scale of a few base pairs. DNA extension has been measured by microneedles, magnetic pull, fluid flow, and optical traps (Bustamante et al., 2000). Initial stretching of long DNA molecules measures entropic straightening of the molecule related to k. At these small deformations, DNA straightens with much less than 0.1 pN of force in a completely reversible way (Smith et al., 1992). At medium extensions (1 pN < force < 65 pN) DNA extends reversibly, even slightly beyond its predicted contour length. Thus, the unique structure of the double helix structure permits additional extensibility to the polymer. The stretch modulus (force/stretch) for this medium regime is greater than 1000 pN (Smith et al., 1996; Wang et al., 1997). Beyond 65 pN of applied force, DNA becomes “overstretched” and exhibits a hysteresis when relaxed, probably a function of lost double helix structure and related base-pair uncoupling (Storm and Nelson, 2003). Torsion and torsion-stretch have also been measured for the medium, reversible regime. To compare with the persistence lengths, moduli are normalized to kBT to produce effective lengths. Torsion length is 120 nm
and torsion-stretch length is much lower at 50 nm (Moroz and Nelson, 1997). The relatively soft torsion-stretch modulus, similar to bending, shows the benefit of combining twist with extension for a helical molecule. 3.1.3 DNA Assembly into Chromatin
DNA rarely exists as a single-double helix for any significant length scale in vivo. DNA winds around histones to package the nearly 1 m of DNA into the nucleus and allows modifiable access to regions of DNA for expression. The DNA-histone complex, called the nucleosome, contains a 10 nm histone octamer (made of core histone proteins H3, H4, H2A, and H2B) which is wound two-times by DNA (Richmond et al., 1984). The DNA sequences that bind to histones statistically show multiples of GC and (AA, TT or TA) (Anderson and Widom, 2001; Kaplan et al., 2009). This may be related to the mechanical character of bending that GC-content allows, but there is increasing evidence from bioinformatics that the DNA sequence is related to the probability of transcription (Segal et al., 2006).To quantify the mechanics associated with DNA wrapping onto histones, experiments have examined both association and dissociation. To measure association, DNA strands were exposed to flow fields in a solution that contained histone octamers. The flow field-induced force can be compared to the speed of the resulting decrease in DNA length as it coils. Thus, it is possible to approximate the force of DNA-association onto a nucleosome. Conversely, pulling on chromatin with an AFM or laser tweezers shows stochastic jumps associated with nucleosomes popping off of the chromatin structures.
