3.1 The forces responsible for DNA stiffness are not understood

As predicted by the WLC model, DNA exhibits a profound local stiffness but global flexibility. Consequently, over nanometer length scales DNA is among the stiffest biopolymers. Why is DNA so stiff? Surprisingly, this simple question remains controversial. The most likely contributors to DNA stiffness are favorable base pair stacking interactions that contract the double helix (Fig. 3a) or mutual phosphate diester charge repulsions that expand it (Fig. 3b). At present, it remains disputed which of these two factors is the dominant contributor to DNA stiffness. It remains possible that each contributes significantly to a balance of forces explaining the unique stiffness of the DNA polymer.

Fig. 3.

Schematic illustration of concepts and experimental approaches to exploring the basis for DNA stiffness. DNA stiffness may involve compressive base pair stacking forces (a) and/or electrostatic stretching forces along the negatively charged sugar–phosphate backbone (b). See discussion of terms in text. (c) Asymmetric phosphate neutralization by targeted methylphosphonate substitution to measure induced DNA bending toward the neutralized helix face. (d) AFM study of apparent DNA stiffness on cationic surfaces. (e) Hemi-charged meroduplex model for measuring DNA stiffness when free bases stack onto a single helix without a second sugar–phosphate backbone.

The roles of local and long-range electrostatic effects in DNA structure and stiffness are not resolved. In his 1978 theory, Manning made predictions concerning residual DNA charge after counterion condensation (Manning, Reference Manning1978). In this model, the high negative charge density of DNA induces a concentrated layer of mobile and hydrated cationic counterions along the DNA surface. The extent to which this ‘condensed’ layer of counterions neutralizes DNA charge is governed by the valence of the counterions present in solution and, surprisingly, not by the bulk counterion concentration. The enthalpic attraction of the counterion to the DNA balances the entropic cost of localizing the ion even at very low bulk concentration. In particular, the parameter ξ governs counterion binding to DNA, and is defined as follows:

(46)

where e is the charge of an electron, ∊ is the bulk dielectric constant of the solvent, k _B is the Boltzmann constant, T is the absolute temperature, and b is the average axial charge spacing of the DNA. The quantity e ²/(∊k _BT)=ℓ_B is the Bjerrum length for the pure solvent, the separation distance at which the electrostatic interaction between two elementary charges (e) is comparable in magnitude to the thermal energy scale (k _BT). According to the theory, counterion condensation occurs when

(47)

where Z is the (unsigned) valence of the counterion. The saturated charge fraction r, that is, the fractional charge of DNA remaining after counterion condensation, in this theory is given by

(48)

It is important to restate this key result. Counterion condensation theory predicts that effective phosphate charge is controlled by counterion valence rather than concentration. Accordingly, DNA is predicted to carry some counterion-dependent residual charge that cannot be quenched by increasing bulk salt concentration. Although increased bulk salt may screen long-range interactions among phosphate charges, local electrostatic stretching interactions persist and make a constant local contribution to DNA stiffness for a given counterion. Manning theory predicts that monovalent cations neutralize ~76% of DNA phosphate charge, divalent cations ~88%, and trivalent cations ~92%. In short, Manning's counterion condensation theory predicts that DNA stiffness should depend on counterion valence because counterions of increasing valence should decrease the residual thermodynamic charge fraction on DNA and thus reduce the electrostatic contribution to DNA stiffness via phosphate screening. This trend has been observed in optical tweezers experiments where the persistence length was fit to force–extension data as a function of counterion valence. Decreasing DNA persistence length was observed for increasing counterion valence (Baumann et al. Reference Baumann, Smith, Bloomfield and Bustamante1997). Additionally, Schurr and co-workers have contributed considerably to the theoretical treatment of experimental polyelectrolyte effects (Fujimoto & Schurr, Reference Fujimoto and Schurr1990; Rangel et al. Reference Rangel, Fujimoto and Schurr2008; Schurr & Allison, Reference Schurr and Allison1981; Schurr & Fujimoto, Reference Schurr and Fujimoto2002), as recently reviewed (Schurr, Reference Schurr and Hud2009).

Manning counterion condensation theory also predicts favorable entropy for the binding of cationic molecules to DNA, which releases condensed counterions into bulk solution. This prediction has been studied in detail by Record and co-workers (deHaseth et al. Reference deHaseth, Lohman and Record1977; Lohman et al. Reference Lohman, Dehaseth and Record1980; Record et al. Reference Record, Dehaseth and Lohman1977, Reference Record, Anderson and Lohman1978).

Manning has recently expanded this analysis to address the contribution of phosphate charge to DNA stiffness (Manning, Reference Manning2006). In this model, bare DNA charge (not residual charge after condensation) produces an electrostatic stretching force (internal tension) on DNA due to phosphate–phosphate repulsions. To quantitatively investigate the effects of this force, Manning devised the notion of a ‘null’ isomer of DNA, the hypothetical structure that would be adopted by a DNA if its electrostatic charge were set to zero (without affecting solvation). This model for null DNA consists of fully charged DNA supplemented by an applied compression force that is equal but oppositely directed to the internal electrostatic tension present in charged DNA. The key result of this model is a prediction for the relationship between the DNA persistence length P and the persistence length of its null isomer P*. This prediction invokes quantities already identified as well as the Debye screening length for the solution, 1/κ, the separation distance beyond which charges are screened (the only term dependent on ionic strength), and the polymer radius, R:

(49)

Thus, through κ there exists a dependence of the persistence length of DNA on salt concentration. Although Eq. (49) has no adjustable parameters, it is shown to give a reasonable value and counterion dependence for P. A key result of this prediction is that the relationship between the bending persistence length of DNA and the persistence length of its null isomer is multiplicative, not additive. In contrast to other theories (Skolnick & Fixman, Reference Skolnick and Fixman1977) there is no ‘electrostatic persistence length’. That is to say, there is no additive electrostatic component. Importantly, the model quantitatively predicts how charge spacing (b) or its reciprocal (linear charge density) governs DNA persistence length. This prediction may be subject to experimental verification. For example, the charge dependence of DNA persistence length and the role of electrostatics in mediating DNA stiffness can be addressed by novel chemistries coupled with traditional assays of DNA stiffness.

Several other theoretical studies have explored whether charge should contribute significantly to DNA stiffness. Results have been mixed. While calculations of charge crowding in bent DNA suggested a strong electrostatic opposition to deformation (Hardwidge et al. Reference Hardwidge, Pang, Zimmerman, Vaghefi, Hogrefe, Maher, Stellwagen and Mohanty2009; Range et al. Reference Range, Mayaan, Maher and York2005), other analyses suggest negligible effects of DNA charge on stiffness under physiological conditions (Ariel & Andelman, Reference Ariel and Andelman2003; Guo et al. Reference Guo, Taubes, Oh, Maher and Mohanty2008; Nguyen & Shklovskii, Reference Nguyen and Shklovskii2002; Skolnick & Fixman, Reference Skolnick and Fixman1977).

There is experimental evidence that DNA shape depends on charge balance (Williams & Maher, Reference Williams and Maher2000). Both theoretical and experimental investigations of asymmetric charge neutralization have been conducted (Kosikov et al. Reference Kosikov, Gorin, Lu, Olson and Manning2002; Manning et al. Reference Manning, Ebralidse, Mirzabekov and Rich1989; Okonogi et al. Reference Okonogi, Alley, Harwood, Hopkins and Robinson2002; Rouzina & Bloomfield, Reference Rouzina and Bloomfield1998). DNAs with one helical face partially modified by incorporation of neutral phosphate analogues have been created (Fig. 3c). These modified DNAs are spontaneously deformed toward the neutralized surface, as would be predicted from Manning electrostatic theory (Strauss & Maher, Reference Strauss and Maher1994). Moreover, in an X-ray crystallography experiment involving tethering of cations (directed radially outward) in the major groove of DNA, it was demonstrated that the bound cations interacted electrostatically with the DNA to induce collapse of the major groove around the bound cations (Moulaei et al. Reference Moulaei, Maehigashi, Lountos, Komeda, Watkins, Stone, Marky, Li, Gold and Williams2005). Crucially, no other apparent structural changes were induced by the bound cations, suggesting that the tethered cations mediated their effect through electrostatics and did not disrupt base stacking. Thus, both phosphate neutralization and cation adduction induce spontaneous DNA bending (Williams & Maher, Reference Williams and Maher2000), and they may cause DNA bending through a common mechanism.

More recently, experiments using AFM of DNA deposited on mica coated with positively charged molecules suggest that surfaces with increasing positive charge densities increase the flexibility of DNA (Podesta et al. Reference Podesta, Imperadori, Colnaghi, Finzi, Milani and Dunlap2004, Reference Podesta, Indrieri, Brogioli, Manning, Milani, Guerra, Finzi and Dunlap2005) (Fig. 3d). Additions of divalent and multivalent cations known to more completely neutralize the phosphate backbone with the potential to condense duplex DNA (Bloomfield, Reference Bloomfield1997; Gosule & Schellman, Reference Gosule and Schellman1978; Hud et al. Reference Hud, Downing and Balhorn1995) enhance the rotational dynamics of DNA, as evidenced by rotational correlation times from steady-state fluorescence anisotropy experiments (Noothi et al. Reference Noothi, Kombrabail, Kundu, Krishnamoorthy and Rao2009). Furthermore, studies have shown that DNA is more compact when complexed with an oppositely charged amphiphile in organic solvent (Sergeyev et al. Reference Sergeyev, Pyshkina, Lezov, Mel'nikov, Ryumtsev, Zezin and Kabanov1999). The hypothesis is that DNA in a DNA–surfactant complex behaves as though it was electrically neutralized and, as a result of enhanced flexibility, assumes a more compact state. These studies suggest dominant effects of DNA charge in modulating DNA flexibility and shape.

Fueling the controversy, there is experimental evidence that DNA stiffness is dominated by base stacking rather than charge repulsion. TEB has been extensively developed to access DNA flexibility via persistence length, as it relates to base pair stacking (Hagerman & Hagerman, Reference Hagerman and Hagerman1996; Hagerman, Reference Hagerman1981; Mills et al. Reference Mills, Vacano and Hagerman1999; Vacano & Hagerman, Reference Vacano and Hagerman1997). In particular, TEB was utilized to explore the flexibility of the so-called ‘meroduplex’, an unstructured single-stranded polypyrimidine that attains duplex character upon addition of excess free purine base (Hagerman & Hagerman, Reference Hagerman and Hagerman1996) (Fig. 3E). A variant of the meroduplex was created with ~20 nucleotides of meroduplex flanked by double-stranded DNA at either end. This ‘gapped’ meroduplex was shown to be much more flexible than the equivalent full duplex, but upon addition of free N ⁶-methyladenine the flexibility became essentially indistinguishable from that of the full duplex, suggesting that base pair stacking is the dominant contributor to DNA stiffness (Mills & Hagerman, Reference Mills and Hagerman2004). There is also evidence that sequence-dependent differences in base stacking forces can measurably influence DNA persistence length (Caserta et al. Reference Caserta, Agricola, Churcher, Hiriart, Verdone, Di Mauro and Travers2009; Protozanova et al. Reference Protozanova, Yakovchuk and Frank-Kamenetskii2004; SantaLucia, Reference Santalucia1998; Virstedt et al. Reference Virstedt, Berge, Henderson, Waring and Travers2004). However, the scale of these stacking effects has never been experimentally compared with electrostatic effects.

Thus, the force (or, likely, balance of forces) responsible for the bending stiffness of DNA remains unresolved. The issue remains of fundamental importance for at least three reasons. First, understanding the forces responsible for DNA stiffness might allow engineering of DNA-like polymers with altered stiffness properties that could be helpful in the creation of novel nanomaterials. Second, such an understanding would illuminate the mechanism responsible for eukaryotic DNA compaction by histone octamers in chromatin. Third, this understanding may suggest design principles for artificial DNA-bending proteins and devices.

4.1 Challenges to the WLC model

T4 DNA-ligase-mediated cyclization studies by Cloutier & Widom (Reference Cloutier and Widom2004, Reference Cloutier and Widom2005) suggested that ~100 bp DNA fragments formed circles at rates 3–5 orders of magnitude faster than predicted by the WLC model (Fig. 4a). In order to explain these unexpected findings, both theoreticians and experimentalists invoked the notion of DNA kinking (local base pair unstacking). Kinking of the DNA duplex would allow unusually large local bend angles as a possible means to explain these findings. DNA kinking is not a new idea. In 1975, Klug and Crick proposed that the energetic cost of forming small circles or loops could be reduced if DNA were to kink rather than uniformly distort (bend) throughout a looping region (Crick & Klug, Reference Crick and Klug1975). Later, experimental evidence for DNA kinking came from the nucleosome, in which a persistence length of DNA is wound nearly twice around a histone octamer (Hogan et al. Reference Hogan, Rooney and Austin1987; Luger et al. Reference Luger, Mader, Richmond, Sargent and Richmond1997). From the high-resolution nucleosome crystal structures it was shown that six of twelve 5′-CA-3′ steps exhibit kinking to narrow the minor groove toward the histone octamer, whereas the remainder of DNA bending in the nucleosome occurs smoothly without kinking (Richmond & Davey, Reference Richmond and Davey2003). The other preferred base step for kinking was 5′-TA-3′, which also exhibits low base stacking energy (Fig. 4b).

Fig. 4.

Controversy surrounding a report of spontaneous sharp bending of double-stranded DNA. (a) Data are taken from Shore & Baldwin (Reference Shore and Baldwin1983) (times signs), Taylor & Hagerman (Reference Taylor and Hagerman1990) (plus signs), Vologodskaia & Vologodskii (Reference Vologodskaia and Vologodskii2002) (open circles), and Rueter & Maher (unpublished results) (stars). Contrasting experimental findings for j-factors of short DNAs by ligase-catalyzed DNA cyclization kinetics where solid black symbols correspond to the data of Cloutier & Widom (Reference Cloutier and Widom2004) and asterisks correspond to the data of Du et al. (Reference Du, Smith, Shiffeldrim, Vologodskaia and Vologodskii2005) collected with particular attention to required assay assumptions (inset). Squares, circles, and triangles reflect data from the Widom group for different sequences. Both datasets have been modeled here using a DNA helical repeat of 10·54 bp/turn and a torsional rigidity of 2·4×10⁻¹⁹ erg cm. Best fits for the DNA persistence length are 31 nm (data of Cloutier and Widom) or 46·5 nm (data of Du et al.). (b) DNA kink that unstacks base pairs and widens the minor groove induced upon strong DNA bending in the X-ray crystal structure of the E. coli catabolite activator protein (Schultz et al. Reference Schultz, Shields and Steitz1991). (c) DNA kink that widens the major groove predicted from the MD simulations of strained DNA circles by Lankas et al. (Reference Lankas, Lavery and Maddocks2006).

Theorists therefore proposed alternative kink-prone models for DNA flexibility. These models suggested the transient appearance of localized weakly stacked segments in the DNA that might be prone to kinking. Such kinks might preserve base pairing but not base stacking, and be accompanied by ‘bubbling’ (local base unpairing to create a flexible hinge), base pair opening (disruption of both base pairing and stacking), or base flipping (where only a flipped base has disrupted base pairing and stacking). Two such models, the kinked WLC (KWLC) model and the single-stranded bubble model, both propose local distortions that could strongly enhance bending and bidirectional torsional flexibility (Wiggins et al. Reference Wiggins, Phillips and Nelson2005; Yan & Marko, Reference Yan and Marko2004). Consideration of the importance of short DNA loops in gene regulation, particularly in bacteria, also prompted models in which short DNA loops readily form with spontaneous kinking to relieve elastic strain, or alternatively that accessory kinking proteins facilitate such loops. At the same time a model including more microscopic detail to supplement the WLC model was shown to predict enhanced apparent flexibility of short DNAs, due to intrinsically curved sequences, without the necessity of kinks (Czapla et al. Reference Czapla, Swigon and Olson2006).

Computationally intense all-atom molecular dynamics (MD) simulations were also applied to determine if kinking could be justified as an explanation for the Cloutier and Widom result. Lankas and co-workers in 2006 predicted the formation of DNA kinks in 94 bp DNA circles, modeled both with and without torsional strain (Lankas et al. Reference Lankas, Lavery and Maddocks2006; Maher, Reference Maher2006) (Fig. 4c). Interestingly, the kinks most commonly occurred at 5′-CG-3′ steps rather than the predicted 5′-TA-3′ and 5′-CA-3′ steps. This simulation again suggested that kinks might be an inherent DNA response to strong bending and twisting strain. More modeling of DNA kinks ensued (Ghatak & Das, Reference Ghatak and Das2007; Popov & Tkachenko, Reference Popov and Tkachenko2005; Randall et al. Reference Randall, Zechiedrich and Pettitt2009). Results of these studies indicated that severe DNA distortions, such as the formation of circles smaller than ~85 bp in length, may require alteration of the WLC model to include sharp bending or kinking of DNA.

Controversy has continued in experiments based on AFM and SAXS. Results of some AFM experiments were interpreted as being consistent with unexpectedly flexible DNA (Wiggins et al. Reference Wiggins, Van Der Heijden, Moreno-Herrero, Spakowitz, Phillips, Widom, Dekker and Nelson2006), while others agreed well with standard persistence lengths (Witz et al. Reference Witz, Rechendorff, Adamcik and Dietler2008). Recent SAXS data examining the equilibrium end-to-end distance distributions of short DNA fragments with gold nanocrystal labels again challenged the WLC model at short DNA lengths (Mathew-Fenn et al. Reference Mathew-Fenn, Das and Harbury2008). In this work, the authors reported that stretching fluctuations were much larger than expected from WLC predictions, and that stretching was correlated over at least two turns of the DNA double helix. This interpretation suggested new flexibility regimes for DNA beyond WLC predictions. There have been further Technical Comments challenging and defending this work in the same journal.

4.2 The WLC model fights back

Amidst the flurry of theoretical and experimental work seeking support for new kink-prone models for DNA flexibility, there was renewed support for the applicability of the WLC model to sub-persistence length DNA. Vologodskii and co-workers revisited cyclization experiments of DNA fragments 105–130 bp in length and demonstrated that the WLC model remains adequate for predicting the cyclization probabilities of these fragments when assumptions of the assay are scrupulously met (Du et al. Reference Du, Smith, Shiffeldrim, Vologodskaia and Vologodskii2005). Their experimental study reported a technical flaw explaining the unusually high cyclization probabilities observed by Cloutier and Widom. Because cyclization becomes an increasingly rare event for short, stiff DNAs at low ligase concentration, addition of increasing ligase had been necessary. However, the requirement that formation of both circular and bimolecular ligation products is proportional to ligase concentration (Eq. (24) above) had not been substantiated for the dimerization reaction under the necessarily high T4 DNA ligase concentrations of the Cloutier and Widom study (Cloutier & Widom, Reference Cloutier and Widom2004). Du et al. showed that the rate of dimerization lacked a dependence on ligase concentration beyond a threshold value (~100 units/ml for their particular cohesive ends) (Du et al. Reference Du, Smith, Shiffeldrim, Vologodskaia and Vologodskii2005). Under conditions where assumptions of the fitting model could be shown to be valid, the WLC chain faithfully predicted the measured values of the j-factor from ligation experiments. Du et al. went on to perform experiments with DNA minicircles under high bending strain (but no twisting strain) using nuclease attack to detect kinks in continuous or gapped control DNAs (Du et al. Reference Du, Kotlyar and Vologodskii2008). Minicircles as small as 85 bp in length resisted kinking or other apparent bending deformations unless torsionally strained. Additionally, recent cryo-EM experiments with the exact sequences studied by Cloutier and Widom suggest that circle formation occurs through smooth bending without DNA kinks (Demurtas et al. Reference Demurtas, Amzallag, Rawdon, Maddocks, Dubochet and Stasiak2009). These results suggest that the WLC model is applicable to DNA lengths down to 85 bp.

Likewise, recent analysis of more extensive SAXS experiments led Mastroianni et al. to conclude that when care is taken to model DNA–gold linkages and to study a broad range of DNA lengths, the WLC model (with a conventional 50 nm persistence length estimate) is completely sufficient to explain the SAXS data (Mastroianni et al. Reference Mastroianni, Sivak, Geissler and Alivisatos2009). This study considers sequence and salt effects, reporting that they contribute negligibly to the conclusions. Monte Carlo simulation is combined with experimentation to carefully consider the implications of non-linear elasticity versus the classical WLC model. The authors find that the WLC model can adequately describe conformational fluctuations of double-stranded DNA in the range of 1/3 to 2/3 of one persistence length.

Thus, although recent high-profile cyclization and SAXS studies raised the provocative possibility that DNA molecules on the length scale of the persistence length (~150 bp) are unexpectedly flexible, both the cyclization and SAXS studies have been contradicted by subsequent clarifying experiments. The subject remains intriguing, controversial, and important. This is because the true character of local DNA behavior determines the energetics of nucleosome positioning, DNA looping, and transcriptional regulation.

5.1 Sequence dependence of DNA curvature

One of the first observations suggesting sequence-dependent DNA curvature was anomalously slow electrophoretic mobility through native polyacrylamide gels for certain DNA molecules. A noteworthy example was a segment of protozoan kinetoplast DNA, part of a natural DNA minicircle chromosome. Sequence analysis and subsequent clever gel assays revealed that A_4–6 tracts phased with the DNA helical repeat are responsible for the observed mobility effects (Hagerman, Reference Hagerman1985; Koo et al. Reference Koo, Wu and Crothers1986; Wu & Crothers, Reference Wu and Crothers1984). This result emphasized a challenging puzzle: what is it about phased A-tracts that causes a gel mobility anomaly? Are the sequences intrinsically curved or anisotropically flexible? Exactly what sub-sequences have the unusual property (the A-tracts or the intervening ‘non-A’-tracts)? What is the molecular basis for the anomaly? Why do phased 5′-A₄T₄-3′ sequences induce curvature, while 5′-T₄A₄-3′ sequences do not?

Work in this area led to classical models of DNA curvature that invoked either virtual wedges in dinucleotide stacks (Bolshoy et al. Reference Bolshoy, Mcnamara, Harrington and Trifonov1991; Cacchione et al. Reference Cacchione, De Santis, Foti, Palleschi and Savino1989; Calladine et al. Reference Calladine, Drew and Mccall1988) or helical axis deformation at junctions between different double-helical forms (Crothers et al. Reference Crothers, Haran and Nadeau1990; Koo & Crothers, Reference Koo and Crothers1988; Koo et al. Reference Koo, Wu and Crothers1986, Reference Koo, Drak, Rice and Crothers1990; Nadeau & Crothers, Reference Nadeau and Crothers1989). The concept of DNA curvature at such junctions had been predicted earlier (Selsing et al. Reference Selsing, Wells, Alden and Arnott1979). The development of these classic models (reviewed by Hagerman, Reference Hagerman1985, Reference Hagerman1990, Reference Hagerman1992) and recent approaches to predict DNA curvature are addressed in the next section. Discussion here will focus on the possible physical basis for sequence-dependent DNA curvature. It is important to note that all of these models were essentially empirical, assigning microscopic properties to junctions or wedges that would explain the experimental data.

5.2 Electrostatic effects in DNA curvature and flexibility

It is evident that different DNA sequences commonly adopt polymorphic geometries in solution over the range of B, B*, and A double helices. Is this polymorphism due only to base pair stacking preferences, or could counterions play a role (Williams & Maher, Reference Williams and Maher2000)? The role of counterions in controlling DNA structure is not understood. As described in section 3 (above), Manning's influential counterion condensation theory expresses the notion that highly charged polyelectrolytes, such as DNA, essentially condense counterions from the diffuse bathing solution into a layer of ~1 M local concentration near the polymer surface (Manning, Reference Manning1978). The concentration of this condensed counterion ‘phase’ is predicted to be essentially independent of the bulk counterion concentration. Substantial (but not complete) polyelectrolyte charge screening accompanies counterion condensation, but the magnitude of stretching forces between residual unscreened nearest-neighbor phosphate anion charges along DNA remains poorly understood. Furthermore, NMR experiments have detected counterion distributions that are asymmetric and sequence dependent (Hud & Feigon, Reference Hud and Feigon1997, Reference Hud and Feigon2002; Hud et al. Reference Hud, Schultze and Feigon1998, Reference Hud, Sklenar and Feigon1999). Related results have been observed using X-ray crystallography (Hamelberg et al. Reference Hamelberg, Mcfail-Isom, Williams and Wilson2000, Reference Hamelberg, Williams and Wilson2001; Howerton et al. Reference Howerton, Sines, Vanderveer and Williams2001; McFail-Isom et al. Reference Mcfail-Isom, Sines and Williams1999; Shui et al. Reference Shui, Mcfail-Isom, Hu and Williams1998a, Reference Shui, Sines, Mcfail-Isom, Vanderveer and Williamsb; Sines et al. Reference Sines, Mcfail-Isom, Howerton, Vanderveer and Williams2000; Williams & Maher, Reference Williams and Maher2000), free electrophoresis (Dong et al. Reference Dong, Stellwagen and Stellwagen2009; Lu & Stellwagen, Reference Lu and Stellwagen2008; Stellwagen et al. Reference Stellwagen, Magnusdottir, Gelfi and Righetti2001), and simulation (Beveridge et al. Reference Beveridge, Young, Sprous, Leontis and Santa Lucia1998; McConnell & Beveridge, Reference Mcconnell and Beveridge2000; Sprous et al. Reference Sprous, Young and Beveridge1998; Young & Beveridge, Reference Young and Beveridge1998; Young et al. Reference Young, Jayaram and Beveridge1997a, Reference Young, Ravishanker and Beveridgeb). This has raised stimulating discussion about the degree to which sequence-dependent asymmetric counterion recruitment into the DNA grooves could alter groove geometry and cause double-helix polymorphism by unbalancing charge repulsions across the groove (McConnell & Beveridge, Reference Mcconnell and Beveridge2000; McFail-Isom et al. Reference Mcfail-Isom, Sines and Williams1999; Williams & Maher, Reference Williams and Maher2000) or across the double helix (Strauss & Maher, Reference Strauss and Maher1994).

These interesting results suggest strong correlations between asymmetry in cation localization, DNA groove geometry, and DNA curvature. However, the cause/effect role of counterion distribution remains both unknown and controversial. Does the asymmetry in counterion distribution arise because preferred cation binding sites are specified by the sequence of base pair edges? Do these cation distributions then exert electrostatic forces that restructure DNA by asymmetrically neutralizing interphosphate stretching forces? Is polymorphism in groove geometry driven by base pair stacking, and counterions simply decorate these sequence-dependent features without influence on DNA structure? These fundamental questions remain unresolved, even in MD simulations.

An important contribution to unifying the concepts of ion distributions, helical polymorphisms, and sequence-dependent DNA curvature has been formulated by Hud and co-workers (Hud & Plavec, Reference Hud and Plavec2003; Hud & Polak, Reference Hud and Polak2001). The revised junction model of Hud and Plavec invokes the correlation between groove polymorphism and counterion localization. The authors conceive of DNA sequences as participating in structural equilibria between different double-helical forms. In particular, they categorize DNA sequences into three groups (A-tracts, G-tracts, and generic DNA) with different equilibrium distributions between B, B*, and A forms (Fig. 5). According to this model, the A-tract group of sequences (length >4, AA, TT, or AT base steps with no TA steps) is more likely to adopt the B*-form with a narrow minor groove rich in counterions. G-tracts are defined as containing only G and C residues with prominent GG steps. These sequences are argued to be more likely to sample the A-DNA conformation featuring a narrow major groove rich in counterions. All other DNA sequences are considered ‘generic’ and most likely to assume B-form. The Hud–Plavec model then proposes a junction explanation for helix curvature. Simple conservation of base stacking between DNA segments with different helical forms alters the helix axis. The phasing of such junctions relative to the DNA helical repeat determines the global curvature of a DNA sequence. The Hud–Plavec model adds coherence to the interpretation of sequence-directed DNA curvature without resolving the cause/effect puzzle of cations and groove geometry.

Fig. 5.

Schematic depiction of the Hud–Plavec model linking counterion distributions, helix polymorphism, and sequence-directed DNA curvature at junctions. (I) Proposed sequence-dependent duplex DNA polymorphism between generic DNA (canonical B-form, center), G-tract sequences (propensity for A-form, left), and A-tract sequences (B*-form, right). Grooves (M, major; m, minor) and simplified cation (+) distributions (magenta) are shown. (II) Example of sequence-dependent DNA curvature due to junctions between B-form DNA and a 5 bp segment of A-form DNA (red). Helical structures were generated with 3DNA (Zheng et al. Reference Zheng, Lu and Olson2009). DNA backbones are shown in yellow.

5.3 Sequence dependence of DNA flexibility

DNA conformation has been shown to be sequence dependent. In fact, local DNA deformability (softness) with respect to bending and twisting is also sequence dependent. It remains unknown how sequence-dependent anisotropic deformability influences anomalous gel mobility. Protein recognition of DNA depends on the initial DNA structure (including groove shape and curvature). For protein–DNA complexes involving distorted DNA, the stability of the complex depends on the sequence-dependent pliability of the double helix. An early study suggested that the DNA persistence length could vary 4-fold between the relatively flexible poly(dA)•poly(dT) and the relatively rigid poly(dG)•poly(dC), and the torsional DNA stiffness could vary at least 40-fold (Hogan et al. Reference Hogan, Legrange and Austin1983). Subsequent work has explored relationships between stacking energy, thermal stability, and persistence length (Protozanova et al. Reference Protozanova, Yakovchuk and Frank-Kamenetskii2004; SantaLucia, Reference Santalucia1998; Sivolob & Khrapunov, Reference Sivolob and Khrapunov1995; Virstedt et al. Reference Virstedt, Berge, Henderson, Waring and Travers2004).

As will be discussed in greater detail below, packaging of eukaryotic DNA onto histone octamers in nucleosomes involves substantial DNA deformation. DNA sequences can be characterized or selected for their histone octamer affinity, thus presumably measuring flexibility rather than curvature (Lowary & Widom, Reference Lowary and Widom1998). Sequences with a high proclivity for nucleosome formation were shown by DNA cyclization analysis to have 2-fold increased longitudinal flexibility and one-third lower torsional constants (Roychoudhury et al. Reference Roychoudhury, Sitlani, Lapham and Crothers2000). Among such sequences, the flexibility of alternating A–T was one-third higher than mixed sequences (Zhang & Crothers, Reference Zhang and Crothers2003). Analysis of nucleosome positioning in genomic DNA has proven to be a fertile approach to deducing apparent sequence requirements for flexibility (Caserta et al. Reference Caserta, Agricola, Churcher, Hiriart, Verdone, Di Mauro and Travers2009; Drew & Travers, Reference Drew and Travers1985; Kaplan et al. Reference Kaplan, Moore, Fondufe-Mittendorf, Gossett, Tillo, Field, Leproust, Hughes, Lieb, Widom and Segal2009; Satchwell et al. Reference Satchwell, Drew and Travers1986; Segal et al. Reference Segal, Fondufe-Mittendorf, Chen, Thastrom, Field, Moore, Wang and Widom2006; Trifonov & Sussman, Reference Trifonov and Sussman1980; Widom, Reference Widom2001). To a first approximation, sequences favored for deformation in nucleosomes are over-populated by AA/TT/TA dinucleotides phased with the DNA helical repeat (i.e. occurring at intervals of ~10 bp), with GC dinucleotide steps phased 5 bp away. Such sequences appear not to be intrinsically curved, but anisotropically flexible (Lowary & Widom, Reference Lowary and Widom1997, Reference Lowary and Widom1998; Segal et al. Reference Segal, Fondufe-Mittendorf, Chen, Thastrom, Field, Moore, Wang and Widom2006). It should be noted, however, that it remains formally possible that the phased AA/TT/TA pattern favored in nucleosomal DNA is not predominantly due to enhanced bend flexibility. Instead, this sequence signature could endow the DNA with a particularly narrow minor groove that enhances local negative electrical potential in the groove, stabilizing histone binding by strengthening electrostatic contacts with protruding cationic arginines that engage the DNA minor groove at these positions (Rohs et al. Reference Rohs, West, Sosinsky, Liu, Mann and Honig2009).

Once assumed to be monotonous in structure, even fully base-paired DNA displays local sequence-dependent groove geometry, axial curvature, and flexibility. These features may be crucial in the energetics of DNA recognition and deformation by sequence-specific proteins. The importance of these properties for indirect DNA readout by sequence-non-specific proteins (including histone octamers) suggests that the DNA sequence also encodes chromatin packaging and gene expression signals (Segal et al. Reference Segal, Fondufe-Mittendorf, Chen, Thastrom, Field, Moore, Wang and Widom2006).

6.1 Base pair step models

Given the significance of sequence-dependent DNA curvature and flexibility, the prediction of such properties is an important challenge. A number of early models deduced or proposed sequence-dependent base pair twist, roll, and tilt values for each of the ten unique base pair steps. Examples of models include those involving curvature at non-A-tract sequences (Calladine et al. Reference Calladine, Drew and Mccall1988; Satchwell et al. Reference Satchwell, Drew and Travers1986), those involving curvature within A-tracts (Bolshoy et al. Reference Bolshoy, Mcnamara, Harrington and Trifonov1991; Cacchione et al. Reference Cacchione, De Santis, Foti, Palleschi and Savino1989), and those involving curvature at junctions between helical forms (Koo & Crothers, Reference Koo and Crothers1988). The various models have both strengths and weaknesses in their predictive power (Goodsell & Dickerson, Reference Goodsell and Dickerson1994). It is important to note that they sought empirically to predict DNA properties without the goal of explaining these properties.

Increasingly sophisticated dinucleotide step models allow the prediction of both DNA curvature (Liu & Beveridge, Reference Liu and Beveridge2001; Young et al. Reference Young, Ravishanker, Beveridge and Berman1995) and flexibility (Czapla et al. Reference Czapla, Swigon and Olson2006, Reference Czapla, Swigon and Olson2008; Matsumoto & Olson, Reference Matsumoto and Olson2002; Olson et al. Reference Olson, Gorin, Lu, Hock and Zhurkin1998, Reference Olson, Swigon and Coleman2004; Olson & Zhurkin, Reference Olson and Zhurkin2000; Swigon et al. Reference Swigon, Coleman and Olson2006; Zheng et al. Reference Zheng, Lu and Olson2009) from the growing databases of high-resolution DNA and DNA–protein structures. The impressive strategy implemented by Olson and co-workers mines average values and deviations for six base pair step parameters in known structures, allowing DNA structure prediction implemented in a web server tool (Lu & Olson, Reference Lu and Olson2003). Empirical energy functions are deduced, allowing specification of the expected range of thermal motion for each base pair step. These estimates substantiate many established features of duplex DNA deformability, including the conclusion that pyrimidine–purine base pair steps are especially flexible. Recent publications have extended the prediction of DNA stiffness to parameters based on trinucleotide step datasets (Gromiha, Reference Gromiha2000).

6.2 MD simulations and other models

Approaches to both understand and predict sequence-dependent DNA curvature and flexibility have also been undertaken using MD simulations. These strategies have grown in sophistication with increasingly facile parallel computing. MD simulations have been applied to sequence-directed DNA curvature. Initial studies were performed with unstrained DNA segments (Beveridge et al. Reference Beveridge, Young, Sprous, Leontis and Santa Lucia1998; Dixit et al. Reference Dixit, Beveridge, Case, Cheatham, Giudice, Lankas, Lavery, Maddocks, Osman, Sklenar, Thayer and Varnai2005; Flatters et al. Reference Flatters, Young, Beveridge and Lavery1997; Jayaram et al. Reference Jayaram, Sprous, Young and Beveridge1998; Sprous et al. Reference Sprous, Young and Beveridge1998; Young & Beveridge, Reference Young and Beveridge1998; Young et al. Reference Young, Ravishanker and Beveridge1997b). An international collaboration has resulted in extended MD simulations of DNA sequences representing multiple samples of the 136 possible unique tetranucleotide sequences in duplex DNA (Beveridge et al. Reference Beveridge, Barreiro, Byun, Case, Cheatham, Dixit, Giudice, Lankas, Lavery, Maddocks, Osman, Seibert, Sklenar, Stoll, Thayer, Varnai and Young2004). Such efforts have allowed the creation of reference datasets from which to deduce trends and compare results with flexibility parameters extracted from crystal structures. The work also firmly addresses issues of reproducibility, sampling, ion fluctuations, and convergence.

More recent simulations have modeled DNA under various bending and twisting forces to explore induced conformational changes (Harris, Reference Harris2006). Forces include bending in small minicircles (Curuksu et al. Reference Curuksu, Zacharias, Lavery and Zakrzewska2009; Lankas et al. Reference Lankas, Lavery and Maddocks2006; Maher, Reference Maher2006), stretching (Harris et al. Reference Harris, Sands and Laughton2005), protein-mediated DNA looping (Balaeff et al. Reference Balaeff, Mahadevan and Schulten2004; Czapla et al. Reference Czapla, Swigon and Olson2008; Swigon et al. Reference Swigon, Coleman and Olson2006; Villa et al. Reference Villa, Balaeff and Schulten2005), and supercoiling (Harris et al. Reference Harris, Laughton and Liverpool2008; Liverpool et al. Reference Liverpool, Harris and Laughton2008). Even more complex challenges to predictive modeling include DNA deformed into loops by proteins or bent onto the surface of proteins.

As discussed in the next section, loop structures are involved in transcriptional repression in bacteria. In eukaryotic cells, DNA commonly exists wrapped tightly onto the histone octamer surface and DNA looping may be important in eukaryotic gene regulation as well. Approaches to modeling these structures and dynamics of such assemblages include several interesting approaches. A statistical mechanical treatment of DNA polymer behavior (Zhang et al. Reference Zhang, Mcewen, Crothers and Levene2006b) has been applied to rationalize length-dependent in vivo DNA looping data in the lac operon (Zhang et al. Reference Zhang, Mcewen, Crothers and Levene2006a). Multiscale modeling and simulation of the same complex were presented by Schulten and co-workers (Balaeff et al. Reference Balaeff, Mahadevan and Schulten2004; Villa et al. Reference Villa, Balaeff and Schulten2005). This approach coupled MD for all-atom models of the protein components with a continuous polymer model of the DNA. Modeling and prediction of lac DNA looping were also undertaken by Olson and co-workers (Swigon et al. Reference Swigon, Coleman and Olson2006) using a theory of sequence-dependent DNA elasticity based on the base pair step sequence. It remains to be seen if tri- or tetranucleotide step data will enrich this approach (Dixit et al. Reference Dixit, Beveridge, Case, Cheatham, Giudice, Lankas, Lavery, Maddocks, Osman, Sklenar, Thayer and Varnai2005). The complexity of even this simplest of bacterial gene regulatory switches represents a daunting challenge for simulation. This is an expansive area for collaboration to generate experimental data that distinguish between the predictions of the different models. It is crucial that highly accurate in vivo gene regulation data are available in order to create meaningful quantitative models of gene regulation.

6.3 Predicting DNA shape

An important recent contribution to the prediction of sequence-dependent DNA structure has come through cataloging patterns of base pair accessibility to damage by hydroxyl radicals. This reactive species is similar in size to water, and hydrogen abstraction reaction rates report solvent accessibility of the DNA grooves. It has been demonstrated that hydroxyl radical reactivity patterns measured for a collection of test sequences can then be used to accurately predict reaction patterns for new sequences through di- and trinucleotide matches. This approach to prediction of DNA ‘topology’ (shape accessible to solvent) has sufficient accuracy to allow a survey of genome-wide protein binding site conservation, even when sequence conservation is difficult to detect (Parker et al. Reference Parker, Hansen, Abaan, Tullius and Margulies2009).

Careful bioinformatics analysis of the 3D structures of protein–DNA complexes has also recently led Honig and co-workers to propose that minor groove negative electrostatic potential is a key recognition element for some proteins (Rohs et al. Reference Rohs, West, Sosinsky, Liu, Mann and Honig2009). This study suggests that minor groove narrowing is a feature of focused electrostatic potential that may be predicted from sequence–structure correlation.

7.1 DNA softening in vivo

There have been hints that the apparent stiffness of DNA is lower in living cells than would be predicted from in vitro measurements. This is an intriguing result. Apparent softening of DNA with respect to both bending and twisting is observed in vivo. Initial results came from classic studies of E. coli lactose (lac) operon transcriptional regulation (Fig. 2g) where a DNA repression loop forms in the presence of lac repressor tetramer (Becker et al. Reference Becker, Kahn and Maher2005; Eismann & Müller-Hill, Reference Eismann and Müller-Hill1990; Kramer et al. Reference Kramer, Niemoller, Amouyal, Revet, Von Wilcken-Bergmann and Müller-Hill1987, Reference Kramer, Amouyal, Nordheim and Müller-Hill1988; Mossing & Record, Reference Mossing and Record1986; Muller et al. Reference Muller, Oehler and Müller-Hill1996; Oehler et al. Reference Oehler, Eismann, Kramer and Müller-Hill1990). Early estimates suggested enhanced DNA softness to bending (7-fold) and twisting (2-fold) relative to naked DNA studied in solution (Bellomy et al. Reference Bellomy, Mossing and Record1988; Law et al. Reference Law, Bellomy, Schlax and Record1993; Mossing & Record, Reference Mossing and Record1986). Using a statistical–mechanical model of DNA bending and protein–DNA looping, recent revised estimates for the bending and twisting anomalies are 1·6-fold and 3-fold, respectively (Zhang et al. Reference Zhang, Mcewen, Crothers and Levene2006a). The DNA flexibility mystery also applies to eukaryotic DNA organized into chromatin. The spooling of DNA onto histone octamers to form nucleosomes should not, in principle, change its inherent flexibility. The naked ‘linker’ segments of DNA between nucleosomes might be expected to determine the flexibility of the resulting fiber. However, careful comparison of DNA persistence length estimates based on genetic recombination in vitro and in vivo suggests a 2-fold reduction in the DNA bending persistence length (from 50 to 27 nm) in vivo (Ringrose et al. Reference Ringrose, Chabanis, Angrand, Woodroofe and Stewart1999).

7.2 Architectural DNA-binding proteins

It has been hypothesized that cellular DNA, both prokaryotic and eukaryotic, displays unexpected apparent flexibility because of negative supercoiling and DNA bending proteins that are abundant in cells. Sequence-non-specific architectural DNA bending proteins have been proposed to decrease the apparent persistence length of DNA by introducing random and transient sites of kinking and bending (Crothers, Reference Crothers1993; Paull et al. Reference Paull, Carey and Johnson1996; Paull et al. Reference Paull, Haykinson and Johnson1993; Paull & Johnson, Reference Paull and Johnson1995; Travers et al. Reference Travers, Ner and Churchill1994). This may be a universal property of architectural DNA-binding proteins including the eukaryotic high mobility group B (HMGB) non-histone chromatin proteins and the heat unstable (HU) protein of bacteria (Bianchi, Reference Bianchi1994; Thomas & Travers, Reference Thomas and Travers2001). A dramatic increase in apparent DNA cyclization propensity was observed when linear DNAs were ligated in the presence of crude heat-treated nuclear extract from human cells, demonstrating the profound capabilities of these proteins (Ross et al. Reference Ross, Hardwidge and Maher2001).

High mobility group (HMG) proteins are small, abundant eukaryotic chromatin-associated proteins of three unrelated families (Bustin, Reference Bustin2001; Grosschedl et al. Reference Grosschedl, Giese and Pagel1994; Hock et al. Reference Hock, Furusawa, Ueda and Bustin2007). HMGA proteins contain AT-hook motifs, HMGN proteins have nucleosome binding domains, and HMGB proteins contain one or two tandem ‘HMG box’ motifs. Structures and DNA bending properties of bacterial HU and eukaryotic HMGB proteins are compared to each other and the histone octamer in Fig. 6. Although all have unrelated structures, HMGB monomers and HU dimers cause strong DNA bending through a combination of minor groove intercalation (by amino acid side chains) and electrostatic interactions involving cationic amino acids that asymmetrically neutralize the DNA double helix.

Fig. 6.

Sequence-non-specific architectural protein complexes with bent DNA. (a) Top and side views of the nucleosome core particle (pdb 1AOI) in which the histone octamer (red) bends 146 bp of DNA by 600°. (b) Bacterial HU protein (red) bending DNA (pdb AHU2). (c) Yeast Nhp6A (pdb 1J5N), a single-box HMGB protein (red) bending DNA through partial minor groove intercalation of amino acid side chains (white and green) and asymmetric charge neutralization (magenta). (d) Two-box mammalian HMGB construct bending DNA (pdb 2GZK). DNA backbones are shown in yellow.

The role of architectural proteins in enhancing the apparent flexibility of DNA and chromatin is under study. Architectural proteins appear to influence DNA looping in bacterial gene control. HU has been shown to participate in bending and kinking DNA in the repression loop of the gal operon in vitro (ensemble and single-molecule experiments) and in vivo (Aki & Adhya, Reference Aki and Adhya1997; Lewis & Adhya, Reference Lewis and Adhya2002; Lia et al. Reference Lia, Bensimon, Croquette, Allemand, Dunlap, Lewis, Adhya and Finzi2003). Despite decades of study it had not been known if HU might be involved in DNA looping at other repression loops such as lac. New evidence raises this possibility. In vivo assays of lac looping have been performed in several variations (Becker et al. Reference Becker, Kahn and Maher2005, Reference Becker, Kahn and Maher2007, Reference Becker, Kahn and Maher2008; Bellomy et al. Reference Bellomy, Mossing and Record1988; Kramer et al. Reference Kramer, Niemoller, Amouyal, Revet, Von Wilcken-Bergmann and Müller-Hill1987; Law et al. Reference Law, Bellomy, Schlax and Record1993; Mossing & Record, Reference Mossing and Record1986; Muller et al. Reference Muller, Oehler and Müller-Hill1996; Oehler et al. Reference Oehler, Eismann, Kramer and Müller-Hill1990). Classic studies by Record and Müller-Hill showed that promoter repression by a weak downstream lac operator is dramatically strengthened by a strong upstream lac operator. Repression as a function of inter-operator distance gives a sensitive readout of the unfavorable energetics associated with DNA (and protein) bending and twisting (Fig. 7a). Repression is leaky when operators are positioned on opposite DNA faces because DNA looping also requires unfavorable DNA twisting. The result is an oscillating dependence of repression looping on inter-operator DNA length, with a period near 10 bp, the helical repeat of DNA (Fig. 7b). Repression is enhanced for properly phased operators because DNA looping increases the effective repressor concentration experienced by the downstream operator by including collisions with repressor tetramers bound upstream. This in vivo looping system can be analyzed quantitatively (for example, Fig. 7b). Data in the lower panels show reporter gene expression as a function of DNA loop size in the absence or presence of IPTG inducer. It was both interesting and unexpected that faint oscillations in repression were observed even in the presence of saturating IPTG inducer concentrations. Data in the upper panels show the +IPTG/−IPTG (induced/repressed) ratio.

Fig. 7.

Experimental model of DNA looping in the control of the lactose operon in E. coli. (A) Control states of the promoter. Strong (O_sym) and weak (O₂) operators for binding lac repressor tetramer (red) flank the lac promoter. Unfavorable operator positions that require DNA bending or twisting strain are poorly repressed (‘on’), while operator spacings compatible with DNA looping allow gene repression (‘off’). (B, C) Example data (Becker et al. Reference Becker, Kahn and Maher2005) comparing repressed and induced lac promoter expression for different operator spacings. (b) Wild-type cells under induced (IPTG) or repressed conditions showing lac promoter activity as normalized reporter activities (bottom), or their ratio (top). (c) Results for E. coli cells lacking the sequence non-specific protein, HU, showing DNA looping disability.

Thermodynamic modeling of lac looping data has been performed in several ways, all based on the notion that the probability of proximal operator occupancy by repressor is inversely proportional to transcription (Becker et al. Reference Becker, Kahn and Maher2005, Reference Becker, Kahn and Maher2007, Reference Becker, Kahn and Maher2008; Bellomy et al. Reference Bellomy, Mossing and Record1988; Bintu et al. Reference Bintu, Buchler, Garcia, Gerland, Hwa, Kondev and Phillips2005; Law et al. Reference Law, Bellomy, Schlax and Record1993; Zhang et al. Reference Zhang, Mcewen, Crothers and Levene2006a). Fitting of the data in Fig. 7b led Zhang et al. (Reference Zhang, Mcewen, Crothers and Levene2006a) to conclude that the apparent in vivo persistence length of DNA was 95 bp (one-third lower than the in vitro value) and the twist constant was 0·7×10⁻¹⁹ erg cm (less than half of the in vitro value). Repression experiments were repeated in isogenic E. coli strains with disruption of the genes encoding HU (Becker et al. Reference Becker, Kahn and Maher2005) (Fig. 7c). DNA looping was strongly disabled. In fact, the fit value for the DNA bending persistence length in this strain (128 bp) is close to that expected based on in vitro analysis (Zhang et al. Reference Zhang, Mcewen, Crothers and Levene2006a). This study suggests that HU protein directly participates in lac repression loops, a hypothesis that is now under further investigation.

This in vivo result should not be interpreted as indicating that lac repressor cannot induce short DNA loops without architectural proteins. Indeed, such loops can be elegantly detected in vitro by single-molecule tethered particle motion and AFM experiments (Han et al. Reference Han, Garcia, Blumberg, Towles, Beausang, Nelson and Phillips2009; Wong et al. Reference Wong, Guthold, Erie and Gelles2008) and by classical methods (Kramer et al. Reference Kramer, Niemoller, Amouyal, Revet, Von Wilcken-Bergmann and Müller-Hill1987). Loop stability may be enhanced in vivo by architectural proteins.

Strikingly, expression of structurally unrelated eukaryotic HMGB architectural proteins can rescue DNA looping in E. coli cells lacking HU (Becker et al. Reference Becker, Kahn and Maher2005, Reference Becker, Kahn and Maher2008; Sebastian et al. Reference Sebastian, Bystry, Becker and Maher2009). This result suggests a fundamental mechanism of architectural proteins in altering DNA physical properties in vivo.

Repression loops comparable to those observed in prokaryotes have not been found in eukaryotic systems, but have been proposed (Zeller et al. Reference Zeller, Griffith, Moore, Kirchhamer, Britten and Davidson1995). Eukaryotic gene activation involves recruitment of both chromatin remodeling factors (Bhaumik & Green, Reference Bhaumik and Green2001) and basal transcription machinery (Buratowski, Reference Buratowski1994; Ptashne & Gann, Reference Ptashne and Gann1997; Tjian & Maniatis, Reference Tjian and Maniatis1994) to promoters. Models for eukaryotic promoter and enhancer function have often invoked DNA loops (Ptashne & Gann, Reference Ptashne and Gann1997; Rippe et al. Reference Rippe, Von Hippel and Langowski1995), but it has been unclear if the looped DNA is naked or assembled into nucleosomal chromatin. Long-range DNA looping in eukaryotes has been suggested by studies of telomeres, locus control regions, and yeast gene transcription termination (Ansari & Hampsey, Reference Ansari and Hampsey2005; Greider, Reference Greider1999; Zhou et al. Reference Zhou, Xin, Song, Di, Liu, Wu, Liu and Liang2006). Proof of short-range DNA looping in transcription activation is lacking, although there are intriguing data (Dobi & Winston, Reference Dobi and Winston2007). An alternative model is that enhancers function by recruiting chromatin remodeling agents that regionally loosen histone octamers, increasing the exposure of promoter DNA to basal transcription factors and RNA polymerase. On the other hand, powerful new mapping techniques such as the chromosome conformation capture (3C) method (Dekker et al. Reference Dekker, Rippe, Dekker and Kleckner2002; Gondor et al. Reference Gondor, Rougier and Ohlsson2008; Lieberman-Aiden et al. Reference Lieberman-Aiden, Van Berkum, Williams, Imakaev, Ragoczy, Telling, Amit, Lajoie, Sabo, Dorschner, Sandstrom, Bernstein, Bender, Groudine, Gnirke, Stamatoyannopoulos, Mirny, Lander and Dekker2009) (Fig. 2h) are being applied to monitor DNA folding and looping after cross-linking in living cells. These studies suggest long-range chromatin flexibility (Tolhuis et al. Reference Tolhuis, Palstra, Splinter, Grosveld and De Laat2002; Vernimmen et al. Reference Vernimmen, De Gobbi, Sloane-Stanley, Wood and Higgs2007; Zhou et al. Reference Zhou, Xin, Song, Di, Liu, Wu, Liu and Liang2006). It is interesting to ask whether the DNA flexibility required for these structures is supported by polymer theory or whether factors such as architectural proteins could play roles. Long-range looping should not be constrained by the stiffness of naked DNA (Allemand et al. Reference Allemand, Cocco, Douarche and Lia2006; Rippe et al. Reference Rippe, Von Hippel and Langowski1995). Short-range looping is a more challenging question.

Spooling onto histone octamers is not a priori expected to change the bend and twist flexibilities of the unbound linker DNA segments that control the overall flexibility of the chromatin fiber. However, single-molecule force–extension studies of reconstituted chromatin fibers have allowed flexibility studies in vitro (Brower-Toland et al. Reference Brower-Toland, Smith, Yeh, Lis, Peterson and Wang2002; Kruithof et al. Reference Kruithof, Chien, Routh, Logie, Rhodes and Van Noort2009). For example, it was found that the stretch behavior of chromatin was not consistent with the classical WLC model, but showed Hookian spring behavior where linear force–extension plots were obtained at low forces.

Constraints on DNA looping in living eukaryotic cells have also been measured. As described above, the rates of site-specific recombination by FLP recombinase have been measured as a function of site separation distance (Ringrose et al. Reference Ringrose, Chabanis, Angrand, Woodroofe and Stewart1999). The authors reported in vitro measurements consistent with WLC polymer theory for naked DNA (persistence length near 50 nm). In contrast, simple fits to data obtained in transfected mammalian cells were interpreted as evidence for a 2-fold shorter apparent in vivo persistence length (~27 nm). If true, this result is reminiscent of DNA behavior in bacteria. The result is striking because of the predominance of nucleosomal DNA packaging in vivo. It remains possible that architectural proteins influence DNA looping in eukaryotes by altering the apparent flexibility of the ~50 bp segments of internucleosomal linker DNA.

A particularly interesting study was a genetic approach to understand what factors limit transcription regulation to a local phenomenon in the compact genome of budding yeast (Dobi & Winston, Reference Dobi and Winston2007). In this organism, long-range effects of cis-regulatory elements could be deleterious. The authors identified mutations that conferred longer-range transcription activation. Interestingly, one of the mutants inactivated the sequence non-specific architectural DNA-binding protein Spt2p. This result raises the intriguing possibility that average DNA loop size might be governed by the concentration of architectural proteins in vivo. On the other hand, Johnston and co-workers found that removal of yeast HMGB proteins Nhp6A/B did not influence the distance dependence of transcription activation, but the potency of the activators themselves (Paull et al. Reference Paull, Carey and Johnson1996). Thus, it remains unclear whether and how enhanced apparent DNA flexibility is required in eukaryotes, and the role played by architectural DNA-binding proteins in eukaryotes versus prokaryotes (Fig. 8).

Fig. 8.

Architectural DNA-binding protein effects on naked DNA. (a) The locally stiff DNA double helix (left) adopts more compact conformations (center) in the presence of randomly bound architectural DNA-binding proteins (red triangles), decreasing the average end–end distance (double-headed arrows) as detected by enhanced cyclization rate (right) in the presence of DNA ligase. (b) Example of ~200 bp circular protein–DNA complex facilitated by HMGB protein Nhp6A (red) in Monte-Carlo simulation. (c) Potential role of architectural protein (e.g. HU, red triangle) in stabilizing bacterial repression loops.