Dna Mesophases

A. Polyelectrolyte Properties of DNA

We can define several levels of DNA organization similarly to (1). Its primary structure is the sequence of base pairs. Its secondary structure is the famous double helix that can exist in several conformations. In solution, the B-helical structure dominates (47). The bases are perpendicular to the axis of the molecule and are 0.34 nm apart, and 10 of them make 1 turn of the helix. These parameters can vary for DNA in solution where up to 10.5 base pairs can make a whole turn of the double helix (48). In the A structure, the bases are tilted with respect to the direction of the helix, and this arrangement yields an internal hole, wider diameter, and closer packing (Fig. 12). Other conformations, such as the left-handed Z form, are rare. In solution, DNA's tertiary structure includes the many bent and twisted conformations in 3 dimensions.

DNA lengths can reach macroscopic dimensions. For instance, the human genome is coded in approximately 3 billion base pairs with a collective linear stretch on the order of a meter. Obviously, this molecule must undergo extensive compaction in order to fit in the cell nucleus. In natural environments, DNA is packaged by basic proteins, which form chro-matin structures to keep DNA organized. In the test tube, DNA can be packaged into very tight and dense structures as well, primarily by various ''condensing'' agents. Their addition typically induces a random coil to globule transition. At large concentrations, DNA molecules, like lipids, form ordered liquid crystalline phases (10) that have been studied extensively at different solution conditions (8).

In vitro, at concentrations above a critical value (49), poly-electrolyte DNA self-organizes in highly ordered mesophases (8). In this respect, it is a lyotropic liquid crystal. But contrary to the case of lipid mesophases, where the shape of constituent molecules plays a determining role, the organization of DNA in condensed phases is primarily a consequence of its relatively large stiffness (8). The orientational ordering of DNA at high concentrations is promoted mostly by the interplay between entropically favored disorder or misalignment and the consequent price in terms of the high interaction energy. The mechanism of orientational ordering is thus the same as in standard short nematogens (50). The main difference being due to the large length of polymeric chains. The discussion that follows concentrates mostly on very long, on the order of 1000 persistence lengths thus microns long, DNA molecules.

B. Flexibility of DNA Molecules in Solution

In isotropic solutions, DNA can be in one of several forms. For linear DNA, individual molecules are effectively straight over the span of a persistence length that can also be defined as the exponential decay length for the loss of angular correlation between 2 positions along the molecule, while for longer

Figure 12 Structural parameters of a DNA molecule. The two relevant configurations of the DNA backbone: A-DNA, common at small hydrations or high DNA densities, and B-DNA common in solution at large hydrations and lower DNA densities. The test tube holds ethanol-precipitated DNA in solution. Its milky color is due to the light scattering by thermal conformational fluctuations in the hexatic phase (see main text). Box: typical persistence lengths for different (bio)polymer chains in nm. See the color insert for a color version of this figure.

Figure 12 Structural parameters of a DNA molecule. The two relevant configurations of the DNA backbone: A-DNA, common at small hydrations or high DNA densities, and B-DNA common in solution at large hydrations and lower DNA densities. The test tube holds ethanol-precipitated DNA in solution. Its milky color is due to the light scattering by thermal conformational fluctuations in the hexatic phase (see main text). Box: typical persistence lengths for different (bio)polymer chains in nm. See the color insert for a color version of this figure.

lengths they form a wormlike random coil. The persistence length of DNA is about 50 nm (1). The persistence length has been determined by measuring the diffusion coefficient of different-length DNA molecules using dynamic light scattering and by enzymatic cyclization reactions (51). It depends only weakly on the base-pair sequence and ionic strength.

DNA can also be circular as in the case of a plasmid. The closed form of a plasmid introduces an additional topological constraint on the conformation that is given by the linking number Lk (2). The linking number gives the number of heli-

cal turns along a circular DNA molecule. Because plasmid DNA is closed, Lk has to be an integer number. By convention, Lk of a closed right-handed DNA helix is positive. The most frequent DNA conformation for plasmids in cells is negatively supercoiled. This means that for such plasmids Lk is less than it would be for a torsionally relaxed DNA circle—negatively supercoiled DNA is underwound. This is a general phenomenon with important biological consequences. It seems that free energy of negative supercoiling catalyzes processes that depend on DNA untwisting, such as DNA replication and transcription, which rely on DNA (52). Although the sequence of bases in exons determine the nature of proteins synthesized, it is possible that such structural features dictate the temporal and spatial evolution of DNA-encoded information.

C. Liquid Crystals

The fact that DNA is intrinsically stiff makes it form liquid crystals at high concentration (8). Known for about 100 years, the simplest liquid crystals are formed by rodlike molecules. Solutions of rods exhibit a transition from an isotropic phase with no preferential orientation to a nematic phase, a fluid in which the axes of all molecules point on average in 1 direction (Fig. 11). The unit vector in which the molecules point is called the nematic director n. Nematic order is orientational order (50), in contrast to positional order that distinguishes between fluid and crystalline phases. Polymers with intrinsic stiffness can also form liquid crystals. This is because a long polymer with persistence length Lp acts much like a solution of individual rods that are all one persistence length long, thus the term ''polymer nematics'' (53).

If the molecules that comprise the liquid crystal are chiral, have a natural twist such as double-helical DNA, then their orientational order tends to twist. This twist originates from the interaction between two molecules that are both of the same handedness. This chiral interaction is illustrated in Fig. 13 for two helical or screwlike molecules. For steric reasons, two helices pack best when tilted with respect to each other. Instead of a nematic phase chiral molecules form a cholesteric phase (50). The cholesteric phase is a twisted nematic phase in which the nematic director twists continuously around the so-called cholesteric axis as shown in Fig. 13. Using the same arguments as for plain polymers, chiral polymers will form polymer cholesterics.

Both cholesteric and hexagonal liquid crystalline DNA phases were identified in the 1960s. This discovery was especially exciting because both phases were also found in biological systems. The hexagonal liquid crystalline phase can be seen in bacterial phages, and the cholesteric phase can be seen in cell nuclei of dinoflagellates (8).

D. Measurements of Forces Between DNA Molecules

Liquid crystalline order lets us measure intermolecular forces directly. With the osmotic stress method, DNA liquid crystals

Figure 13 Chiral interaction for two helical or screwlike molecules. For steric reasons, two helices just as two screws (depicted on the figure) pack best when slightly tilted with respect to each other. Because of DNA's double-stranded, helical nature, it is a type of molecular screw and exhibits chiral interactions. Instead of a nematic phase depicted on Fig. 11, characterized by the average constant direction of molecules, chiral molecules form a cholesteric phase (50). The cholesteric phase is a twisted nematic phase in which the nematic director twists continuously around a ''cholesteric axis'' depicted on the middle drawing. Under crossed polarizers (bottom), the DNA cholesteric phase creates a characteristic striated texture. For long DNA molecules, the striations appear disordered.

Figure 13 Chiral interaction for two helical or screwlike molecules. For steric reasons, two helices just as two screws (depicted on the figure) pack best when slightly tilted with respect to each other. Because of DNA's double-stranded, helical nature, it is a type of molecular screw and exhibits chiral interactions. Instead of a nematic phase depicted on Fig. 11, characterized by the average constant direction of molecules, chiral molecules form a cholesteric phase (50). The cholesteric phase is a twisted nematic phase in which the nematic director twists continuously around a ''cholesteric axis'' depicted on the middle drawing. Under crossed polarizers (bottom), the DNA cholesteric phase creates a characteristic striated texture. For long DNA molecules, the striations appear disordered.

are equilibrated against neutral polymer (e.g., PEG or PVP) solutions of known osmotic pressure, pH, temperature, and ionic composition (54). Equilibration of DNA under osmotic stress of external polymer solution is effectively the same as exerting mechanical pressure on the DNA subphase with a piston [see Fig. 4]. In this respect, the osmotic stress technique is formally much similar to the Boyle experiment where one compresses a gas with mechanical pistons and measures the ensuing pressure. After equilibration under this known stress, DNA separation is measured either by X-ray scattering, if the DNA subphase is sufficiently ordered, or by straightforward densitometry (55). Known DNA density and osmotic stress immediately provide an equation of state (osmotic pressure as a function of the density of the DNA subphase) to be codified in analytical form for the entire phase diagram. Then, with the local packing symmetry derived from X-ray scatter ing (7,54), and sometimes to correct for DNA motion (42), it is possible to extract the bare interaxial forces between molecules that can be compared with theoretical predictions as developed in Chapter 2. In vivo observation of DNA liquid crystals (56) shows that the amount of stress needed for compaction and liquid crystalline ordering is the same as for DNA in vitro.

E. Interactions Between DNA Molecules

Performed on DNA in univalent salt solutions, direct force measurements reveal two types of purely repulsive interactions between DNA double helices (4):

1. At interaxial separations less than ~3 nm (surface separation ~1 nm), an exponentially varying ''hydration'' repulsion believed to originate from partially ordered water near the DNA surface.

2. At surface separations greater than 1 nm, measured interactions reveal electrostatic double-layer repulsion, presumably from negative phosphates along the DNA backbone.

Measurements give no evidence for a significant DNA-DNA attraction expected on theoretical grounds (57). Although charge fluctuation forces must certainly occur, they appear to be negligible at least for liquid crystal formation in monovalent-ion solutions. At these larger separations, the double-layer repulsion often couples with configurational fluctuations to create exponentially decaying forces whose decay length is significantly larger than the expected Debye screening length (42).

Bare short-range molecular interactions between DNA molecules appear to be insensitive to the amount of added salt. This has been taken as evidence that they are not electrostatic in origin, as attested also by similar interactions between completely uncharged polymers such as schizophilline (Fig. 5). The term hydration force associates these forces with perturbations of the water structure around DNA surface (54). Alternatively, short-range repulsion has been viewed as a consequence of the electrostatic force specific to high DNA density and counterion concentration (58).

F. High-density DNA Mesophases

Ordering of DNA can be induced by two alternative mechanisms. First of all, attractive interactions between different DNA segments can be enhanced by adding multivalent counterions believed to promote either counterion correlation forces (59) or electrostatic (60) and hydration attraction (22). In these cases, DNA aggregates spontaneously. Alternatively, one can add neutral crowding polymers to the bathing solution that phase separate from DNA and exert osmotic stress on the DNA subphase (61). In this case the intersegment repulsions in DNA are simply counteracted by the large externally applied osmotic pressure. DNA is forced in this case to condense under externally imposed con straints. This latter case is formally (but only formally) analogous to a Boyle gas pressure experiment but with osmotic pressure playing the role of ordinary pressure. The main difference being that ordinary pressure is set mechanically, whereas osmotic pressure has to be set through the chemical potential of water, which is in turn controlled by the amount of neutral crowding polymers (e.g., PEG, PVP, dextran) in the bathing solution (55).

At very high DNA densities, where the osmotic pressure exceeds 160 atm, DNA can exist only in a (poly)crystalline state (62). Nearest neighbors in such an array are all oriented in parallel and show correlated (nucleotide) base stacking between neighboring duplexes (Figs. 11 and 14). This means that there is a long-range correlation in the positions of the backbone phosphates between different DNA molecules in the crystal. The local symmetry of the lattice is monoclinic. Because of the high osmotic pressure, DNA is actually forced to be in an A conformation characterized by a somewhat larger outer diameter as well as a somewhat smaller pitch than in the canonical B conformation (see Fig. 12), which persists at smaller densities. If the osmotic pressure of such a crystal is increased above 400 atm, the helix begins to crack and the sample loses structural homogeneity (62).

Lowering the osmotic pressure does not have a pronounced effect on the DNA crystal until it is down to ~ 160 atm. Then the crystal as a whole simultaneously expands while individual DNA molecules undergo an A-B conformational transition (see Fig. 14) (62). This phase transformation is thus first order, and besides being a conformational transition for single DNAs, is connected also with the melting of the base stacking as well as positional order of the helices in the lattice. The ensuing low-density mesophase, where DNA is in the B conformation, is therefore characterized by short range base stacking order, short range 2-dimensional positional order and longrange bond orientational order (Fig. 15) (63). This order is connected with the spatial direction of the nearest neighbors (64). It is for this reason that the phase has been termed a ''line hexatic'' phase. Hexatics usually occur only in 2-dimensional systems. They have crystalline bond orientational order but liquidlike positional order. There might be a hexatic-hexago-nal columnar transition somewhere along the hexatic line, though a direct experimental proof is lacking.

The difference between the 2 phases is that the hexagonal columnar phase has also a crystalline positional order and is thus a real 2-dimensional crystal (see Fig. 15) (65). It is the long-range bond orientational order that gives the line hexatic phase some crystalline character (66). The DNA duplexes are still packed in parallel, while the local symmetry perpendicular to the long axes of the molecules is changed to hexagonal. The directions of the nearest neighbors persist through macroscopic dimensions (on the order of mm) while their positions tend to become disordered already after several (typically 5 to 10) lattice spacings. This mesophase has a characteristic X-ray scattering fingerprint (see Fig. 15). If the X-ray beam is directed parallel to the long axis of the molecules, it will show a hexagonally symmetric diffraction pattern of broad liquidlike peaks (67).

Figure 14 Schematic phase diagrams for DNA (left) and lipids (right). In both cases, the arrow indicates increasing density in both cases. DNA starts (bottom) as a completely disordered solution. It progresses through a sequence of blue phases characterized by cholesteric pitch in two perpendicular directions (68), then to a cholesteric phase with pitch in only one direction. At still larger densities, this second cholesteric phase is succeeded by a hexatic phase, characterized by short-range, liquidlike positional order and long-range, crystallike bond orientational (or hexatic order, indicated by lines). At highest densities, there is a crystalline phase characterized by long-range positional order of the molecules and long-range base stacking order in the direction of the long axes of the molecules. Between the hexatic and the crystalline forms, there might exist a hexagonal columnar liquid-crystalline phase, that is similar to a crystal, but with base stacking order only on short scales. The lipid-phase diagram (77) is a composite of results obtained for different lipids. It starts from a micellar solution and progresses through a phase of lipid tubes to a multilamellar phase of lipid bilayers. This is followed by an inverted hexagonal columnar phase of water cylinders and possibly goes to an inverted micellar phase. Most lipids show only a subset of these possibilities. Boundaries between the phases shown here might contain exotic cubic phases not included in this picture. See the color insert for a color version of this figure.

Typical lattice spacings in the line hexatic phase are between 25 and 35 A (i.e., between 600 and 300 mg/mL of DNA) (63). The free energy in this mesophase is mostly a consequence of the large hydration forces stemming from removal of water from the phosphates of the DNA backbone. Typically independent of the ionic strength of the bathing solution, these hydration forces (54) depend exponentially on the interhelical separation and decay with a decay length of about 3 A (11) at these large densities. This value of the hydration decay length seems to indicate that it is determined solely by the bulk properties of the solvent (i.e., water).

It is interesting to note that the behavior of short-fragment DNA in this range of concentrations is different from the long DNA (65). The short-fragment DNA, typically the nucleoso-mal DNA fragment of 146 bp, makes a 2-dimesional hexagonal phase at interaxial spacing of ~30 A, that progressively orders into a 3-dimensional hexagonal phase on decrease of the interaxial spacing to ~23 A (65). At still larger concentrations, the short-fragment DNA makes a 3-dimensional ortho-rhombic crystal, with a deformed hexagonal unit cell perpendicular to the c-axis. Concurrently to this symmetry transformation, the helical pitch of the condensed phase decreases continuously from 34.6 to 30.2 A (65). The reasons for this fundamental difference between the behavior of long as opposed to short-fragment DNA is still not well understood.

When the osmotic pressure is lowered to about 10 atm (corresponding to interaxial spacing of about 35 A, or DNA density of about 300 mg/mL), the characteristic hexagonal X-ray diffraction fingerprint of the line hexatic mesophase disappears continuously. This disappearance suggests the presence of a continuous, second-order transition into a low-density cholesteric (63). It is characterized by short-range (or effectively no) base stacking order, short-range positional order, short-range bond orientational order, but long-range cholesteric order, manifested in a continuing rotation of the long axis of the molecules in a preferred direction. In this sense, the cholesteric DNA mesophase would retain the symmetry of a 1-dimensional crystal. X-ray diffraction pattern of the DNA in the cholesteric phase is isotropic and has the form of a ring. Crossed polarizers, however, reveal the existence of long-range cholesteric order just as in the case of short chiral molecules. The texture of small drops of DNA choles-teric phase (spherulites) under crossed polarizers (Fig. 16) reveals the intricacies of orientational packing of DNA, where its local orientation is set by a compromise between interaction forces and macroscopic geometry of a spherulite. It is thus only at these low densities that the chiral character of the DNA finally makes an impact on the symmetry of the mesophase. It is not yet fully understood why the chiral order is effectively screened from the high-density DNA mesophases.

At still smaller DNA densities, the predominance of the chiral interactions in the behavior of the system remains. Recent work on the behavior of low-density DNA mesophases indicates (68) that the cholesteric part of the phase diagram might end with a sequence of blue phases that would emerge as a consequence of the loosened packing constraints coupled to the chiral character of the DNA molecule. At DNA density

Figure 15 Bond orientational or hexatic order. With a real crystal if one translates part of the crystal by a lattice vector, the new position of the atoms completely coincides with those already there. (Adapted from ref. 67.) In a hexatic phase the directions to the nearest neighbors (bond orientations) coincide (after rotation by 60°), but the positions of the atoms do not coincide after displacement in 1 of the 6 directions! Consequently, a real crystal gives a series of very sharp Bragg peaks in X-ray scattering (upper half of box), whereas a hexatic gives hexagonally positioned broad spots. The pattern of X-ray scattering by high- density DNA samples gives a fingerprint of a hexatic phase. The densitogram of the scattering intensity (right half of figure) shows 6 pronounced peaks that can be Fourier decomposed with a marked sixth-order Fourier coefficient, another sign that that the scattering is due to long-range bond orientational order (63). See the color insert for a color version of this figure.

Figure 15 Bond orientational or hexatic order. With a real crystal if one translates part of the crystal by a lattice vector, the new position of the atoms completely coincides with those already there. (Adapted from ref. 67.) In a hexatic phase the directions to the nearest neighbors (bond orientations) coincide (after rotation by 60°), but the positions of the atoms do not coincide after displacement in 1 of the 6 directions! Consequently, a real crystal gives a series of very sharp Bragg peaks in X-ray scattering (upper half of box), whereas a hexatic gives hexagonally positioned broad spots. The pattern of X-ray scattering by high- density DNA samples gives a fingerprint of a hexatic phase. The densitogram of the scattering intensity (right half of figure) shows 6 pronounced peaks that can be Fourier decomposed with a marked sixth-order Fourier coefficient, another sign that that the scattering is due to long-range bond orientational order (63). See the color insert for a color version of this figure.

of about 10 mg/mL, the cholesteric phase line would end with DNA reentering the isotropic liquid solution where it remains at all subsequent densities, except perhaps at very small ionic strengths (69).

G. DNA Equation of State

The free energy of the DNA cholesteric mesophase appears to be dominated by the large elastic shape fluctuations of its constituent DNA molecules (70) that leave their imprint in the very broad X-ray diffraction peak (55). Instead of showing the expected exponential decay characteristic of screened electrostatic interactions (71), where the decay length is equal to the Debye length, it shows a fluctuation-enhanced repulsion similar to the Helfrich force existing in the flexible smectic multilamellar arrays (41). Fluctuations not only boost the magnitude of the existing screened electrostatic repulsion, but also extend its range through a modified decay length equal to 4 times the Debye length. The factor-of-4 enhancement in the range of the repulsive force is a consequence of the coupling between the bare electrostatic repulsions of exponential type and the thermally driven elastic shape fluctuations described through elastic curvature energy that is proportional to the square of the second derivative of the local helix position (42). In the last instance, it is a consequence of the fact that DNAs in the array interact via an extended, soft-screened electrostatic potential and not through hard bumps as assumed in the simple derivation in Chapter 2.

The similarity of the free energy behavior of the smectic arrays with repulsive interactions of Helfrich type and the DNA arrays in the cholesteric phase that can also be understood in the framework of the Helfrich-type-enhanced repulsion satisfies a consistency test for our understanding of flexible supermolecular arrays.

Wr S

Figure 16 Texture of small drops of DNA cholesteric phase (spherulites) in a PEG solution under crossed polarizers. These patterns reveal the intricacies of DNA orientational packing when its local orientation is set by a compromise between interaction forces and the macroscopic geometry of a spherulite. The change from a bright to a dark stripe indicates that the orientation of the DNA molecule has changed by 90 degrees.

Figure 16 Texture of small drops of DNA cholesteric phase (spherulites) in a PEG solution under crossed polarizers. These patterns reveal the intricacies of DNA orientational packing when its local orientation is set by a compromise between interaction forces and the macroscopic geometry of a spherulite. The change from a bright to a dark stripe indicates that the orientation of the DNA molecule has changed by 90 degrees.

Was this article helpful?

0 0

Post a comment