Toroidal DNA Condensates: Unraveling the Fine Structure and the Role of Nucleation in Determining Size

Hud, Nicholas V.; Vilfan, Igor D.

doi:10.1146/annurev.biophys.34.040204.144500

Cited by 210 publications

(274 citation statements)

References 86 publications

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“…The non-linearity in this latter case is clearly present and is captured in a single parameter describing the onset of DNA kink formation. This clearly exhibited elastic nonlinearity is taken as the motivation for the present study that attempts to derive the macroscopic consequences of this interesting microscopic elastic behavior of DNA.Another interesting facet of DNA behavior is that under specific solution conditions, it condenses into highly compact structures with pronounced symmetry [8][9][10][11]. This condensation phenomenon serves as an example of high polymer density packing in biology and of polymer phase transitions and phase separations in general, being relevant also for artificial gene delivery [12,13].…”

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confidence: 94%

“…Another interesting facet of DNA behavior is that under specific solution conditions, it condenses into highly compact structures with pronounced symmetry [8][9][10][11]. This condensation phenomenon serves as an example of high polymer density packing in biology and of polymer phase transitions and phase separations in general, being relevant also for artificial gene delivery [12,13].…”

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confidence: 99%

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Phase diagram of the ground states of DNA condensates

et al. 2015

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Phase diagram of the ground states of DNA in a bad solvent is studied for a semi-flexible polymer model with a generalized local elastic bending potential characterized by a nonlinearity parameter x and effective self-attraction promoting compaction. x = 1 corresponds to the worm-like chain model. Surprisingly, the phase diagram as well as the transition lines between the ground states are found to be a function of x. The model provides a simple explanation for the results of prior experimental and computational studies and makes predictions for the specific geometries of the ground states. The results underscore the impact of the form of the microscopic bending energy at macroscopic observable scales.The non-linear elasticity of DNA at short length scales, probed by non-equilibrium DNA cyclization experiments [1,2], AFM imaging on surfaces [3], as well as by equilibrium mechanically constrained DNA experiments [4][5][6], is still not well understood. While the conclusions regarding the first two methods for probing non-linear ds-DNA elasticity have been criticized [7], the experiments on stressed DNA ring molecules are performed by a different methodology based on thermodynamic methods via DNA high-curvature states through partial hybridization of a ss-DNA loop with a linear complementary strand [6]. This methodology does not depend on thermal fluctuations to realize high-curvature states and thus appears to have a far better accuracy and reliability. The non-linearity in this latter case is clearly present and is captured in a single parameter describing the onset of DNA kink formation. This clearly exhibited elastic nonlinearity is taken as the motivation for the present study that attempts to derive the macroscopic consequences of this interesting microscopic elastic behavior of DNA.Another interesting facet of DNA behavior is that under specific solution conditions, it condenses into highly compact structures with pronounced symmetry [8][9][10][11]. This condensation phenomenon serves as an example of high polymer density packing in biology and of polymer phase transitions and phase separations in general, being relevant also for artificial gene delivery [12,13]. Several distinct morphologies of the DNA condensates have been observed including a toroid, a spheroid as well as a rodlike configuration [10,[14][15][16]. Our principal goal is to explore the rich interplay between the strong tendency for compactness, arising from the presence of multivalent cations or osmolytes in the solution, and the intrinsic stiffness of the DNA molecule promoting the chain to be locally straight. In the absence of stiffness, one would expect the chain to adopt a densely compact spheroidal globule configuration. The key issue is to understand how local stiffness and the detailed way it enters the elastic energy result in the spheroidal configuration becoming unstable w.r.t. other lower energy configurations. In particular, one would like to map out a phase diagram and understand the different condensate geometries.The topolog...

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Phase diagram of the ground states of DNA condensates

et al. 2015

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“…On the molecular level, the torus shape is preferred by numerous biological and chemical macromolecules, such as DNA condensates [4], proteins [5] and oligosaccharides [6], to name just a few. Toroidal symmetries are also encountered frequently in solid-state systems including carbon nanotubes [7] and ferroelectrics [8,9].…”

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Gyrotropy of a Metamolecule: Wire on a Torus

et al. 2009

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In this letter, we present the first experimental study of a new chiral metamaterial consisting of toroidal wire windings. We show that the metamaterial exhibits three bands of circular dichroism in the GHz range. We discuss the response of the structure in terms of multipole moments, including the (magnetic) toroidal dipole moment.Toroidal, doughnut-shaped structures are ubiquitous in nature, appearing on scales which range from the subatomic [1, 2] to the astronomical [3]. On the molecular level, the torus shape is preferred by numerous biological and chemical macromolecules, such as DNA condensates [4], proteins [5] and oligosaccharides [6], to name just a few. Toroidal symmetries are also encountered frequently in solid-state systems including carbon nanotubes [7] and ferroelectrics [8,9]. Although the behavior of such systems has been studied extensively, their interaction with electromagnetic radiation is not well understood. Indeed, within the framework of classical electrodynamics, unusual phenomena associated with violation of Lorentz reciprocity [10] and non-radiating configurations [11] have been predicted for toroidal structures and their interactions. Nevertheless, such phenomena are usually weak [12,13] and, therefore, experimental investigations are rare. In this letter, we study a new artificial chiral medium, originally suggested in [14], consisting of an array of toroidal wire windings in a metamaterial' configuration. We show that such a metamaterial exhibits strong gyrotropic response which is attributed to different terms of its multipole expansion.In contrast to artificial gyrotropic media, where handedness is usually associated with the direction of a "twist vector" following a cork-screw law along the helicity axis, the situation is more complicated when the structure possesses toroidal symmetry. Here, the twist vector rotates along the torus, and therefore a corresponding direction can not be defined. However, although no helicity axis exists, the structure has two well-defined enantiomeric forms, corresponding to different directions of the winding (see Fig. 1a). Based on this concept, we manufactured a chiral toroidal metamaterial with a unit cell consisting of four connected square loops that were formed by horizontal and vertical copper wire segments (see Fig. 1b). The resulting windings were embedded in dielectric bars with permittivity = 4.5 − 0.081i. The size of the unit cell was 15x15 mm rendering the metamaterial non-diffracting up to 20 GHz. Transmission experiments were performed at normal incidence, from 2 to 14 GHz, in an anechoic chamber using two broadband horn antennas (Schwarzbeck M. E. model BBHA 9120D). The transmission spectra were recorded with a vector network analyzer. The intensity and phase of the structure's response to right and left circularly polarized light are presented in Figs. 2a and 2b, respectively. As it can be seen in Fig. 2a, experimental results (solid line) are in good agreement with finite element numerical simulations (solid circles). Two resonan...

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“…[1][2][3][4][5] Polyelectrolyte theory has figured out that the attractive potential that leads to DNA compaction originates from correlated fluctuation of counterions shared between DNA segments. 6 Experimental observations have revealed that DNA condensates have generally a toroidal geometry with a typical size of ∼100 nm in diameter.…”

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Compaction Dynamics of Single DNA Molecules under Tension

Wang

Zhang

et al. 2006

J. Am. Chem. Soc.

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The compaction of DNA by multivalent cations has been the subject of many investigations, not only because it is biologically important, but also because it poses a fascinating challenge to our understanding of semiflexible polymers. [1][2][3][4][5] Polyelectrolyte theory has figured out that the attractive potential that leads to DNA compaction originates from correlated fluctuation of counterions shared between DNA segments. 6 Experimental observations have revealed that DNA condensates have generally a toroidal geometry with a typical size of ∼100 nm in diameter. It is generally believed that DNA within a toroid is organized in a hexagonal close-packed lattice, 7 but how such a structure is formed is still not fully understood.Single-molecule measurements have proven helpful to understanding the nucleation and growth of DNA condensates. [8][9][10][11][12][13] A few recent experiments concentrated on the kinetics of DNA compaction. They showed that DNA condenses continuously and linearly with time once the compaction process begins. [14][15][16][17] The results seemed to support the widely accepted opinion that the toroid is formed by continuously absorbing DNA to a primary loop randomly nucleated on DNA. The temporal resolution of the experiments was, however, relatively low. They might not be able to resolve the time trajectories of the DNA compaction.Exerting forces on DNA is a useful way to study processes relevant to DNA. 18 The force may slow down the dynamical process so that details can be observed using an apparatus of finite temporal resolution. Here we report single-molecule studies on the dynamics of hexaammine cobalt chloride-induced DNA compaction under tension. It turns out that the compaction process is more sophisticated than the static structural model has suggested. DNA condenses into toroid in a quantized manner.The measurements were performed using transverse magnetic tweezers similar to the one recently developed by Yan and Marko. 19 Two micrometer-sized beads are tethered to the two ends of a λ-phage DNA (16.4 µm). One bead is fixed in space by a micropipette, and the other is free in solution. A magnetic rod is inserted into the solution to generate a constant force to the free magnetic bead. The experiments were done in phosphate-buffered saline (10 mM PBS, 5 mM NaCl, pH ) 7.4). After adjusting the force on DNA, 10 µL of 10 mM hexaammine cobalt chloride solution was added into the sample cell. The final concentration of the trivalent cations was 100 µM. Figure 1a shows the time course of DNA compaction at a force F ) 0.5 pN. Time courses measured at other concentrations of the trivalent cations (from 35 to 200 µM) are quite similar. After addition of the cations, a long induction period was observed before the compaction started. The induction time becomes longer when a less concentrated solution of trivalent cations is added. The compaction is discontinuous and stepwise. The two big steps in Figure 1a consist of multiple small steps. Such discontinuous compactions were also observed...

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Toroidal DNA Condensates: Unraveling the Fine Structure and the Role of Nucleation in Determining Size

Cited by 210 publications

References 86 publications

Phase diagram of the ground states of DNA condensates

Phase diagram of the ground states of DNA condensates

Gyrotropy of a Metamolecule: Wire on a Torus

Compaction Dynamics of Single DNA Molecules under Tension

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