Theory of H1-mediated control of higher orders of structure in chromatin

It is known that the lysine-rich histone H1 induces both higher orders of folding in chromatin and donut shapes in DNA. However, these phenomena occur only on the high-salt side of a narrow transition range located at about 0.02M salt. Previous theoretical analyses of the ionic-strength dependencies of DNA persistence length and denaturation rate have provided the information that the basic rigid-rod unit in high-molecular-weight DNA is a segment 60 base pairs in length and that if the phosphate charge is neutralized, this segment will spontaneously adopt a bent conformation with radius of curvature 170 Å. On the assumption that an H1 molecule does not completely neutralize the DNA charge in its vicinity, the theory has been extended here to determine the onset of spontaneous bending as a function of salt concentration and extent of phosphate neutralization. A salt transition of the kind observed has been found for the realistic value of 82% charge neutralization, with the actual value likely to be in the neighborhood of 90%, as suggested by the measurements of Wilson and Bloomfield.¹ It is recalled that the spacer DNA length in chromatin is of about the same length as the DNA rigid-rod unit. If binding of H1 to the spacer induces, as predicted, a bent conformation of radius about 170 Å, then the observed value of about 150 Å for the outer radius of the solenoid presently thought to be the basic mode of folding for a nucleosome chain can be understood as a reflection of the inherent maximum curvature of DNA in aqueous salt solution.     

Breathing and bending fluctuations in DNA modeled by an open-base-pair kink coupled to axial compression

We develop a model designed to show that flexibility in the DNA molecule can arise from relatively improbable transient opening of base pairs. The axial direction changes at the site of an open base pair. The region between open base pairs is a double helix of hydrogen-bonded base pairs with a slightly decreased rise per residue and a slightly increased helical winding angle. An analysis of the model yields several testable predictions. For example, we predict probability 0.026 for a base pair to be open at 25°C, a value close to that measured by hydrogen-exchange experiments. Other predictions involve matters like the variation of persistence length with ionic strength and temperature, the variation of helical winding angle with temperature, and the kinetics of heat denaturation. An additional result of the analysis is an explanation of the high degree of local stiffness of the DNA molecule. Strong resistance to bending fluctuations is provided from two sources: increased polyelectrolyte repulsion among phosphate groups in the axially compressed stacks between open base pairs and the tendency of stacking forces to oppose opening of a base pair. Stacking forces, however, also support compression of the stacks between open base pairs, so that the net effect of stacking forces on elastic bending of DNA is small relative to the polyelectrolyte effect. If the ionic charges on the phosphate groups were absent, DNA would spontaneously fold, driven by the entropy gained when about 1% of its base pairs open.     

Sequence-induced curvature of Tenebrio molitor satellite DNA

Single satellite DNA constitutes about 50% of the Tenebrio molitor genome. Electrophoresis of 142 base pair long satellite monomers on nondenaturating polyacrylamide gel shows retarded mobility, a characteristic of fragments with sequence-induced DNA curvature. Migrational analysis of circularly permuted satellite monomers revealed the existence of 2 bend centers in the monomer sequence. We calculated the trajectory of DNA helix axis according to the algorithm of De Santis et al. This model predicts that T molitor naked satellite DNA forms a solenoid structure with left-handed superhelix. One turn of the superhelix has approximately 310 base pairs and a 33 nm pitch. Point mutations found in the satellite DNA (1.8%) influence bending characteristics, but do not distort the general geometry of satellite superhelix.     

Computer simulation of the 30-nanometer chromatin fiber

A new Monte Carlo model for the structure of chromatin is presented here. Based on our previous work on superhelical DNA and polynucleosomes, it reintegrates aspects of the "solenoid" and the "zig-zag" models. The DNA is modeled as a flexible elastic polymer chain, consisting of segments connected by elastic bending, torsional, and stretching springs. The electrostatic interaction between the DNA segments is described by the Debye-Hückel approximation. Nucleosome core particles are represented by oblate ellipsoids; their interaction potential has been parameterized by a comparison with data from liquid crystals of nucleosome solutions. DNA and chromatosomes are linked either at the surface of the chromatosome or through a rigid nucleosome stem. Equilibrium ensembles of 100-nucleosome chains at physiological ionic strength were generated by a Metropolis-Monte Carlo algorithm. For a DNA linked at the nucleosome stem and a nucleosome repeat of 200 bp, the simulated fiber diameter of 32 nm and the mass density of 6.1 nucleosomes per 11 nm fiber length are in excellent agreement with experimental values from the literature. The experimental value of the inclination of DNA and nucleosomes to the fiber axis could also be reproduced. Whereas the linker DNA connects chromatosomes on opposite sides of the fiber, the overall packing of the nucleosomes leads to a helical aspect of the structure. The persistence length of the simulated fibers is 265 nm. For more random fibers where the tilt angles between two nucleosomes are chosen according to a Gaussian distribution along the fiber, the persistence length decreases to 30 nm with increasing width of the distribution, whereas the other observable parameters such as the mass density remain unchanged. Polynucleosomes with repeat lengths of 212 bp also form fibers with the expected experimental properties. Systems with larger repeat length form fibers, but the mass density is significantly lower than the measured value. The theoretical characteristics of a fiber with a repeat length of 192 bp where DNA and nucleosomes are connected at the core particle are in agreement with the experimental values. Systems without a stem and a repeat length of 217 bp do not form fibers.     

A study of phi X-174 DNA torus and lambda DNA torus tertiary structure and the implications for DNA self-assembly

Hydrated torus shaped complexes were examined by transmission electron microscopy in both spermidine-condensed linear and nicked circular phi X-174 DNA and lambda DNA preparations. Freeze-etch replicas of both these torus samples, produced with very low Pt metal deposition levels (9APt/C), were found to have circumferentially wound single DNA double helix size surface fibers in the range of 30A width. Measurements of torus inner and outer circumference as well as ring thickness were performed. Observed differences in the torus dimension distributions from circular phi X-174 DNA and linear phi X-174 DNA may be related to the different topological constraints on DNA folding in these two samples (1). On the basis of annulus thickness measurements phi X-174 DNA toruses, in contrast to lambda DNA toruses, were observed to fall into two classes identified as being formed from monomer DNA condensation and multimer DNA condensation. All of the torus substructure and population dimensions observed here are consistent with the continuous circumferential DNA winding model of torus organization proposed by Marx and Reynolds (1) to explain the micrococcal nuclease cleavage properties of the toruses. End-on view measurements of the torus thickness were made from micrographs obtained by extensive tilting of the object replica. These direct measurements confirmed quaternary structure interpretations made from simple strand packing models. We compared the measured torus properties in this linear DNA size series (5386-48000 bp). With increasing DNA length the pattern of DNA strand self-assembly was found to be more varied producing lambda DNA toruses of varying shape. The relevance of our study to the problem of lambda bacteriophage DNA head packaging was discussed.     

A Study of øX-174 DNA Torus and Lambda DNA Torus Tertiary Structure and the Implications For DNA Self-Assembly

Abstract

Hydrated torus shaped complexes were examined by transmission electron microscopy in both spermidine-condensed linear and nicked circular øX-174 DNA and lambda DNA preparations. Freeze-etch replicas of both these torus samples, produced with very low Pt metal deposition levels (9APt/C), were found to have circumferentially wound single DNA double helix size surface fibers in the range of 30A width. Measurements of torus inner and outer circumference as well as ring thickness were performed. Observed differences in the torus dimension distributions from circular øX-174 DNA and linear øX ?174 DNA may be related to the different topological constraints on DNA folding in these two samples (1). On the basis of annulus thickness measurements øX ?174 DNA toruses, in contrast to lambda DNA toruses, were observed to fall into two classes identified as being formed from monomer DNA condensation and multimer DNA condensation. All of the torus substructure and population dimensions observed here are consistent with the continuous circumferential DNA winding model of torus organization proposed by Marx and Reynolds (1) to explain the micrococcal nuclease cleavage properties of the toruses. End-on view measurements of the torus thickness were made from micrographs obtained by extensive tilting of the object replica. These direct measurements confirmed quaternary structure interpretations made from simple strand packing models. We compared the measured torus properties in this linear DNA size series (5386–48000 bp). With increasing DNA length the pattern of DNA strand self- assembly was found to be more varied producing lambda DNA toruses of varying shape. The relevance of our study to the problem of lambda bacteriophage DNA head packaging was discussed.     

Forces and pressures in DNA packaging and release from viral capsids

In a previous communication (Kindt et al., 2001) we reported preliminary results of Brownian dynamics simulation and analytical theory which address the packaging and ejection forces involving DNA in bacteriophage capsids. In the present work we provide a systematic formulation of the underlying theory, featuring the energetic and structural aspects of the strongly confined DNA. The free energy of the DNA chain is expressed as a sum of contributions from its encapsidated and released portions, each expressed as a sum of bending and interstrand energies but subjected to different boundary conditions. The equilibrium structure and energy of the capsid-confined and free chain portions are determined, for each ejected length, by variational minimization of the free energy with respect to their shape profiles and interaxial spacings. Numerical results are derived for a model system mimicking the lambda-phage. We find that the fully encapsidated genome is highly compressed and strongly bent, forming a spool-like condensate, storing enormous elastic energy. The elastic stress is rapidly released during the first stage of DNA injection, indicating the large force (tens of pico Newtons) needed to complete the (inverse) loading process. The second injection stage sets in when approximately 1/3 of the genome has been released, and the interaxial distance has nearly reached its equilibrium value (corresponding to that of a relaxed torus in solution); concomitantly the encapsidated genome begins a gradual morphological transformation from a spool to a torus. We also calculate the loading force, the average pressure on the capsid's walls, and the anisotropic pressure profile within the capsid. The results are interpreted in terms of the (competing) bending and interaction components of the packing energy, and are shown to be in good agreement with available experimental data.     

A refined calculation of the solution dimensions of the complex between gene 32 protein and single stranded DNA based on estimates of the bending persistence length

The rotation diffusion coefficient of a complex of GP32, the single stranded DNA binding protein of the bacteriophage T4, with a single stranded DNA fragment with about 270 bases was determined to obtain further information on the flexibility of this particle. The rotation diffusion of these molecules is used as a sensitive measure of the flexibility of different DNA protein complexes. Using the theory of Hagerman and Zimm (Biopolymers 20, 1481 (1981)) and assuming a bending persistence length of about 35 nanometer it can be shown that the axial increment for GP32 complexes with single stranded DNA is close to 0.5 nm per base. The value for the bending persistence length is in agreement with values found for much larger DNA protein complexes using light scattering experiments. This value for the persistence length also implies that the complex is thin. The radius is estimated to be around 1.7 nm, which shows a moderate degree of hydration. With this set of parameters we can describe all the hydrodynamic experiments on GP32 complexes from 76 to more than 7000 bases obtained using electric birefringence, quasi-elastic light scattering and sedimentation experiments performed in our group over the last few years.     

Hexagonally packed DNA within bacteriophage T7 stabilized by curvature stress.

A continuum computation is proposed for the bending stress stabilizing DNA that is hexagonally packed within bacteriophage T7. Because the inner radius of the DNA spool is rather small, the stress of the curved DNA genome is strong enough to balance its electrostatic self-repulsion so as to form a stable hexagonal phase. The theory is in accord with the microscopically determined structure of bacteriophage T7 filled with DNA within the experimental margin of error.     

X-ray small-angle scattering study of mononucleosomes and of the close packing of nucleosomes in polynucleosomes

The radius of gyration of mononucleosomes determined by X-ray small-angle scattering is 4.35 nm. The maximum dimension determined from the distance distribution function and the volume amount to 12.9 nm and 370 nm³, respectively. For a particular fraction of polynucleosomes a mean radius of gyration 16 nm, a maximum dimension 65 nm, and a mean volume 25,240 nm³ is obtained.The shape is approximated by an elongated cylinder having a diameter of 28 nm. A polynucleosome is built up from 69 nucleosomes, on the average. The distance of neighbouring nucleosomes in the polynucleosome amounts to 5.2 nm. Moreover, this distance shows that the nucleosomes in the polynucleosome are very closely packed.     

Probing DNA conformational changes with high temporal resolution by tethered particle motion

The tethered particle motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dynamical level: we analyze how the relaxation time grows with both DNA contour length (from 401 to 2080 base pairs) and particle radius (from 20 to 150 nm). Notably we demonstrate that, for a particle of radius 20 nm or less, the hydrodynamic friction induced by the particle and the surface does not significantly slow down the DNA. This enables us to determine the optimal time resolution of TPM in distinct experimental contexts which can be as short as 20 ms.     

Helix–coil transition in nucleoprotein—theory and applications

A general theory of helix–coil transition of irreversibly complexed nucleoproteins is presented. The equations are tested by experimental results in basic polypeptide–DNA complexes, nucleohistone I and pea bud nucleohistones. They show good agreement between theory and experiments. The theory provides direct measurement of a fraction of DNA base pairs covered by proteins, yielding a value of about 75% histone-covered base pairs in pea bud nucleohistone. It also provides a measurement of an average number of amino acid residues per nucleotide in protein-bound regions. This number varies from 1.0 to 1.4 in DNA–polylysine or DNA–polyarginine and from 2.9 to 3.3 in nucleohistone Ia, Ib, f1, and pea bud nucleohistone.     

Nucleosome structure.

Electron microscopic and biochemical results are presented supporting the following conclusions: (1) Two molecules of each histone H2A, H2B, H3 and H4 are necessary and sufficient to form a nucleosome with a diameter of 12.5 +/- 1 nm and containing about 200 base pairs of DNA. (2) H3 plus H4 alone can compact 129 +/- 8 DNA base pairs into a sub-nucleosomal particle with a diameter of 8 +/- 1 nm. In such a particle the DNA duplex is under a constraint equivalent to negative superhelicity. (3) Chromatin should be viewed as a dynamic structure, oscillating between a compact structure (the nucleosome) and more open structures, depending on the environmental conditions.     

Flexibility of duplex DNA on the submicrosecond timescale

Using a site-specific, Electron Paramagnetic Resonance (EPR)-active spin probe that is more rigidly locked to the DNA than any previously reported, the internal dynamics of duplex DNAs in solution were studied. EPR spectra of linear duplex DNAs containing 14-100 base pairs were acquired and simulated by the stochastic Liouville equation for anisotropic rotational diffusion using the diffusion tensor for a right circular cylinder. Internal motions have previously been assumed to be on a rapid enough time scale that they caused an averaging of the spin interactions. This assumption, however, was found to be inconsistent with the experimental data. The weakly bending rod model is modified to take into account the finite relaxation times of the internal modes and applied to analyze the EPR spectra. With this modification, the dependence of the oscillation amplitude of the probe on position along the DNA was in good agreement with the predictions of the weakly bending rod theory. From the length and position dependence of the internal flexibility of the DNA, a submicrosecond dynamic bending persistence length of around 1500 to 1700 A was found. Schellman and Harvey (Biophys. Chem. 55:95-114, 1995) have estimated that, out of the total persistence length of duplex DNA, believed to be about 500 A, approximately 1500 A is accounted for by static bends and 750 A by fluctuating bends. A measured dynamic persistence length of around 1500 A leads to the suggestion that there are additional conformations of the DNA that relax on a longer time scale than that accessible by linear CW-EPR. These measurements are the first direct determination of the dynamic flexibility of duplex DNA in 0.1 M salt.     

Folding of red blood cells in capillaries and narrow pores.

The geometric features of red blood cells in narrow channels in vivo and in vitro were studied by electron microscopy. In rabbit myocardial capillaries about half of the red cells were folded. In polycarbonate filters with pore diameters of 2.2-4.5 microns approximately one third of the trapped red blood cells were folded. The frequency of folding did not depend on the applied pressure, which ranged from 0.1 to 8.0 cm H2O. The folding of the red blood cells in filter pores was used to estimate the bending stiffness of the membrane. An analysis based on the large deformation theory of bending of an elastic sheet was developed. Using pressures of 0.2 and 1.0 cm H2O, the bending stiffness of human red cell membranes was estimated to be approximately 2.4 - 11.6 x 10(-12) dyn-cm, which is in good agreement with other methods. A limiting radius of curvature of about 85 nm was found at higher pressures.     

Interaction of chromatin with NaCl and MgCl2: Solubility and binding studies,transition to and characterization of the higher-order structure

Chicken erythrocyte chromatin containing histones H1 and H5 was carefully separated into a number of well-characterized fractions. A distinction could be made between chromatin insoluble in NaCl above about 80 mm, and chromatin soluble at all NaCl concentrations. Both chromatin forms were indistinguishable electrophoretically and both underwent the transition from the low salt “10 nm” coil to the “30 nm” higher-order structure solenoid by either raising the MgCl₂ concentration to about 0.3 mm or the NaCl concentration to about 75 mm. The transitions were examined in detail by elastic light-scattering procedures. It could be shown that the 10 nm form is a flexible coil. For the 30 nm solenoid, the assumption of a rigid cylindrical structure was in good agreement with 5.7 nucleosomes per helical turn. However, disagreement of calculated frictional parameters with values derived from quasielastic light-scattering and sedimentation introduced the possibility that the higher-order structure, under these conditions, is more extended, flexible, or perhaps a mixture of structures. Values for density and refractive index increments of chromatin are also given.To understand the interaction of chromatin with NaCl and with MgCl₂, a number of experiments were undertaken to study solubility, precipitation, conformational transitions and binding of ions over a wide range of experimental conditions, including chromatin concentration.     

Conformation and circular dichroism of DNA.

CD spectra of calf thymus, C. perfringens, E. coli, and M. luteus DNA have been measured in the vacuum-uv region to about 168 nm for the A-, B-, and C-forms. The positive band at about 187 nm and the negative band at about 170 nm found for each type and form of DNA are sensitive to the source of the DNA and the base–base interactions of the double-stranded helix. The A-form spectra confirm that these bands are indeed sensitive to secondary structure. In the near-uv, the CD of B-form DNA is well analyzed as a linear combination of 27% A-form and 78% C-form. However, an analysis of the extended spectrum demonstrates that the near-uv analysis is not correct. The extended analysis shows that the base–base interactions are similar for B- and C-forms in solution, which implies that these two forms have nearly the same number of base pairs per turn. Various types of CD difference spectra are also discussed.