Protein–DNA and ion–DNA interactions revealed through contrast variation SAXS

Abstract

Understanding how DNA carries out its biological roles requires knowledge of its interactions with biological partners. Since DNA is a polyanionic polymer, electrostatic interactions contribute significantly. These interactions are mediated by positively charged protein residues or charge compensating cations. Direct detection of these partners and/or their effect on DNA conformation poses challenges, especially for monitoring conformational dynamics in real time. Small-angle x-ray scattering (SAXS) is uniquely sensitive to both the conformation and local environment (i.e. protein partner and associated ions) of the DNA. The primary challenge of studying multi-component systems with SAXS lies in resolving how each component contributes to the measured scattering. Here, we review two contrast variation (CV) strategies that enable targeted studies of the structures of DNA or its associated partners. First, solution contrast variation enables measurement of DNA conformation within a protein–DNA complex by masking out the protein contribution to the scattering profile. We review a specific example, in which the real-time unwrapping of DNA from a nucleosome core particle is measured during salt-induced disassembly. The second method, heavy atom isomorphous replacement, reports the spatial distribution of the cation cloud around duplex DNA by exploiting changes in the scattering strength of cations with varying atomic numbers. We demonstrate the application of this approach to provide the spatial distribution of monovalent cations (Na⁺, K⁺, Rb⁺, Cs⁺) around a standard 25-base pair DNA. The CV strategies presented here are valuable tools for understanding DNA interactions with its biological partners.

Introduction

The double helical structure of DNA enables the efficient storage, replication, repair and transcription of this fundamental macromolecule. These functions and others require macromolecular partners, and are carried out on the background of physiological solutions with ionic strengths that exceed 0.1 M (Mouat and Manchester 1998). Because of the high negative charge of the DNA backbone, long-range electrostatic forces affect DNA’s interactions with essential cellular partners. These partners range in size and complexity from small cations to large macromolecular protein complexes (Bloomfield et al. 2001; Martin and Saenger 2013).

The majority of macromolecules that interact with DNA are proteins (Luscombe et al. 2000; Hernan et al. 2007; Luger and Phillips 2010; Rohs et al. 2010). Many DNA binding proteins possess positively charged side chains and exploit electrostatics in their interactions with DNA’s backbone (Korolev et al. 2007). For example, positively charged regions in histone proteins help fold DNA into stable structures that lead to efficient storage in chromatin (Clark and Kimura 1990; Widom 1998; Hansen 2002; Korolev et al. 2010; Andrews and Luger 2011). Not all interactions are passive, as enzymes like helicases exploit electrostatic interactions to actively unwind DNA (Thommes and Hubscher 1992; Liu et al. 2009).

In addition to proteins, smaller, charged molecules also serve as essential partners of DNA (Wong and Pollack 2010). They are more challenging to study because, unlike many DNA-binding proteins, these smaller molecules or ions can interact non-specifically with DNA structures and are therefore not amenable to characterization by standard methods like x-ray crystallography. Because much of the charge compensation of DNA in cells is accomplished by small salt ions, a detailed understanding of their interactions with DNA is essential in gaining an accurate view of electrostatic interactions between DNA and other partners, including proteins (Lohman and Overman 1985). Simple systems such as DNA duplexes in salt solutions of monovalent or divalent ions are important benchmarks for modeling electrostatic effects and are essential for validating force fields or theories that accurately capture DNA electrostatics (Anderson 1995; Zuo et al. 2006; Park et al. 2009; Nguyen et al. 2014; Meisburger et al. 2015). Accurate and experimentally validated parameters are essential for developing models of protein–DNA interactions.

Our understanding of DNA is intricately linked with knowledge of how it interacts with partners. In this review, we describe recent updates to two contrast variation (CV) methods employed with solution small-angle x-ray scattering (SAXS) that highlight the interactions between DNA and protein or solvent/ion partners. The first example describes the use of dense solvents to mask the scattering of proteins in a protein–DNA system. In conjunction with time-resolved methods and changing solution conditions, contrast variation SAXS provides new insights into the electrostatic interactions that stabilize protein–DNA complexes, as well as DNA conformational changes within these complexes. We also discuss recent progress in using heavy atom replacement methods to quantify the hydration and ionic environment around double-stranded DNA. The new information provides stringent tests of theories and also yields fundamentally important information about the ubiquitous, but difficult to visualize partners that influence DNA interactions with all other molecules in the cell.

General SAXS overview and two contrast variation strategies

We begin with a brief overview of solution SAXS, a remarkably simple, yet powerful technique that provides information about the structures of biological macromolecules. SAXS studies can be easily carried out under a variety of solution conditions and as a function of time, allowing ready access to measurements of large-scale conformational changes and assembly/disassembly processes important for biological function (Lipfert and Doniach 2007; Jacques and Trewhella 2010; Skou et al. 2014). Recent advances in x-ray sources, data collection and analysis tools have greatly expanded the biological problems that may be investigated with SAXS (Pérez and Nishino 2012; Graewert and Svergun 2013; Vestergaard and Sayers 2014; Chaudhuri 2015; Curry 2015). The theoretical principles behind SAXS and novel applications are covered in great detail in other reviews (Koch et al. 2003; Svergun and Koch 2003). Here, we provide only the relevant introductory information to understand the contrast variation methods, whose application to DNA–partner interactions is the subject of this review.

The SAXS signal originates as illustrated in Fig. 1, when a dilute solution of macromolecules is exposed to x-rays. X-rays scatter elastically in response to electron density variations throughout the illuminated volume, and yield a diffraction pattern. Although the spatial and orientational averaging of macromolecules in solution result in a loss of atomic-scale resolution, the resulting 1-dimensional intensity profile contains information about macromolecular features with a resolution that is typically of order 10 Å for SAXS. Global structural properties such as molecular weight, radius of gyration, and low-resolution shape envelopes are readily obtained for any homogeneous macromolecular system. However, in the case of multi-component systems (e.g., protein–DNA complexes, or DNA and its ion cloud), interpretation of SAXS data is obscured by our limited ability to discern how each component contributes to the total scattering.

Fig. 1.

Small-angle X-ray scattering (SAXS) is a solution-based approach that yields the low-resolution structures of macromolecules. Left A schematic of a typical SAXS experiment is shown. The sample is typically a buffered solution containing 2 mg/mL of protein, DNA, or protein–DNA complex. This sample oscillates through a quartz capillary to reduce radiation damage from the x-ray beam. The scattered x-rays are imaged onto an area detector while the primary beam is either blocked or greatly attenuated (as shown) by a beamstop. Right The images are pooled, averaged, and converted into profiles of intensity as a function of scattering vector, I(q), through azimuthal integration. For each sample, a corresponding measurement of the buffer alone is made and the resulting buffer profile is subtracted from the sample profile to obtain the macromolecular SAXS profile. SAXS intensities can be calibrated onto an absolute scale (in units of e²) through the measurement of water as a standard

In order to understand the principles behind these contrast variation approaches, we briefly discuss the origin of the SAXS signal (for more details, see Guinier and Fournet 1955; Glatter and Kratky 1982). In most SAXS experiments, macromolecules have a higher electron density than the solvent that surrounds them. This density difference gives rise to the scattering, and can be expressed in terms of the (average) electron density difference between the macromolecule and the solution: Δρ _M = ρ _M − ρ _solv. The number of excess electrons present in the volume occupied by the macromolecule (relative to an identical volume occupied by the solvent) is given by the scattering factor: f ₁ = Δρ _M V _M, where V _M indicates the volume of the macromolecule. If the macromolecule were in vacuum, f ₁ would equal the number of electrons present in the macromolecule. Since the solvent is essential for physiological measurements, the relevant value reflects the number of excess electrons above that contained by the solvent in the same volume.

The amplitude of the SAXS signal is described by the product of this scattering factor, f ₁, and an angle (or q)-dependent form factor, F ₁(q), that reflects the arrangement of electrons in the macromolecule. For a single component system, the scattering amplitude is given by: A = f ₁ F ₁(q). This equation neglects density fluctuations internal to the macromolecule (Svergun and Koch 2003). SAXS experiments measure intensity: the product of the scattering amplitude and its complex conjugate. For a single particle system, this “squaring” is not of concern. The measured scattering intensity can be written as:

$$I\left(q\right)={f_1}^2{P}_1\left(q\right)\text{,}$$ 1

where P ₁(q) is the partial scattering form factor of this molecule, given by F ₁(q)F ₁*(q) integrated over all space. P ₁(q) reflects the shape of the macromolecule and is unity at q = 0.

For a two-component system, the total scattering amplitude is the sum of that from each component: A = f ₁ F ₁(q) + f ₂ F ₂(q), where the subscripts reflect each of the two components. The resulting expression for scattering intensity contains cross terms, proportional to various products of the form factors, F ₁(q) and F ₂(q). These terms, which depend on the structures of both particles, introduce new challenges and present new opportunities for the study of multicomponent systems (i.e. DNA–protein, or DNA–ion). For this system, the scattering intensity I(q) is given by:

$$I\left(q\right)={f_1}^2{P}_1\left(q\right)+2f_1{f}_2{P}_{12}\left(q\right)+{f_2}^2{P}_2\left(q\right)\text{,}$$ 2

where P ₁(q) and P ₂(q) are the partial scattering form factors for each of the two components and reflects their individual contributions. The cross term, P ₁₂(q), contains information about the relative distributions of electrons between the two components.

The two experimental strategies we describe vary the scattering factors (f ₁ or f ₂) in the above equations. In solution contrast variation, which is applied to DNA–protein systems, the solvent is manipulated to eliminate the contribution from one of the components. If DNA is component 1 and a protein partner is component 2, the contrast variation experiment essentially drives f ₂ to zero. In the second method, heavy atom isomorphous replacement, consider the case where DNA is component 1 and the ion cloud is component 2. Varying f ₂ in a predictable way leads to a solvable system of simultaneous equations, which allows us to extract both the cross term and the much weaker scattering term P ₂, providing the distribution of counterions. Absolute calibration of the intensities allows us to extrapolate to the case of f ₂ = 0, providing information about the hydrating waters associated to the DNA.

Principles behind solution contrast variation

Solution contrast variation (Fig. 2) allows the SAXS signal from individual components to be measured within a multi-component complex if the components have different electron densities. The signal is isolated by varying the electron density of the bulk solvent until it matches that of one of the components. Under this condition, the matched component no longer contributes to the measured signal and details from the remaining components can be obtained. This approach is detailed in Stuhrmann and Kirste (1965), Jacques and Trewhella (2010), and Svergun et al. (2013). Below, we demonstrate how solution CV can be applied to reveal the conformational details of DNA within a protein–DNA complex. This information is valuable when addressing important issues, for example, understanding how proteins modulate DNA structure for further processing in the cell.

Fig. 2.

Cartoon illustration of the principle behind solution contrast variation. a A color scale bar is shown with average electron density values for DNA, protein, and water. b, c Cartoon schematics of the nucleosome core particle (1AOI, Luger et al. 1997) in buffers with electron densities that vary according to the addition of 0 % (b) and 50 % (c) sucrose. The resulting contrasts (excess electron densities) are shown below each condition. d SAXS profiles for the DNA and histone proteins measured separately with and without sucrose. Note: in 50 % sucrose, the histone SAXS signal disappears, but the DNA is still visible due to its higher electron density

If component 1 represents the DNA and component 2 represents the protein, then Eq. 2 can be rewritten as:

$$I\left(q\right)={f_{DNA}}^2{P}_{DNA}\left(q\right)+2f_{DNA}{f}_{\mathit{prot}}{P}_{DNA•\mathit{prot}}\left(q\right)+{f_{\mathit{prot}}}^2{P}_{\mathit{prot}}\left(q\right)\text{,}$$ 3

where f _DNA, P _DNA(q) and f _prot, P _prot(q) represent the scattering factors and partial form factors for the two components, respectively. P _{DNA • prot}(q) is the cross-term form factor. The scattering factors are related to electron densities as f _DNA ∝ (ρ _DNA − ρ _solv) and f _prot ∝ (ρ _prot − ρ _solv). If the solvent electron density (ρ _solv) is increased to equal that of the protein (ρ _prot), then f _prot = 0 and the second and third terms of Eq. 3 vanish (note: Eq. 3 becomes Eq. 1, which describes a single component system). As stated above, this analysis does not account for internal density fluctuations within the DNA or protein components—a valid approximation in most cases since these fluctuations are typically much smaller that the differences between the components. Nevertheless, the resulting scattering profile is dominated by the DNA shape and conformational details of the DNA emerge that are otherwise obscured in standard SAXS measurements. The addition of 50–65 % (w/v) sucrose to the solvent typically suffices to match the electron density of most proteins. Note that the effective scattering factor for the DNA is also reduced when the solvent electron density is increased, which results in a weaker but otherwise unchanged signal. This approach is visualized in Fig. 2.

Theoretically, if the electron density of the solvent was increased further to match that of the DNA, the protein signal from the complex can be isolated. Sucrose cannot be used to achieve this matching condition due to solubility limits; however, the use of other highly soluble additives with heavier atoms may enable such studies in the future. Small-angle neutron scattering (SANS) is better suited for this type of contrast matching due to the remarkable difference in scattering between hydrogen and deuterium. In SANS, the scattering from various components can be selected by varying the H₂O/D₂O composition of the solvent. This approach has been applied with great success in the pioneering studies of nucleosomes (Baldwin et al. 1975; Bram et al. 1975; Pardon et al. 1975) as well as a variety of other biomolecular complexes (Stuhrmann and Kirste 1965; Hjelm et al. 1977; Svergun et al. 1994, 2013; Svergun and Koch 1994; Jacques and Trewhella 2010). Solution CV has proven to be a powerful tool in SAXS studies for elucidating the structural details of multi-component systems in which each component has a distinct electron density. Measurements carried out at multiple contrast levels can be used to identify the best match point for one component, or to reveal finer structural details. Though outside the scope of work described here, these approaches have been described (Ibel and Stuhrmann 1975; Sardet et al. 1976; Tardieu et al. 1976; Ueki et al. 1986; Inoko et al. 1992). Recent advancements in x-ray technologies and high flux of x-ray sources significantly decreases the measurement time and uniquely enables time-resolved studies (Chen et al. 2014). Contrast variation SAXS and SANS methods have been reviewed (Stuhrmann 1974; Stuhrmann and Miller 1978; Jacques and Trewhella 2010; Svergun et al. 2013).

Solvent CV SAXS reveals partially unwrapped states for DNA in nucleosome core particles

The power of solvent CV methods to reveal biologically important changes in a protein–DNA system is highlighted in recent studies that focus on the salt-induced disassembly of nucleosomes (Chen et al. 2014). To package and regulate access to nuclear genetic information, eukaryotic cells organize the DNA in repeated structural units called nucleosome core particles (NCPs) (Kornberg and Lorch 1999; Andrews and Luger 2011). NCPs consist of approximately 147 base pairs (bp) of DNA wrapped in ≈1.7 superhelical turns around a symmetric octamer of histone proteins. Although high-resolution structures for the most stable conformations have been well characterized (Luger et al. 1997; Richmond and Davey 2003), little is known about the transient and partially unwrapped structures relevant to nucleosome dynamics (Li and Widom 2004; Mihardja et al. 2006; Gansen et al. 2009a, b; Shlyakhtenko et al. 2009; Zlatanova et al. 2009; Prinsen and Schiessel 2010; Tims et al. 2011; Li and Wang 2012; Ngo et al. 2015; Ngo and Ha 2015; Vlijm et al. 2015). These dynamics regulate the accessibility of DNA for processing by proteins. Since these protein–DNA interactions are mediated by electrostatic interactions, the addition of salt weakens the protein’s affinity for the DNA, and populates partially disrupted species (Yager et al. 1989; Hoch et al. 2007; Gansen et al. 2009a, 2015; Buning and Van Noort 2010). Contrast variation is an ideal method to monitor DNA release as the complex is destabilized by salt.

The first step in a solvent CV experiment is to determine how much sucrose needs to be added to increase the density of the buffer until it matches that of the proteins (Fig. 2c). To accomplish this goal, SAXS profiles of isolated histone proteins are acquired in solutions containing different concentrations of sucrose. In 50 % (w/v) sucrose, the protein signal was effectively eliminated (Fig. 2d). Because variations in the sucrose concentration can lead to small changes in scattering, one of the greatest challenges associated with this technique is the need to closely match the sucrose concentration in the buffer sample with that of the NCP sample. SAXS profiles of the DNA alone were also acquired at this solution condition, and confirmed that sufficient signal exists to determine DNA conformation. In this case, where it is possible to extract only the scattering of one component in a multicomponent system, it is straightforward to compute the pairwise distance distribution function, P(R), which is related to the Fourier transform (FT) of the SAXS profile as shown in Eq. 4 (Svergun and Koch 2003):

$$P\left(R\right)=\frac{1}{2{\pi }^2}{\displaystyle {\int }_0^{\infty }I\left(q\right)·qR·sin\left(qR\right)dq}\text{.}$$ 4

In practice, only approximate solutions for P(R) are obtained through indirect Fourier transform methods due to experimental limitations (e.g., finite measureable q-range). Detailed instructions for obtaining reliable P(R) curves are reviewed in Skou et al. (2014). This procedure allows a conversion of SAXS data from reciprocal (q) to real space (R), and can be very informative if well-defined shapes are present. Peaks in the P(R) distributions represent length scales that are prominent or repeated in the particles, and assist in interpreting structural changes reported by SAXS. These P(R) computations are relatively straightforward to apply using readily available software such as GNOM (Svergun 1992).

SAXS profiles were measured (q-range: 0.007–0.26 Å⁻¹) for NCPs equilibrated in buffers with NaCl concentrations ranging from 0.2 to 2.0 M. At low salt concentrations, the DNA is stably wound around the histone core. At high salt concentrations (≈ 2 M NaCl), complete dissociation is observed, and the DNA assumes a rod-like shape due to its long persistence length (Hagerman 1988; Marko and Siggia 1995; You et al. 2012). These expected end states (fully wrapped vs. fully released) are shown in Fig. 3a. Figure 3b shows pairwise distance distributions, P(R), computed from data acquired on NCP particles in a salt titration without sucrose. In 0.2 M NaCl, the NCPs are compact with the DNA predominantly wrapped tightly. The general extension observed in the P(R) curves as the salt concentration increases reflects the increasing population of partially unwrapped species. However, the trends observed in the P(R) curves are extremely challenging to interpret when both protein and DNA scatter. The addition of sucrose to mask the signal from the protein significantly clarifies the situation and illustrates the power of this approach.

Fig. 3.

Application of solution contrast variation to monitor DNA unwrapping during the salt-induced disassembly of nucleosome core particles (NCP). a DNA models for the expected end states of the NCP at low [NaCl] (completely wrapped) and high [NaCl] (completely unwrapped). b P(R) curves for the NCP measured in 0 % sucrose and varied [NaCl]. c P(R) curves for the NCP measured in 50 % sucrose and varied [NaCl]. d P(R) curves determined for the models in (a). Peaks in the P(R) curves can be associated with structural features as follows: d ₁, diameter of the duplex DNA; d ₂, distance between overlapping DNA ends; d ₃, diameter of the overall wrapped structure. These curves, specifically the difference between P(R) illustrate highlight how structural features emerge in the contrast matched condition

When the NCP in the same salt series is measured with 50 % sucrose, the protein scattering is effectively eliminated and identifiable features emerge from the P(R) distributions (Fig. 3c). These peaks reveal conformational details of the nucleosomal DNA with varying degrees of unwrapping. In order to interpret these features, the peaks are compared with theoretical P(R)s (Fig. 3c) calculated for the expected end states of Fig. 3a. As the DNA unwraps with increasing salt, several trends proceed as follows: (1) the peak at d₁ ≈ 20 Å increases, reflecting the extension of duplex DNA, (2) the peak at d₂ ≈ 40 Å decreases, coinciding with the reduction of overlap between the DNA ends, and (3) the peak at d₃ ≈ 80 Å decreases, corresponding to the disruption of the overall wrapped structure. These results illustrate the advantage of applying solution contrast variation to provide insight into DNA conformation within a protein–DNA complex.

In order to visualize the DNA conformations present at each salt concentration, the SAXS profiles collected for NCPs in 50 % sucrose can be used as a constraint to select DNA conformations that best recapitulate the data. This approach is preferred over ab initio reconstructions which struggle to generate certain structural features (e.g., holes, as found in wrapped DNA, and structures with large aspect ratios, as found in unwrapped DNA). First, a pool of DNA structures is generated with varying degrees of unwrapping (see methods in Chen et al. 2014). Since multiple DNA conformations may be present at each salt concentration, a genetic algorithm selects an ensemble of structures that produce SAXS profiles that best match the data at each condition. Although this approach, called ensemble optimization method (EOM) (Bernadó et al. 2007; Bernadó and Svergun 2012), was initially designed for flexible proteins, this strategy has been successfully adapted to identify conformational details of nucleic acids measured with SAXS (Stoddard et al. 2010; Kazantsev et al. 2011; Gopal et al. 2012; Chen et al. 2014). An example fit of the experimental data with the theoretical profile generated from the ensemble selected for the data collected at 1.0 M NaCl and 50 % sucrose is shown in Fig. 4a. The DNA models selected for each salt concentration are shown in Fig. 4b. These structures independently confirm the interpretation of the P(R) curves provided above, and highlight the power of this approach for determining the structures of DNA within protein–DNA complexes.

Fig. 4.

DNA models selected by ensemble optimization method (EOM) that best recapitulate the [NaCl]-dependent SAXS data for NCPs measured in 50 % sucrose. a Fit of the experimental data collected at 1.0 M NaCl with the theoretical SAXS curve generated from the ensemble of structures selected by EOM. Similar fits (not shown) were found for other [NaCl] concentrations. b Models representing the ensemble of structures selected by EOM that generate SAXS profiles that best fit the data measured at the indicated salt concentrations. χ ² values assessing the overall fit to the experimental data and percentages reporting the weight of each model are shown. These models show how the DNA unwraps with increasing [NaCl]

The combination of this approach with time-resolved methods available at bright x-ray synchrotron sources uniquely enables measurements of the dynamics of the conformational change. Chen et al. proceeded to resolve transient structures with millisecond time resolution by incorporating a stopped flow mixer that effected a salt jump from the initial, wrapped state (0.2 M) to the final extended state (≈ 2 M). A transient, asymmetric state was detected, with a short lifetime of about 1 s. This DNA conformation may serve as an important biological substrate for gene regulation.

CV-SAXS methods that focus on DNA’s partners: water and counterions

In the absence of protein partners, DNA is surrounded by charge compensating salt ions and water (Manning 1969; Draper 2004). A full understanding of biological processes requires knowledge of the solvent structure around DNA as binding and release of these small ions and molecules facilitate all other interactions (Lohman and Overman 1985; Wong and Pollack 2010; Lipfert et al. 2014). Commonly applied electrostatic theories that describe the structure and composition of salt ions in the solvent are based on mean-field treatments, for example the Poisson–Boltzmann equation (Chin et al. 1999; Grochowski and Trylska 2007). Although these theoretical treatments are straightforward to apply, they insufficiently capture the details necessary to fully describe ion–DNA interactions (Bardhan 2012). Improved theories with varying degrees of sophistication have been proposed to predict the spatial arrangement of ions around DNA (Holst et al. 2000; Rocchia et al. 2001; Das et al. 2003; Tang et al. 2004; Bai et al. 2007; Chu et al. 2007; Giambaşu et al. 2014; Nguyen et al. 2014). However, assessment of the validity of any approach requires comparison with measurements that are sensitive to DNA’s ionic and solution environment. Contrast variation SAXS methods offer several ways to detect localized but not exclusively site bound ions.

Anomalous SAXS, or ASAXS, has been successfully used to count the number of excess positively charged counterions around nucleic acids relative to the number that would exist in solution without the DNA (Pabit et al. 2009b, 2010). ASAXS also provides their positions relative to the macromolecule (Andresen et al. 2004, 2008; Ballauff and Jusufi 2006; Pabit et al. 2009a; Pollack 2011; Sztucki et al. 2012). Here, the counterion contrast is varied by probing the system with different energy x-rays. If the x-ray energy is close to the binding energy of a core electron in a particular element, its scattering strength is reduced relative to a measurement far from this atomic absorption edge (Bradley et al. 2006a, b). Measurements at different energies can be used to vary the contrast of one atomic species within a sample. These energy-dependent changes can be exploited to provide the information of interest. ASAXS methods have been recently reviewed in Pabit et al. (2009a), and will not be discussed here. Instead, we revisit the method of heavy atom isomorphous replacement, as previously used to study ions around DNA (Luzzati 1967; Chang et al. 1990; Das et al. 2003; Morfin et al. 2004; Meisburger et al. 2015). Recently, this method was powerfully updated (Meisburger et al. 2015) by combining absolute calibration with a new systematic approach that solves a series of simultaneous equations, carried out at different values of counterion contrast.

Heavy atom isomorphous replacement reveals the number and spatial distribution of monovalent ions around DNA

In heavy atom isomorphous replacement, the strength of the scattering from the ion atmosphere is systematically varied by substituting the associated ions with heavier counterparts. Recent work focused on measurements of a series of monovalent ions around dilute, non-interacting solutions of 25-bp DNA ([DNA] = 50 μM). The duplex was buffer-exchanged extensively in different salt solutions, containing either 100 mM NaCl, KCl, RbCl, or CsCl and 1 mM Na-MOPS, pH 7.0. Returning to Eq. 2, if the DNA is component 1 and the ions are component 2, the scattering intensity from these ion–DNA systems is represented as follows:

$$I\left(q\right)={f_M}^2{P}_M\left(q\right)+2f_M\left(N_{\mathit{Ion}}{f}_{\mathit{Ion}}\right)P_{MI}\left(q\right)+{\left(N_{\mathit{Ion}}{f}_{\mathit{Ion}}\right)}^2{P}_I\left(q\right)\text{,}$$ 5

where f _M is the number of excess electrons contributed by the DNA and its associated water molecules, N _Ion and f _Ion are the number of associated counterions and the number of excess electrons per ion, and P _M(q) and P _I(q) are the partial scattering factors associated with the hydrated macromolecule and the counterions. P _MI(q) is the cross term, with contributions from both the structure of the macromolecule and the ions.

The use of different counterions (with known values of contrast) is equivalent to varying f _Ion and yields a series of simultaneous equations that can be solved to extract information about DNA hydration and the distribution of counterions. This strategy is illustrated in Fig. 5a, where progressively larger ions are distributed around a DNA duplex. An underlying assumption for this analysis is that the ion distribution remains the same, despite the increase in atomic number.

Fig. 5.

Application of heavy atom isomorphous replacement to study the ion atmosphere around a 25-base pair DNA duplex. a Cartoon illustration of how increasing the atomic number of the monovalent cation cloud affects the scattering profile of the DNA–ion system. Ion size differences have been exaggerated to emphasize the increasing scattering factor. The dynamic spatial distributions of the different species of cations are assumed to be the same. b SAXS profiles for 50 μM DNA measured in 100 millimolar solutions of the monovalent chloride salts shown in (a). The increasing contrast for the heavier cations results in larger scattering signals. c The square root of the extrapolated forward scattering is shown to vary linearly with the effective ion contrast (see Eq. 5). This linearity is consistent with the assumption that the number and arrangement of these (excess) cations are identical (Meisburger et al. 2015)

These experiments benefit from absolute calibration of the data (Orthaber et al. 2000). Here, the measured intensity on the detector is converted into absolute scattering strength in terms of the square of the number of electrons in the sample. Equation 5 reveals a very useful application of this calibration. At q = 0, the form factors are unity: P _M(0) = P _MI(0) = P _I(0) = 1. Therefore, we can write:

$$I\left(q=0\right)={\left(f_M+N_{\mathit{Ion}}{f}_{\mathit{Ion}}\right)}^2\text{.}$$ 6

Here, f _Ion is the effective number of electrons, derived from the number of electrons per ion (in vacuum) minus the density of the solvent times the partial molar volume of the ion (Meisburger et al. 2015). Figure 5b shows the scattering profiles of DNA in the presence of the different monovalent ions. Note the increased scattering signal as the compensating cations increase in atomic number. A fit to the data provides the value of I(q = 0), which can be used in the above equation.

Given the linear nature of Eq. 6, a plot of the $\sqrt{I\left(0\right)}$ versus f _Ion in Fig. 5c yields the value of f _M as the y-intercept. This value of f _M includes information about the number of tightly associated waters as discussed in detail in Meisburger et al. (2015). The slope of the line provides the number of ions, N _Ion. For the case of monovalent ions around DNA, the value obtained, 36.5 ± 2.4, is in good agreement with ion counting via ASAXS measurements, 39 ± 2 (Pabit et al. 2010; Nguyen et al. 2014). The straight line validates our assumption of identical distributions for the different monovalent ions. All these parameters provide useful experimental benchmarks for comparison with theories of ion and water association to DNA.

In addition, the partial scattering form factors P _M(q), P _MI(q), P _I(q) can be extracted from the data for comparison to theory. Figure 6 shows the partial scattering form factors scaled by the scattering factors determined for Rb (terms from Eq. 5). Most useful are the latter two curves, which reflect the ion–DNA interference term, and the pure ion scattering term. We note that a similar decomposition can be used in ASAXS to extract these terms if measurements at more than three energies are acquired (Ballauff and Jusufi 2006). However, the ion contributions measured using heavy atom isomorphous replacement can be obtained with greater signal-to-noise relative to ASAXS since the relevant ion scattering signal (third term in Eq. 5) is significantly larger than that measured from the anomalous signal (Pabit et al. 2009a). The shapes of the ion–DNA and ion scattering terms provide insight into the spatial arrangement of ions around the DNA and can be used to assess theoretical models of the ion cloud. As shown in Meisburger et al. (2015), comparison of these shape-functions to predicted scattering profiles based on the non-linear Poisson Boltmann equations suggest that this mean field theory underestimates the number of ions present near the DNA surface.

Fig. 6.

Mathematical decomposition of the measured scattering of DNA duplexes and associated ions into contributions from partial structure factors. Shown here are the terms in Eq. 4 calculated for the DNA surrounded by a cloud of Rb⁺ ions. Details for this calculation are provided in Meisburger et al. (2015). Regularized fits to the data (black) were calculated using GNOM (Svergun 1992). Since DNA is always surrounded by a cloud of charge compensating ions, the mathematical decomposition illustrates the strong contributions of the DNA–ion cross term and the ion–ion scattering to the scattering profile of the DNA–ion system

Conclusions and outlook

This review focused on recent developments in measuring the distribution of partner molecules that are critical to the structure and function of DNA, demonstrating how SAXS contrast variation methods can be applied to focus on one component in a multi-component system. The first example illustrated how the contributions from lower density proteins could be ‘masked’ in a protein–DNA system, to reveal only the scattering from the DNA. The second example illustrated how the scattering from counterions could be enhanced in an ion–DNA system to extract critical information about their number and distribution around DNA. The overall goal of this work is to enable measurements that focus on only one component, although both are present. This strategy allows for more direct comparison with predictions and elucidates DNA interactions with its biological partners.

Although neither contrast variation, nor heavy atom replacement techniques are new, the advent of high brightness x-ray sources enables the new opportunities described here. For the case of the counterion scattering, the large signal sizes (relative to the noise) allows the extraction of weaker terms, such as the ion partial scattering factor. Extension to ions of higher valence is in progress, but caution must be exercised to ensure that the assumption about identical ion distribution holds. For divalent ions, specific interactions are known to occur, which may alter ion distributions according to ion type.

It is also exciting to consider future opportunities to monitor structural dynamics by the inclusion of time-resolved methods with the solvent contrast variations methods described. Time resolution as short as 10 ms has recently been demonstrated (manuscript in preparation), and extension to longer time scales, as warranted by the biological questions, is also possible. This tool can also be extended to the study of RNA–protein systems. Planned experiments include watching enzymes, such as polymerases or helicases, as they modify nucleic acid substrates in real time, as well as the ejection of genomic material from viruses.

Compliance with ethical standards

Conflict of interest

Joshua M. Tokuda declares that he has no conflict of interest.

Suzette A. Pabit declares that she has no conflict of interest.

Lois Pollack declares that she has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.