Opto-Electrostatic Determination of Nucleic Acid Double-Helix Dimensions and the Structure of the Molecule-Solvent Interface

Abstract

A DNA molecule is highly electrically charged in solution. The electrical potential at the molecular surface is known to vary strongly with the local geometry of the double helix and plays a pivotal role in DNA-protein interactions. Further out from the molecular surface, the electrical field propagating into the surrounding electrolyte bears fingerprints of the three-dimensional arrangement of the charged atoms in the molecule. However, precise extraction of the structural information encoded in the electrostatic "far field" has remained experimentally challenging. Here, we report an optical microscopy-based approach that detects the field distribution surrounding a charged molecule in solution, revealing geometric features such as the radius and the average rise per basepair of the double helix with up to sub-Angstrom precision, comparable with traditional molecular structure determination techniques like X-ray crystallography and nuclear magnetic resonance. Moreover, measurement of the helical radius furnishes an unprecedented view of both hydration and the arrangement of cations at the molecule-solvent interface. We demonstrate that a probe in the electrostatic far field delivers structural and chemical information on macromolecules, opening up a new dimension in the study of charged molecules and interfaces in solution.

Figure 1

High-precision ETe measurements on nucleic acid fragments. (a) Schematic representation (not-to-scale) of fluorescently labeled nucleic acid molecules confined in an array of electrostatic fluidic traps and imaged using wide-field optical microscopy (top). Maximum intensity projection of 500 fluorescence images of parallel arrays of ≈700 traps imaged for 20 s (bottom). (b) Calculated spatial distribution of minimum axial electrostatic free energy, , in a representative trap (top). Labels “1” and “2” denote locations of the molecule outside and inside the potential well, respectively, and refer to spatial locations in the trapping nanostructure depicted in the device schematic in (a). A time course of optical images in a single trap (bottom) displays the duration of a single recorded residence event of duration, Δt. (c) Probability density distributions, P(Δt), of escape times, Δt, for N = 10⁴ escape events for measurements on double-stranded B-DNA (solid lines) and A-RNA (dashed lines) in 1.23 mM LiCl for fragment length n_b = 30 (red), 40 (blue), and 60 (green) basepairs fitted to the expression . In order to enable comparison across different molecular species, P(Δt) data series are rescaled such that the maximum value is 1. Average escape times, t_esc, and measured effective charge values, q_m, are as follows: t_esc,30B = 52.2 ± 0.3 ms (q_m,30B = −25.28 ± 0.07e), t_esc,40B 93.9 ± 0.4 ms (30.46 ± 0.06e), and 242.5 ± 1.1 ms (40.71 ± 0.07e) for B-DNA and 46.3 ± 0.2 ms (−23.86 ± 0.04e), 70.4 ± 0.8 ms (−28.35 ± 0.13e), and 192.5 ± 0.6 ms (−37.26 ± 0.04e) for A-RNA. B-DNA systematically displays 10–20% longer escape times and higher magnitudes of effective charge than A-RNA. Space filling structures of B-DNA and A-RNA reproduced with permission from ref (3) (right).

Figure 2

Modeling the double helix as a smooth charged cylinder of finite length. (a) Distributions of surface electrostatic potential, ϕ, for two molecular models of a 30 bp fragment of B-DNA (IB and IIB—left) and A-RNA (IA and IIA—right) generated based on atomic coordinates with rolling probe radius (r_p = 1 Å) and solvent accessible surface (w) parameter values as listed and pictured (inset) alongside axial projections of the molecular models (top panel). Surface potential distributions for corresponding smooth charged cylinders equivalent to models IIB and IIA carrying a total charge 60e with radii, 10.8 Å and 11.7 Å, respectively, and length 30b Å in each case. The radius of the equivalent cylinder, (dashed lines), may be compared with a nominal double-helical radius r_c = 10 Å (dotted lines). (b) Calculated trends for the renormalization factor, , for cylinders of radius and length 30b Å, with nominal values of b = 3.4 Å for B-DNA (red line) and 2.6 Å for A-RNA (gray line). η values for the four molecular models can be related to those for smooth cylinders and correspond to 8.8 Å(effective vdW surface), 10.8 Å (effective SAS), 5 Å (vdWS), and 11.7 Å (SAS), two of which are depicted in (a). Panels are reproduced from ref (48), with the permission of AIP Publishing.

Figure 3

Measuring the helical rise per basepair and radius of the double helix. (a) Principle behind the measurement of the helical rise per basepair, b, and radius, r, of the double helix, for an ideal experiment, free of systematic measurement uncertainty (i.e., f_M = 1). Schematic representations of three lengths of a double-stranded nucleic acid species surrounded by a cloud of screening counterions (left). A measured value for each molecular species of length n bp, in conjunction with the corresponding calculated 2D function (colored surface) for the effective charge, , generates a curve of possible solutions in b and r. Intersection of three such curves for n = 30, 40, and 60 bp yields a probability-weighted manifold of solutions from which measured values, b_m and r_m, for the rise and radius, respectively, of each helix form can be obtained. (b) Measured b–r probability manifolds for B-DNA (top) and A-RNA (bottom) for an experiment performed in 1.2 mM CsCl. Since f_M ≠ 1 in experiments, measured b–r manifolds are broader than those in the ideal case depicted in (a) yielding 3.2 Å and 10.4 Å and 2.6 Å and 12.5 Å for B-DNA and A-RNA, respectively.

Figure 4

Inferring the structure of the molecule–electrolyte interface. (a) Measured helical rise per basepair, b_m (top), and radius, r_m (bottom), as a function of the hydrated cation radius, a_H. Error bars denote s.e.m. Rise per basepair values show no significant variation with a_H and yield average values of 3.1 ± 0.1 Å and 2.5 ± 0.1 Å. Helical radius data were fit with a function of the form , yielding 10.5 ± 0.6 Å and 11.8 ± 0.6 Å. The slope, k = 0.8 ± 0.2, is a shared fit parameter in both relationships. (b) Cylinder of radius 10.5 (blue dashed cylinder) depicting that the effective cylinder in model-IIB of B-DNA is superimposed for comparison on the vdW molecular surface in model-IB (gray dashed cylinder). k = 0.8 ± 0.2 suggests that the distance of the closest approach of screening cations to the molecular surface is directly related to the radius of the hydrated cation species, a_H. The resulting effective “ion accessible surface” (IAS) is the distance from the molecular axis beyond which the point-ion description of the electrolyte may be invoked (red, green, and blue dotted lines). The molecular structure may carry bound ions (yellow spheres) whose charge is included in . (c) For A-RNA, model-IIA which includes a SAS of thickness w = 3 Å meets the condition 12 Å (blue dashed cylinder). (d) Extrapolating the inferred structure of the molecule–electrolyte interface in (b) to a view of a macroscopic interface in solution where w < 3 Å.