DNA Counterions Research Articles

Unusual bending patterns of spermidine3+ bound to DNA double helix

Natural polyamines play a fundamental role in the cell cycle. Despite being recognized as the most abundant organic counterions of DNA in the cell nucleus, their interactions with DNA have not been fully characterized. In a recent work [S. Perepelytsya, T. Vasiliu, A. Laaksonen, L. Engelbrecht, G. Brancato, and F. Mocci, J. Molec. Liq.389, 122828 (2023)], we have shown how the interactions between spermidine3+ and the DNA double helix induce significant conformational variations in the polyamine molecule. Specifically, we found that DNA induces conformations that are not observed in solution. Following that study, we present here a detailed investigation of the most compact conformation of the polyamine, analyzing its connection to the interaction with the DNA duplex. The analysis reveals that anomalous bent conformations of the spermidine3+ molecule result from the interaction of all three amino groups of the polyamine with the DNA phosphate groups on the minor groove side of the double helix. The changes in dihedral angles of the bent spermidine3+ molecule can be explained in terms of conformational transformations of six- and seven-membered rings, analogous to cyclohexane and cycloheptane. The analysis of the position of spermidine3+ molecule along the DNA surface reveals a sequence specificity of this binding mode with a marked preference for the narrow minor groove of A-tracts. The formation of the anomalous bent conformations of spermidine3+ in the complex with the DNA double helix is expected to be of paramount importance in understanding the mechanisms underlying DNA’s biological function.

Nanoscale hydration dynamics of DNA-lipid blend dry films: DNA-size dependency.

In this study, nanoscale hydration dynamics of DNA-lipid blend dry films are investigated via small angle X-ray diffraction. Compared to the hydration of lipid films, fragmented short DNA strands and counterions in stacked lipid layers dramatically accelerate both the relaxation of the lamellar distance to a metastable interval and the subsequent peeling-off process of lipid bilayers. Moreover, genome-sized long DNA and counterions accelerate the relaxation process, but suppress the peeling-off process and simultaneously induce a damped-oscillation of the lamellar interval; this is probably due to the viscoelastic properties of the entangled long DNA dissolved in hydrated water between the stacked lipid bilayers. This study's findings can pave the way for producing cell-sized liposomes, which efficiently encapsulate any arbitrary sized DNA through natural swelling.

Ultrafast vibrational dynamics of the DNA backbone at different hydration levels mapped by two-dimensional infrared spectroscopy.

DNA oligomers are studied at 0% and 92% relative humidity, corresponding to N < 2 and N > 20 water molecules per base pair. Two-dimensional (2D) infrared spectroscopy of DNA backbone modes between 920 and 1120 cm−1 maps fluctuating interactions at the DNA surface. At both hydration levels, a frequency fluctuation correlation function with a 300 fs decay and a slow decay beyond 10 ps is derived from the 2D lineshapes. The fast component reflects motions of DNA helix, counterions, and water shell. Its higher amplitude at high hydration level reveals a significant contribution of water to the fluctuating forces. The slow component reflects disorder-induced inhomogeneous broadening.

Understanding the mechanism of DNA deactivation in ion therapy of cancer cells: hydrogen peroxide action*

Changes in the medium of biological cells under ion beam irradiation has been considered as a possible cause of cell function disruption in the living body. The interaction of hydrogen peroxide, a long-lived molecular product of water radiolysis, with active sites of DNA macromolecule was studied, and the formation of stable DNA-peroxide complexes was considered. The phosphate groups of the macromolecule backbone were picked out among the atomic groups of DNA double helix as a probable target for interaction with hydrogen peroxide molecules. Complexes consisting of combinations including: the DNA phosphate group, H2O2 and H2O molecules, and Na+ counterion, were considered. The counterions have been taken into consideration insofar as under the natural conditions they neutralise DNA sugar-phosphate backbone. The energy of the complexes have been determined by considering the electrostatic and the Van der Waals interactions within the framework of atom-atom potential functions. As a result, the stability of various configurations of molecular complexes was estimated. It was shown that DNA phosphate groups and counterions can form stable complexes with hydrogen peroxide molecules, which are as stable as the complexes with water molecules. It has been demonstrated that the formation of stable complexes of H2O2-Na+-PO4 - may be detected experimentally by observing specific vibrations in the low-frequency Raman spectra. The interaction of H2O2 molecule with phosphate group of the double helix backbone can disrupt DNA biological function and induce the deactivation of the cell genetic apparatus. Thus, the production of hydrogen peroxide molecules in the nucleus of living cells can be considered as an additional mechanism by which high-energy ion beams destroy tumour cells during ion beam therapy.

Structurization Of Counterions Around DNA Double Helix: A Molecular Dynamics Study

The structurization of DNA counterions around the double helix has been studied by the molecular dynamics method. A DNA dodecamer d(CGCGAATTCGCG) in a water solution with alkali metal counterions Na+, K+, and Cs+ has been simulated. The systems have been considered in the regimes without excess salt and with different added salts (0.5 M of NaCl, KCl, or CsCl). The results have shown that the Na+ counterions interact with the phosphate groups directly from outside of the double helix and via water molecules at the top edge of the DNA minor groove. The potassium ions are mostly localized in the grooves of the double helix, and the cesium ions penetrate deeply inside the minor groove, being bonded directly to atoms of the nucleic bases. Due to the electrostatic repulsion, the chlorine ions tend to be localized at large distances from the DNA polyanion, but some Cl− anions have been detected near atomic groups of the double helix, by forming electrically neutral pairs with counterions already condensed on DNA. The DNA sites, where counterions are incorporated, are characterized by local changes in the double helix structure. The lifetime of Na+ and K+ in the complex with DNA atomic groups is less than 0.5 ns, while it can reach several nanoseconds in the case of cesium ions. On this time scale, the Cs+ counterions form a structured system of charges in the DNA minor groove that can be considered as ionic lattice.

Simulation study of the effects of surface chemistry and temperature on the conformations of ssDNA oligomers near hydrophilic and hydrophobic surfaces

We study the effects of the presence of a hydrophilic and a hydrophobic surface on the conformations and interactions of a single-stranded DNA (ssDNA) oligomer using atomistic molecular dynamics, umbrella sampling, and temperature-replica exchange. Our simulations capture the expected interactions between the ssDNA and the two surfaces (e.g., hydrogen bonds, hydrophobic interactions), but we find that the surface chemistry does not strongly affect the exposure of the relatively hydrophobic nucleobases or the hydrophilic phosphate backbone in a 16-base ssDNA. Likewise, the surfaces do not strongly affect the preferred size of the ssDNA compared to bulk solution, although the hydrophilic surface does favor slightly more compact ssDNA conformations than the hydrophobic surface. In more compact conformations, the negative charge of the ssDNA is more concentrated, and the energetic interactions of the DNA and DNA-bound counterions with the hydrophilic surface are more favorable, which consequently favors smaller ssDNA sizes. Increasing temperature, regardless of the presence or chemistry of a surface, makes it less unfavorable for the ssDNA to assume both compact and extended conformations. With increasing temperature the free energy cost of assuming a compact conformation is reduced to a greater extent than the cost of assuming an extended conformation. The reason for this difference is the entropically favorable release of DNA-bound water molecules upon assuming a compact conformation. Increasing temperature decreases water-DNA interactions while surprisingly increasing counterion-DNA interactions, changes which are attributed to the relative balance of entropic and energetic contributions for water molecules and counterions bound to the ssDNA.

MD and NMR Analyses of Choline and TMA Binding to Duplex DNA: On the Origins of Aberrant Sequence-Dependent Stability by Alkyl Cations in Aqueous and Water-Free Solvents

It has been known for decades that alkylammonium ions, such as tetramethyl ammonium (TMA), alter the usual correlation between DNA GC-content and duplex stability. In some cases it is even possible for an AT-rich duplex to be more stable than a GC-rich duplex of the same length. There has been much speculation regarding the origin of this aberration in sequence-dependent DNA duplex stability, but no clear resolution. Using a combination of molecular dynamics simulations and NMR spectroscopy we demonstrate that choline (2-hydroxy-N,N,N-trimethylethanaminium) and TMA are preferentially localized in the minor groove of DNA duplexes at A·T base pairs and these same ions show less pronounced localization in the major groove compared to what has been demonstrated for alkali and alkali earth metal ions. Furthermore, free energy calculations show that single-stranded GC-rich sequences exhibit more favorable solvation by choline than single-stranded AT-rich sequences. The sequence-specific nature of choline and TMA binding provides a rationale for the enhanced stability of AT-rich sequences when alkyl-ammonium ions are used as the counterions of DNA. Our combined theoretical and experimental study provides one of the most detailed pictures to date of cations localized along DNA in the solution state, and provides insights that go beyond understanding alkyl-ammonium ion binding to DNA. In particular, because choline and TMA bind to DNA in a manner that is found to be distinct from that previously reported for Na(+), K(+), Mg(2+), and Ca(2+), our results reveal the important but underappreciated role that most other cations play in sequence-specific duplex stability.

Dielectric measurements of aqueous DNA solutions up to 110 GHz.

A measurement system for broadband dielectric spectroscopy of biological samples for frequencies between 25 MHz and 110 GHz is presented. It is based on a vector network analyzer and a 1.19 mm-diameter open-ended coaxial probe. Complex reflection coefficients of aqueous Na-DNA solutions are measured in the frequency domain at a constant temperature of 25 °C. Complex permittivity spectra are analysed at various solute concentrations and two dispersions are observed. The first one is located at about 19 GHz and is due to the reorientation of water molecules. The second one is located at approximately 100 MHz and is interpreted as being caused by DNA counterion fluctuations. The relaxation frequency of free water in solutions appears to be practically unaffected by the presence of DNA. For the relaxation in the MHz region the dielectric loss maximum shifts to higher frequencies and the distribution of relaxation times becomes broader with increasing polymer concentration.

Global analysis of ion dependence unveils hidden steps in DNA binding and bending by integration host factor

Proteins that recognize and bind to specific sites on DNA often distort the DNA at these sites. The rates at which these DNA distortions occur are considered to be important in the ability of these proteins to discriminate between specific and nonspecific sites. These rates have proven difficult to measure for most protein-DNA complexes in part because of the difficulty in separating the kinetics of unimolecular conformational rearrangements (DNA bending and kinking) from the kinetics of bimolecular complex association and dissociation. A notable exception is the Integration Host Factor (IHF), a eubacterial architectural protein involved in chromosomal compaction and DNA recombination, which binds with subnanomolar affinity to specific DNA sites and bends them into sharp U-turns. The unimolecular DNA bending kinetics has been resolved using both stopped-flow and laser temperature-jump perturbation. Here we expand our investigation by presenting a global analysis of the ionic strength dependence of specific binding affinity and relaxation kinetics of an IHF-DNA complex. This analysis enables us to obtain each of the underlying elementary rates (DNA bending/unbending and protein-DNA association/dissociation), and their ionic strength dependence, even under conditions where the two processes are coupled. Our analysis indicates interesting differences in the ionic strength dependence of the bi- versus unimolecular steps. At moderate [KCl] (100-500 mM), nearly all the ionic strength dependence to the overall equilibrium binding affinity appears in the bimolecular association/dissociation of an initial, presumably weakly bent, encounter complex, with a slope SK(bi) ≈ 8 describing the loglog-dependence of the equilibrium constant to form this complex on [KCl]. In contrast, the unimolecular equilibrium constant to form the fully wrapped specific complex from the initial complex is nearly independent of [KCl], with SK(uni) < 0.5. This result is counterintuitive because there are at least twice as many ionic protein-DNA contacts in the fully wrapped complex than in the weakly bent intermediate. The following picture emerges from this analysis: in the bimolecular step, the observed [KCl]-dependence is consistent with the number of DNA counterions expected to be released when IHF binds nonspecifically to DNA whereas in the unimolecular reorganization step, the weak [KCl]-dependence suggests that two effects cancel one another. On one hand, formation of additional protein-DNA contacts in the fully wrapped complex releases bound counterions into bulk solution, which is entropically favored by decreasing [salt]. On the other hand, formation of the fully wrapped complex also releases tightly bound water molecules, which is osmotically favored by increasing [salt]. More generally, our global analysis strategy is applicable to other protein-DNA complexes, and opens up the possibility of measuring DNA bending rates in complexes where the unimolecular and bimolecular steps are not easily separable.

Non-uniform Velocity of Homogeneous DNA in a Uniform Electric Field: Consequence of Electric-Field-Induced Slow Dissociation of Highly Stable DNA–Counterion Complexes

Identical molecules move with identical velocities when placed in a uniform electric field within a uniform electrolyte. Here we report that homogeneous DNA does not obey this fundamental rule. While most DNA moves with similar velocities, a fraction of DNA moves with velocities that vary within a multiple-fold range. The size of this irregular fraction increases several orders of magnitude when exogenous counterions are added to DNA. The irregular fraction decreases several orders of magnitude when DNA counterions are removed by dialysis against deionized water in the presence of a strong electric field (0.6 kV/cm). Dialysis without the field is ineffective in decreasing the size of irregular fraction. These results suggest that (i) DNA can form very stable complexes with counterions, (ii) these complexes can be dissociated by an electric field, and (iii) the observed non-uniform velocity of DNA is caused by electric-field-induced slow dissociation of these stable complexes. Our findings help to better understand a fundamental property of DNA: its interaction with counterions. In addition, these findings suggest a practical way of making electromigration of DNA more uniform: removal of strongly bound DNA counterions by electro-dialysis against deionized water.

Optical, electro-optic and optoelectronic properties of natural and chemically modified DNAs

This article reviews recent findings on the optical, electro-optic and optoelectronic properties of natural and modified DNAs. When the sodium (Na+) ions of DNA are replaced with long alkyl quaternary ammonium (Q+) ions, the resulting compositions (Q+DNA−) are organic-soluble, and thin films produced using these materials reveal many interesting optical and optoelectronic properties. These films tend to form well-structured supramolecular assemblies. In contrast, natural DNAs are water-soluble and hygroscopic. DNAs are strong absorbers of UV wavelengths in the region of 260 nm. The Q+DNA− films are excellent dielectrics that can be utilized as insulating layers in organic thin film transistors. Chemical modification of the Q+ parts results in many interesting structures that can be used in a wide variety of optical and optoelectronic devices. This review specifically deals with the optical and fluorescence properties of, organic lasing composites, the nonlinear optical characteristics of, light-emitting diodes, and photovoltaic cells based on natural and modified DNAs. This article reviews recent findings on the optical, electro-optic, and optoelectronic properties of natural and chemically modified DNAs. This review specifically deals with photoluminescence and ET, lasing, NLO, organic light-emitting diode, and photovoltaic characteristics of various compositions based on natural and modified DNAs. Replacement of the Na+ counter-ions of natural DNA with functionalized cationic moieties is rapidly broadening the possible utilizations of DNA-based novel materials.

Reentrant Behavior of Divalent-Counterion-Mediated DNA-DNA Electrostatic Interaction

The problem of DNA-DNA interaction mediated by divalent counterions is studied using computer simulation. Although divalent counterions cannot condense free DNA molecules in solution, we show that if DNA configurational entropy is restricted, divalent counterions can cause DNA reentrant condensation similar to that caused by tri- or tetravalent counterions. DNA-DNA interaction is strongly repulsive at small or large counterion concentration and is negligible or slightly attractive for a concentration in between. Implications of our results to experiments of DNA ejection from bacteriophages are discussed. The quantitative result serves to understand electrostatic effects in other experiments involving DNA and divalent counterions.

Self-Assembly of Lamellar Lipid−DNA Complexes Simulated by Explicit Solvent Counterion Model

The dissipative particle dynamics simulations with explicit solvent and counterions are used to mimic the self-assembly of lamellar cationic lipid-DNA (CL-DNA)complexes. We found that the formation of the complexes is associated with the releasing of 70% DNA counterions and 90% lipid counterions. The trapped DNA and CL charges together with their counterions inside the complex still keep the interior neutral, which stabilized the structure. Simulations in constant pressure ensemble following the self-assembly show that the DNA interaxial spacing as a function of the inversed CL concentrations 1/phi(c) is linear at low phi(c) and nonlinear at high phi(c). The attraction between the DNA and the CLs as well as the repulsion between the DNA strands impose stretching stress on the membrane so that the averaged area per lipid is dependent on the CL concentration, which in turn determines the behavior of the DNA spacing.

Vertical Ionization Potentials of Nucleobases in a Fully Solvated DNA Environment

Vertical ionization potentials (IPs) of nucleobases embedded in a fully solvated DNA fragment (12-mer B-DNA fragment + 22 sodium counterions + 5760 water molecules equilibrated to 298 K) have been calculated using a combined quantum mechanical molecular mechanics (QM/MM) approach. Calculations of the vertical IP of the anion Cl(-) are reported that support the accuracy of the application of a QM/MM method to this problem. It is shown that the pi nucleotide HOMO origin for the emitted electron is localized on the base by the hydration structure surrounding the DNA in a way similar to that recently observed for pyrimidine nucleotides in aqueous solutions (Slavicek, P.; et al. J. Am. Chem. Soc. 2009, 131, 6460). In a first step, a high level of theory, CCSD(T)/aug-cc-pVDZ, was used to calculate the vertical IP of each of the four single bases isolated in the QM region while the remaining DNA fragment, counterions, and water solvent molecules were included in the MM region. The calculated vertical IPs show a large positive shift of 3.2-3.3 eV compared to the corresponding gas-phase values. This shift is similar for all four DNA bases. The origin of the large increase in vertical IPs of nucleobases is found to be the long-range electrostatic interactions with the solvation structure outside the DNA helix. Thermal fluctuations in the fluid can result in IP changes of roughly 1 eV on a picosecond time scale. IPs of pi-stacked and H-bonded clusters of DNA bases were also calculated using the same QM/MM model but with a lower level of theory, B3LYP/6-31G(d=0.2). An IP shift of 4.02 eV relative to the gas phase is found for a four-base-pair B-DNA duplex configuration. The primary goal of this work was to estimate the influence of long-range solvation interactions on the ionization properties of DNA bases rather than provide highly precise IP evaluations. The QM/MM model presented in this work provides an attractive method to treat the difficult problem of incorporating a detailed long-range structural model of physiological conditions into investigations of the electronic processes in DNA.

SCREW MOTION OF DNA DUPLEX DURING TRANSLOCATION THROUGH PORE I: INTRODUCTION OF THE COARSE-GRAINED MODEL

Based upon the structural properties of DNA duplexes and their counterion-water surrounding in solution, we have introduced here a screw model which may describe translocation of DNA duplexes through artificial nanopores of the proper diameter (where the DNA counterion–hydration shell can be intact) in a qualitatively correct way. This model represents DNA as a kind of "screw," whereas the counterion-hydration shell is a kind of "nut." Mathematical conditions for stable dynamics of the DNA screw model are investigated in detail. When an electrical potential is applied across an artificial membrane with a nanopore, the "screw" and "nut" begin to move with respect to each other, so that their mutual rotation is coupled with their mutual translation. As a result, there are peaks of electrical current connected with the mutual translocation of DNA and its counterion–hydration shell, if DNA is possessed of some non-regular base-pair sequence. The calculated peaks of current strongly resemble those observed in the pertinent experiments. An analogous model could in principle be applied to DNA translocation in natural DNA–protein complexes of biological interest, where the role of "nut" would be played by protein-tailored "channels." In such cases, the DNA screw model is capable of qualitatively explaining chemical-to-mechanical energy conversion in DNA–protein molecular machines via symmetry breaking in DNA–protein friction.

DNA surface hybridization regimes

Surface hybridization reactions, in which sequence-specific recognition occurs between immobilized and solution nucleic acids, are routinely carried out to quantify and interpret genomic information. Although hybridization is fairly well understood in bulk solution, the greater complexity of an interfacial environment presents new challenges to a fundamental understanding, and hence application, of these assays. At a surface, molecular interactions are amplified by the two-dimensional nature of the immobilized layer, which focuses the nucleic acid charge and concentration to levels not encountered in solution, and which impacts the hybridization behavior in unique ways. This study finds that, at low ionic strengths, an electrostatic balance between the concentration of immobilized oligonucleotide charge and solution ionic strength governs the onset of hybridization. As ionic strength increases, the importance of electrostatics diminishes and the hybridization behavior becomes more complex. Suppression of hybridization affinity constants relative to solution values, and their weakened dependence on the concentration of DNA counterions, indicate that the immobilized strands form complexes that compete with hybridization to analyte strands. Moreover, an unusual regime is observed in which the surface coverage of immobilized oligonucleotides does not significantly influence the hybridization behavior, despite physical closeness and hence compulsory interactions between sites. These results are interpreted and summarized in a diagram of hybridization regimes that maps specific behaviors to experimental ranges of ionic strength and probe coverage.

H4 histone tail mediated DNA–DNA interaction and effects on DNA structure, flexibility, and counterion binding. A molecular dynamics study

All-atom molecular dynamics (MD) simulations were performed during 30-45 ns for a system of three identical DNA 22-mers, 14 short fragments of the charged H4 histone tail peptide fragment (amino acids 5-12, KGGKGLGK) with K(+) counterions, and explicit water. The simulation setup mimics the crowded conditions of DNA in eukaryotic chromatin. To assess the influence of tail fragments on DNA structure and dynamics, a "control" 20 ns MD simulation was carried for a system with the same DNA and water content but in the absence of oligopeptides. Results of DNA interaction with the histone tail fragments, K(+), and water is presented. DNA structure and dynamics and its interplay with the histone tail fragments binding are described. The charged side chains of the lysines play a major role in mediating DNA-DNA attraction by forming bridges and coordinating to phosphate groups and electronegative sites in the minor groove. Binding of all species to DNA is dynamic. Some of the tail fragments while being flexible and mobile in each of its functional groups remain associated near certain locations of the DNA oligomer. The present work allows capturing typical features of the histone tail-counterion-DNA structure, interaction, and dynamics.

Dielectric relaxation of DNA aqueous solutions

We report on a detailed characterization of complex dielectric response of Na-DNA aqueous solutions by means of low-frequency dielectric spectroscopy (40 Hz-110 MHz). Results reveal two broad relaxation modes of strength 20<Deltaepsilon(LF)<100 and 5<Deltaepsilon(HF)<20, centered at 0.5 kHz<nu(LF)<70 kHz and 0.1 MHz<nu(HF)<15 MHz. The characteristic length scale of the low-frequency (LF) process, 50<L(LF)<750 nm, scales with DNA concentration as c(DNA)(-0.29+/-0.04) and is independent of the ionic strength in the low added salt regime. Conversely, the measured length scale of the LF process does not vary with DNA concentration but depends on the ionic strength of the added salt as I(s)(-1) in the high added salt regime. On the other hand, the characteristic length scale of the high-frequency (HF) process, 3<L(HF)<50 nm, varies with DNA concentration as c(DNA)(-0.5) for intermediate and large DNA concentrations. At low DNA concentrations and in the low added salt limit the characteristic length scale of the HF process scales as c(DNA)(-0.33). We put these results in perspective regarding the integrity of the double stranded form of DNA at low salt conditions as well as regarding the role of different types of counterions in different regimes of dielectric dispersion. We argue that the free DNA counterions are primarily active in the HF relaxation, while the condensed counterions play a role only in the LF relaxation. We also suggest theoretical interpretations for all these length scales in the whole regime of DNA and salt concentrations and discuss their ramifications and limitations.

DNA counterion current and saturation examined by a MEMS-based solid state nanopore sensor

Reports of DNA translocation measurements have been increasing rapidly in recent years due to advancements in pore fabrication and these measurements continue to provide insight into the physics of DNA translocations through MEMS based solid state nanopores. Specifically, it has recently been demonstrated that in addition to typically observed current blockages, enhancements in current can also be measured under certain conditions. Here, we further demonstrate the power of these nanopores for examining single DNA molecules by measuring these ionic currents as a function of the applied electric field and show that the direction of the resulting current pulse can provide fundamental insight into the physics of condensed counterions and the dipole saturation in single DNA molecules. Expanding on earlier work by Manning and others, we propose a model of DNA counterion ionic current and saturation of this current based on our experimental results. The work can have broad impact in understanding DNA sensing, DNA delivery into cells, DNA conductivity, and molecular electronics.

Role of Monovalent Counterions in the Ultrafast Dynamics of DNA

This paper examines the contribution of counterion motion to the electric-field dynamics in the interior of DNA. The electric field is measured by a coumarin fluorophore that is synthetically incorporated into an oligonucleotide, where it replaces a native base pair. The DNA is a 17-base-pair oligomer with no A- or G-tracts. Time-resolved Stokes-shift measurements on the coumarin are made from 40 ps to 40 ns with each of the alkali ions and or one of several tetraalkylammonium ions as the DNA counterion. With the possible exception of rubidium, there are no indications of site-specific binding of the counterions. For sodium and other ions with a smaller hydrodynamic radius, the dynamics are identical and are fit to a power law. For larger ions, there is a progressive increase in the rate of shifting after 1 ns. This effect correlates with the hydrodynamic radius of the counterion. The lack of change in the spectral shape of the emission shows that neither the broadly distributed power-law relaxation nor the extra nanosecond dynamics are due to heterogeneity in the relaxation rates of different helices.