Range, Magnitude, and Ultrafast Dynamics of Electric Fields at the

Letter pubs.acs.org/JPCL

Range, Magnitude, and Ultrafast Dynamics of Electric Fields at the Hydrated DNA Surface Torsten Siebert, Biswajit Guchhait, Yingliang Liu, Benjamin P. Fingerhut, and Thomas Elsaesser* Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, D-12489 Berlin, Germany S Supporting Information *

ABSTRACT: Range and magnitude of electric fields at biomolecular interfaces and their fluctuations in a time window down to the subpicosecond regime have remained controversial, calling for electric-field mapping in space and time. Here, we trace fluctuating electric fields at the surface of native salmon DNA via their interactions with backbone vibrations in a wide range of hydration levels by building the water shell layer by layer. Femtosecond two-dimensional infrared spectroscopy and ab initio based theory establish water molecules in the first two layers as the predominant source of interfacial electric fields, which fluctuate on a 300 fs time scale with an amplitude of 25 MV/cm due to thermally excited water motions. The observed subnanometer range of these electric interactions is decisive for biochemical structure and function.

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experimental work for benchmarking the wide range of theoretical predictions has remained scarce. Vibrations of the DNA backbone experience and, thus, probe fluctuating electric fields at the DNA−water interface. Such fields induce spectral diffusion, that is, time-dependent frequency excursions of vibrational excitations within a time interval set by the respective vibrational lifetime. Spectral diffusion is mapped by nonlinear two-dimensional (2D) infrared spectroscopy with a 100 fs time resolution and manifests in the 2D lineshapes.15 A lineshape analysis allows for extracting the time-frequency correlation function of the fluctuating forces acting on the vibrational potential of a selected mode, in particular the field-induced fluctuation amplitudes and the correlation times. To assess the role of water, we measure 2D infrared spectra of salmon testes DNA at different hydration levels from less than 2 to approximately 150 water molecules per base pair. This concept of building the aqueous environmentlayer by layerallows for identifying water’s contribution to the overall interfacial electric field and for quantifying the effective spatial range of electric forces. This approach goes far beyond existing 2D infrared studies of short artificial DNA helices16−19 and provides the first direct insight in electric fields at a native DNA surface under physiologically relevant conditions. Salmon testes DNA consists of double-helical strands of up to 2000 base pairs with a 41% guanine−cytosine and a 59% adenine−thymine base pair fraction. At hydration levels of more than 20 water molecules per base pair, the double helix exists in B-geometry (Figure 1A).4,20 The helix is embedded in

iological interfaces are characterized by highly complex electrical interactions among ionic or zwitterionic groups as well as with the dipolar water molecules of the environment. The many-body and inherent long-range character of Coulomb interaction together with thermally activated structure fluctuations on a multitude of time scales present major challenges for an understanding at the molecular level. This calls for model systems with a well-defined yet controllable molecular structure and novel experimental concepts for mapping fluctuating electric interactions in space and time. As a prototype system, we study native salmon testes DNA at different levels of hydration. Its backbone contains a sequence of negatively charged phosphate groups with two oxygen atoms in the backbone and two free oxygens which interact with hydrating water molecules via local hydrogen bonds and longerrange Coulomb forces.1−3 Local polar structures from oxygen atoms within the deoxyribose main chain and the ring moieties further contribute to the well-defined pattern of water sites at the DNA surface.4 The negative phosphate charges are compensated for by positively charged counterions such as Na+ that are located close to the DNA surface and solvated by water molecules.5−7 The water molecules hydrating DNA are both sources of electric fields and polarizable constituents of a dielectric. In spite of extensive theoretical and simulation work, central issues such as the effective spatial reach, radial dependence and interfacial amplitude of electric fields have remained highly controversial.7−13 A treatment of electric interactions in static Poisson−Boltzmann pictures is inadequate in view of the fluctuations of structure and electric fields at up to terahertz frequencies8,9 together with the critical dependency on the assumption of the radial dielectric function at the interface.10 Moreover, induction effects of highly polarizable ionic groups and water molecules need to be taken into account.14 So far, © 2016 American Chemical Society

Received: June 21, 2016 Accepted: July 28, 2016 Published: July 28, 2016 3131

DOI: 10.1021/acs.jpclett.6b01369 J. Phys. Chem. Lett. 2016, 7, 3131−3136

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spectra of the backbone modes at lower frequency, all showing lifetimes in the picosecond range. In Figure 2A−C, 2D infrared spectra in the spectral range between 920 and 1120 cm−1 are presented for the three hydration levels. The spectra were recorded at a waiting time of T = 500 fs. The absorptive 2D signal, that is, the real part of the sum of the rephasing and nonrephasing third-order response,25 is plotted as a function of excitation frequency ν1 and detection frequency ν3. Along the diagonal ν1 = ν3, one discerns, with increasing frequency, the contributions of the L3/R2, R1, L2/L1, and P2 modes. Each diagonal signal consists of a positive peak (yellow−red contours) due to ground state bleaching and stimulated emission on the v = 0 to 1 transition, as well as a negative component (blue contours) at lower detection frequency ν3, which is caused by the transient, anharmonically red-shifted v = 1 to 2 absorption. All diagonal peaks display elliptical lineshapes with a substantial inhomogeneous broadening along the diagonal. These lineshapes undergo minor changes with increasing waiting times as shown in Figures S1−S3 of the Supporting Information (SI). The respective signal amplitudes decay with time constants on the order of a picosecond, due to population relaxation and energy transfer by intermode coupling among the backbone modes. The latter is reflected by a rich pattern in pairs of negative and positive off-diagonal or cross peaks observed in parallel to the diagonal signals. A kinetic analysis of the relative amplitude changes in these signals as a function of waiting time gives a time-constant on the order of 2 ps for downhill population transfer from high-frequency to low-frequency modes, as described in detail for short DNA oligomers in ref 18. The pattern of diagonal and cross peaks is largely preserved upon changing the hydration level (Figure 2) with some variations in the amplitude ratios of the diagonal and cross peaks. There are, however, significant changes in lineshape and spectral position of the diagonal signals. Figure 3 displays cross sections of diagonal peaks along an antidiagonal that crosses the ν1 = ν3 line close to the position of the maximum positive signal of (A) the P2 mode, (B) the L2 mode, and (C) the R2/L3 mode. The profiles consist of a positive contribution from the v = 0 to 1 transition and a negative component from the v = 1 to 2 transition. For all modes, the spectral width of the positive and negative components is similar for the DNA water film (Na+ counterions) and the DNA lipid film (CTMA+ counterions) at 92% r.h., whereas the profiles measured with the DNA lipid film at 0% r.h. are systematically narrower. The line widths along the antidiagonals are smaller than the spectral widths along the diagonal ν1 = ν3, which were derived from diagonal cuts (not shown) and are summarized in Figure 4A. Here, the largest values occur for the DNA lipid film at 0% r.h. In evaluating other sources of electric interactions parallel to the effect of interfacial water, the influence of the counterion atmosphere is examined. Switching from the spaceous trimethylammonium headgroup (CMTA+) in lipid films at 92% r.h. to the natural monovalent Na+ and further to the divalent Mg2+ counterion of DNA water films shows minor effects on the lineshapes (Figure 3) as well as the cross- and diagonal-peak pattern (Figure S4 of the SI). The present experiments cover a very wide range of DNA hydration and address the influence of different counterions. At 0% r.h. with N < 2 water molecules per base pair, the hydration shell is essentially absent and the phosphate and counterion charges interact without attenuation by the aqueous “dielectric”. At 92% r.h. with N ≈ 20−30, statistically two closed water

Figure 1. (A) Surface structure of a hydrated DNA double helix in a Bgeometry and (B) a magnifcation of (A) showing water molecules around a phosphate group in the deoxyribose-phosphodiester segment of the backbone (atomic positions taken from ref 4., hydrogens implied). Blue spheres in (A) represent Mg2+ counterions. The distances marked in (B) indicate water oxygens at a radial distance within the first and second water layer around the hydrated double helix. (C) Linear infrared spectra of salmon testes DNA in different environments, displaying absorption bands of different backbone modes: P1, P2: asymmetric and symmetric PO2 stretching bands, L1− L3: linker modes, R1, R2: ribose ring modes. The spectrum of salmon testes DNA with Na+ counterions in H2O at N > 150 water molecules per base pair is shown as blue line. The black and the red line represent the spectrum of salmon testes DNA with CTMA + counterions in a film sample for a water content of N ≈ 20−30 and N < 2 water molecules per base pair.

a water shell3,4 with the first and second minimum in the radial distribution function of the water oxygens occurring at ∼0.35 and ∼0.7 nm and defining the first and second water layer (cf. Figure 1B).13 At a low hydration level of N < 2 water molecules per base pair, the helix forms an A-geometry.4,20 Linear infrared spectra of salmon testes DNA are presented in Figure 1C for hydration levels of 0% relative humidity (r.h.) corresponding to N < 2, 92% r.h. with N ≈ 20−30, and a DNA water film with N ≥ 150. A total of seven backbone normal modes contribute to the spectra between 900 and 1400 cm−1, the asymmetric (P1) and symmetric (P2) stretching modes of the PO2 moiety, the diester linker modes L1 to L3, and the deoxyribose ring modes R1 and R2.21,22 With decreasing hydration, the P1 mode undergoes a pronounced blue shift23 while the P2 mode displays a substantial decrease of absorption strength. All other bands show smaller changes in position and strength upon dehydration. For salmon testes DNA in water (blue line), the onset of water’s librational L2 absorption is visible as a broad absorption feature below 1000 cm−1. The P1 mode of DNA displays a short vibrational lifetime on the order of 300 fs, limiting the time window over which spectral diffusion can be followed.18,24 We, thus, focus on 2D 3132

DOI: 10.1021/acs.jpclett.6b01369 J. Phys. Chem. Lett. 2016, 7, 3131−3136

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Figure 2. Nonlinear 2D infrared spectra of the backbone modes measured with salmon testes DNA in different environments. The absorptive 2D signal is plotted as a function of the excitation frequency ν1 and the detection frequency ν3. Red yellow contours are positive signals, blue contours represent negative signals. The signal changes by 5% between adjacent contour lines. Panels (A) to (C) show experimental spectra recorded at a waiting time T = 500 fs, whereas calculated 2D spectra are presented in panels (D) to (F).

the depopulation of the v = 1 state. The v = 1 lifetimes make a contribution on the order of 5 cm−1, only weakly affected by a change of hydration level. At the low hydration level of 0% r.h. (N < 2), lifetime broadening dominates the observed spectral widths by far (red lines in Figure 3).19 In contrast, the substantially larger line widths at N ≈ 20−30 and N ≥ 150 (black and blue lines in Figure 3) give evidence of spectral diffusion caused by fluctuating forces from the hydration shell. The line widths of the P2 and R2/L3 modes, which dominate helix elongations in regions of the ionic phosphate and polar sugar ring structures, show the most pronounced effect in the line broadening upon hydration while the ester linkage region of the L2 mode is less affected. This is in line with the spatial distribution of hydration sites as determined from X-ray crystal structures.4 It is important to note that the spectral widths for N ≈ 20− 30 and N ≥ 150 are practically the same for all modes, that is, addition of more than two water layers around the DNA helix does not enhance spectral diffusion. In other words, electric fields from water molecules beyond the first two layers are screened with high efficiency and, thus, make a negligible contribution to the amplitude of fluctuating forces at the DNA surface. Moreover, the exchange of counterions from CTMA+ at N ≈ 20−30 to Na+ at N ≥ 150 has a negligible influence on the antidiagonal lineshapes. For N ≥ 150, an exchange of Na+ for Mg2+ leaves the profiles unchanged (Figure S4). We summarize that (i) the contribution of electric fields from counterions to spectral diffusion is minor to negligible and (ii) the fluctuating electric forces at the DNA surface are primarily generated by water molecules in the first two layers. For quantitative insight in the underlying fluctuation dynamics, the experimental 2D spectra were analyzed by calculating the third-order response functions to the photonecho pulse sequence in an approach derived from perturbation theory, Kubo lineshape analysis, and a rate equation approach to account for vibrational population transfer (cf. supplement of ref 18 for a detailed description). On this level of theory,

layers are present around the double helix in B-geometry, whereas even more water layers exist in the water film at N ≥ 150. In the latter two cases, electric forces generated by the counterions close to the DNA surface are reduced by the highly polar and polarizable water environment, whereas the first few water layers themselves generate significant electric fields at the surface of the helix. We now focus on the lineshapes and time evolution of diagonal peaks as they reflect the influence of fluctuating electric forces on the v = 0 to 1 and v = 1 to 2 transitions of the backbone modes most directly. The spectral width of all 2D diagonal peaks along the ν1 = ν3 direction (Figure 4A) decreases with increasing hydration level corresponding to a decrease in inhomogeneous broadening. This is clearly seen in the spectral separation of the backbone resonances along the frequency diagonal in Figure 2A−C. Obviously, structural heterogeneity of the double helix is highest in the dehydrated case (N < 2), whereas increasing hydration generates a more homogeneous solvation shell in which the structural differences between the many sites along the backbone of the long DNA sequence are reduced. Inhomogeneous broadening is, however, always present and exceeds the antidiagonal width of the 2D lineshapes. Its independence on the waiting time T shows that a variety of local environments persists at the DNA surface even at full hydration and for times beyond the observation window defined by the vibrational lifetimes. Apart from structural defects of the salmon testes double helix, structural heterogeneity originates from a variation in the positions of counterions and in the local patterns of hydrogen bonds between the DNA backbone and the first water layer.3 The positive (v = 0 to 1) and negative (v = 1 to 2) components of the spectral cuts along the antidiagonal frequency axis (Figure 3) are separated by the diagonal anharmonicity of the respective oscillator. In the present case of a quasistatic inhomogeneous broadening, the antidiagonal spectral width of the v = 0 to 1 components is primarily determined by spectral diffusion and lifetime broadening due to 3133

DOI: 10.1021/acs.jpclett.6b01369 J. Phys. Chem. Lett. 2016, 7, 3131−3136

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Figure 3. Cuts through the 2D diagonal peaks of the (A) P2 mode, (B) L2 mode, and (C) R2/L3 mode along the antidiagonal direction for salmon testes DNA with Na+ counterions in water (blue lines), with CTMA+ counterions at 92% r.h. (black lines) and 0% r.h. (red lines). The spectral width of the positive and negative signal components are similar for DNA in a full and partial hydration state whereas narrower profiles are found for a nearly dehydrated state. The profiles display additional contributions from cross peaks for larger frequency separations from the central zero crossings.

Figure 4. (A) Diagonal line width of the backbone modes P2, L2 and R2/L3 at different hydration levels obtained from the 2D infrared spectra in Figure 2. (B) Normalized frequency fluctuation correlation functions (FFCFs) derived from theoretical simulations of the 2D infrared spectra at different hydration levels. The FFCFs consist of a fast 300 fs decay and a slow component with a decay time longer than 10 ps. The ratio in amplitudes of the two components vary for the different normal modes of the backbone. (C) Fast 300 fs FFCF component with its absolute amplitude (in (cm−2)) for different normal modes and hydration levels. Similar amplitudes for the fast component are found at approximately N ≈ 20−30 and N > 150 water molecules per base pair for 92% r.h. and the water film, respectively.

spectral diffusion is described by frequency fluctuation correlation functions (FFCFs) which are comprised of two Kubo terms with amplitudes (Δν1,2)2 and correlation decay times τ1,2.15 As a benchmark, the linear infrared spectra were calculated with the parameters extracted from the 2D spectra (Figure S6). The calculated 2D spectra in Figure 2D−F reproduce the experimental spectra in Figure 2A−C in a quantitative way. Experimental and calculated spectral profiles along antidiagonal cross sections are compared in Figure S5. The 2D and the linear absorption spectra for all hydration levels and different counterions are reproduced by FFCFs with a first τ1 = 300 fs correlation decay and a slow component with τ2 > 10 ps (Figure 4B). The former is responsible for spectral diffusion and the later accounts for inhomogeneous broadening. The τ1 = 300 fs correlation time characterizes the time scale of electric fluctuations at the DNA-water interface. The induced excursions of vibrational frequency vary for the different normal modes, resulting in mode-specific amplitudes of this fast FFCF component (cf. Tables S1−S3). The amplitudes of the slow (>10 ps) component describe the mode-specific extent of inhomogeneity in the local environment of each oscillator persisting significantly beyond its lifetime.

In Figure 4C, we plot the 300 fs components of the FFCFs with their absolute amplitudes (Δν1,i)2 for the P2, L2, and R2/ L3 modes at the three hydration levels. The amplitudes for 92% r.h. and the water film are very similar, in accordance with the similar experimental line widths along the antidiagonals. In other words, the addition of water beyond the first two water layers leaves the fluctuation amplitudes Δν1,i essentially unchanged, confirming that the fluctuating electric forces originate primarily from the first two water layers. The 300 fs correlation decay differs from the sub-100 fs and ∼1 ps time scales observed in neat bulk water.26,27 This change in water dynamics in direct proximity to the DNA−water interface can be seen as the result of the modified structure in the hydrating water layers, as determined by the morphology and local electric potential of the DNA surface.28−30 In the most elementary approach, the amplitudes Δν1,i are related to the fluctuation amplitude of the interfacial electric field ΔE by Δν1,i = ai·ΔE, where ai is the tuning rate of the vibrational transition frequency in an external electric field. Tuning rates of ai = 0.4 to 0.53 cm−1/(MV/cm) have been reported for the symmetric and asymmetric PO2 stretching vibrations.12,31 Taking the value Δν1,P2 ≈ 10 cm−1 derived from our 2D spectra of the hydrated 3134

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The Journal of Physical Chemistry Letters DNA, one derives a fluctuation amplitude ΔEexp = 19−25 MV/ cm of the interfacial electric field. For a theoretical modeling of hydration dynamics and fluctuating electric forces at the phosphate−water interface, we employ the dimethyl phosphate (CH3O)2PO2− anion (DMP). DMP constitutes the smallest realistic model system of the phosphodiester moiety in the backbone of nucleic acids and is a common model to simulate phosphate group properties of biomolecules. We consider DMP solvated in bulk water. The fluctuating electric forces exerted on the PO2 moiety are calculated by combining the ab initio based effective fragment potential approach that accounts for electric fields due to static multipoles (up to quadrupoles) and polarization contributions due to induced dipoles, with molecular dynamics (for details see SI). The total time-averaged electric field generated by water molecules and evaluated as a function of radial distance from the phosphate group (Figure S7) has an amplitude on the order of 90 MV/cm and arises to approximately 76% from the first water layer while the second layer contributes some 18%, with noticeable contributions from induction. The results on DMP compare well with the sigmoidal shape of the radial relative dielectric permittivity at the DNA−water interface reported by Young et al. 7 The considered induction contribution to the electrical field due to many-body polarization closely resembles the radial electric field dictated by static multipoles. Our calculations give a fluctuation amplitude of the interfacial electric field of ΔEtheory ≈ 25 MV/cm, in good agreement with the range of ΔEexp derived from the 2D lineshapes. Thus, our theoretical model strongly supports both the picture of short-range electric forces that arise locally from the first two water layers and the observed magnitude of electric field fluctuations. Vice versa, this agreement underlines the strong potential of 2D infrared spectroscopy for mapping local electric interactions in complex biomolecular environments.

ACKNOWLEDGMENTS

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REFERENCES

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EXPERIMENTAL METHODS The preparation of the DNA samples is described in the SI. The 2D infrared spectra were derived from heterodyne detected three-pulse photon echoes where three pulses of 125 fs duration interact sequentially with the DNA samples and a fourth pulse serves as a local oscillator for heterodyning the photon echo signal in a phase-resolved detection scheme. Details of pulse generation, the photon echo setup and the data analysis are given in the SI. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b01369. Preparation of DNA samples, methods of 2D infrared spectroscopy and additional 2D spectra, analysis of 2D spectra, theoretical model of electric phosphate−water interactions. (PDF)

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B.P.F. gratefully acknowledges support through the DFG within the Emmy Noether Programme (Grant No. FI 2034/1-1). T.S. and B.G. contributed equally to this work.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 30 63921400. Fax: +49 30 63921409. Notes

The authors declare no competing financial interest. 3135

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