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Anharmonic Backbone Vibrations in Ultrafast Processes at the DNA-Water Interface Torsten Uwe Siebert, Biswajit Guchhait, Yingliang Liu, Rene Costard, and Thomas Elsaesser J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b04499 • Publication Date (Web): 30 Jun 2015 Downloaded from http://pubs.acs.org on July 7, 2015

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The Journal of Physical Chemistry

Anharmonic Backbone Vibrations in Ultrafast Processes at the DNA-Water Interface Torsten Siebert, Biswajit Guchhait, Yingliang Liu, Rene Costard, and

Thomas Elsaesser

∗

Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, Max-Born-Str. 2a, D-12489 Berlin, Germany

E-mail: [email protected]

Abstract

The vibrational modes of the deoxyribose-phosphodiester backbone moiety of DNA and their interactions with the interfacial aqueous environment are addressed with twodimensional (2D) infrared spectroscopy on the femto- to picosecond time scale. Beyond the current understanding in the harmonic approximation, the anharmonic character and delocalization of the backbone modes in the frequency range from 900 to 1300 cm−1 are determined with both diagonal anharmonicities and inter-mode couplings of the order of 10 cm−1 . Mediated by the inter-mode couplings, energy transfer between the backbone modes takes place on a picosecond time scale, parallel to vibrational relaxation and energy dissipation into the environment. Probing structural dynamics noninvasively via the time evolution of the 2D lineshapes, limited structure uctuations are observed on a 300 fs time scale of low-frequency motions of the helix, counterions, and water shell. Structural disorder of the DNA-water interface and DNA-water hydrogen bonds are, however, preserved for times beyond 10 ps. The dierent interactions of ∗

To whom correspondence should be addressed 1

ACS Paragon Plus Environment


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limited strength ensure ultrafast vibrational relaxation and dissipation of excess energy in the backbone structure, processes which are important for the structural integrity of hydrated DNA.

Keywords: DNA double helix, hydration, ultrafast infrared spectroscopy, anharmonicity, vibrational energy transfer.

Introduction The conformation of the DNA backbone depends critically on the interactions with the aqueous environment and in turn dictates a particular type of helical structure such as the B-form (Fig. 1A) predominant under physiological conditions. 13 The time-averaged global DNA structures together with the spatial distributions of counterions have been determined by a variety of methods and primary hydration sites such as the phosphate groups as well as hydration geometries in the groove structure of the helix have been identied. 37 Structural dynamics of DNA helix geometries occur on a multitude of time scales and are connected with vibrational motions in a frequency range from a few up to 1500 cm −1 . 810 Vibrational excitations of the sugar-phosphate backbone are of particular relevance for dynamic changes, uctuations, and distortions of the helix. Moreover, backbone vibrations are carriers of energy transport within the helical structure, involving inter-mode couplings as a key mechanism. They are involved in dissipation of excess energy, both within the helix and to the aqueous environment. In such processes, anharmonic couplings between dierent backbone modes are essential and determine the pathways and rates of energy transport and redistribution. 11,12 Beyond their involvement in helix dynamics and energy transport, backbone vibrations with molecular elongations at the DNA-water interface are subject to changes and uctuations of the hydration shell surrounding the DNA. Hydration dynamics of DNA have been studied by a variety of experimental methods 1318 and by theoretical simulations. 9,10,1924 2


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A

B O5 O4

O4

Normalized Absorbance

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L2 L1   P2 1.0 L3 R2

P1

C

R1 0.5

0.0

1000 1200 Frequency  (cm-1)

1400

Figure 1: (A) Schematic representation of a double-stranded DNA helix in the B-form taken

from the PDB crystal structure 3BSE highlighting the deoxyribose-phosphodiester moiety (Ref. 2). (B) Detailed view of the deoxyribose-phosphodiester segment. (C) Stationary infrared absorption spectrum (black line) of a 23 base-pair double-stranded DNA oligomer with an alternating AT sequence at a hydration level of 92% r.h. The symbols indicate the backbone vibrations listed in Table 1. The individual line proles (colored lines) were calculated with parameters derived from 2D spectra and in sum (blue line) reproduce the experimental spectrum.

However, the femto- to picosecond time scales of water motions in the hydration shell and at the interface, the lifetimes of DNA-water hydrogen bonds and water residence times at the interface have remained highly controversial. 25,26 The lack of specic knowledge originates from the invasive character of some of the experimental probes, the fact that dierent methods map hydration dynamics in dierent time windows only, and that most methods provide spatially averaged signals without a specic sensitivity to interfacial water. Here, time-resolved studies of backbone vibrations hold a strong potential for generating new insight. The uctuating hydration shell and positively charged counterion environment of DNA

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exert uctuating electric forces on the backbone modes and - due to their vibrational anharmonicity - modulate the vibrational transition frequencies. Backbone modes with vibrational elongations located at the DNA-water interface are particularly sensitive to local interactions such as hydrogen bonds with water molecules and to electric forces exerted by them and by the counterions located close to the interface. In this sense, backbone vibrations represent spatially selective interfacial probes. The characteristic time scales and frequency excursions of spectral diusion processes are accessible via nonlinear 2D infrared spectroscopy which probes interfacial hydration dynamics non-invasively. So far, knowledge on backbone vibrations of DNA and their role in nonequilibrium processes has remained very limited. Stationary infrared (IR) and Raman spectra have been analyzed by normal mode calculations in the harmonic limit only 27,28 and frequency positions of particular bands have been used as - rather indirect - indicators of a particular helix geometry. 29,30 Both (diagonal) anharmonicities of backbone modes and anharmonic couplings between them have remained unknown and not been addressed by theory. While dynamics around DNA has been the subject of - mostly classical - molecular dynamics simulations, the inuence of water uctuations and counterion distributions on backbone excitations and their linear and nonlinear vibrational spectra are not understood. In the present study, the pronounced anharmonic character, concomitant coupling, and delocalization of DNA backbone modes are revealed by nonlinear 2D-IR spectroscopy in the frequency range from 900 to 1300 cm −1 and on the femtosecond time scale of molecular motions. Inter-mode couplings of the order of 10 cm −1 result in picosecond energy transfer between backbone modes. Using vibrational backbone excitations as noninvasive dynamic probes, we establish a basic time scale of structure uctuations of 300 fs and show that phosphate-water hydrogen bonds and structural inhomogeneity at the DNA-water interface persist for longer than 10 ps.

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Materials and Methods Thin-cast DNA-lipid complexes

Double-stranded DNA oligomers are composed of an articial sequence of 23 alternating adenine-thymine base pairs in a Watson-Crick geometry. DNA-lipid complexes in thincast lipid lms (DNA concentration c ≈ 1.5 × 10−2 M, thickness d≈10 µm) are obtained by exchange of sodium with cetylmethyl-ammonium chloride (CTMA) counterions. 31 The DNA-lipid lm was cast on a BaF 2 substrate and mounted in a humidity cell. At 92 % r.h. in the sample cell, a hydration level is obtained for a statistical distribution of more than 20 water molecules per base pair in the rst and second hydration layer. 32 At this hydration level, the double-stranded oligomers take on a B-helix geometry. For details see the supplementary information (SI). 2D-IR Spectroscopy

Heterodyne-detected three-pulse photon echoes were recorded in the frequency range from 900 to 1300 cm−1 with mid-IR pulses of approximately 100 fs in duration, using a standard folded-box-CARS geometry on the sample. Two passively phase-locked pairs of pulses were generated in a diractive optics based setup rendering absorptive 2D spectra from the sum of the rephasing and non-rephasing signal contributions. 33,34 For details see the SI. Data Analysis

Simulations of the 2D spectra are carried out by calculating the third-order response functions of the backbone modes to the photon-echo pulse sequence as derived in the standard approach from perturbation theory. 33,34 The congested spectral signatures are approached with a model using a minimal number of free parameters, while maintaining a subset of variables as global parameters applied to all backbone modes. Overlap of the diagonal and cross peak signatures are considered by simulation of the full 2D spectrum of the backbone 5



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region in the frequency range of 920 to 1120 cm −1 . The analysis is further aided by utilizing auxiliary data from pump-probe experiments and controlling the parameter set employed for simulation with a calculation of and comparison to the linear vibrational spectrum. This is described in detail in the SI.

Results Linear vibrational spectra

The deoxyribose-phosphodiester moiety highlighted in Figs. 1A,B incorporates characteristic backbone vibrational modes within the selected spectral range of 900 to 1300 cm −1 . Fig. 1C shows the stationary IR spectrum of double-stranded DNA oligomers composed of 23 base pairs with an alternating adenine(A)-thymine(T) sequence and CTMA counterions prepared as thin cast lipid lms. At the hydration level of more than 20 water molecules per base pair, a statistical distribution within the rst and a second hydration layer makes the vibrational spectra highly sensitive to interfacial water, while providing a free spectral window to the backbone resonances void of the background from water librations. Assignments of the individual bands in the highly congested spectrum to vibrational normal modes are summarized in Table 1, together with molecular parameters derived in the present study. The assignments are based on the normal mode analysis within the harmonic limit of Refs. 27 and 28 which is documented in more detail in the SI (Table S1). Ref. 27 includes an ab-initio normalized potential energy distribution (PED) which suggests contributions from dierent local coordinates to the overall normal mode elongations. As listed in Table 1, such elongations include the phosphate group ( νP 2 ), the phosphodiester linkage ( νL1 , νL2 , νL3 ) and the furanose main chain and rings ( νR1 , νR2 ). The asymmetric phosphate stretching mode (νP 1 ) represents an exception and is localized on the PO −2 moiety.

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Table 1: Vibrational modes of the DNA backbone. The population decay times T10 were measured in pump-probe experiments. The diagonal anharmonicity ∆ and the FFCF parameters are derived from the analysis of the linear and 2D infrared spectra. The FFCF consists of two Kubo terms with amplitudes ∆ν1 and ∆ν2 and decay times τ1 = 0.3 ps and τ2 = 50 ps.

Mode Character

Frequency Anharm. Decay Time ν01

νP 1 νP 2 νL1 νL2 νR1 νR2 νL3

Asym. phosphate stretch: νas (PO− 2) Sym. phosphate stretch: νs (PO− 2 ), νs (OPO), νs (CO) Diester linkage: νs (CO), νs (PO− 2 ), νs (CC) Diester linkage: νas (CO), νas (PO− 2 ), νas (CC) Furanose ring: (C1'C2'O4'C3') Ribose main chain: undened coordinates Diester linkage: νas (CC), νs (OPO)

∆

T10

FFCF ∆ν1

∆ν2

cm−1 1230

cm−1 5

ps 0.34

cm−1 6

cm−1 16

1092

8

1.24

8

7

1071

10

1.55

7

7

1052

10

2.28

8

9

1016

10

1.84

9

12

976

7

1.74

7

7

962

7

1.65

6

6

Two-dimensional infrared spectra and pump-probe transients

Nonlinear 2D-IR spectra of the DNA backbone modes were derived from heterodyne-detected 3-pulse photon echoes (cf. SI). In Figs. 2A and 3, we present absorptive 2D spectra in which the real part of the sum of the rephasing and non-rephasing signal is plotted as a function of the excitation frequency ν1 and the detection frequency ν3 . The 2D spectrum of Fig. 2A was measured at a waiting time T =250 fs, i.e., for sequential interaction of the third pulse, and displays prominent diagonal peaks of the asymmetric (PO −2 ) stretch vibration νP 1 around (ν1 , ν3 )=(1230,1230) cm−1 , the symmetric (PO−2 ) stretch vibration νP 2 around (1095,1095) cm−1 and other modes at lower ( ν1 , ν3 ). The yellow-red contours represent positive signals caused by ground-state bleaching and stimulated emission on the v=0 →1 transitions while the blue features are negative signals from to v=1 →2 excitations, red-shifted by the diagonal anharmonicity ∆i of normal mode i. The pronounced inter-mode anharmonic coupling of νP 1 and νP 2 gives rise to the pairs of (o-diagonal) cross peaks at ν1 = νP 1 and νP 2 . As

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a function of waiting time T , such cross peaks decay in parallel to the diagonal peaks (cf. Fig. S3 of the SI). Absent are cross peaks between νP 1 and the diester linkage modes νL1 and νL2 that indicate a signicant delocalization of νP 1 or a noteworthy energy transfer to delocalized backbone modes. This region of the 2D spectrum is dominated by the coupling of the νP 1 and νP 2 modes (see Fig. S3 of the SI for an analysis of this spectral region for T = 250, 500 and 1000 fs). It has been shown in Ref. 12 that excess energy released in the

Excitation Frequency 1 (cm-1)

vibrational relaxation of νP 1 is preferentially transferred into the water shell. 1300

A P1

1200

P2

1100

T = 250 fs 1100

1200

1300

Detection Frequency 3 (cm-1)

B Normalized FFCF Amplitude

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1.0

H2O

L2

P1

R1

0.5

0.0

0

500

1000

1500

2000

Population Time T (fs)

Figure 2: (A) 2D infrared spectrum in the range of the phosphate stretch vibrations νP 1 and νP 2

at a waiting time T=250 fs. The absorptive 2D signal is plotted as a function of excitation (ν1 ) and detection frequency (ν3 ). (B) Frequency uctuation correlation functions (FFCFs) of selected backbone vibrations [(νP 1 ) asymmetric phosphate stretch, (νL2 ) diester stretch, (νR1 ) sugar ring mode] as derived from the 2D-IR spectra in Figs. 2 and 3. For comparison, the FFCF of bulk H2 O from Ref. 42 is shown.

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950 1000 1050 1100

950 1000 1050 1100

A

1050 1000 950 1100

T = 500 fs

C

nP2 nL1 nL2 nR1 nR2 n L3

1000

nP2 nL1 nL2 nR1

950

nR2 n L3

1050

T = 500 fs

B

1050 1000 950

1100

T = 2000 fs

D

1050 1000 950

T = 2000 fs 950 1000 1050 1100

950 1000 1050 1100

Detection Frequency n3

1100

Excitation Frequency n1 (cm-1)

1100

Excitation Frequency n1 (cm-1)

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Detection Frequency n3 (cm-1)

(cm-1)

Figure 3: (A, B) 2D infrared spectra measured at waiting times T = 500 and 2000 fs in the frequency range of the phosphate (νP 2 ), phosphodiester linkage (νL1 , νL2 , νL3 ) and sugar ring structure (νR1 , νR2 ) modes. (C, D) 2D infrared spectra calculated from a third-order perturbation theory with the FFCFs of Fig. 2B and molecular parameters summarized in Table 1. The increase of cross peak amplitudes with T is due to a picosecond downhill population transfer. Dashed lines: positions of the cross-sections given in Fig. 4A-C.

The 2D spectra measured between 920 to 1120 cm −1 for waiting times T =500 fs (Fig. 3A) and 2000 fs (Fig. 3B) exhibit a complex pattern of diagonal and cross peaks due to the multitude of backbone modes νi . The multitude of cross peaks is due to the inter-mode couplings and their pronounced T -dependent amplitudes above the frequency diagonal reect population/energy ow between them. The couplings are most evident from the extended 'stripe-like' patterns of positive and negative cross peaks with a similar separation in detection frequency ν3 . The frequency separation of corresponding cross peaks is a measure of the anharmonic inter-mode coupling ∆ij with i 6= j , while the superimposed T -dependent rise in the cross-peak amplitudes above the diagonal reect the anharmonicity ∆j of the mode 9



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accepting population in the inter-mode energy exchange of the anharmonically coupled i-th and j -th mode. The spectral envelopes of the diagonal peaks undergo insignicant changes with increasing T ,

i.e.

, during the development of system between excitation ( ν1 ) and de-

tection (ν3 ). This points to minor spectral diusion of the dierent vibrational transitions within a frequency range limited to their linewidths along and perpendicular to the diagonal ν1 = ν3 . With increasing T , the diagonal signals decrease due to the depopulation of the v = 1 states as is evident from the frequency cuts along the diagonal ν1 = ν3 (Fig. 4A). In

the SI, we present a 2D spectrum of DNA oligomers with Na + counterions dissolved in bulk H2 O as a benchmark. Both the 2D lineshapes and the cross peak pattern are very similar to the data shown in Fig. 3. In parallel to the 2D experiments, pump-probe measurements were performed for extracting the decay times T10 of the vibrational absorption changes of each mode. Such decay times are summarized in Table 1. While spectrally resolved pump-probe signals correspond to the integral of the 2D signal along the ν1 axis, the kinetics of diagonal and cross peaks in the 2D spectrum allow for separating the contributions from population decay and intermode transfer, respectively. These are manifested in the signicant changes of the relative amplitudes in the cross peaks with development of the system during T . Fig. 4B shows frequency cuts along ν3 for a xed ν1 = 1050 cm−1 and normalized to the positive signal at ν3 = 1050 cm−1 while cuts along ν1 for a xed ν3 = 975 cm−1 are presented in Fig. 4C (normalized at ν1 = 973 cm−1 ). This behavior is a hallmark of downhill population and, thus, energy transfer from high-frequency vibrations to modes at lower frequencies mediated by inter-mode couplings. Two-color pump-probe experiments performed with selective excitation of a subset of DNA vibrations give independent evidence of the downhill population transfer. The time resolved transients in Fig. 5 represent the change of vibrational absorbance ∆A on the v = 0 → 1 transition of the modes νR2 and νL3 at 975 cm−1 , after excitation with pulses

centered at 1005 cm−1 (squares) and after excitation centered at 1095 cm −1 (triangles). In 10


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T = 500fs ( T = 2000fs (

Amplitude (norm.) Amplitude (scaled)

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exp.; exp.;

theo.) theo.)

A

1.0

0.5

0.0 1.0

B

0.5 0.0 -0.5 -1.0

950 1000 1050 1100 Detection Frequency 3 (cm-1)

Amplitude (scaled)

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C

1.5 1.0 0.5 0.0

950 1000 1050 1100 Excitation Frequency 1 (cm-1)

Figure 4: Cross-sections of the 2D infrared spectra in Figs. 3A,B (solid lines) and of the calculated

spectra in Figs. 3C,D (broken lines) for waiting times T = 500 and 2000 fs. (A) Diagonal crosssections along the line ν1 = ν3 - 10 cm−1 . (B) Cross-sections parallel to the ν3 axis at ν1 =1050 cm−1 showing the diagonal signals of the νL2 mode at 1050 cm−1 and the pronounced cross-peak signatures from the coupled excitations of the νR1 , νL3 and νR2 modes. (C) Cross-sections parallel to the ν1 axis for a detection frequency of ν3 =975 cm−1 . The increase of amplitude of cross peaks at high ν1 is due to down-hill transfer of vibrational energy from high-frequency modes.

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the rst case, the low-frequency modes are excited resonantly and the 1.7 ps decay of ∆A change reveals their v = 1 lifetimes. The pump pulses centered at 1095 cm −1 primarily excite higher-lying modes and the ∆A kinetics at 975 cm−1 reect the downhill population transfer into the low-frequency modes. The slower decay with a 2.5 ps time constant is due to the delayed proliferation of v = 1 population from the directly excited high-frequency modes. An analysis of such transients based on a kinetic model for the population transfer within the desoxyribose-phosphodiester is presented in the SI. Absorbance Change #A (norm.)

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0.0

1.7 ps ± 0.1 ps

-0.2 2.5 ps ± 0.2 ps

-0.4 -0.6

!pump = 1095 cm-1

-0.8

!probe = 975 cm-1

-1.0

""""""""""""" !probe = 975 cm-1

!pump = 1005 cm-1

-4

-2

0

2

4

6

8

10

Delay Time #t (ps)

Figure 5: Two-color pump-probe data conrming the downhill energy transfer from the νP 2 , νL1 ,

νL2 modes pumped with pulses centered at 1095 cm−1 to the νR2 and νL3 vibrations at 975 cm−1 in comparison to direct pumping of the latter. The change of absorbance ∆A=-log(T/T0 ) is plotted

as a function of pump-probe delay (T, T0 : sample transmission with and without excitation). The long-range oset in the pump-probe signals originating from the formation of a hot ground state of the helix is not considered in the model. For details see the SI.

Theoretical analysis of the 2D spectra

The measured 2D spectra were analyzed by theoretical calculations of the third-order nonlinear vibrational response to a photon-echo pulse sequence 33,34 as described in detail in the SI. To account for changes of cross-peak amplitudes with waiting time T , a rate equation model of incoherent inter-mode population transfer is included. In the calculations, we con12


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sider the normal modes listed in Table 1 and derive vibrational anharmonicities and coupling parameters from a comparison of theory and experiment (for details, see the SI). The 2D lineshapes depend sensibly on the frequency uctuation correlation function (FFCF) hδν(t)δν(0)i where δν(t) is the deviation from the average vibrational frequency at time t, and the brackets hi stand for the average over the ensemble of oscillators. The FFCF correlates frequency uctuations at dierent instants in time and, thus, maps the uctuations of both the DNA helix geometry and embedding water/counterion shell, as well as potential long-lived frequency correlations. To account for the full set of experimental 2D spectra, we use a Kubo Ansatz for the FFCF with an initial τ1 = 300 fs decay and a τ2 = 50 ps component (Fig. 2B). The amplitudes ∆ν1 and ∆ν2 of such two components were

adjusted for each individual mode as given in Table 1. In Fig. 2B, FFCFs derived from this analysis are plotted for 3 of the backbone modes, together with the FFCF of bulk water from Ref. 42. The latter displays a much faster decay without a long-lasting kinetic component. As a benchmark, the linear IR absorption spectrum (Fig. 1C) is calculated with the same parameters. The 2D spectra of Figs. 2A and 3 give quantitative information on the diagonal anharmonicities ∆i =ν01i - ν12i of mode i (ν01i , ν12i : frequency of the v = 0→1 and 1→2 transition) where ν01i and ν12i determine the respective position along ν3 of the positive (yellow-red) and the negative (blue) diagonal peak. For the asymmetric ( νP 1 ) and symmetric (νP 2 ) (PO−2 ) stretch vibrations (Fig. 2A), one derives diagonal anharmonicities ∆i ≈ 5-8 cm−1 which are small compared to the frequency splitting ∆P = νP 1 − νP 2 = 135 cm−1 between the two modes. 35 In a normal mode picture, the coupling of these modes imposes the spectral shifts documented by the separation of the cross-peak signal pairs above and below the diagonal. For an analysis of the much more complex 2D spectra in Figs. 3A,B, we rst focus on the diagonal peaks. Introducing the individual transition dipoles and diagonal anharmonicities ∆i of the six modes (cf. Table 1) and using FFCFs with mode-specic uctuation amplitudes

(Fig. 2B), the 2D envelopes of the positive (v=0 →1) and negative (v=1→2) diagonal peaks 13



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are calculated as presented in Figs. 3C,D and the diagonal cuts shown in Fig. 4A (dash-dotted lines). There is good agreement of calculation and experiment. The diagonal anharmonicities have values of 5 to 10 cm −1 while the uctuation amplitudes cover a range from 5 to 16 cm −1 (Table 1). The 300 fs and the 50 ps FFCF component are present for all modes. Using the relative transition dipoles µi (v=0→1) from the calculated 2D spectra, the IR absorption proles of the dierent modes are shown in Fig. 1C scaled with their relative amplitudes |µi (v = 0 → 1)|2 . The calculated stationary IR spectrum (blue line) reproduces the experimental spectrum (black line). To correctly account for the 1120 cm −1 shoulder in the linear absorbance, we introduced an additional line prole centered at 1120 cm −1 for which no vibrational assignment exists so far. The combination of linear and 2D infrared spectroscopy allows for a much more accurate analysis of the highly congested linear vibrational spectrum than steady-state infrared and Raman spectroscopies. The analysis of the very rich cross peak patterns (Figs. 3A,B, 4B,C) includes the kinetic model for inter-mode population transfer which is manifested in the increase of relative cross peak amplitudes with waiting time T . For an anharmonic coupling ∆ij = 10 cm−1 between all pairs ij of (normal) modes which is in line with the very similar separation of positive and negative cross peaks along ν3 , such simulations account for the cross peak pattern in a quantitative way and reproduce the amplitude changes caused by vibrational population transfer with a rate kd ≈ 0.5 ps−1 , corresponding to a time constant of τd = 2 ps.

Discussion These results give new and quantitative insight into anharmonicities and inter-mode couplings of DNA backbone vibrations and into interactions between the backbone and its aqueous environment. We rst discuss vibrational couplings and energy transfer within the backbone. Normal mode calculations 27 have suggested that elongations of the asymmetric (PO−2 ) stretching mode at 1230 cm −1 are localized on the (PO −2 ) group while the 14


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modes between 900 and 1100 cm −1 involve motions of several subunits of the deoxyribosephosphodiester moiety shown in Fig. 1B. Such linear superpositions of local elongations in a harmonic potential must not be confused with anharmonic couplings between normal modes, resulting in mixed quantum states and pairs of cross peaks of opposite sign in 2D-IR spectra. 34 From the analysis of the 2D spectra, we conclude that the backbone modes between 950 and 1100 cm−1 display diagonal anharmonicities and inter-mode couplings of similar strength. The inter-mode couplings mix and, thus, delocalize vibrational excitations over the desoxyribose-phosphdiester segment (Fig. 1B). Moreover, there is a pronounced downhill transfer of vibrational populations and energy within this spectral window that occurs on a time scale of a few picoseconds, due to the global inter-mode coupling of the backbone modes. This energy transfer makes a signicant contribution to the depopulation of the backbone modes at high frequency, in this way additionally randomizing energy in the backbone. Intermode couplings play a key role also for spatial energy transport along the helix. While the present experiments imply a statistical distribution of excitation sites on the DNA helix, the addition of particular marker groups with distinct frequencies would allow for a spatial mapping of energy transport. 11 The randomization of excess population among backbone modes and their relaxation transfers excess energy to a multitude of low-frequency degrees of freedom and eventually establishes a heated vibrational ground state of the helix and the surrounding water shell. 12,18 An exception from this behavior is the highly localized asymmetric (PO −2 ) stretch vibration with a lifetime of 340 fs, much shorter than the energy transfer times of τd = 2 ps determined for the other backbone modes. A similar lifetime of this mode has been found for phosphate ions in H2 O 36 and for phospholipids, 37 strongly suggesting a vibrational relaxation pathway via modes localized on the phosphate group. The excess energy released in this process is preferentially transferred to the surrounding water shell but not into the backbone. 12 This is further documented by the distinctly dierent behavior of cross-peak amplitudes in the 15



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2D spectra of Fig. 2A and Fig. 3A,B. The asymmetric phosphate stretching vibration ( νP 1 ) clearly shows a pronounced coupling to the symmetric phosphate stretching mode ( νP 2 ) as is evident from the cross peak pairs in Fig. 2A. The missing asymmetry of cross peak amplitudes above and below the frequency diagonal and the lack of a change in their relative amplitudes as a function of waiting time T (see Fig. 3 of the SI) document the kinetic suppression of a transfer channel to the backbone in favor of a faster pathway that directs energy into the interfacial environment. This underscores that energy management in the backbone is specic with respect to the types of modes participating in the dierent transfer channels, far from an exchange of energy among all available modes of this structural element in the double-helix. The backbone modes located at the DNA surface are spatially selective probes of uctuating interactions of DNA with the surrounding water and counterions. The elliptic envelopes of the 2D diagonal peaks which remain essentially unchanged up to the longest waiting time of T =2000 fs, are oriented along the diagonal with a spectral width larger than along the anti-diagonal. The fast 300 fs decay of the FFCF (Fig. 2B) accounts for the anti-diagonal width and is caused by uctuations with frequencies of the order of 100 cm −1 . The 50 ps component introduces the inhomogeneous width along the diagonal. Calculations with different FFCFs (Fig. S4 of the SI) set a lower limit of 10 ps for the decay time of this component which reects combined structural disorder of the hydration pattern and the helix. At the water content limited to the proximate hydration and a specic counterion interaction given by the lipid geometry, this disorder results in a distribution of local interaction strengths and, thus, inhomogeneous broadening of the 2D envelopes. Coulomb interactions between the charged phosphate groups and counterions, electric forces from water dipoles, and local hydrogen bonds between DNA and interfacial water are the key interactions at the DNA-water interface. Thermally activated low-frequency motions of the DNA helix itself and of the environment 38,39 generate uctuating electric forces inducing the 300 fs FFCF decay. Our results show for the rst time that the FFCF decay 16


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of backbone vibrations (Fig. 2B) is substantially slowed down compared to neat H 2 O 4042 or hydrated phosphate ions 36 and remains incomplete on a 10 ps time scale. This behavior is rationalized as follows. Counterions are arranged in a 0.5 nm thick hydrated layer around the DNA helix. 4 The resulting electric elds between them and the DNA backbone are typically one order of magnitude larger than the water dipole elds and, thus, dominate the electric interaction between DNA and the aqueous environment. Counterions contribute to uctuating electric forces at frequencies mainly below 100 cm −1 because of their slow motions. 43 Furthermore, water motions at the interface are restricted by the steric constraints of the DNA surface, in particular the minor groove, and by molecular orientation in the strong counterion elds, both slowing down water uctuations and extending lifetimes of water-DNA hydrogen bonds. 43,44 The slow FFCF component sets a lower limit of 10 ps for the lifetime of such hydrogen bonds.

Conclusions This work provides the rst direct evidence for the delocalized anharmonic character of DNA backbone vibrations and signicant inter-mode couplings among the subset of backbone modes located between 900 and 1300 cm −1 . 2D-IR spectroscopy in this spectral range demonstrates a unique sensitivity for specic local interactions in an extended and diverse biomolecular geometry. The character and coupling of the backbone modes as well as the nature of the interfacial dynamics are representative of the double helix interacting with water in the rst and second hydration layer. In this conguration, the dominant dynamics of the interface are characterized by correlation times of structural uctuations of 300 fs and a longlived interfacial disorder and hydrogen bonds that persists for times beyond 10 ps. These time scales are observed uniformly in all lineshapes of the backbone modes at varying amplitudes together with a global and very similar inter-mode coupling that mediates population transfer and energy dissipation within a few picoseconds in the backbone structure. In competition to these intra-helical processes, excess energy is transferred to the water shell as a whole. 17



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Acknowledgement

This research has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2012)/ERC Grant Agreement No. 247051. The authors wish to thank Dr. Margitta Dathe and Heike Nikolenko from the Leibniz-Institut für Molekulare Pharmakologie (FMP), Berlin, for providing the opportunity to obtain CD spectra of the DNA-lipid lms.

Supporting Information Sample preparation and characterization, experimental methods, supplementary 2D spectra, data analysis. The Supporting Information is available free of charge via the internet at http://pubs.acs.org. References

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Graphical TOC Entry Excitation Frequency (cm-1)

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24

1100 1050 1000 950

T = 500 fs 950 1000 1050 1100

Detection Frequency (cm-1)


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Anharmonic Backbone Vibrations in Ultrafast ... - ACS Publications

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