Low-frequency vibrations of water molecules in minor groove of the DNA double helix
aa r X i v : . [ q - b i o . B M ] D ec Low-frequency vibrations of water molecules in minorgroove of the DNA double helix
T.L. Bubon and S.M. PerepelytsyaBogolyubov Institute for Theoretical Physics of the National Academy ofSciences of Ukraine, 14-b Metrolohichna Str., Kyiv 03143, UkraineDecember 9, 2020
Abstract
The dynamics of the structured water molecules in the hydration shell of the DNAdouble helix is of paramount importance for the understanding of many biological mech-anisms. In particular, the vibrational dynamics of a water spine that is formed in theDNA minor groove is the aim of the present study. Within the framework of the devel-oped phenomenological model, based on the approach of DNA conformational vibrations,the modes of H-bonds stretching, backbone vibrations, and water translational vibra-tions have been established. The calculated frequencies of translation vibrations of watermolecules vary from 167 to 205 cm − depending on the nucleotide sequence. The modeof water vibrations higher than the modes of internal conformational vibrations of DNA.The calculated frequencies of water vibrations have shown a sufficient agreement with theexperimental low-frequency vibrational spectra of DNA. The obtained modes of water vi-brations are observed in the same region of the vibrational spectra of DNA as translationvibrations of water molecules in the bulk phase. To distinguish the vibrations of watermolecules in the DNA minor groove from those in the bulk water, the dynamics of DNAwith heavy water was also considered. The results have shown that in the case of heavywater the frequencies of vibrations decrease for about 10 cm − that may be used in theexperiment to identify the mode of water vibrations in the spine of hydration in DNAminor groove. The natural DNA consists of two chains of nucleotides (adenine, guanine, thymine, and cy-tosine) winding around each other as the double helix [1]. The hydrophobic nucleotide basesform the complementary H-bonded pairs (A-T and G-C) inside the macromolecule to reducethe contact with water molecules, while the negatively charged phosphate groups of the doublehelix backbone are exposed to the solution to be neutralized by the positively charged ions ofmetals. Starting with the very first X-ray and modeling studies of the DNA molecular struc-ture, the ion-hydration environment was known to stabilize the macromolecule structure [2–4].The hydration shell of DNA macromolecule ranges over several layers from the surface withinthe region of 10–15 ˚A and can be conditionally divided into primary and secondary hydrationshells [5–7]. The conformational dynamics of the DNA double helix and the dynamics of itshydration shell are interrelated [8,9] that is determinative for the mechanisms of nucleic-protein1ecognition and the interaction with the biologically active compounds [10–12]. Thus, to un-derstand the physical mechanisms of DNA biological functioning the structure and dynamicsof the hydration shell of the double helix should be studied.Under the physiological conditions, DNA takes the specific B -form with a hydration shellconsisted of about 30–50 water molecules per nucleotide pair [6, 13, 14]. The hydration shell ofDNA macromolecule has different structure in different compartments of the double helix: mi-nor groove, major groove, and outer region of the macromolecule. Earliest X-ray studies of thestructure of the crystals of DNA fragment d(CGCGAATTCGCG), known as Drew-Dickersondodecamer, showed that in AATT nucleotide region in the minor groove the water moleculesare ordered in the specific structure known as spine of hydration [15]. The hydration spineis composed of water molecules bridging N and O atoms of purines (A, G) and pyrimidines(C, T) nucleotide bases of opposite strands of DNA. Such structure has been also observed infurther X-ray experiments [16], nuclear magnetic resonance (NMR) studies [17, 18] and chiralnonlinear vibrational spectroscopy [19]. The formation of the hydration spine was also observedin molecular dynamics (MD) simulation studies [20, 21].The dynamics of hydration shell is heterogeneous and depends on water molecule locationin the double helix. The residence time of water molecules near phosphate groups are about10 ps [22, 23], while in the bulk water it is about 1 ps [24, 25]. In the grooves of the doublehelix the dynamics of water molecules is even slower than near phosphate groups. In the minorgroove, the residence time of water molecules is very long (more than 1 ns) compared to thosein the major groove (0,5 ns) [18]. However, the NMR studies [26, 27] showed that the residencetime of water molecules in the minor groove is within the range 0.2–0.9 ns, while in the majorgroove it is about 0.1 ns. These results quantitatively agree with MD simulations, where veryslow water molecules in the minor groove (residence time more than 100 ps) and in the majorgroove (about 60 ps) [8, 28] were detected. The residence time of water molecules is determinedby the lifetime of H-bonds that are formed with the atoms of DNA. The MD simulation studiesshowed that in the minor groove the lifetime of water H-bonds is about 50 ps, while in themajor groove it is more than two times lower [9,29]. The characteristic residence times of watermolecules in the DNA binding sites are much longer than the period of water vibrations ( < − , while librational (hindered rotational) motionsare above 300 cm − [30–33]. In the Raman spectra, two bands at about 175 and 60 cm − areobserved that attributed to H-bonds stretching and bending vibration, respectively [30, 31, 34].These vibrations are also observed in the infra-red absorption (IR) spectra [35–37], neutronscattering experiments [38], analytical estimations [39] and MD simulations [40, 41]. At thesame spectra range the DNA conformational vibrations characterized by the displacements ofthe atomic groups in the nucleotide pairs are observed [42,43]. The DNA low-frequency spectraare characterized by the narrow peak about 20 cm − and a broad band near 85 cm − [43–45]. Ina higher frequency range (100–200 cm − ) the modes that depend on concentration and type ofthe counterions have been observed [46, 47]. The low-frequency spectra of the DNA have beendescribed by different analytical approaches [48–52]. In particular, the detailed interpretationof the DNA low-frequency spectra was done within the framework of the approach of theconformational vibrations of the double helix [49, 50]. According to this approach, the lowestmode around 20 cm − is related to the vibrations of DNA backbone, while the broad band near85 cm − characterizes the vibrations of H-bond stretching in the bases pairs and intranucleosidevibrations due to the conformational flexibility of sugar rings. The ion-depended modes inDNA low-frequency spectra [46, 47, 53] have been determined as shown to be related to thevibrations of counterions with respect to the phosphate groups of the double helix backbone2 N3 A N3 A N3 T O2 T O2 C O2 G N3 C O2 A N A N N G T O T O C O N G O C ww ’ w ’ w ’ ww ’ ww ’ ’ ww ’ w Base BaseHydrationspineBackbone Backbone
Figure 1:
The scheme of the structure of the first and second layers of water molecules in the hydrationspine in the DNA minor groove according to [15,16]. Circles with w and w’ indicate water molecules ofthe first and second layer, respectively. The atoms of acceptors of the nucleotide bases are indicated. (ion-phosphate vibrations) [54–56]. To determine the modes of water molecules vibrations inthe DNA low-frequency spectra, the theoretical approach should be developed.The goal of the present study was to determine the low-frequency vibrations of watermolecules in the DNA minor groove. To solve this problem, the analytical model has beenelaborated based on the phenomenological approach of the DNA conformational vibrations [49].The developed model is described in the Section 2. In the Section 3, the parameters of themodel have been determined. In the Section 4, the frequencies and amplitudes of vibration ofDNA with water molecules have been calculated. As a result, the mode of water translationalvibrations in the DNA minor groove has been established within the frequency range 167–205cm − depending on nucleotide sequence. In the Section 5, the obtained frequencies of vibrationshave been compared with the experimental spectra of DNA in an aqueous environment. Thefrequencies of water vibrations in the DNA minor groove in the same spectral range as trans-lation vibrations of bulk water. To distinguish the vibrations of water molecules in the minorgroove from those in the bulk, the vibrations of DNA with heavy water have been considered. To built the model of vibrations of water molecules in the hydration spine of DNA minor groovethe approach for the description of the conformation dynamics of DNA double-helix developedby Volkov and Kosevich [49] has been used. In the present model, the sugar-phosphate backboneof the double helix is modelled by rigid walls. The nucleosides with mass M are presented asthe physical pendulums with the reduced length ℓ suspended to the backbone at the angle θ .The physical pendulums rotate in the plane orthogonal to the helical axis. The nucleoside basesin different DNA stands are connected by the hydrogen bonds modelling the nucleotide pairs.Water molecules are represented as the masses bonded to the pendulum-nucleosides, bridgingthe nucleotide bases of one stand with the nucleotide base of another stand (Fig.1). The3 l i=1 i=2 mM M n n-1n+1 a) XYZ w Y X X Y Y X a b θ φ θ θ θ θ r n b) Figure 2:
Model for the vibrations of water molecules in DNA minor groove. a) The chain of monomerlinks consisted of two nucleotides bounded by one water molecule. The monomer links are shown bydotted frames. ℓ is the reduced length of physical pendulum; M and m are masses of nucleosideand water molecule, respectively; i and n enumerate the monomer links and chains of the doublehelix, respectively. b) Two pairs of complementary bases in the plane orthogonal to the axis of thedouble helix. The nucleotides bridged by water molecule represent the selected monomer link (water-bounded pair). Water molecule placed in the centre of the coordinate system. φ is the equilibriumangle between nucleoside and water molecule masses. θ is the equilibrium angle between nucleosidemass and backbone; θ i,n and r n are vibrational coordinates of the model. The arrows indicate positivedirections of displacements. a and b are distances from the centre of coordinate system to suspensionpoint (backbone) of nucleosides mass on OX and OY direction, respectively. nucleosides of opposite stands bridged by water molecule form the monomer link in our model(Fig.2a). The nucleic bases that interact with the water molecules belong to different nucleotidepairs will be referred as water-bounded pairs. The interactions between complementary basesin the nucleotides pairs and interaction of the bases among chain are taken into account. Inthe present work, the nucleotides of different types (adenine, thymine, guanine and cytosine)have been characterized by averaged values of the parameters θ , ℓ and M .To consider the dynamics of structural elements of presented model, the following systemof coordinates has been used. The centre of coordinates is related to the water molecule. Theaxis OZ is directed along the axis of the double helix. The axis OY is directed to the majorgroove. The axis OX is orthogonal to the plane Y OZ . The nucleotides pairs placed in theplane
XOY , where axis OX defines the positive direction for each nucleoside to the outsideof the double helix. The vibrations of nucleosides with respect to the phosphate groups aredescribed by deviations θ i,n from the equilibrium angle θ , where n enumerates the monomer link( n = 0 , ± , .., ± N ) and i is the number of DNA strand ( i = 1 , a and b in OX and OY directions, respectively. The position of water molecules with mass m withrespect to nucleotides is characterized by the equilibrium angle φ describing the orientationof water molecule. The displacements of water molecules from the equilibrium positions in themonomer link are described by the deviation r n (Fig.2b). The coordinates of the displacementsfor the system are presented as follows: X n,i = a − ℓ cos( θ + θ i,n ); (1) Y n,i = ℓ sin( θ + θ i,n ) − b ; (2) u x,n = r n cos φ ; (3) u y,n = r n sin φ . (4)4ithin the framework of the introduced coordinates, the energy of vibrations of structuralelements of the double helix and water molecules may be written as follows: E = X n [ K n + U n + U n − ] , (5)where K n and U n are the kinetic and potential energies of the monomer link n ; U n − describesthe interactions in the complementary pairs and interactions of the staked bases along thechain.Taking into account that in the present work small displacements of the masses in the modelare considered the coordinates (1)-(4), the kinetic energy may be written in the following form: K n = 12 " X i =1 M ( ℓ ˙ θ i,n ) + m ˙ r n . (6)The potential energy of the monomer link in harmonic approximation may be written asfollows: U n = 12 X i =1 h βθ i,n + k ( θ i,n ℓC + r n C ) i . (7)Here C = ( a sin θ − b cos θ )/ R and C = ( a cos φ + b sin φ − ℓ cos( θ − φ )) /R , where R is the equlibrium distance in water-bounded pair and R = ( a + b + ℓ − aℓ b + bℓ a )) / . ℓ a = ℓ sin θ and ℓ b = ℓ cos θ . β is the force constant of the rotation of nucleosides with respectto the backbone chain in the plane of nucleosides pair without interaction between adjacentbases; k is the force constant of changes in the equilibrium distance between water moleculeand nucleoside.The potential energy of displacements in complementary nucleotide pairs and the energy ofinteraction along the chain may be written as follows: U n − = 12 h αℓ a ( θ ,n + θ ,n − ) + X i =1 g ( θ i,n − θ i,n − ) i , (8)where α is the force constant of H-bonds stretching in complementary pairs; g is the forceconstant of interactions between the stacked adjacent base pairs.Using the formulae (6)-(8), the equations of motion have been obtained: M ℓ ¨ θ ,n + βθ ,n + αℓ a ( θ ,n + θ ,n − )++ g ( θ ,n − − θ ,n + θ ,n +1 ) + kℓC ( θ ,n ℓC + r n C ) = 0; M ℓ ¨ θ ,n + βθ ,n + αℓ a ( θ ,n − + θ ,n )++ g ( θ ,n − − θ ,n + θ ,n +1 ) + kℓC ( θ ,n ℓC + r n C ) = 0; m ¨ r n + kC ( θ ,n ℓC + r n C ) + kC ( θ ,n ℓC + r n C ) = 0 . (9)The system of equations (9) consists of the second-order differential equations. The solutionsof the equations (9) may be found in the following form: θ i,n = ˜ θ i e i ( ωt − κ n ) , r n = ˜ re i ( ωt − κ n ) , (10)where κ is the projection of the wave vector to the axis Z ; ˜ θ and ˜ r are the amplitudes ofvibrations.In the present work, the modes observed in the experimental vibrational spectra in the scopeof interest. Therefore, we interested in finding the vibrations of optic type. In the case of the5pproach of dynamical lattice theory, this is equivalent to the long-wave limit ( κ → θ + ˜ θ = ˜ θ and ˜ θ − ˜ θ = ˜ ξ are split as follows: ( ˜ θl (cid:0) ω − β − k C mM − α sin θ (cid:1) + ˜ r (cid:0) − k C C mM (cid:1) = 0;˜ θℓ ( − k C C ) + ˜ r ( ω − k C ) = 0 . (11)˜ ξ (cid:16) ω − β − k C mM (cid:17) = 0 , (12)where α = α/M, β = β/M ℓ , k = k/m. Using the existence condition for a solution of equations (11), the expression for frequenciesof longwave vibrations has been determined in the form: ω − ω (cid:16) β + 2 α sin θ + k (cid:0) C + C mM (cid:1)(cid:17) ++ 2 k C (cid:0) β + 2 α sin θ (cid:1) = 0 . (13)From the equation (12) the following equation for frequency has been determined: ω − β − k C mM = 0 . (14)The solutions of the equation (13) have been found in the following form: ω , = 12 n β + 2 α sin θ + k ( C Mm + 2 C ) ±± (cid:2)(cid:0) β + 2 α sin θ + k (cid:0) C Mm + 2 C (cid:1)(cid:1) − k C ( β + 2 α sin θ ) (cid:3) / o . (15)The solution of equation (14) has been obtained as follows: ω = β + k C mM . (16)According to the character of frequency of vibration of the DNA with water molecules,the vibrational modes ω , ω , ω can be classified as the modes of water molecules vibrations( ω W ), H-bonds stretching vibrations ( ω H ) and nucleoside vibrations ( ω N ), respectively. Fromthe equations (15)-(16), the obtained modes of vibration significantly depend on the forceconstants and appropriate parameters.The ratio between the amplitudes of coupling vibrations may be obtained from the systemof equations (11) in the following form:˜ θℓ ˜ r = 2 k C C mM ω − β − α sin θ − k C mM . (17)The amplitudes of vibrations have been estimated accordingly to the [49]. To obtain theamplitudes of the DNA with water molecules vibrations (˜ θ , ˜ ξ and ˜ r ), the solutions (10) weresubstituted to the equations of potential energy (7),(8) and resulting expression was averagedover the time. As a result, the averaged potential energy has the form: h U i = 18 (cid:2) U + + U − (cid:3) , (18)6here U + = 2 αℓ a ˜ θ + β ˜ θ + k (cid:16) ˜ θℓC + 2˜ rC (cid:17) and U − = β ˜ ξ + k (cid:16) ˜ ξℓC (cid:17) . According to Boltzmann hypothesis about the uniform energy distribution by degrees offreedom the average energy per one degree of freedom is equal to k B T /
2, where T is thetemperature and k B is the Boltzmann constant [57]. Using the amplitudes ratio (17) andequation for averaged energy (18), the vibrational amplitudes of the water molecules can bedetermined is as follows: ˜ r = 2 s k B TU +˜ r . (19)Here U +˜ r has the form: U +˜ r = 2 α sin θ ˜ θℓ ˜ r ! + βℓ ˜ θℓ ˜ r ! + k ˜ θℓ ˜ r C + 2 C ! . Using the formulae (15),(16),(18) and (19) the frequencies and amplitudes of the vibrationsmay be determined.
To estimate the frequencies of vibrations of the system, the structural parameters ( θ , ℓ, φ , M and m ) and the force constants ( α, β, k ) of the model should be determined. The parameters θ , ℓ for B -DNA double helix have been taken from [49, 50]. The force constant of H-bondsstretching in the complementary base pairs α and the force constant of nucleoside vibrations β are equal to 80 kcal/mol˚A and 40 kcal/mol, respectively. The values of equilibrium angle θ and reduced length ℓ are equal to 28 ◦ and 4.9 ˚A, respectively [49, 50]. The mass of nucleoside M has been taken 199 u.m.a.. The distances a and b from selected centre of coordinate system(water molecule) to the suspension point of nucleosides (backbone) are approximately equal7.3 ˚A and 1.7 ˚A, respectively (Fig.2b). Using the X-ray structure of the Drew-Dickersondodecamer [16] the angle φ have been calculated. The average value of angle φ over thewater-bounded pairs in the minor groove is equal to 39 ◦ . The mass m of water molecule is 18u.m.a..In the present work, the force constant of water vibrations k has been estimated usingthe potential of mean force (PMF) derived from the molecular dynamics simulation data [58].Water molecules are trapped in the potential well and to obtain its shape, the PMF has beenused. The PMFs for water molecules in each water-bonded pair have been calculated from thedefinition [59]: U PMF = − k B T ln( g ( r )) , (20)where k B is the Boltzmann constant, T is the temperature and g ( r ) is the radial distributionfunction (RDF). The RDFs have been derived using molecular dynamics simulations trajectoriesobtained in [58], where the system of Drew-Dickerson dodecamer surrounded by water moleculesand counterions was studied. The RDFs have been built for oxygen atoms of water moleculeswith the respect to reference atoms of nucleotides: O of cytosine and thymine, N of guanineand adenine. The radial distribution functions have been calculated using the plugin [60]implemented to the VMD software [61]. RDFs have been obtained for each base bounded withwater molecule in the DNA minor groove. The potential of mean force calculated by (20) hasbeen fitted by the fourth degree polynomial: U PMF ≈ A + B r + B r + B r + B r , (21)7able 1: The values of force constant k averaged for the water-bonded pairs derived from MDsimulation. In the present work, the water-bounded pair is the nucleic bases that interact withthe water molecules belong to different nucleotide pairs.Water-bounded pair G-G A-C A-T T-T T-A C-A G-G k ,(kcal/mol˚A ) 37 38 31 26 32 40 39Table 2: The frequency of vibrations of DNA with water molecules. ω W is the frequency ofwater vibrations; ω H is the frequency of H-bond stretching vibrations; ω N is the frequency ofnucleoside vibrations. Water-bounded pair G-G A-C A-T T-T T-A C-A G-G ω W ,(cm − ) 199 201 181 167 184 205 203 ω H ,(cm − ) 47 47 47 47 47 47 47 ω N ,(cm − ) 16 16 15 14 15 16 16 where A, B , B , B , B are the fitting coefficients and r is the distance.From the other side, the potential of mean force may be presented as Taylor expansion ofpotential energy with respect to the equilibrium point: U PMF ≈ U PMF | r = r + 12! ∂ U PMF ∂r | r = r ( r − r ) ++ 13! ∂ U PMF ∂r | r = r ( r − r ) + + 14! ∂ U PMF ∂r | r = r ( r − r ) , (22)where r is the position of minimum.Using equations (21) and (22), the force constant k has been obtained as follows: k = ∂ U PMF ∂r | r = r = 2 B + 6 B r + 12 B r . (23)The force constants k have been estimated for each nucleotide in the minor groove of theDrew-Dickerson dodecamer using the equation (23). The obtained values of k have been aver-aged for the water-bounded nucleotide pairs. The calculated force constants for water moleculeswith nucleic bases in water-bounded pairs in the minor groove are shown in 1. The values of frequencies of vibrational modes have been estimated using the formulas (15),(16)and the parameters determined in the previous section. The obtained frequencies of vibrationsare presented in the Table 2. The mode of the water molecule vibration in the DNA minorgroove ω W ranges from 167 to 205 cm − . Our calculations have shown that the frequency ofwater vibration depends on nucleotide sequence: the frequency ω W increases from the centreof the Drew-Dickerson fragment (CGCGAATTCGCG) to its periphery where the cytosine andguanine bases are located. The lowest value of the frequency of water molecule vibration (167cm − ) is observed in the centre of the spine of hydration. The analysis has shown that thewater dynamics in the water-bounded pairs may depend on type of acceptor atoms of nucleicbases (binding site).The frequency of the mode of H-bond stretching vibrations ( ω H ) is about 47 cm − . It isabout twice lower than in the case of the approach of the four-mass model and experimental8ata (about 85 cm − ) [45, 49, 50]. According to the four-mass model, the H-bond stretchingoccurs due to the symmetrical rotations of nucleosides around phosphates and motions of themasses of phosphates groups. However, in the present model, the phosphates are fixed andin this case, the H-bonds stretching vibrations in complementary pairs are caused only bypendulum-nucleosides vibration around the phosphate groups. At the same time, the analysis,performed in the present work, showed that variation of the force constant α does not influencethe water molecule vibrations.The frequency of the mode ω N ranges from 14 to 16 cm − which depends on nucleosidetype. The calculated result in good agreement with results of four-mass model [49, 50], wherethis mode is referred to pendulums-nucleoside vibrations. In turn, calculated frequencies ofpendulums-nucleoside vibrations ( ω N ) are in good agreement with experimental studies. Inthis spectra range, experimental data [44, 62, 63] have defined mode around 20 cm − , whichvalue significantly depend on macromolecule hydration and associated it with vibration ofstaked bases.To determine a character of the DNA conformational vibration with water molecules inthe hydration spine of the DNA minor groove, the amplitudes of the displacements of thenucleosides and water in water-bouned pairs are calculated using formulae (22). The amplitudesof the vibrations describe the displacements of the mass centres from their equilibrium positions.The obtained amplitudes of water and nucleosides masses displacements are presented in Table3. The value of H-bonds stretching in complementary pairs have been also calculated usingexpression δ = l a ˜ θ .As follows from the equations (11) and (12), the amplitudes of vibration ˜ θ and ˜ ξ character-ize symmetrical and asymmetrical vibrations of pendulum-nucleosides, respectively, while theamplitudes of vibration ˜ r characterize vibrations of the water molecule in water-bounded pairs.Analysis of obtained amplitude values shows that asymmetrical movements of nucleosides occurwithout participation of water molecule and H-bonds stretching vibrations. Whereas symmet-rical movements of the masses in the model occur with H-bonds stretching in the base pairsand water molecules vibration.The amplitudes of water molecules in the case of the modes ω W depend on nucleotidevibration. In the centre of the spine of hydration, the amplitudes ˜ r are slightly higher than in theends, as well as in the case of amplitude ˜ θ . In turn, the amplitudes of the symmetrical vibrationsof pendulums-nucleosides in the case of the modes ω H are similar for all selected nucleosides thatare caused by constant value of vibrational mode of H-bonds stretching for all selected pairs(Table 2). From Table 3 follows that vibrational modes ω N caused by asymmetrical vibrationsof pendulums-nucleosides are not affect on the amplitudes of vibrations of water molecules andH-bonds stretching.The analysis of calculated amplitudes of displacements demonstrates that the water moleculesvibrations are interrelated with the conformational vibrations of the DNA double-helix. The ob-tained frequencies and amplitudes of vibrations show that dynamics of water molecule dependson nucleotide sequence and binding sites. 9able 3: The amplitudes of the DNA conformational vibrations with the water moleculeswhich are located in the minor groove of double helix. ˜ θ and ˜ ξ are the amplitudes of pendulum-nucleoside vibrations; ˜ r is the amplitude of water molecule vibrations in water-bonded pairs; δ is the value of H-bonds stretching in base pairs. ω W , ω H , ω N are the frequency of vibration(cm − ). G-G ˜ θ ( ◦ ) ˜ r (pm) ˜ ξ ( ◦ ) δ (pm) ω W ω H -2.97 3.85 0 -11.9 ω N A-C ω W ω H -2.97 3.84 0 -11.9 ω N A-T ω W ω H -2.97 3.89 0 -11.9 ω N T-T ω W ω H -2.97 3.94 0 -11.9 ω N T-A ω W ω H -2.97 3.88 0 -11.9 ω N C-A ω W ω H -2.97 3.83 0 -11.9 ω N G-G ω W ω H -2.97 3.84 0 -11.9 ω N -G A-C A-T T-T T-A C-A G-G H O D O F r equen cy , ( c m - ) Figure 3:
The frequency of vibration of light and heavy water bridging bases in water-bounded pairsin the DNA minor groove. The black line with squares identifies the modes of vibration of light water(H O) and red line with circles identifies the modes of vibration of heavy water (D O).
The low-frequency vibrational modes calculated in the present work should be observed inthe experimental spectra of DNA. At the same time, the observation of these modes may be acomplicated task due to the presence of the translational water vibrations, observed around 180cm − [30]. The Raman spectroscopy experiments [33] for liquid water showed that symmetricand asymmetric stretch of H-bonds are about 111 and 157 cm − , respectively, while coupledmode of translation and rotation vibrations is about 220 cm − . Therefore, our calculationsshould be compared with experimental data observed in the frequency range from 150–220cm − , where our calculated frequencies are obtained.In the far-infrared spectroscopic experiments [46] for various polynucleotides at 300 K, theDNA vibrations modes lower than 250 cm − are present. In particular, the characteristicpeaks in the spectra of poly(dA)poly(dT) around 170 and 214 cm − and in the spectra ofpolynucleotide poly(dA-dT)poly(dA-dT) around 195 cm − are indicated. Our results showthat vibrational modes of water molecules bridging bases in nucleotide sequence AATT arearound 181,167 and 184 cm − (Table 2). The vibrational modes of poly(dG)poly(dC) indicatedby experimental data ranged from 160 to 235 cm − , while our calculations show vibrationalmodes within the range 199–205 cm − . The obtained results sufficiently agree with experimentaldata. Therefore, it may be expected that the modes observed by spectroscopy experiments maycharacterize the modes of water molecules vibrations.To find the mode of water vibrations in the hydration spine of the DNA minor groove thedynamics of the double helix with heavy water (D O) may be considered. For this analysis, thedeveloped approach was used. The frequencies of vibrations of heavy water in the DNA minorgroove have been obtained using equations (15) and (16). Our calculations have shown that thefrequency mode of heavy water vibrations ranges from 158 to 195 cm − . The comparison of thefrequencies of vibrations of heavy water and light water in the DNA minor groove are shownin Fig. 3. The obtained frequencies modes of vibrations of heavy water softened for about 1011m − comparing to H O that may be explained due to the increasing mass. Decreasing in thefrequency value should be observed in the experimental vibrational spectra. In the case of liquidwater, the experimental data for D O has shown that the mode of translation vibrations softenfor about 10 cm − compared to the H O [35]. Therefore, the comparison of the low-frequencyspectra DNA with heavy water can provide additional information for identifying the watermodes in the DNA minor groove.
The model of the low-frequency water vibrations in the DNA minor groove has been developed.Our calculations have shown that the frequency of translational vibrations of water moleculeswithin the frequency range 167–205 cm − . The obtained values of the frequencies and ampli-tudes of vibrations indicate that the character of the dynamics of water molecules significantlydepends on the conformational vibrations of the DNA double helix and the binding site of watermolecules with atoms of nucleotide bases. The calculated modes of water molecules vibrationsobserved in the same spectra range as translational vibrations of the water in the bulk phase.To distinguish the vibrations of water molecules in the DNA minor groove from those in thebulk, the dynamics of DNA with heavy water has been considered. The calculations have shownthat the frequency of vibration of heavy water in the DNA minor groove ranges from 158 to195 cm − . Decreasing of vibrational mode of heavy water for about 10 cm − compared to thelight water was obtained in our calculations and is expected to be observed in the experimentalspectra. The mode softening due to the heavy water may be used for identifying the mode ofwater vibration in the spine of hydration in DNA minor groove. The authors gratefully acknowledge Prof. Sergey Volkov and the colleagues of the Labora-tory of Biophysics of Macromolecules of the BITP for the stimulative discussion. The presentwork was partially supported by the Project of the National Academy of Sciences of Ukraine(0120U100855).
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