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Cite this: Phys. Chem. Chem. Phys., 2014, 16, 11256
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Dielectric measurements of aqueous DNA solutions up to 110 GHz Elena Ermilova,* Frank F. Bier and Ralph Ho ¨ lzel 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 1C. Complex permittivity spectra are analysed at various solute concentrations and two dispersions are observed. The first one is located at about
Received 13th December 2013, Accepted 23rd April 2014
19 GHz and is due to the reorientation of water molecules. The second one is located at approximately
DOI: 10.1039/c3cp55272a
of free water in solutions appears to be practically unaffected by the presence of DNA. For the relaxation in
100 MHz and is interpreted as being caused by DNA counterion fluctuations. The relaxation frequency the MHz region the dielectric loss maximum shifts to higher frequencies and the distribution of relaxation
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times becomes broader with increasing polymer concentration.
Introduction For many years the electric properties of biological materials, such as tissues and cell suspensions as well as of aqueous protein and DNA solutions have attracted scientific interest.1–3 Investigation of their response to electric fields is useful for the understanding of the structure and dynamics of these biological systems and, moreover, this knowledge can be exploited for numerous practical applications. Especially radiowaves and THz radiation are increasingly applied for medical diagnostic and therapy. The availability of modern and fast techniques allows the investigation of dielectric relaxations of biological material over many orders of frequency using methods of frequency as well as time domain spectrometry.4,5 The interaction of DNA macromolecules with water and the surrounding ionic environment under the influence of an electric field has been a subject of research for many years.2,6,7 Several dielectric relaxations of DNA solutions have been reported.8–22 At present the counterion condensation theory8–10,23 is generally accepted for the explanation of their origin at low (kHz range) and intermediate (MHz range) frequencies. On account of the high charge density of the DNA polyion chain in solution the counterions stay in the vicinity of the DNA molecule, to a certain extent neutralizing this excess charge and lowering the repulsions between the negatively charged phosphate groups. One portion of the counterions is territorially bound,
Fraunhofer Institute for Biomedical Engineering (IBMT), Branch Potsdam, ¨hlenberg 13, 14476 Potsdam-Golm, Germany. Am Mu E-mail: [email protected]; Fax: +49-331-58187-199; Tel: +49-331-58187-216
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it is located close to the DNA chain and is called condensed, whereas the other part is more loosely bound and is considered as free or diffused counterions.10–12 The relaxation at low frequencies in the Hz–kHz spectral region is called a-relaxation, which has been found to be strongly molecular weight depended.2,5,11 It arises from the polarization of condensed counterions along the polyion chain. The so-called b-relaxation takes place in the spectral range between 1 MHz and 1 GHz. Its magnitude is much smaller than that of the a-relaxation and is independent of molecule size. For a long time the origin of the b-relaxation has been a subject of numerous dielectric studies.1,4,5,8–15 The movement of the counterions over short segments of DNA in response to the applied electric field is likely to account for this polyion relaxation which is dependent on DNA concentration.8–12 In addition to the mentioned model, the hypotheses of the motion of some polar groups of the DNA molecule13 as well as of relaxations of bound water have been proposed to explain the dielectric b-relaxation.21,22 The third dispersion, named g-relaxation, with the maximum of its dielectric loss peak at about 19 GHz (at 25 1C), is related to the orientational polarization of water dipoles in the applied alternating field. Recent technical advances in radio frequency techniques, especially of vector network analyzers in the upper GHz and lower THz range make it possible to conduct broadband dielectric measurements over a wide frequency range. Reflection methods, and among them open-ended coaxial line sensors, are particularly suitable for a fast and accurate investigation of the dielectric properties of many materials and can be used for engineering as well as medical application.24–31 In the present work we report results on dielectric studies of aqueous solutions
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of Salmon sperm Na–DNA in a spectral region from 25 MHz up to 110 GHz.
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Experimental setup All measurements were carried out with a computer controlled vector network analyser (VNA) Anritsu MS 4647A operating in the frequency range between 70 kHz and 70 GHz. The high frequency region up to 110 GHz was covered by extension of this experimental system with two fast microwave generators (Anritsu MG37022), a broadband test set (Anritsu 3738A), coupler (Anritsu WR10 66670-3) and a transmission-reflection module (Anritsu 3740A-EW) (Fig. 1). One of the distinguishing features of this system is the integration of an external mixer as part of the broadband test set and a coupler, providing the coverage of the whole frequency range in a single sweep. This kind of measurements results in low measurement uncertainties at high frequencies and fast scanning speeds – with a single sweep taking only a few seconds. An open-ended coaxial line was used as sensing element. To prevent the propagation of higher order modes of the high frequency signal the sensor was prepared from a 1.19 mm precision 50 Ohm semirigid coaxial cable (CA100FF, Kawashima Manufacturing, Japan) with solid dielectric PTFE. The centre conductor is made from silver plated copper, the outer conductor from Cu/Sn/Zn plated copper. It was cut flat, carefully polished and inspected through a stereo microscope (Fig. 2). A short (15 cm) and flexible coaxial cable (Gore, 3671 W1-50-3) was used to connect the output of the microwave coupler to the sensor. We have used W-type connectors to provide proper TEM operation of the sensor at high frequencies. The complex input reflection coefficient G*(o) = S11ejj was measured at the tip of the probe immersed into the solution. Here S11 and j are the magnitude and the phase of the reflection pffiffiffiffiffiffiffi coefficient, respectively, and j ¼ 1 is the imaginary unit. All samples were investigated in the frequency domain at 25 1C. Solutions under test with a volume of 1 ml were placed in polypropylene test tubes. Temperature was controlled using a test tube incubator (Peqlab Thriller) with a temperature stability 0.5 K. Standard one-port S11-calibration procedures of the whole system with the reference plane at the end of the 15 cm flexible
Fig. 1
Experimental setup.
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Fig. 2
Tip of the open-ended coaxial sensor.
coaxial cable were performed using a W1 Calibration Kit (3656B, Anritsu). To calculate the complex permittivity, e*(o), of the investigated DNA solutions using the measured reflection coefficients relationship (1) was applied:32,33 e ðoÞ ¼
a1 G ðoÞ a2 a3 G ðoÞ
(1)
where ai with i = 1. . .3 are complex frequency dependent coefficients. They were determined from additional reference measurements using the semirigid coaxial sensor being shorted, left open or immersed in a standard liquid, respectively. Open was obtained by measurements in air with G = 1. To achieve a proper short-circuit at the probe’s open end metal sheets of aluminium, silver, gold and freshly polished copper were tested as well as a silicon rubber sheet with silver particles.34 The phase shift by measuring the complex reflection coefficient G*(o) should amount to 1801 with respect to the open coaxial line, whilst its magnitude S11 should remain the same. Aluminium foil gave the best results and, hence, was chosen for the shortcalibration. Value G = 1 corresponds to the shortened end of the coaxial probe. As standard liquid ultrapure water (Ariums 611VF, Sartorius) was used with an electrical conductivity lower than 0.1 mS cm1, whose dielectric parameters were taken from the literature.35 All measurements were carried out after stabilization of the measured reflection coefficient36 applying an averaging factor of 5. Salmon sperm DNA with lengths of 500–1000 base pairs was purchased from AppliChem GmbH (Germany) and was used without further purification. The stock solution was prepared by dissolving the DNA in ultrapure water to a concentration of 50 mg ml1 and was subsequently diluted to the final concentrations required. The concentration of the stock solution
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was determined using a UV absorption spectrophotometer (Nanodrop ND-1000, Thermo Fisher Scientific). Conductivities of the samples were measured at 4 kHz with a 2-electrode cell CDC 749 (Radiometer Analytical SAS, France) connected to a conductivity meter (LF DIGI 550, WTW GmbH, Germany). In order to take account of the small volume (1 ml) and, hence, possible errors, e.g. by field effects at the test tube walls, the setup was calibrated with a Cond 197i (WTW GmbH) conductivity meter and a 4-electrode TetraCons 325 (WTW GmbH) cell.
Results and discussion The dielectric response of Salmon sperm DNA was analysed in terms of complex permittivities. The resulting dielectric spectra contain the real part, e 0 , called permittivity and the imaginary part, e00 , known as dielectric loss, which are mutually connected by means of eqn (2):37,38 e*(o) = e 0 (o) je00 (o).
(2)
The permittivity reflects the ability of the material to be polarized under the influence of the external electric field, while the dielectric loss represents dissipative effects in a medium. At high frequencies, when the dipoles are not able to follow the changes of the field immediately, the medium’s permittivity decreases and dielectric loss increases. The phase lag between field and polarization causes conversion of electric energy into heat. The frequency, at which the dielectric loss e00 reaches its maximum, is known as the relaxation frequency fr and it is connected with the relaxation time by eqn (3): 1 t¼ : 2pfr
(3)
On the other hand, an increase of the imaginary part of the complex dielectric function to lower frequencies indicates contributions of the ionic conductivity of a solution. Relaxation processes of polar liquids, attributed to orientational relaxation, can be analysed by the Debye model:37–39 e ðoÞ ¼ e1 þ
es e1 ; 1 þ jot
(4)
where eN is the permittivity at very high frequencies, es is the static permittivity and o = 2pf is the angular frequency. The dielectric strength De = es eN characterises the magnitude of the dielectric relaxation. Applying the empirical Cole–Cole formula (5) one can take into account the distribution of the relaxation times of molecules, where the exponent a(0 o a r 1) is a measure of the symmetrical broadening of the dielectric loss peak: e ðoÞ ¼ e1 þ
es e1 : 1 þ ð jotÞa
(5)
Several relaxation processes simultaneously contribute to the dielectric response of the DNA solution to the applied field. They correspond to the polarization of the ion atmosphere around the DNA, the polarization of water dipoles and to possible bound water effects.21,22 Their frequency ranges partially overlap and
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Fig. 3 Electrical conductivity of aqueous Salmon sperm DNA solution at 25 1C (obtained from the fitting procedure) as a function of its concentration.
lead to a rather complex character of dielectric spectra. Above that, to a great extent significant conductivity effects complicate detection and analysis of these processes as well as the precise determination of the amplitude of the high frequency g-relaxation. Therefore, measurements of the DC electrical conductivity s0 of the Salmon sperm DNA solution were performed in order to exclude its contribution to the true dielectric loss: 00
e00 ¼ etot
s0 ; e0 o
(6)
where etot00 is the total dielectric loss and e0 = 8.85 1012 A s V1 m1 is the permittivity of vacuum. The variation of the conductivity of Salmon sperm DNA solution was measured as a function of concentration (Fig. 3). It clearly exhibits a linear dependence, even at high concentrations of DNA in solution. These values and those obtained from fitting the measured dielectric spectra were in very good agreement. Dielectric dispersion and absorption curves of water and of 12 mg ml1 DNA solution are presented in Fig. 4. In comparison with water DNA spectra exhibit a second dispersion region around 100 MHz with significantly smaller amplitude, which is evident after the subtraction of the conductivity term. For quantitative analysis of the dielectric spectra model function (7) was simultaneously fitted to both the real and imaginary parts of the experimentally obtained complex permittivities using a nonlinear least square minimization. The complex permittivity spectra were fitted starting at 25 MHz up to 110 GHz. As a model function we used the sum of two Cole–Cole relaxation terms corresponding to the relaxation in the MHz range as well as to the orientational polarization of water dipoles: e ðoÞ ¼ e1 þ
De De g a þ b a : 1 þ jotg g 1 þ jotb b
(7)
The complex permittivity spectra with their spectral decomposition according to eqn (7) are presented in Fig. 5. It is well known that the crucial factors for the extraction of dielectric parameters from the fit are the frequency range and
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Fig. 4 The real and imaginary parts of the complex permittivity of water (green line) according to ref. 35, and of the measured Salmon sperm DNA solution (points) at 25 1C and at a concentration of 12 mg ml1.
Fig. 5 The measured complex dielectric function of 12 mg ml1 Salmon sperm DNA at 25 1C (points) and its fit to a superposition of two Cole–Cole functions: b-dispersion (red), g-dispersion (green) and the sum of two dispersions (blue).
the magnitude of relaxations. However, due to the instrumental limitation of the VNA in the high kHz and low MHz regions only the high frequency tail of the low magnitude b-relaxation is covered in our experiments. That complicates the fitting procedure and leads to higher errors in the parameter evaluation for the b-relaxation. Calculation models for the translation of reflection coefficients to complex permittivity values assume a semi-infinite sample volume. This condition can be satisfied when measuring lossy liquids at high frequencies. At low frequencies the skin depth in the liquids under investigation
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can be substantial and affects the measurements.40 Ultrapure water as a calibration standard liquid presents reflection coefficient value close to 1 at frequencies in the low-MHz region. With increasing conductivity of the DNA samples the reflection coefficient becomes smaller and the skin depth decreases due to losses caused by ionic conduction. In the case of ultra pure water and conductive samples there is no complete elimination of skin depth effects. Moreover, reflection measurements using VNAs are best performed by the sample impedances close to the system impedance Z0 = 50 Ohm38 and, therefore, to a reflection coefficient G a 1. At the same time, for the evaluation of dielectric parameters corresponding to the g-relaxation our experimental setup provides very good conditions owing to the wide frequency range reaching 110 GHz. It is possible to cover the water absorption peak nearly completely, the high magnitude of which in turn allows the parameters to be determined with high accuracy. Therefore the maximum standard errors of fits are not more than 0.5% for Deg and tg for all concentrations. The standard fit errors for Deb and tb reach 12% at concentrations lower than 3 mg ml1, and their values are between 3% and 5% at higher concentrations. For a more detailed analysis we fitted the complex dielectric function e*(o) to the Cole–Cole function setting: (i) ab = 1, i.e. for the Debye case, and (ii) leaving ab as a free parameter to be optimised by the fitting routine. In both cases the g-relaxation was presumed to follow the Cole–Cole function with free ag. By addition of the s0 to fit function (7) the electrical conductivity conductivity term je0 o of the investigated solutions was taken into account. Despite the low signal-to-noise ratio in the low frequency region it is obvious that for a proper fit a sum of two Cole–Cole functions has to be assumed in order to take account of both dielectric dispersions. Therefore all presented diagrams correspond to this fit. The concentration dependence of the relaxation time tb, attributed to the movement of DNA counterions, is shown in Fig. 6a. With DNA concentration increasing up to 16 mg ml1 the relaxation time of DNA rapidly falls. At higher concentrations tb decreases to a lesser extent. The obtained dependence can be well fitted with a logarithmic function. The relaxation frequency shifts from approximately 60 to 130 MHz (Fig. 6b). A broad concentration dependent dielectric dispersion of aqueous DNA solution has been observed by Takashima and co-workers.13 Using various experimental techniques for the investigation of calf thymus DNA solution, they reported the loss peak’s maximum at approximately 80 MHz at 20 1C for a 1% solution. On the basis of measurements of frozen Calf thymus DNA Gabriel and Grant15 performed the extrapolation of the activation enthalpy values to 20 1C. They predicted the relaxation frequency to be between 80 and 90 MHz. For the same concentration of DNA we observed a relaxation frequency of 84 MHz at 25 1C. Taking into account the decrease of relaxation time with temperature this is a very good agreement. Fig. 7 shows the variation of dielectric strength Deb with concentration. It rises with increasing amount of DNA in solution
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of dielectric parameters on the ionic strength of aqueous DNA solutions as well as the presence of concentration regimes, where interactions between polyions can be relevant. For preliminarily dialysed and freeze-dried Calf thymus and Herring testes Na–DNA, which were dissolved in deionised water, they observed the relaxation times at least by a factor of 15 higher compared to those obtained in the present study. According to the model of Manning,9 condensation of counterions occurs on the polyion chain if the critical parameter x Z 1/z. x¼
Fig. 6 (a) Variation of the relaxation time tb of Salmon sperm DNA with concentration and its logarithmic fit. (b) Fit curves of the dielectric loss peak of the b-relaxation at 4 (black), 12 (red), 25 (green) and 45 mg ml1 (blue) concentrations (for clarity experimental data are not shown).
q2 4pe0 er kB Tb
(8)
where z is the valence of counterions, q is the electronic charge, er = 78.35 is the permittivity of the solvent, kB is the Boltzmann constant, T is the absolute temperature and b = 0.17 nm is the average distance between charged phosphate groups. For DNA in solution, which has a B-conformation, the value of the critical parameter is x = 4.2. The part of condensed counterions 1 and amounts to f = 0.76 for monois defined as f ¼ 1 zx + valent Na ions in water. The residual negative charges are compensated by loosely associated diffuse ions. According to the Mandel model,8,10,23 the polyion can be represented by a sequence of rigid subunits. As it was mentioned above, the dielectric dispersion of DNA solution at intermediate frequencies is considered to be due to the relaxation of the induced dipole moment caused by counterion fluctuations along these short subunits with the length Ls. Applying formula (9) the subunit length Ls (ref. 8, 10, 11, 19 and 23) can be estimated: De ¼
Cz2 q2 nALs2 ; 36e0 kB T
(9)
where n is the number of condensed counterions: n¼
fLs : zb
(10)
The factor A is connected with the ionic strength of the solution and is defined as: A¼
1 ; 1 2ðzx 1Þ lnðkbÞ
(11)
where k is the Debye screening parameter, which is given by
k¼
Fig. 7 Dielectric strength Deb of Salmon sperm DNA as a function of DNA concentration, line: logarithmic fit.
and fits well to a logarithmic function. Using time domain reflectometry Bone and co-workers19,20 have shown the dependence
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4pNA
q2 4pe0 er kB T
12 1 2 Ci z þ Cp ; x
(12)
Ci is the molar concentration of bulk ions, De is the dielectric strength of the intermediate frequency relaxation (Deb) due to the fluctuation of condensed counterions, C is the number of subunits per m3: b : (13) C ¼ NA C p Ls NA is the Avogadro number and Cp denotes the molar concentration of monomers per m3.
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The second approach to calculate the subunit length Ls is provided by expression (14), which includes the relaxation time of the measured dispersion:8,19
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t¼
Ls2 Aq p2 kB Tu
(14)
where u is the counterion mobility. The higher fit errors in the course of the evaluation of dielectric parameters at low polymer concentration do not allow precise extrapolation to zero DNA concentration, and, therefore, we estimated the subunit lengths from (9) and (14) for the DNA concentration of 4 mg ml1. To determine the concentration Ci, we assume (in the first approximation), that only diffuse and bulk excess ions are responsible for the conductivity. The contribution of DNA polyions is not considered. The contribution of diffuse ions to the electrical conductivity can be calculated as: sdiff = u+qNACp(1 f)
(15)
where u+ = 5.19 108 m2 s1 V1 is the mobility of Na+ ions.41 The excess of conductivity can be determined as: Ds = s0 sdiff.
However, at concentrations above 25 mg ml1 with ionic strength increasing, the relaxation time tb exhibits only small changes. In this range the dielectric strength of this dispersion, Deb, increases only slightly as compared to lower concentrations. The successful logarithmic fit to the experimental data represents more an empirical approach than a mechanistic explanation of the underlying phenomena. In such multicomponent system consisting of polyions, co- and counterions it is difficult to separate individual contributions of the various components and to explain what kind of physical effects are behind the logarithmical correlation. Also mutual interactions of macromolecules could contribute to the obtained relaxation behaviour. Whilst tb shows pronounced dependence on DNA concentration, the relaxation time of water was found to be practically unaffected by variation of DNA concentration. As a result of the reduced water content per unit volume and the restricted mobility of water in a hydration layer close to the polymer surface, the increase of bulk water relaxation time could be expected. Fig. 8a demonstrates the values of tg obtained for different DNA concentrations. It is seen that these values are close to 8.27 ps – the
(16)
Referring to electro neutrality of solutions we suppose the presence of monovalent salt NaCl in the samples. The mobility of chlorine ions is u = 7.91 108 m2 s1 V1.41 Taking into account the measured electric conductivity of s0 = 0.0592 S m1 and its part from diffuse counterions being sdiff = 0.0147 S m1 at this DNA concentration, the concentration of bulk ions can be derived by: Ci ¼
2Ds : u qNA uþ 1 þ uþ
(17)
As result we obtain Ci = 7.07 mol m3. The molar concentration of the DNA’s phosphate groups for an average molecule size of about 750 bp is Cp = 12.33 mol m3. Finally, we get subunit lengths of Ls1 = 35.88 nm and Ls2 = 27.17 nm. These values are only about 40% of those reported in ref. 19 and 20 at comparable ionic strengths. A subunit length of 23.5 nm has been reported in ref. 12 for a plasmid DNA dispersion at 11.7 MHz. The ionic strength was calculated from the concentration of NaCl. This value was found to rise from 1.57 mmol l1 to 26 mmol l1 linearly with polyion concentration. Under the influence of electric field a bulk ions gradient is built up around the polyion chains. On the other hand, it is known that for highly charged polyelectrolytes like DNA the counterions gradient is insensitive to the changes in the monovalent bulk salt concentration.42 It is not clear yet, to which extend bulk ions influence the relaxation behaviour of counterions. It is obvious that the charge density around polyions is much higher than in the bulk medium. Counterions mobility decreases with increasing concentration and viscosity of the solution and DNA chains become more flexible with increasing salt concentration. To a certain extent these mechanisms lead to a decrease of ionic relaxation times and, therefore, shift the relaxation frequencies.
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Fig. 8 (a) Relaxation time tg of Salmon sperm DNA solution (points) as a function of DNA concentration and of pure water (line, according to ref. 35) and (b) dielectric loss peak at 4 (black), 12 (red), 25 (green) and 45 mg ml1 (blue) concentrations at 25 1C.
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relaxation time of pure water.35 The presence of the DNA polymer in solution does not cause an increase of relaxation time or any shift of the relaxation peak (Fig. 8b). A shift of the relaxation frequency in DNA solutions towards lower frequencies has been mentioned by Takashima et al.13 However, their observation was based on measurements up to just 10 GHz plus a single frequency point at 70 GHz, whilst in the present study the spectrum up to 110 GHz was covered in a nearly continuous manner. The absence of any significant frequency shift of the loss peak has also been reported by Cametti et al. in a recent dielectric study on protein solutions up to 50 GHz.43 According to the results presented in ref. 44, the degree of polymer–water interactions and changes in water relaxation time depend not only on the polymer concentration in solution, but also on the hydrophilicity of polymers. In comparison to hydrophilic polymers the distribution of water relaxation times for those ones with pronounced hydrophobic properties is narrower, because the structure of water close to the polymer surface is assumed to be more stable and uniform. The relaxation time of water in such solutions was found to be higher than that for hydrophilic ones.44 On the other hand, the presence of ions45,46 leads to the opposite effect – a reduction of the water relaxation time. However, the estimated concentrations of residual salt in our study could not give a considerable contribution to the decrease of tg. The observations in ref. 44 are related to the solute concentrations between 10% and 50%, whereas the maximum concentration applied in our study is 5%. Moreover, taking into account a great number of hydrophilic groups in DNA we can suggest, that polymer concentrations used in our study are not high enough to detect any significant changes in tg. The dependence of dielectric strength, Deg, on DNA concentration is shown in Fig. 9. It is clear that the value of Deg decreases linearly with increasing DNA concentration. This effect is due to the dilution of water by solute molecules and diminished contribution of much less mobile water molecules bound to the DNA polymer surface in the hydration layer.
Fig. 9 Dielectric strength Deg of Salmon sperm aqueous solution at 25 1C. The inset shows the number of bound water molecules per one base pair.
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The hydration of DNA is an important and intriguing question because of its relevance for biochemical processes such as DNA–protein interactions as well as for the stabilization of the double-helix structure. The ordered structure of DNA and the high number of negatively charged hydrophilic phosphate groups result in strong hydration of DNA. By bonding to the bases in the major and minor grooves water participates in the forming of aqueous networks.6 Moreover, the presence of ions seems to contribute to reduction of the mobility of water molecules near the surface of biopolymers.47 On the basis of the concentration dependence of Deg and using the eqn (18), as reported in ref. 43 and 48, the number of water molecules affected by the polymer surface can be calculated as: N¼
Cw Cw CDNA
(18)
where Cw is the analytical molar water concentration, Cw ¼ Deg r is the apparent water concentration, CDNA is the Deg ðwÞ Mw molar concentration of DNA (the average size of the molecule was taken as 750 bp). The density of water at 25 1C is r = 997 kg m3, its molar mass Mw = 18.02 g mol1 and its dielectric strength at the same temperature Deg(w) = 73.15.35 From this a value of about 40 water molecules per base pair at a DNA concentration of 10 mg ml1 results, and this value remains practically constant at higher DNA concentrations. It should be emphasized that application of eqn (18) to non-spherical polymers is a rough approximation, still the obtained results are in a good correlation with a reported value of about 20 water molecules per nucleotide, required for the maintenance of B-conformation of DNA.47,49 The broadening parameter, ag, for water was found to decrease slightly with an increase of DNA concentration (Fig. 10). Applying a fit with a variable ab we got ag = 0.985 at the highest DNA concentration of 50 mg ml1. This corresponds to a very slight broadening of the water relaxation peak by the dissolved DNA. The value of ab falls from 0.98 at 2 mg ml1 DNA concentration to approximately 0.81 at 50 mg ml1, corresponding to a broader
Fig. 10 Cole–Cole exponents ab (triangles) and ag (circles).
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distribution of the relaxation times of DNA with increasing polymer concentration. Such a wide distribution can be a consequence of the molecular weight distribution of the polymer sample (500–1000 bp), the molecules unsymmetrical shape as well as increasing solute molecule interactions with rising concentration.2 Summing up, our experiments show that the presence of DNA polymers at concentrations up to 50 mg ml1 does not affect the relaxation time of free water. The frequency dependence of the complex permittivities exhibits only slight deviations from the Debye-type relaxation. By increasing the concentration of DNA polyions in solution the broad shoulder between 50 MHz and 1 GHz becomes more and more pronounced. At 50 mg ml1 a satisfactory fit of the complex permittivity curves can be achieved only by introduction of an additional third relaxation term into the model function. For the sake of simplicity we assign it the name delta. We found that in this case the dielectric spectra can be fitted very well to the superposition of a relaxation term of the Cole– Cole type for the g-dispersion of free water and two relaxation terms of the Debye type for the dispersion region between 25 MHz and 1 GHz (Fig. 11). The maximum of this additional loss peak is at 306 MHz corresponding to a relaxation time td = 0.52 ns. Its dielectric strength Ded = 7.87 nearly reaches that of the b-dispersion Deb = 9.63. For the process at lower frequencies we now get a value of the relaxation time tb = 2.69 ns. In this case the standard errors amount to about 15% for those parameters describing the b- and d-relaxations. In the previous case assuming only one broad relaxation of Cole–Cole type in this region we obtain tb = 1.34 ns at ab = 0.81. As it was mentioned above, the accuracy of the fit in the low frequency range of the spectrum is limited by the high noise amplitude in this spectral region. Moreover, the high electrical conductivity of the solutions and the small probe radius could
Fig. 11 Measured dielectric permittivity of 50 mg ml1 Salmon sperm DNA (black circles) and its fit (blue line) with representation as the superposition of three dispersions (green corresponds to the b-relaxation, red – to the g-relaxation, lilac – d-relaxation).
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lead to significant electrode polarization. Local concentration of DNA might be changed by dielectrophoresis7 as well as by adherence of the negatively charged DNA at the electrode surface. Still, it is obvious that introduction of a third term in the model function leads to a satisfying fit, especially in the high frequency range. The nature of this third dispersion is not clear yet. Therefore, further investigations with improved accuracy and even higher DNA concentration should be performed.
Conclusion Using a vector network analyzer we have determined the complex dielectric properties of DNA solutions over the wide frequency range from 25 MHz to 110 GHz. It was possible to resolve at least two dispersions. The first dispersion, centred at 19 GHz, originates from the relaxation of free water. Its relaxation time was found to be practically unaffected by the presence of DNA polyions. Only a slight broadening of the dielectric loss peak occurs at high solute concentrations. The dielectric loss peak of the dispersion, which can be attributed to DNA shifts with concentration from 60 MHz to 130 GHz and becomes broader. Inspection of dielectric spectra at high DNA concentrations reveals the presence of a third dispersion whose origin remains to be clarified.
Acknowledgements This work was supported by the European Regional Development Fund and by the federal state of Brandenburg (projects TeraSens and 031IS2201A ‘‘Taschentuchlabor’’).
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Cite this: Phys. Chem. Chem. Phys., 2014, 16, 11256
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Dielectric measurements of aqueous DNA solutions up to 110 GHz Elena Ermilova,* Frank F. Bier and Ralph Ho ¨ lzel 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 1C. Complex permittivity spectra are analysed at various solute concentrations and two dispersions are observed. The first one is located at about
Received 13th December 2013, Accepted 23rd April 2014
19 GHz and is due to the reorientation of water molecules. The second one is located at approximately
DOI: 10.1039/c3cp55272a
of free water in solutions appears to be practically unaffected by the presence of DNA. For the relaxation in
100 MHz and is interpreted as being caused by DNA counterion fluctuations. The relaxation frequency the MHz region the dielectric loss maximum shifts to higher frequencies and the distribution of relaxation
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times becomes broader with increasing polymer concentration.
Introduction For many years the electric properties of biological materials, such as tissues and cell suspensions as well as of aqueous protein and DNA solutions have attracted scientific interest.1–3 Investigation of their response to electric fields is useful for the understanding of the structure and dynamics of these biological systems and, moreover, this knowledge can be exploited for numerous practical applications. Especially radiowaves and THz radiation are increasingly applied for medical diagnostic and therapy. The availability of modern and fast techniques allows the investigation of dielectric relaxations of biological material over many orders of frequency using methods of frequency as well as time domain spectrometry.4,5 The interaction of DNA macromolecules with water and the surrounding ionic environment under the influence of an electric field has been a subject of research for many years.2,6,7 Several dielectric relaxations of DNA solutions have been reported.8–22 At present the counterion condensation theory8–10,23 is generally accepted for the explanation of their origin at low (kHz range) and intermediate (MHz range) frequencies. On account of the high charge density of the DNA polyion chain in solution the counterions stay in the vicinity of the DNA molecule, to a certain extent neutralizing this excess charge and lowering the repulsions between the negatively charged phosphate groups. One portion of the counterions is territorially bound,
Fraunhofer Institute for Biomedical Engineering (IBMT), Branch Potsdam, ¨hlenberg 13, 14476 Potsdam-Golm, Germany. Am Mu E-mail: [email protected]; Fax: +49-331-58187-199; Tel: +49-331-58187-216
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it is located close to the DNA chain and is called condensed, whereas the other part is more loosely bound and is considered as free or diffused counterions.10–12 The relaxation at low frequencies in the Hz–kHz spectral region is called a-relaxation, which has been found to be strongly molecular weight depended.2,5,11 It arises from the polarization of condensed counterions along the polyion chain. The so-called b-relaxation takes place in the spectral range between 1 MHz and 1 GHz. Its magnitude is much smaller than that of the a-relaxation and is independent of molecule size. For a long time the origin of the b-relaxation has been a subject of numerous dielectric studies.1,4,5,8–15 The movement of the counterions over short segments of DNA in response to the applied electric field is likely to account for this polyion relaxation which is dependent on DNA concentration.8–12 In addition to the mentioned model, the hypotheses of the motion of some polar groups of the DNA molecule13 as well as of relaxations of bound water have been proposed to explain the dielectric b-relaxation.21,22 The third dispersion, named g-relaxation, with the maximum of its dielectric loss peak at about 19 GHz (at 25 1C), is related to the orientational polarization of water dipoles in the applied alternating field. Recent technical advances in radio frequency techniques, especially of vector network analyzers in the upper GHz and lower THz range make it possible to conduct broadband dielectric measurements over a wide frequency range. Reflection methods, and among them open-ended coaxial line sensors, are particularly suitable for a fast and accurate investigation of the dielectric properties of many materials and can be used for engineering as well as medical application.24–31 In the present work we report results on dielectric studies of aqueous solutions
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of Salmon sperm Na–DNA in a spectral region from 25 MHz up to 110 GHz.
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Experimental setup All measurements were carried out with a computer controlled vector network analyser (VNA) Anritsu MS 4647A operating in the frequency range between 70 kHz and 70 GHz. The high frequency region up to 110 GHz was covered by extension of this experimental system with two fast microwave generators (Anritsu MG37022), a broadband test set (Anritsu 3738A), coupler (Anritsu WR10 66670-3) and a transmission-reflection module (Anritsu 3740A-EW) (Fig. 1). One of the distinguishing features of this system is the integration of an external mixer as part of the broadband test set and a coupler, providing the coverage of the whole frequency range in a single sweep. This kind of measurements results in low measurement uncertainties at high frequencies and fast scanning speeds – with a single sweep taking only a few seconds. An open-ended coaxial line was used as sensing element. To prevent the propagation of higher order modes of the high frequency signal the sensor was prepared from a 1.19 mm precision 50 Ohm semirigid coaxial cable (CA100FF, Kawashima Manufacturing, Japan) with solid dielectric PTFE. The centre conductor is made from silver plated copper, the outer conductor from Cu/Sn/Zn plated copper. It was cut flat, carefully polished and inspected through a stereo microscope (Fig. 2). A short (15 cm) and flexible coaxial cable (Gore, 3671 W1-50-3) was used to connect the output of the microwave coupler to the sensor. We have used W-type connectors to provide proper TEM operation of the sensor at high frequencies. The complex input reflection coefficient G*(o) = S11ejj was measured at the tip of the probe immersed into the solution. Here S11 and j are the magnitude and the phase of the reflection pffiffiffiffiffiffiffi coefficient, respectively, and j ¼ 1 is the imaginary unit. All samples were investigated in the frequency domain at 25 1C. Solutions under test with a volume of 1 ml were placed in polypropylene test tubes. Temperature was controlled using a test tube incubator (Peqlab Thriller) with a temperature stability 0.5 K. Standard one-port S11-calibration procedures of the whole system with the reference plane at the end of the 15 cm flexible
Fig. 1
Experimental setup.
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Fig. 2
Tip of the open-ended coaxial sensor.
coaxial cable were performed using a W1 Calibration Kit (3656B, Anritsu). To calculate the complex permittivity, e*(o), of the investigated DNA solutions using the measured reflection coefficients relationship (1) was applied:32,33 e ðoÞ ¼
a1 G ðoÞ a2 a3 G ðoÞ
(1)
where ai with i = 1. . .3 are complex frequency dependent coefficients. They were determined from additional reference measurements using the semirigid coaxial sensor being shorted, left open or immersed in a standard liquid, respectively. Open was obtained by measurements in air with G = 1. To achieve a proper short-circuit at the probe’s open end metal sheets of aluminium, silver, gold and freshly polished copper were tested as well as a silicon rubber sheet with silver particles.34 The phase shift by measuring the complex reflection coefficient G*(o) should amount to 1801 with respect to the open coaxial line, whilst its magnitude S11 should remain the same. Aluminium foil gave the best results and, hence, was chosen for the shortcalibration. Value G = 1 corresponds to the shortened end of the coaxial probe. As standard liquid ultrapure water (Ariums 611VF, Sartorius) was used with an electrical conductivity lower than 0.1 mS cm1, whose dielectric parameters were taken from the literature.35 All measurements were carried out after stabilization of the measured reflection coefficient36 applying an averaging factor of 5. Salmon sperm DNA with lengths of 500–1000 base pairs was purchased from AppliChem GmbH (Germany) and was used without further purification. The stock solution was prepared by dissolving the DNA in ultrapure water to a concentration of 50 mg ml1 and was subsequently diluted to the final concentrations required. The concentration of the stock solution
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was determined using a UV absorption spectrophotometer (Nanodrop ND-1000, Thermo Fisher Scientific). Conductivities of the samples were measured at 4 kHz with a 2-electrode cell CDC 749 (Radiometer Analytical SAS, France) connected to a conductivity meter (LF DIGI 550, WTW GmbH, Germany). In order to take account of the small volume (1 ml) and, hence, possible errors, e.g. by field effects at the test tube walls, the setup was calibrated with a Cond 197i (WTW GmbH) conductivity meter and a 4-electrode TetraCons 325 (WTW GmbH) cell.
Results and discussion The dielectric response of Salmon sperm DNA was analysed in terms of complex permittivities. The resulting dielectric spectra contain the real part, e 0 , called permittivity and the imaginary part, e00 , known as dielectric loss, which are mutually connected by means of eqn (2):37,38 e*(o) = e 0 (o) je00 (o).
(2)
The permittivity reflects the ability of the material to be polarized under the influence of the external electric field, while the dielectric loss represents dissipative effects in a medium. At high frequencies, when the dipoles are not able to follow the changes of the field immediately, the medium’s permittivity decreases and dielectric loss increases. The phase lag between field and polarization causes conversion of electric energy into heat. The frequency, at which the dielectric loss e00 reaches its maximum, is known as the relaxation frequency fr and it is connected with the relaxation time by eqn (3): 1 t¼ : 2pfr
(3)
On the other hand, an increase of the imaginary part of the complex dielectric function to lower frequencies indicates contributions of the ionic conductivity of a solution. Relaxation processes of polar liquids, attributed to orientational relaxation, can be analysed by the Debye model:37–39 e ðoÞ ¼ e1 þ
es e1 ; 1 þ jot
(4)
where eN is the permittivity at very high frequencies, es is the static permittivity and o = 2pf is the angular frequency. The dielectric strength De = es eN characterises the magnitude of the dielectric relaxation. Applying the empirical Cole–Cole formula (5) one can take into account the distribution of the relaxation times of molecules, where the exponent a(0 o a r 1) is a measure of the symmetrical broadening of the dielectric loss peak: e ðoÞ ¼ e1 þ
es e1 : 1 þ ð jotÞa
(5)
Several relaxation processes simultaneously contribute to the dielectric response of the DNA solution to the applied field. They correspond to the polarization of the ion atmosphere around the DNA, the polarization of water dipoles and to possible bound water effects.21,22 Their frequency ranges partially overlap and
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Fig. 3 Electrical conductivity of aqueous Salmon sperm DNA solution at 25 1C (obtained from the fitting procedure) as a function of its concentration.
lead to a rather complex character of dielectric spectra. Above that, to a great extent significant conductivity effects complicate detection and analysis of these processes as well as the precise determination of the amplitude of the high frequency g-relaxation. Therefore, measurements of the DC electrical conductivity s0 of the Salmon sperm DNA solution were performed in order to exclude its contribution to the true dielectric loss: 00
e00 ¼ etot
s0 ; e0 o
(6)
where etot00 is the total dielectric loss and e0 = 8.85 1012 A s V1 m1 is the permittivity of vacuum. The variation of the conductivity of Salmon sperm DNA solution was measured as a function of concentration (Fig. 3). It clearly exhibits a linear dependence, even at high concentrations of DNA in solution. These values and those obtained from fitting the measured dielectric spectra were in very good agreement. Dielectric dispersion and absorption curves of water and of 12 mg ml1 DNA solution are presented in Fig. 4. In comparison with water DNA spectra exhibit a second dispersion region around 100 MHz with significantly smaller amplitude, which is evident after the subtraction of the conductivity term. For quantitative analysis of the dielectric spectra model function (7) was simultaneously fitted to both the real and imaginary parts of the experimentally obtained complex permittivities using a nonlinear least square minimization. The complex permittivity spectra were fitted starting at 25 MHz up to 110 GHz. As a model function we used the sum of two Cole–Cole relaxation terms corresponding to the relaxation in the MHz range as well as to the orientational polarization of water dipoles: e ðoÞ ¼ e1 þ
De De g a þ b a : 1 þ jotg g 1 þ jotb b
(7)
The complex permittivity spectra with their spectral decomposition according to eqn (7) are presented in Fig. 5. It is well known that the crucial factors for the extraction of dielectric parameters from the fit are the frequency range and
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Fig. 4 The real and imaginary parts of the complex permittivity of water (green line) according to ref. 35, and of the measured Salmon sperm DNA solution (points) at 25 1C and at a concentration of 12 mg ml1.
Fig. 5 The measured complex dielectric function of 12 mg ml1 Salmon sperm DNA at 25 1C (points) and its fit to a superposition of two Cole–Cole functions: b-dispersion (red), g-dispersion (green) and the sum of two dispersions (blue).
the magnitude of relaxations. However, due to the instrumental limitation of the VNA in the high kHz and low MHz regions only the high frequency tail of the low magnitude b-relaxation is covered in our experiments. That complicates the fitting procedure and leads to higher errors in the parameter evaluation for the b-relaxation. Calculation models for the translation of reflection coefficients to complex permittivity values assume a semi-infinite sample volume. This condition can be satisfied when measuring lossy liquids at high frequencies. At low frequencies the skin depth in the liquids under investigation
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can be substantial and affects the measurements.40 Ultrapure water as a calibration standard liquid presents reflection coefficient value close to 1 at frequencies in the low-MHz region. With increasing conductivity of the DNA samples the reflection coefficient becomes smaller and the skin depth decreases due to losses caused by ionic conduction. In the case of ultra pure water and conductive samples there is no complete elimination of skin depth effects. Moreover, reflection measurements using VNAs are best performed by the sample impedances close to the system impedance Z0 = 50 Ohm38 and, therefore, to a reflection coefficient G a 1. At the same time, for the evaluation of dielectric parameters corresponding to the g-relaxation our experimental setup provides very good conditions owing to the wide frequency range reaching 110 GHz. It is possible to cover the water absorption peak nearly completely, the high magnitude of which in turn allows the parameters to be determined with high accuracy. Therefore the maximum standard errors of fits are not more than 0.5% for Deg and tg for all concentrations. The standard fit errors for Deb and tb reach 12% at concentrations lower than 3 mg ml1, and their values are between 3% and 5% at higher concentrations. For a more detailed analysis we fitted the complex dielectric function e*(o) to the Cole–Cole function setting: (i) ab = 1, i.e. for the Debye case, and (ii) leaving ab as a free parameter to be optimised by the fitting routine. In both cases the g-relaxation was presumed to follow the Cole–Cole function with free ag. By addition of the s0 to fit function (7) the electrical conductivity conductivity term je0 o of the investigated solutions was taken into account. Despite the low signal-to-noise ratio in the low frequency region it is obvious that for a proper fit a sum of two Cole–Cole functions has to be assumed in order to take account of both dielectric dispersions. Therefore all presented diagrams correspond to this fit. The concentration dependence of the relaxation time tb, attributed to the movement of DNA counterions, is shown in Fig. 6a. With DNA concentration increasing up to 16 mg ml1 the relaxation time of DNA rapidly falls. At higher concentrations tb decreases to a lesser extent. The obtained dependence can be well fitted with a logarithmic function. The relaxation frequency shifts from approximately 60 to 130 MHz (Fig. 6b). A broad concentration dependent dielectric dispersion of aqueous DNA solution has been observed by Takashima and co-workers.13 Using various experimental techniques for the investigation of calf thymus DNA solution, they reported the loss peak’s maximum at approximately 80 MHz at 20 1C for a 1% solution. On the basis of measurements of frozen Calf thymus DNA Gabriel and Grant15 performed the extrapolation of the activation enthalpy values to 20 1C. They predicted the relaxation frequency to be between 80 and 90 MHz. For the same concentration of DNA we observed a relaxation frequency of 84 MHz at 25 1C. Taking into account the decrease of relaxation time with temperature this is a very good agreement. Fig. 7 shows the variation of dielectric strength Deb with concentration. It rises with increasing amount of DNA in solution
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of dielectric parameters on the ionic strength of aqueous DNA solutions as well as the presence of concentration regimes, where interactions between polyions can be relevant. For preliminarily dialysed and freeze-dried Calf thymus and Herring testes Na–DNA, which were dissolved in deionised water, they observed the relaxation times at least by a factor of 15 higher compared to those obtained in the present study. According to the model of Manning,9 condensation of counterions occurs on the polyion chain if the critical parameter x Z 1/z. x¼
Fig. 6 (a) Variation of the relaxation time tb of Salmon sperm DNA with concentration and its logarithmic fit. (b) Fit curves of the dielectric loss peak of the b-relaxation at 4 (black), 12 (red), 25 (green) and 45 mg ml1 (blue) concentrations (for clarity experimental data are not shown).
q2 4pe0 er kB Tb
(8)
where z is the valence of counterions, q is the electronic charge, er = 78.35 is the permittivity of the solvent, kB is the Boltzmann constant, T is the absolute temperature and b = 0.17 nm is the average distance between charged phosphate groups. For DNA in solution, which has a B-conformation, the value of the critical parameter is x = 4.2. The part of condensed counterions 1 and amounts to f = 0.76 for monois defined as f ¼ 1 zx + valent Na ions in water. The residual negative charges are compensated by loosely associated diffuse ions. According to the Mandel model,8,10,23 the polyion can be represented by a sequence of rigid subunits. As it was mentioned above, the dielectric dispersion of DNA solution at intermediate frequencies is considered to be due to the relaxation of the induced dipole moment caused by counterion fluctuations along these short subunits with the length Ls. Applying formula (9) the subunit length Ls (ref. 8, 10, 11, 19 and 23) can be estimated: De ¼
Cz2 q2 nALs2 ; 36e0 kB T
(9)
where n is the number of condensed counterions: n¼
fLs : zb
(10)
The factor A is connected with the ionic strength of the solution and is defined as: A¼
1 ; 1 2ðzx 1Þ lnðkbÞ
(11)
where k is the Debye screening parameter, which is given by
k¼
Fig. 7 Dielectric strength Deb of Salmon sperm DNA as a function of DNA concentration, line: logarithmic fit.
and fits well to a logarithmic function. Using time domain reflectometry Bone and co-workers19,20 have shown the dependence
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4pNA
q2 4pe0 er kB T
12 1 2 Ci z þ Cp ; x
(12)
Ci is the molar concentration of bulk ions, De is the dielectric strength of the intermediate frequency relaxation (Deb) due to the fluctuation of condensed counterions, C is the number of subunits per m3: b : (13) C ¼ NA C p Ls NA is the Avogadro number and Cp denotes the molar concentration of monomers per m3.
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The second approach to calculate the subunit length Ls is provided by expression (14), which includes the relaxation time of the measured dispersion:8,19
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t¼
Ls2 Aq p2 kB Tu
(14)
where u is the counterion mobility. The higher fit errors in the course of the evaluation of dielectric parameters at low polymer concentration do not allow precise extrapolation to zero DNA concentration, and, therefore, we estimated the subunit lengths from (9) and (14) for the DNA concentration of 4 mg ml1. To determine the concentration Ci, we assume (in the first approximation), that only diffuse and bulk excess ions are responsible for the conductivity. The contribution of DNA polyions is not considered. The contribution of diffuse ions to the electrical conductivity can be calculated as: sdiff = u+qNACp(1 f)
(15)
where u+ = 5.19 108 m2 s1 V1 is the mobility of Na+ ions.41 The excess of conductivity can be determined as: Ds = s0 sdiff.
However, at concentrations above 25 mg ml1 with ionic strength increasing, the relaxation time tb exhibits only small changes. In this range the dielectric strength of this dispersion, Deb, increases only slightly as compared to lower concentrations. The successful logarithmic fit to the experimental data represents more an empirical approach than a mechanistic explanation of the underlying phenomena. In such multicomponent system consisting of polyions, co- and counterions it is difficult to separate individual contributions of the various components and to explain what kind of physical effects are behind the logarithmical correlation. Also mutual interactions of macromolecules could contribute to the obtained relaxation behaviour. Whilst tb shows pronounced dependence on DNA concentration, the relaxation time of water was found to be practically unaffected by variation of DNA concentration. As a result of the reduced water content per unit volume and the restricted mobility of water in a hydration layer close to the polymer surface, the increase of bulk water relaxation time could be expected. Fig. 8a demonstrates the values of tg obtained for different DNA concentrations. It is seen that these values are close to 8.27 ps – the
(16)
Referring to electro neutrality of solutions we suppose the presence of monovalent salt NaCl in the samples. The mobility of chlorine ions is u = 7.91 108 m2 s1 V1.41 Taking into account the measured electric conductivity of s0 = 0.0592 S m1 and its part from diffuse counterions being sdiff = 0.0147 S m1 at this DNA concentration, the concentration of bulk ions can be derived by: Ci ¼
2Ds : u qNA uþ 1 þ uþ
(17)
As result we obtain Ci = 7.07 mol m3. The molar concentration of the DNA’s phosphate groups for an average molecule size of about 750 bp is Cp = 12.33 mol m3. Finally, we get subunit lengths of Ls1 = 35.88 nm and Ls2 = 27.17 nm. These values are only about 40% of those reported in ref. 19 and 20 at comparable ionic strengths. A subunit length of 23.5 nm has been reported in ref. 12 for a plasmid DNA dispersion at 11.7 MHz. The ionic strength was calculated from the concentration of NaCl. This value was found to rise from 1.57 mmol l1 to 26 mmol l1 linearly with polyion concentration. Under the influence of electric field a bulk ions gradient is built up around the polyion chains. On the other hand, it is known that for highly charged polyelectrolytes like DNA the counterions gradient is insensitive to the changes in the monovalent bulk salt concentration.42 It is not clear yet, to which extend bulk ions influence the relaxation behaviour of counterions. It is obvious that the charge density around polyions is much higher than in the bulk medium. Counterions mobility decreases with increasing concentration and viscosity of the solution and DNA chains become more flexible with increasing salt concentration. To a certain extent these mechanisms lead to a decrease of ionic relaxation times and, therefore, shift the relaxation frequencies.
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Fig. 8 (a) Relaxation time tg of Salmon sperm DNA solution (points) as a function of DNA concentration and of pure water (line, according to ref. 35) and (b) dielectric loss peak at 4 (black), 12 (red), 25 (green) and 45 mg ml1 (blue) concentrations at 25 1C.
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relaxation time of pure water.35 The presence of the DNA polymer in solution does not cause an increase of relaxation time or any shift of the relaxation peak (Fig. 8b). A shift of the relaxation frequency in DNA solutions towards lower frequencies has been mentioned by Takashima et al.13 However, their observation was based on measurements up to just 10 GHz plus a single frequency point at 70 GHz, whilst in the present study the spectrum up to 110 GHz was covered in a nearly continuous manner. The absence of any significant frequency shift of the loss peak has also been reported by Cametti et al. in a recent dielectric study on protein solutions up to 50 GHz.43 According to the results presented in ref. 44, the degree of polymer–water interactions and changes in water relaxation time depend not only on the polymer concentration in solution, but also on the hydrophilicity of polymers. In comparison to hydrophilic polymers the distribution of water relaxation times for those ones with pronounced hydrophobic properties is narrower, because the structure of water close to the polymer surface is assumed to be more stable and uniform. The relaxation time of water in such solutions was found to be higher than that for hydrophilic ones.44 On the other hand, the presence of ions45,46 leads to the opposite effect – a reduction of the water relaxation time. However, the estimated concentrations of residual salt in our study could not give a considerable contribution to the decrease of tg. The observations in ref. 44 are related to the solute concentrations between 10% and 50%, whereas the maximum concentration applied in our study is 5%. Moreover, taking into account a great number of hydrophilic groups in DNA we can suggest, that polymer concentrations used in our study are not high enough to detect any significant changes in tg. The dependence of dielectric strength, Deg, on DNA concentration is shown in Fig. 9. It is clear that the value of Deg decreases linearly with increasing DNA concentration. This effect is due to the dilution of water by solute molecules and diminished contribution of much less mobile water molecules bound to the DNA polymer surface in the hydration layer.
Fig. 9 Dielectric strength Deg of Salmon sperm aqueous solution at 25 1C. The inset shows the number of bound water molecules per one base pair.
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The hydration of DNA is an important and intriguing question because of its relevance for biochemical processes such as DNA–protein interactions as well as for the stabilization of the double-helix structure. The ordered structure of DNA and the high number of negatively charged hydrophilic phosphate groups result in strong hydration of DNA. By bonding to the bases in the major and minor grooves water participates in the forming of aqueous networks.6 Moreover, the presence of ions seems to contribute to reduction of the mobility of water molecules near the surface of biopolymers.47 On the basis of the concentration dependence of Deg and using the eqn (18), as reported in ref. 43 and 48, the number of water molecules affected by the polymer surface can be calculated as: N¼
Cw Cw CDNA
(18)
where Cw is the analytical molar water concentration, Cw ¼ Deg r is the apparent water concentration, CDNA is the Deg ðwÞ Mw molar concentration of DNA (the average size of the molecule was taken as 750 bp). The density of water at 25 1C is r = 997 kg m3, its molar mass Mw = 18.02 g mol1 and its dielectric strength at the same temperature Deg(w) = 73.15.35 From this a value of about 40 water molecules per base pair at a DNA concentration of 10 mg ml1 results, and this value remains practically constant at higher DNA concentrations. It should be emphasized that application of eqn (18) to non-spherical polymers is a rough approximation, still the obtained results are in a good correlation with a reported value of about 20 water molecules per nucleotide, required for the maintenance of B-conformation of DNA.47,49 The broadening parameter, ag, for water was found to decrease slightly with an increase of DNA concentration (Fig. 10). Applying a fit with a variable ab we got ag = 0.985 at the highest DNA concentration of 50 mg ml1. This corresponds to a very slight broadening of the water relaxation peak by the dissolved DNA. The value of ab falls from 0.98 at 2 mg ml1 DNA concentration to approximately 0.81 at 50 mg ml1, corresponding to a broader
Fig. 10 Cole–Cole exponents ab (triangles) and ag (circles).
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distribution of the relaxation times of DNA with increasing polymer concentration. Such a wide distribution can be a consequence of the molecular weight distribution of the polymer sample (500–1000 bp), the molecules unsymmetrical shape as well as increasing solute molecule interactions with rising concentration.2 Summing up, our experiments show that the presence of DNA polymers at concentrations up to 50 mg ml1 does not affect the relaxation time of free water. The frequency dependence of the complex permittivities exhibits only slight deviations from the Debye-type relaxation. By increasing the concentration of DNA polyions in solution the broad shoulder between 50 MHz and 1 GHz becomes more and more pronounced. At 50 mg ml1 a satisfactory fit of the complex permittivity curves can be achieved only by introduction of an additional third relaxation term into the model function. For the sake of simplicity we assign it the name delta. We found that in this case the dielectric spectra can be fitted very well to the superposition of a relaxation term of the Cole– Cole type for the g-dispersion of free water and two relaxation terms of the Debye type for the dispersion region between 25 MHz and 1 GHz (Fig. 11). The maximum of this additional loss peak is at 306 MHz corresponding to a relaxation time td = 0.52 ns. Its dielectric strength Ded = 7.87 nearly reaches that of the b-dispersion Deb = 9.63. For the process at lower frequencies we now get a value of the relaxation time tb = 2.69 ns. In this case the standard errors amount to about 15% for those parameters describing the b- and d-relaxations. In the previous case assuming only one broad relaxation of Cole–Cole type in this region we obtain tb = 1.34 ns at ab = 0.81. As it was mentioned above, the accuracy of the fit in the low frequency range of the spectrum is limited by the high noise amplitude in this spectral region. Moreover, the high electrical conductivity of the solutions and the small probe radius could
Fig. 11 Measured dielectric permittivity of 50 mg ml1 Salmon sperm DNA (black circles) and its fit (blue line) with representation as the superposition of three dispersions (green corresponds to the b-relaxation, red – to the g-relaxation, lilac – d-relaxation).
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lead to significant electrode polarization. Local concentration of DNA might be changed by dielectrophoresis7 as well as by adherence of the negatively charged DNA at the electrode surface. Still, it is obvious that introduction of a third term in the model function leads to a satisfying fit, especially in the high frequency range. The nature of this third dispersion is not clear yet. Therefore, further investigations with improved accuracy and even higher DNA concentration should be performed.
Conclusion Using a vector network analyzer we have determined the complex dielectric properties of DNA solutions over the wide frequency range from 25 MHz to 110 GHz. It was possible to resolve at least two dispersions. The first dispersion, centred at 19 GHz, originates from the relaxation of free water. Its relaxation time was found to be practically unaffected by the presence of DNA polyions. Only a slight broadening of the dielectric loss peak occurs at high solute concentrations. The dielectric loss peak of the dispersion, which can be attributed to DNA shifts with concentration from 60 MHz to 130 GHz and becomes broader. Inspection of dielectric spectra at high DNA concentrations reveals the presence of a third dispersion whose origin remains to be clarified.
Acknowledgements This work was supported by the European Regional Development Fund and by the federal state of Brandenburg (projects TeraSens and 031IS2201A ‘‘Taschentuchlabor’’).
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