epl draft Short-fragment Na-DNA dilute aqueous solutions: fundamental length scales and screening S. Tomic´1 (a), S. Dolanski Babic´1 (b), T. Ivek1, T. Vuletic´1, S. Krcˇa2, F. Livolant3 and 8 R. Podgornik4,5,6 0 0 1 Institut za fiziku - HR-10001 Zagreb, Croatia 2 2 Rudjer Boˇsković Institute - HR-10001 Zagreb, Croatia n 3 Laboratoire de Physique des Solides, Université Paris Sud - F-91405 Orsay, France a 4 Department of Physics, University of Ljubljana - SI-1000 Ljubljana, Slovenia J 5 J. Stefan Institute - SI-1000 Ljubljana, Slovenia 1 6 Laboratory of Physical and Structural Biology, NICHD, National Institutes of Health - Bethesda, MD 20892, USA 3 ] t f o PACS 87.15.H-–Dynamics of biomolecules s PACS 82.39.Pj–Nucleic acids, DNAand RNAbases t. PACS 77.22.Gm–Dielectric loss and relaxation a m Abstract. - Dielectric spectroscopy is used to investigate fundamental length scales of 146bp - short-fragment (nucleosomal) dilute Na-DNA solutions. Two relaxation modes are detected: the d high- and the low-frequency mode. Dependence of the corresponding length scales on the DNA n and on the (uni-valent) salt concentration is studied in detail, being different from the case of o long, genomic DNA, investigated before. In low added salt regime, the length scale of the high- c frequency mode scales as the average separation between DNAs, though it is smaller in absolute [ magnitude, whereas the length scale of the low-frequency mode is equal to the contour length 1 of DNA. These fundamental length scales in low added salt regime do not depend on whether v DNA is in a double stranded or single stranded form. On the other hand, with increasing added 5 salt, thecharacteristic length scale oflow-frequency modediminishes at low DNAconcentrations 8 probably due to dynamical formation of denaturation bubbles and/or fraying in the vicinity of 8 DNAdenaturation threshold. 4 . 1 0 8 0 : Semiflexible polyelectrolytes are fundamental compo- ing the amount of added salt, as well as valency of the v i nents of biological environment, ranging from charged counterions[2,3]. A full descriptionandunderstanding of X polymers such as deoxyribonucleic acid (DNA) and pro- single DNA chain structure together with the structural r teins, all the way to molecular aggregates such as bac- organization of DNA chains in aqueous solutions are of a terial fd viruses and the tobacco mosaic virus [1]. DNA fundamental importance in the study of living systems. is in many respects a paradigm of a semiflexible highly Let us first reiterate the results of a recent dielectric charged polymer. In aqueous solutions it assumes a con- spectroscopy study of polydisperse Na-DNA [4,5] in the formation of an extended statistical coil, whereas in vivo caseofsemidiluteaqueoussolutionsoflong(2−20kbp), quite long genomic DNA is usually folded in dense and genomic DNA. It revealed two relaxation modes that can compact states to fit within the micron-sized nucleus of be attributed to diffusive motion of DNA counterions, eukaryoticcellsorevensmallerviralcapsids[2]. Suchwide with fundamental length scales consistent with theoreti- range of complex behaviors of DNA is due to its connec- cal estimates [3,6,7]. Both relaxationmodes are found to tivity, stiffness and strong electrostatic interactions. To a be strongly DNA concentration-dependent, setting them large degree this behavior seen in vivo can be closely re- apartfrompreviouslyobservedconcentration-independent producedin vitrobytuningtheDNAconcentration,vary- processesthatarecontingentonthedegreeofpolymeriza- tion N (number of monomers in a given molecule) [8]. (a)E-mail: stomic@ifs.hr (b)Permanent address: Department of Physics and Biophysics, The measured fundamental length scale, probed by the MedicalSchool,UniversityofZagreb-Zagreb,Croatia low-frequency(LF)mode,characterizessinglechainprop- p-1 S. Tomić et al. erties, being equal to the size of the Gaussian chain com- a) 25 °C b) 25 °C posed of correlation blobs that scales as c−0.25 in the low 10 a1 DNA added salt limit [3]. In the high added salt limit the LF b1 a2 mode length scale equals the persistence length L and b2 p scales as L =L +aI−1 (in ˚A) which is nothing but the b4 well-knownpOdijk0-Skolnsick-Fixman(OSF)result. HereL ''ε 1 a4 a3 b3 0 is close to the structural persistence length of 500˚A and I is the ionic strength of the added salt (in M). On the s other hand, the high-frequency (HF) mode is probing the collective properties of the DNA solution which are char- 0.1 acterized by the de Gennes-Pfeuty-Dobrynin (GPD) cor- 103 104 105 106 107 108 103 104 105 106 107 108 relation length or the mesh size, that scales as c−0.5. At ν (Hz) ν (Hz) DNA low DNA concentrations and in the low added salt limit the LF mode length scale reflects the locally fluctuating Fig.1: Doublelogarithmicplotofthefrequencydependenceof DNAregionswithpartiallyexposedhydrophobiccorethat theimaginarypartofthedielectricfunction(ε′′)atT =25◦C yields the scaling form c−0.33. Even when the denatura- ofa)purewater146bpDNAsolutions(forDNAconcentrations DNA tionprotocolisapplied,unzippingofthetwoDNAstrands a1-a4(5,0.5,0.15,0.05mg/mL))andb)146bpDNAsolutions with added salt I = 1mM (for DNA concentrations b1-b4 appears to be at most local and complete separation of s (1.5,0.8,0.4,0.3mg/mL)). Thefulllinesarefitstothesumof the strands in semidilute solutions is never really accom- two Cole-Cole forms (see text); the dashed lines represent the plished. For both modes the high and the low salt are single form. characterized by the competition between added salt and intrinsic DNA counterions. Due to the size of DNA used in these experiments, all ∗ A very crude estimate of c based on de Gennes argu- DNA length dependence was already saturated and none ∗ ments[7]yieldsc ofthe orderof1mg/mL,whichisclose of the two modes show any. For shorter chains other ex- totheupperconcentrationboundinourexperiments[12]. periments show that even N-dependent modes can often Thismeans thatweareeffectivelyalwaysindilute regime be concentration-dependent [9], leading to a complicated which, in contrast to the semidilute one, has not been interdependence of the two effects. Another intriguing is- much studied experimentally. Concurrently we have also sue is if and how the screening and fundamental length consideredtowhatextenttheinterpretationofourresults scales will change in the limit of very low DNA density, depends on DNA conformation in low salt and in pure that is, below the semidilute-dilute crossover. Contrary water solutions, more specifically on whether DNA is in to the semidilute regime, where polyelectrolyte chains are a single stranded or double stranded form. Denaturation in general entangled with each other, the dilute regime studies(performedbydielectricspectroscopyasdescribed with no or low added salt is characterized by extended previously [5]) indicate that for these dilute conditions DNA conformations where each chain is well separated DNAdouble-helixisdenaturedinpurewatersolutionsfor from all other ones, leading to an average separation between chains that scales as c−0.33 [3]. In addition, the DNA concentrations below about 0.4mg/mL, which cor- DNA respondsto 1mMof intrinsic DNA counterions[13]. This low concentrationof chains alsoaffects the characteristics value is also in accord with results obtained by UV spec- oftheManning-Oosawacounterioncondensationwhichin trophotometry on solutions of varying DNA and added facttakesplaceintwoseparatezonesofvolumeassociated salt concentrations in that they gave a limit on the order with each chain [10]. of1mMoftotalcounterions(intrinsicandaddedsalt)be- Inthis Letterweaddresssomeoftheseissueswhiletry- ing to characterizethe structure of dilute DNA solutions low which double stranded DNA denatures. We detected no change in the scaling behavior of fundamental lengths composed of short-fragment DNA. To this effect we used nucleosomalDNA(∼146bp)chainspreparedasdescribed ofthe twodielectricmodes aswecrossthese solutioncon- ditions; nevertheless a decrease in magnitude of the LF previously [11]. The low protein content was verified and length scale is observed in the presence of added salt in DNA concentration was determined by UV spectropho- the vicinity of the denaturation threshold. tometry. Weperformasystematicinvestigationofhowthe dielectricpropertiesofthesemonodisperseshort-fragment Fig. 1 shows the frequency dependent imaginary part DNA aqueous solutions evolve upon change of DNA con- of the dielectric function for solutions with selected DNA centration and added salt over a range of two to three concentrations. Theresultsfor purewatershort-fragment ordersof magnitude. DNA solutions werepreparedas de- DNA solutions are shown in panel a), while results for scribed previously (see Materials and Methods in ref. [5], DNAsolutionswithaddedsaltofionicstrengthI =1mM s preparationprotocolsIandII.3). Sincethecontourlength are shown in panel b). The observed dielectric response L ofDNA chains is onthe order of500˚A, the concentra- is complex [14] and the data can only be successfully fit- c tion of polyelectrolyte solutions that we deal with here ted to a formula representing the sum of two Cole-Cole is always below the chain overlap concentration c∗ [3]. forms (ε(ω)−ε = (ε −ε )/(1+(iωτ )1−α)), equiv- HF 0 HF 0 p-2 Short-fragment Na-DNA solutions alent to the Havriliak-Negami type with skewness pa- rameter β = 1 [15]. The spectra consist of two broad 100 25 °C 20 modes that show a symmetrical broadening of the relax- m) ation time distribution function described by the param- (n 10 eter 1−α ≈ 0.8. The mode in the high-frequency region HF L (HF mode) has a strength 2 < ∆ε < 15 and is cen- ) 5 HF m tered in the range 0.3MHz < ν < 15MHz. The mode n HF ( in the low-frequency region (LF mode) has a strength F 0.1 1 10 H 0.5 < ∆εLF < 50 and for pure water solutions does not L 10 Is (mM) movemuchinfrequencyremainingcenteredaround80kHz (60kHz<ν <110kHz). LF ThepolarizationresponseofDNAsolutionsinthekHz- MHz range is due to an oscillating flow of net charge associated with DNA counterions induced by an applied ac field. Since the counterion displacement is facilitated 0.01 0.1 1 10 throughdiffusion,thedielectricresponseisbasicallychar- acterizedbythemeanrelaxationtimeτ ∝L2/D ,where c (mg/mL) 0 in DNA L is the associated length scale, and D is the diffusion in constant of counterions. This constant is sufficiently well Fig. 2: Main panel: Characteristic length of the HF mode approximatedbythediffusionconstantofbulkions[14,16] (L ) for pure water short-fragment DNA solutions (open HF leading to a value of D = 1.33· 10−9m2/s. In other squares)andforshort-fragmentDNAsolutionswithaddedsalt in words, the fit to the Cole-Cole functions allows us to ex- Is = 1mM (full squares) as a function of DNA concentration (c ). ThefulllineisafittothepowerlawL ∝c−0.33. In- tract the characteristic time τ0 and calculate the corre- DNA HF DNA set: L for short-fragment DNAsolutions vs. addedsalt (I ) sponding length scale for each of the relaxation modes. HF s for c = 0.5mg/mL (full triangles). The full line denotes Similarlycomplexspectrahavealsobeenobservedforlong DNA Debyescreeninglengthfortheinvestigatedrangeofaddedsalt. polydisperse DNA semidilute solutions [4,5]. However the DNA concentration and added salt dependence mea- suredforshort-fragmentDNAareratherdistinct,indicat- of 1mg/mL. Finally, we remark that in semidilute solu- ing that mechanisms of counterion relaxation for short- tions, but only in semidilute solutions, this scaling form fragment as opposed to long Na-DNA solutions are not wouldbetypicalforchargedchainswithpartiallyexposed identical. hydrophobic cores [3]. Letusfirstdescribethe characteristicsoftheHFmode. For pure water short-fragmentDNA solutions the charac- Withadded1mMsalt,thebehaviorofLHF remainsun- teristiclengthLHFincreaseswithdecreasingDNAconcen- changed(main panelof fig.2), thus LHF ∝cD−N0.A33, as long tration in almost three decades wide concentration range as the concentration of intrinsic counterions cin (propor- (mainpaneloffig.2)followingthepowerlawLHF ∝cD−N0.A33 tional to cDNA) is larger than the concentration of added as a function of the DNA concentration. In dilute solu- salt ions. At lower DNA concentrations, the LHF appar- tions this scaling form is typical for the average distance entlyshowsalevelingoff,withalimitingvalueclosetothe between chains [3]. This result also confirms our claim Debyelengthappropriateforthissaltconcentration. Aset in the case of long, genomic DNA that the HF relaxation of additional data (inset of fig. 2) for cDNA = 0.5mg/mL processdescribesthecollectivestructuralpropertiesofso- withvaryingaddedsaltconcentrationshowthatLHF does lution composed of many chains [4,5]. It is noteworthy not change with Is in most of the measured range. How- that although the DNA double-helix appears to be dena- ever,thisbehaviorseemstoremaineveninthelimitwhen tured for c < 0.4mg/mL, the overall change in the added salt concentration is larger than the concentration DNA prefactor of the scaling law is small and is within the er- of DNA intrinsic counterions, showing LHF values appar- ror bar of the experiment. This result is not too surpris- ently above the corresponding Debye length. This is in ing. First, the same scaling law is expected to be valid contrastto1mMdata(showninthe mainpaneloffig.2). alsofor single strandedDNA, and second,such a solution Wearetemptedtobelievethatthisapparentcontradiction should contain twice the number of chains corresponding is related to a poorer accuracy of these data, in compar- to only about 20% decrease in the average distance be- ison to 1mM ones, due to the progressive merging of the tween chains, which is at the resolution limit of our mea- HFandLFmodeswhenoneapproachestheregimeofhigh surement. Also, the two chains that partake in the orga- added salt. nizationofthe commoncounterioncloudshouldprobably Second,weaddresstheLFmode. Forpurewatershort- remain in relatively close proximity even after they are fragmentDNAsolutions,thecharacteristiclengthL re- LF nominally dissociated. Furthermore even at high DNA mains approximately constant in more than two decades concentrations there is still no sign of a dilute-semidilute wide concentration range (open squares in fig. 3) at the crossover,confirming our estimate that c∗ is on the order level of L ≈500˚A. The latter value suggests that in this c p-3 S. Tomić et al. 10 25 °C 25 °C ) 100 ) 1000 nm →0 ( LF 50 Is L ( ) 30 LF 1 m L n /F L( LF 100 0.1 Is (m1M) 10 LL 0.1 0.1 1 10 Lc = 50 nm 2Is/cin 10 0.01 0.1 1 10 Fig.4: CharacteristiclengthoftheLFmode(LLF)normalized c (mg/mL) with the value in pure water solutions LLF(Is → 0) ≈ Lc vs. DNA added salt concentration normalized by the concentration of intrinsiccounterions(2I /c ). Dataareforonerepresentative s in Fig. 3: Main panel: Characteristic length of the LF mode DNA concentration c = 0.5mg/mL and varying I (open DNA s (LLF) for pure water short-fragment DNA solutions (open triangles) and forIs =1mMandvaryingDNAconcentrations squares)andforshort-fragmentDNAsolutionswithaddedsalt (full squares). I = 1mM (full squares) as a function of DNA concentration s (c ). The full line denotes the contour length L ≈ 500˚A. DNA c Inset: L forshort-fragmentDNAsolutionswithvaryingionic LF length. Our data (see fig. 2 and 3, main panels) are strength of added salt for c = 0.5mg/mL (full triangles). DNA at variance with this expectation: although L scales HF The grey and full lines denote the contour length of studied as expected for the average distance between chains, it short-fragment DNA and the persistence length as predicted is smaller than L in the whole range of DNA concen- bythe OSFtheory,respectively (ref. [6]). LF trations. In order to rationalize this finding, we deem it plausible that L corresponds to a shorter scale in- HF regime LLF is proportional to the contour length of the side the spherical cell zone of the size Rcell around the polyelectrolyte chain [17]. This result confirms that the polymer. Indeed, theoretically the dilute regime is mod- LFrelaxationrepresentsasinglechainproperty[4,5]. For elled by placing the polymer at the center of a cell of size DNA solutions with added salt Is = 1mM (full squares Rcell ∝ c−0.33 that is subdivided into two zones [3,10]: in fig. 3) L is the same as for pure water DNA solu- a smaller cylindrical one, inside which the electrostatic LF tions at high DNA concentrations. At the concentrations interaction energy is large, and a larger spherical zone, ofintrinsic counterionsc (proportionalto c ) smaller where the electrostatic interactions are described by the in DNA than the concentration of added salt ions, L starts to low coupling Debye-Hu¨ckel approximation. As a result, LF deviate from the L ∝ L behavior and decreases to at- the response of DNA counterions to an applied ac field LF c tain a value of about 250˚A. Additional data (inset of would be mostly confined to a smaller cylindrical volume fig. 3) for c = 0.5mg/mL with varying added salt withinthelargesphericalvolumeofradiusequaltotheav- DNA show that L does not vary with I in most of the mea- erage distance between chains. We remark that a similar HF s suredrangeofaddedsalt. Whenaddedsaltconcentration relationshipbetweenLHF andthecontourlengthindilute islargerthanDNAconcentration,thebehaviorofL in- regime, although not discussed, can be discerned in the LF dicates only a minor decrease, in contrast to a more sub- datareportedbyItoet al.(ref.[18])andbyKatsumotoet stantial one shown by 1mM data (main panel of fig. 2). al. (ref. [19]). This discrepancy might be ascribed, similarly as for the It is noteworthy that the contour length remains the HF process, to a poor accuracy of former data, which are relevantsinglechainlengthscaleaslongastheconcentra- severely influenced by high salt environment. The added- tion of intrinsic counterions is larger than the concentra- salt-independent behavior in the limit of low added salt tionofaddedsalt,ascanbeclearlynoticedfromfig.4. In is not surprising since the contour length of the short- otherwords,thesinglechainlengthscaleisindependentof fragmentDNAchainsisontheorderoftheDNAintrinsic the DNA concentration due to the fact that in the dilute persistence length. This factimmediately excludes the ef- regime interchain interactions are negligible compared to fectsofelectrostaticinteractionsonthepersistencelength intrachain interactions, in contrast with the behavior of as predictedby OSF theory [6]andshownfor comparison long DNA chains in semidilute solutions [4,5]. The data in inset of fig. 3. for L deviate from the L only in the high salt limit, LF c In the dilute regime it is expected that the averagedis- for 2I > 2c , where we expect that the effects of added s in tance between chains (R ) is larger than the contour salt become dominant. In this regime on addition of salt, cell p-4 Short-fragment Na-DNA solutions (fig. 4), we note that the fundamental single chain length NewYork) 2003. scale shrinks in size, becoming smaller than the nominal [2] Bloomfield V. A., Crothers D. M. and Tinocco I., contour length of the chain. Taking into accountthat the Jr., Nucleic Acids (University Science Books, Sausalito) short fragments of DNA are almost exactly one persis- 2000. [3] Dobrynin A. V.andRubinstein M.,Prog. Polym. Sci., tencelengthlong,itisdifficulttoenvisionanydecreasein 30 (2005) 1049; Dobrynin A. V.,Colby R. H. and Ru- the rigidity, as quantified by the persistence length, that binstein M., Macromolecules, 28 (1995) 1859. would lead to a smaller effective contour length. A possi- [4] Tomic´ S., Vuletic´ T., Dolanski Babic´ S., Krcˇa S., blespeculativeexplanationforthisstrangebehaviorcould Ivankovic´ D., Griparic´ L. and Podgornik R., be soughtinthe incipientdynamic dissociationofthe two Phys. Rev. Lett., 97 (2006) 098303. strands of DNA that is fully established for DNA con- [5] Tomic´ S., Dolanski Babic´ S., Vuletic´ T., Krcˇa S., centrations below 0.4mg/mL. Short bubbles of separated Ivankovic´ D., Griparic´ L. and Podgornik R., strandsalongDNA and/orpronouncedfrayingatthe two Phys. Rev. E, 75 (2007) 021905. endscouldshortenitseffectivecontourlengthwhichwould [6] Odijk T.,J. Polym. Sci. B: Polym. Phys.,15 (1977) 477; thencorrespondtothemeasuredfundamentalsinglechain Skolnick J. and Fixman M.,Macromol., 10 (1977) 944. length scale. [7] de Gennes P. G., Pincus P., Velasco R. M. and Brochard F., J. Phys. (Paris), 37 (1976) 1461; In summary, our results demonstrate that the LF and Pfeuty P., J. Phys. (Paris), 39 (1978) C2-149. HF processes, detected by dielectric spectroscopy mea- [8] Takashima S., J. Phys. Chem., 70 (1966) 1372. surements of short-fragment DNA solutions, are associ- [9] Molinari R. J., Cole R. H. and Gibbs J. H., Biopoly- ated with structural properties of single chains as well mers, 20 (1981) 977. as collective properties of the solution composed of many [10] Deshkovski A., Obukhov S., and Rubinstein M., chains, respectively. In dilute conditions and in the low Phys. Rev. Letts., 86 (2001) 2341 added salt limit, the characteristic lengths of the two re- [11] Sikorav J. L., Pelta J. and Livolant F., Biophys. J., laxation modes are given either by the contour length of 67 (1994) 1387. ∗ a single DNA chain or the reduced average distance be- [12] c is given by the concentration where there is only one ∗ tweenchainsofthewholesolution,consistentwiththetwo polymermolecule inthevolumeof apolymerglobule c = zonemodelofcounterioncondensation[3,10]. Inthe high molecule mass/Vc, where molecule mass is N ·mbp, and V ≈L3 =N3·a3;m isamassofabasepair≈10−18mg, added salt limit for 2I > 2c our data indicate that the c c bp s in N =146, L =N·a;a=3.4˚A; a is themonomer size. added salt effects are relevant for both length scales. For c [13] The concentration of intrinsic counterions is given by thesinglechainlengthscale,saltapparentlyfacilitatesthe c [mM]=c [mg/mL]·3µmol/mg. in DNA formation of denaturation bubbles and/or fraying at the [14] BordiF.,CamettiC.andColbyR.H.,J.Phys.:Con- two ends close to DNA concentrations where the strand dens. Matter, 16 (2004) R1423. separation is clearly seen. For the collective length scale, [15] HavriliakS.andNegamiS.,J.Polym.Sci.C,14(1966) on addition of salt the Debye screening length seems to 99. taketheroleofthefundamentallengthscaleforthewhole [16] Angelini T. E., Golestanian R., Cori- solution. The latter statement should be taken with cau- dan R. H., Butler J. C., Beraud A., Krisch M., tion, however, due to poor accuracy of the data at higher Sinn H., Schweizer K. S. and Wong G. C. L., addedsalt. Finally,ourresultsindicatethat,atthedilute Proc. Natl. Acad. Sci. USA, 103 (2006) 7962. [17] For c < 0.2mg/mL the LF mode decreases in DNA conditions and in low added salt regime, the same DNA strengthandmergesintothelargerHFmode.Intherange fundamental length scales are obtained, even under the 0.04mg/mL < c < 0.2mg/mL, two-modes fits with conditions where the dissociation of the DNA strands is DNA constraint on the relaxation time of LF mode were done likely to be expected. in order to keep L close to L . The constraint did not LF c influence the parameters obtained for the HF mode. For ∗∗∗ c <0.04mg/mL,theLFmodeisofnegligiblestrength DNA and completely overwhelmed by the HF one, so that only We wouldlike to thank DonRauand AdrianParsegian single mode fits to theHFmode were performed. for valuable and illuminating discussions. This work was [18] ItoK.,YagiA.,OokuboN.andHayakawaR.,Macro- supportedbytheCroatianMinistryofScience,Education mol.,23 (1990) 857. and Sports under grant 035-0000000-2836. R.P. would [19] Katsumoto Y., Omori S., Yamamoto D., Yasuda A., like to acknowledge the financial support of the Agency and Asami K., Phys. Rev. E, 75 (2007) 011911. forResearchandDevelopmentofSloveniaundergrantP1- 0055(C) and partial financial support by the Intramural ResearchProgramofthe NIH,NationalInstitute ofChild Health and Human Development. REFERENCES [1] DauneM.,MolecularBiophysics(OxfordUniversityPress, p-5

Short-fragment Na-DNA dilute aqueous solutions: fundamental length scales and screening

Similar Short-fragment Na-DNA dilute aqueous solutions: fundamental length scales and screening