Confinement, spatial correlations and flexibility in the melting transition of DNA

Confinement, spatial correlations and flexibility in the melting transition of DNA University of Burgos and Institut Laue-Langevin Adri´an Gonz´alez Rodr´ıguez Advisors: Andrew Wildes and Santiago Cuesta L´opez December 20, 2017 2 Contents 1 Introduction 5 2 Methods and theory 10 2.1 Samplepreparation................................ 10 2.1.1 Production of oriented DNA fibers . . . . . . . . . . . . . . . . . . . 10 2.1.2 Widom-sequence ............................. 15 2.2 Differential scanning calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.1 Thermodynamical principles . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.2 DSCtechnique .............................. 17 2.2.3 Instruments................................ 18 2.2.4 Experimental protocol . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.5 Dataanalysis ............................... 21 2.3 Introduction to scattering theory . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.1 Basic principles of a scattering experiment . . . . . . . . . . . . . . . 23 1 2.3.2 Scattering by a single fixed atom . . . . . . . . . . . . . . . . . . . . 26 2.3.3 Scattering from an assembly of atoms . . . . . . . . . . . . . . . . . . 27 2.3.4 FiberDiffraction ............................. 28 2.3.5 Small angle scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.4 DiffractionInstruments.............................. 36 2.4.1 Neutron diffractometers . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.4.2 X-raydevices ............................... 41 2.5 Data collection and reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.5.1 Wide angle neutron scattering . . . . . . . . . . . . . . . . . . . . . . 45 2.5.2 Small angle neutron scattering . . . . . . . . . . . . . . . . . . . . . . 51 2.5.3 Small angle X-ray scattering . . . . . . . . . . . . . . . . . . . . . . . 53 3 Literature review 54 3.1 Previous diffraction studies in fiber DNA . . . . . . . . . . . . . . . . . . . . 54 3.1.1 Conformation of humidified fibers. A and B form DNA as seen by neutronscattering ............................ 55 3.1.2 Conformation of DNA fibers submerged in ethanol solutions. The Bto-Atransition .............................. 58 3.1.3 DNA fibers submerged in PEG solutions. The osmotic pressure method 59 3.2 ConfinementofDNA............................... 60 2 3.3 Meltingtransition................................. 63 3.3.1 Effect of the confinement of DNA in the melting transition . . . . . . 64 3.3.2 Effect of PEG in the melting transition . . . . . . . . . . . . . . . . . 66 3.3.3 Effect of ethanol in the melting transition . . . . . . . . . . . . . . . 67 3.4 Models of DNA and the melting transition . . . . . . . . . . . . . . . . . . . 69 3.4.1 Peyrard-Bishop-Dauxois model . . . . . . . . . . . . . . . . . . . . . 69 3.4.2 Kratky-Porod model . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4 Study of submerged DNA fibers 76 4.1 Structural characterization with X-rays . . . . . . . . . . . . . . . . . . . . . 76 4.2 Room temperature study with neutrons . . . . . . . . . . . . . . . . . . . . . 79 4.2.1 Fibers submerged in PEG solutions . . . . . . . . . . . . . . . . . . . 79 4.2.2 Fibers submerged in ethanol solutions . . . . . . . . . . . . . . . . . . 83 4.3 Melting transition studied by calorimetry . . . . . . . . . . . . . . . . . . . . 93 4.3.1 Fibers submerged in PEG solutions . . . . . . . . . . . . . . . . . . . 93 4.3.2 Fibers submerged in ethanol . . . . . . . . . . . . . . . . . . . . . . . 100 4.4 Study of the melting transition with neutron scattering . . . . . . . . . . . . 105 4.4.1 Fibers submerged in PEG . . . . . . . . . . . . . . . . . . . . . . . . 105 4.4.2 Fibers submerged in ethanol . . . . . . . . . . . . . . . . . . . . . . . 120 5 Widom-601 investigated by SAS 129 3 5.1 Room temperature study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.2 Temperature-dependent study . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.2.1 SANS ................................... 147 5.2.2 SAXS ................................... 152 5.2.3 Discussion................................. 156 6 Conclusions 159 4 Chapter 1 Introduction Deoxyribonucleic acid (DNA) is a macromolecule which carries the genetic information essential for every living organism. It is a biopolymer built by the repetition of monomers called nucleotides. Each nucleotide consists of a phosphate group, a sugar group and a nitrogen base. The phosphate and sugar groups alternate in sequence and form a linear chain. Two of these chains are linked by hydrogen bonds between nitrogen bases generating the famous double helix. Each couple of linked nitrogenous bases is called a base pair. The melting transition (thermally induced helix-to-coil transition) of DNA is a first order phase transition induced in DNA molecules by heat. In such a process the hydrogen bonds between base pairs break as the temperature is increased. Local openings of consecutive base pairs can occur at a temperature below the transition resulting in zones of open base pairs (called denaturation bubbles) which are surrounded by closed zones in which the double helix is intact. As the temperature is raised and more base pairs break, the open zones expand to larger sizes and eventually the two strands of the double helix separate. Fig. 1.1 illustrates the process. The melting transition of this life-essential molecule has been heavily studied to learn about the intramolecular interactions, the impact of the base pair sequence in DNA unwinding and the effect of the solvent in DNA stability [2, 3, 4]. A better understanding of the 5 Figure 1.1: DNA openings as Tincreases. Adapted from [1]. transition could have an immediate impact in applications such as high resolution melting analysis or polymerase chain reactions, which are widely used in bio-labs around the world [5, 6]. However, the melting of DNA itself is interesting to study from a theoretical point of view since it is, essentially, a phase transition in a one dimensional system. In this thesis, a better understanding of the melting transition of DNA and its effects in the functionality of the molecule is attempted by following two avenues: i) the study of highly oriented DNA fibers with wide angle diffraction techniques and calorimetry. ii) the investigation of a short chain, biologically relevant, sequence with small angle scattering techniques (SAS). Highly oriented DNA fibers Experimentally, the transition has been studied with techniques that either probe the bulk sample, like calorimetry, UV-Vis absorption and circular dichroism spectroscopy, or localized points on the molecule, like fluorescence spectroscopy. The spatial structure of DNA molecules is not accessible using these techniques, and therefore, the distribution of open and closed base pairs during the phase transition can not be determined. Knowledge of 6 the spatial correlations and how they evolve with temperature is necessary for a complete understanding of the transition. Scattering techniques allow to access structural information and thus the spatial correlations within the molecule. Such information is more easily accessible when the sample has long-range order, which gives rise to Bragg peaks. DNA fibers, in which the molecules are coaligned and are close packed, have sufficient long-range order to exhibit Bragg peaks in their diffraction patterns. By studying these peaks, the information of interest is collected in a measurement which is only weakly perturbed by sample imperfections and incoherent contributions to the scattering. The melting transition of oriented DNA fibers equilibrated with a humid atmosphere has been previously studied [7, 8] using neutron scattering. The results have been successfully modeled with the mesoscopic statistical-mechanical Peyrard-Bishop-Dauxois (PBD) model [9]. Therefore, these works were able to access the spatial correlations of the molecules during the transition and reinforce the validity of the PBD model, which is already widely used to describe complex DNA denaturation curves. During the analysis, the question of whether the confinement of the DNA molecules in the fibers has an effect on the transition arose. The restricted degrees of spatial freedom due to the confinement of the molecules could arguably have an impact on the interpretation of the results since the model does not account for intermolecular interactions. In order to test the effects of the molecular confinement, a new experiment was designed in which the fibers were submerged in a solution with a given osmotic pressure. The osmotic pressure method has been reported in numerous articles [10, 11]. It consists of submerging the DNA fibers in a saline solution with a high-molecular-weight polymer such as polyethylene glycol (PEG). If the PEG does not penetrate the DNA fibers, the osmotic pressure acts analogously to a mechanical and permeable piston preventing DNA from dissolving, thus preserving the long-range order, while allowing water and salt to be exchanged between the fibers and the solution. X-ray diffraction has proved that fibers equilibrated with these kind of solutions show a well-defined interaxial distance between molecules, which increases with 7 Figure 2.3: Picture of the final films produced by the wet spinning apparatus. Submerged fibers Na−and Li-DNA oriented fibers submerged in PEG solutions made with 2H2O(heavy water) and ethanol/2H2Omixtures have been investigated in this work using calorimetry, X-ray and neutron scattering. Using heavy water is an advantage when investigating samples with neutrons because it minimizes the incoherent scattering [12]. 2H2Owas used in the samples studied with other techniques for consistency. Since the chemical properties of heavy water and normal water are almost identical the range of application of the results is not hindered by the use of heavy water. The PEG solutions were made by dissolving the specific amount of PEG in a buffer made with 2H2Owith 10 mM Tris (tris(hydroxymethyl)aminomethane), 1 mM EDTA (ethylenediaminetetraacetic acid). Unless mentioned otherwise the solutions contained 0.1M NaCl for samples made with Na-DNA and 0.1M LiCl for samples made with Li-DNA. The PEG solutions will be identified by the amount of PEG in weight percent. The ethanol/water mixtures were prepared with the same buffer and will be identified by the amount of ethanol in volume percent. Also, for the sake of simplicity the mixtures will be addressed as ethanol solutions. For the neutron samples fully deuterated ethanol was used (ethanol-d6), for the other techniques protonated ethanol was used due to the cost of 14 ethanol-d6. A specific sample for neutron scattering consisted of a number of films with a total DNA mass close to 0.6gthat were concertina folded and stacked with their axes coaligned. The dimensions of the final sample were approximately 2.5×2.5×0.2cm3. The DNA was placed in a niobium envelope which in turn was placed inside an aluminum cassette. The niobium is necessary since the DNA can react chemically with aluminum at high temperatures. Around 0.8ml of a given PEG or ethanol solution was degassed and placed in the cassette so the DNA was totally submerged. Then the cassette was screwed closed and sealed with a lead-wire gasket. 2.1.2 Widom-sequence The short DNA sequence chosen for the small angle scattering experiments described in this document is the so called Widom-601 sequence. It has great affinity to bind around protein histone octamers and it is called a strong positioning sequence. It was discovered by Lowary and Widom [19]. It has 145 base pairs with a total length of around 485 ˚ A. Fig. 2.4 presents the primary structure of the sequence with the binding site highlighted in red. The artificial DNA needed for the experiments was synthesized by collaborators in the ICCRAM at the university of Burgos, Spain (Marta Marty Roda, Lorena Romero Santacreu), and in the INMG at the university of Lyon, France (Ramachandran Boopathi, Dimitar Angelov). The exact protocol differed slightly from one lab to another but a general summary Figure 2.4: The 145 base-pair sequence corresponding to the NCP-601 nucleosome investigated in [13] also known as Widom-601 sequence. The fragment highlighted in red is the strong positioning element characteristic of this sequence. 15 is presented below. The starting material was a solution of plasmid pGEM-3z/601 purchased from Addgene, which contains the Widom sequence. A polymerase chain reaction (PCR) was performed with the proper primers in order to duplicate the Widom sequence. After enough duplications, the result was processed with a purification column kit (Gene Matrix Basic) for separating the Widom sequences from the remanent plasmid. PCR alone is not an optimal method to obtain the quantities of DNA needed for neutron scattering (in the order of the mg) but the amount of widom-DNA out of the first PCR allowed to use another multiplication technique, called competent cells. In cell biology, competence is defined as the ability of a cell to take extracellular DNA and incorporate it in its vital cycle, including reproduction. Thus, for reproducing a given sequence which has been assimilated by a cell culture it is sufficient to allow the cell culture to grow. Cells will not assimilate a short sequence such as the Widom-601 in this way but they can assimilate and multiply a plasmid including the Widom sequence. Therefore the Widom DNA from the first PCR and purification was used in a ligation process with ligase T4 in which plasmids pGEM/3z-601 were reformed. The plasmids were introduced in competent cells DH5α. After adequate growing time the plasmids were extracted from the cells by GeneJET Plasmid Miniprep Kit from Thermo Scientific. Finally, repeating the PCR and column purification stated above and performing further purification using ethanol/chloroform/fenol extraction as well as precipitation via centrifugation allowed the desired quantities of Widom-sequence DNA molecules to be obtained. 2.2 Differential scanning calorimetry Differential scanning calorimetry (DSC) is a thermo-analytical technique designed to gauge the change in specific heat of a sample as a function of temperature. Many thermodynamical quantities may be calculated from calorimetry data including transition enthalpies, melting temperatures, specific heat and free energy. Apart from the references specifically highlighted 16 in the text, general information for the elaboration of this section has been collected from the book by Hohne [20]. 2.2.1 Thermodynamical principles A given conformational or phase transition can be described by the change in the thermodynamical properties: internal energy (∆U), enthalpy (∆H), Gibbs free energy (∆G), Helmholtz free energy (∆F) and entropy (∆S). When the pressure is constant the enthalpy is a quantity equivalent to the total heat content of a system. The entropy represents the amount of energy in a system which is unavailable for performing work. It also is understood as the degree or disorder within the system [21, 22]. If the pressure is kept constant the difference in enthalpy and entropy during a transition induced by a change in temperature can be calculated from the specific heat (Cp): (∆H)p=ZT2 T1 CpdT (2.1) (∆S)p=ZT2 T1 Cp TdT (2.2) Where the specific heat is defined as the amount of heat per unit mass needed to raise the temperature of the system by one degree at constant pressure. 2.2.2 DSC technique There are two types of DSC experiments: the power-compensated DSC; and the heat flux DSC which is the technique of choice for the present work. In a heat flux differential scanning calorimeter two thermally isolated cells, one for the sample under study and another for the reference, are placed in a furnace connected to a heater. If the temperature of the furnace is raised the temperature of the sample and the reference cell will differ because they contain 17 samples with different Cp. The difference in temperature relates to the differential heat flux through Ke, the heat exchange coefficient of the furnace: ∆P=Ke∆T.Kecan be obtained with a calibration using a material of well known thermal properties. The differential heat capacity of the sample with respect to the reference can be expressed in function of the differential heat flux (derivation can be found in [23]): ∆Cp=−∆P β−τins d(∆P) dT (2.3) where β=dT0 dt is the scanning rate of the experiment (T0is the furnace temperature) and τis the so called thermal time constant of the calorimeter [24]. This constant is related with the thermal lag of the set-up of the instrument and can be approximated by controlling the time it takes for the instrument to respond to a swift power change. Figure 2.5 is an example of a calorimetry scan presenting heat flux (J/s) as a function of temperature during a heating ramp. If the sample does not undergo a physico-chemical transition in a given range of temperatures then the heat flux into the sample is constant in this range. On the contrary, when a thermal process takes place within the sample the heat flux changes and the sign of this change depends on whether the process is exothermic, like the crystallization transition of the figure, or endothermic, like the melting. In the former case heat is produced by the sample during the transition and so a lower heat flux is going into the sample. The opposite is true for the latter case. 2.2.3 Instruments The differential scanning calorimeter used for collecting the data of the fiber samples of the present work was a MicroDSC III from Setaram instrumentation. It has two 1 ml volume Hastelloy C (Nickel and Chromium alloy) cells, the sample cell and the reference. The cells are placed in highly conductive tubes, thermally isolated from each other and from the outside environment. Thermocouples are fixed to the tubes for temperature measurement. 18 Figure 2.5: Example of differential scanning calorimetry scan. Three different transitions can be observed: a glass transition, a crystallization and a melting. reproduced from [25]. Figure 2.6: MicroDSC III from Setaram instrumentation company. Reproduced from [27]. During a scan both cells are subjected to a temperature ramp. Constant circulating toluene allows for a very precise temperature stability. The cooling is achieved through an external stabilization water bath which was kept at 27 ◦C for all experiments. The temperatures ranged from room temperature to 120 ◦C and the programmable scanning rate is 0.001 to 1.2◦C/min. The thermal time constant (τins) as provided by the manufacturer is 60 s [26, 27]. A sample of dissolved DNA was measured in a different calorimeter from the rest of samples (a Nano DSC III from Calorimetry Sciences corp.) due to sensitivity reasons. The DNA concentration of the dissolved sample was 2 mg/ml and the volume of solution measured was 0.33 ml. The working principle of this calorimeter is the same as for the MicroDSC III and the methods used are identical. The sample was measured by Herv´e Guillou in the 19 Institut N´ EEL, Grenoble, France. 2.2.4 Experimental protocol Most of the calorimetry work performed for the thesis was on samples of highly oriented fiber Na/Li-DNA submerged in PEG solutions or ethanol/2H2Omixtures described in 2.1.1. For the sake of convenience the liquid in which a given fiber sample was submerged would be referred to simply as solution in this section. In a typical experiment the DNA amount under study was a piece of film that weighted around 25 mg when dry. The solution used for the experiment was degassed using ultrasound for 20 min and then 0.5ml was used to submerge the DNA. The degassing minimized the quantity of bubbles introduced during the process since they may increase the noise of the signal or generate unstable baselines [28]. The DNA was left to equilibrate with the aqueous medium for around a week before being measured. The scanning rate βwas fixed at 1 ◦C/min for all the experiments. Increasing it to 1.2 ◦C/min or decreasing it to 0.5 ◦C/min made no significant difference in the data recorded. Before the DNA sample was measured, a ”solution versus solution” scan was performed where 0.5ml of degassed buffer was place in both sample and reference cell. The thermal program for these scans consisted of successive cycles of heating and cooling from room temperature to around 110 ◦C. The calorimetric curve evolves during the first cycles but eventually stabilized to a constant value of around zero. The instability of the curve in the first scans is a well known instrumental artifact related to the fact that there is a natural instrumental baseline for a particular set of scan conditions which disappears after several heating cycles [29]. The curve of the heating ramp of the last cycle was reproducible and it was taken as the reference curve for the DNA sample and used in the data analysis. Thus, exactly the same conditions of the solution-solution scan must be used for the sample in order to avoid the reappearance of this artifact. 20 After the reference curve was obtained the sample (DNA+solution) was introduced in the sample cell and the DNA melting experiment was launched, with the same 0.5ml of buffer in the reference cell. Since approximately the same amount of buffer (0.5ml) is in both cells, features in the final curve could be ascribed only to the internal DNA or the DNA-buffer interactions. 2.2.5 Data analysis The raw output data of a heat flux DSC device is a curve of differential heat flux in power units versus temperature (∆P(T)), c.f. fig. 2.5. The aim of this subsection is to explain how to use these data to calculate thermodynamical quantities that are relevant to characterize a transition. Quantities of choice are the melting (or denaturation) temperature, the width of the transition, and the fraction of open base pairs. The final methodology used for data analysis as well as most of the content of this section have been heavily based on several works of Charles H. Spink [29, 30]. The reference curve was subtracted from the measured ∆P(T). Then ∆P(T) can be converted to ∆C(T) in J/◦C via eq. 2.3. The differential heat capacity per unit mass (J/g◦C) can be obtained by: ∆c(T) = ∆C(T) mDNA (2.4) where mDNA is the mass of the DNA in the sample cell. The resulting curve usually has a single peak over a straight-line baseline. Tmin and Tmax are respectively the minimun and maximum temperatures of the scan. Before further treatment a baseline was defined as the connection line between ∆c(Tmin) and ∆c(Tmax) and then subtracted from the data. This curve could be fitted with a Gaussian function and so the full width at half maximum (FWHM) could be determined. This parameter was taken as the width of the transition. The differential heat capacity allows the calculation of the fraction of base pairs which 21 Figure 2.7: Example of data reduction and analysis performed on the calorimetric curve of a sample of Na-DNA submerged in a PEG solution. Left y-axis: ∆cin blue, Gaussian fit to the data in red and baseline in green. Right y-axis: Fraction of open base pairs in black. The melting temperature is highlighted. have opened at a given temperature: fSS, where SS stands for single strand. fSS(T) was calculated as done in [31] with the equation: fSS(T) = (∆H)n(T) ∆H(2.5) Where (∆H)n=RT Tmin ∆Cp(T)dT is called the cumulative enthalpy at temperature T. Once the fraction of open base pairs is known the fraction of base pairs which are closed at a specific temperature is calculated as: fDS(T) = 1 −fSS(T) (2.6) where DS stands for double strand. The melting temperature, Tmis the temperature at which half of the base pairs are open so it is the temperature for which fDS = 0.5. Figure 2.7 summarizes the data analysis described in this section. The figure shows a model example of ∆c(T), the fit with a Gaussian function, the straight-line baseline and the 22 calculated fraction of open base pairs. All the calorimetric data presented in the result chapters of this work are obtained by measuring three identical samples and averaging the results. The error bars shown are the standard deviation of the three measurements. 2.3 Introduction to scattering theory The theoretical and experimental descriptions in this section will cover only the techniques used for this work. Thus, no inelastic scattering is mentioned, neither the spin or magnetic contributions to the scattering are presented. Information for this section was collected from the books by Sivia [32] and Squires [33]. 2.3.1 Basic principles of a scattering experiment In a scattering experiment most of the information about the system is extracted from the change of momentum and energy of the scattered particles with respect to the incident particles. The momentum change is described mathematically by: ~ Q=~ ki−~ kf(2.7) where ~ Qis the momentum transfer (also called scattering vector), ~ kiand ~ kfare the initial and final wavevectors of the scattered particle. The work described in this document is based in elastic scattering in which Ei=Ef, so ki=kf=2π λ, where λis the wavelength of the incident particles. The vector diagram for an elastic scattering event is shown in fig. 2.8 where an incoming particle is deflected through an angle of 2θ. Trigonometry then leads to the result: 23 (a) (b) Figure 2.11: a) Usual geometry of DNA fiber diffraction. b) Schematic of the construction of the layer-lines in the X-ray diffraction pattern of a linear array of point scatterers. RL stands for real lattice; ES for Ewald sphere; CA for cone axis; LP of layer-planes; S for observation screen; BS for beam stop and; LL for layer lines. Adapted from [34]. molecule are aligned along a regular circular helix. The full general theory for calculating the form factor of a helix was published by Cochran, Crick and Vand [37] and is summarized with the CCV formula. This formula computes the scattering amplitude of a continuous helix of radius Rand pitch P, for such a system the cylindrical coordinates ~rj= (ρj, ϕj, zj) of identical atoms placed at axial intervals pacan be defined with relation to an arbitrary atom taken as the origin (R, ϕ0, z0). The step-by-step derivation can be found at [37] and the formula is: A(~ Q) = 2π Pf(Q)X n,m Jn(QrR)ein(Qϕ−ϕ0+pi/2)e(Qzz0)δ(Qz−n2π P−m2π pa ) (2.16) where ~ Q= (Qr, Qϕ, Qz) in cylindrical coordinates and Jn(x) is the cylindrical Bessel functions of integer order n. 30 The δ-function in eq. 2.16 makes it clear that the diffraction patterns will still be organized in layer lines. The δ-function imposes the selection rule: l Pa =n P+m pa (2.17) With this selection rule the δ-function can be rewritten and it can be concluded that non-zero intensity will be seen at Qz= 2πl/Pa. Thus the scattering pattern of a phosphorous helix in a single strand DNA backbone can be calculated with eq. 2.16 setting Pa=P= 10pa= 34 ˚ A−1and R= 10 ˚ A−1. The result can be seen in fig. 2.12 reproduced from [34]. The figure shows a very characteristic cross pattern. The selection rule for this system is then l=n+ 10m. As an, example the selection rule gives (n= 0, m = 0) (i.e. J0) as leading term in the diffraction amplitude for the equatorial line (l= 0). For the l= 1,2,3,4,5 the equation selects as leading terms (1,0), (2,0), (3,0), (4,0), (5,0). Keeping in mind that nis the order of the Bessel function the cross pattern of the first five lines can be explained. Moreover the same selection rule imposes the repeat of the cross patterns along the direction of the axis of the helix every ten layer-lines. This creates a diamond pattern in the diffraction picture with the interior of the diamond approximately empty of intensity. These diamonds are characteristic of an helical distribution of matter in the diffracting object. In order to complement this theoretical introduction to fiber diffraction, two very important results will be commented. They will allow the main differences between the secondary A and B form of DNA to be highlighted, which will be significantly important for the discussion of future chapters. Fig. 2.13 show diffraction diagrams of Na-DNA fibers. The measurements were made with a geometry similar to that shown in fig. 2.11a. The fiber comprises a macroscopic number of long, parallel DNA molecules, Na+ions and water molecules. The cations and 31 Figure 2.12: Simulated diffraction pattern by an atomic phosphorus helix. Reproduced from [34]. the water are in amorphous state and give only diffuse scattering. Fig. 2.13a shows the pattern classically associated with the A-form of DNA, Fig. 2.13b the one associated with the B-form. After the discovery of these two forms of DNA it was proved that the transition between A to B form is reversible [39, 40]. In these works the water content of a sample was modified between two states. The drier state of the sample gave pattern A and was interpreted as crystalline, with long range order, due to the sharp spots specially close to the center. The wetter state of the sample gave pattern B and due to its broader features was called semycristalline and was considered to have less long range order due to the disordering effect of the increased amount of water surrounding the molecules. Both patterns are organized in regularly spaced layer-lines as expected from long molecules having a repeating structural unit (the base pair). The dramatic change of the features between patterns was interpreted not only as a change in the long range arrangement or the sample but as a change in the internal structure of the DNA molecules. This is why the DNA is said to adopt different conformations depending on the environmental conditions. The discovery of A and B form was followed by many other conformations such as C, D, Z...[41]. The B-form is believed to be the conformation of chromosomic DNA in vivo and will be 32 (a) (b) (c) Figure 2.13: X-ray fiber diffraction patterns of a) A-DNA, b) Semycristalline B-DNA. Reproduced from [34] and c) Crystalline B-DNA reproduced from [38]. 33 the focus of the present work. Its pattern is qualitatively very similar to fig. 2.13, showing the helical structure of the molecule. The reflexion of the 10th layer line of this form will be instrumental in the study of the melting transition in DNA fibres. Soon after the discovery of the B-form it was proven that this reflexion was related with a nucleotide repeat of 3.4˚ A−1[42]. This reflection was modeled as the result of a concatenation of flat nucleotides (even though in reality the sugar and nitrogenous base do not lie in the same plane) stacked on top of each other and covalently linked to the phosphate backbone. The bases scatter coherently despite being irregular in their chemical composition and geometrical structure because they behave like thin scattering slabs seen edge-on by the incident beam (perpendicular to the fiber). In summary the stacked base pairs act somewhat like a parallel slit grating to produce the large 10th layer reflections. Since the B-pattern shows ten layer-intervals separating the center from this reflexion it follows that in this conformation the pitch of the DNA is 34 ˚ A−1. The cross pattern in the center of the picture is the second strongest feature, it is, as stated above, a footprint of the helical conformation of the DNA backbone. A last crucial piece of information that can be extracted easily from the B-pattern is the radius of this form (≈10 ˚ A−1), which is patent due to the distance between the equatorial reflections. Fig. 2.13c shows a pattern very similar to fig. 2.13b but the blurred reflections are substituted with sharp points and lines which indicates both samples are in the same conformation but the former has better crystalline order. Because of this, patterns like fig. 2.13b are usually said to relate to the ”semicrystalline” B-form and patterns like fig. 2.13c are related to the crystalline B-form. The A-form has 11 nucleotides per pitch with an average distance between base pairs of 2.56 ˚ A. The removal of water with respect to the B-form contracts the molecule along its axis and, the base pairs become inclined with respect to the horizontal plane (with a tilt angle as large as 20◦). The effect of this tilt is that most of the base pairs are not seen edge-on by the incident beam and thus they no longer act as a horizontal slit grating. The base pair stacking no longer gives a strong reflexion on the 10th layer but two pairs of smear 34 reflexions appear on the sixth, seventh and eighth layer lines which are sometimes refereed to as off-axis Bragg peaks. 2.3.5 Small angle scattering When studying the scattering from a conglomerate of atoms, the characteristics will depend on the spacial distribution, number and f(λ, θ) parameters of the atoms. The spacial distribution weighted by the f(λ, θ) of each atom can be quantified by the so called scattering length density function, β. The scattering length density at a position ~r in a system is given by: β(~r) = ρ(~r)¯ f(λ, θ)(~r) where ρ(~r) is the local atomic number density and ¯ f(λ, θ)(~r) is the mean scattering length which varies as a function of atom and isotope for neutrons and as the Thomson scattering length times the local number of electrons for X-rays [43]. Then a continuum generalization of the discrete case of eq. 2.14 can be made: (dσ dΩ)el ∝N Vh|ZZZV β(~ R)ei~ Q•~ Rd3~ R|2iΘ(2.18) where the system contains Nparticles in a volume of Vand the angular brackets indicate an ensemble average over all the orientations of the particles. As mentioned previously (sec. 2.3.3), the differential cross section equates the Fourier transform of the scattering length density of the sample. A basic property of Fourier transforms is the inverse relationship between length scales in real, ~r, and reciprocal space, ~ Q. Thus experiments focusing in small Qranges provide low resolution structural information but are optimal for studying the configuration of macromolecules in the mesoscopic scale (such as short DNA chains). Equation 2.8 demonstrates that low-Q experiments should prioritize measurements at small θs and use large λs. Small diffraction angles are reached by having a long flight-path between sample and detector. Many small angle scattering experiments are performed on solutions so the sample consists of Nobject of interest placed within the solvent. The small angle scattering (SAS) 35 experiments described in the present work were performed on a dilute solution of short chain DNA molecules so the objects of interest were Nisolated molecules isotropically oriented and randomly located within the sample. Under these circumstances equation 2.18 reduces to a one dimensional integral: dσ dΩ∝Zdmax 0 P(r)sin(Qr) Qr dr (2.19) where dmax is the longest dimension of the scattering object. P(r) is the pair-distribution function. It represents the average of the shapes of the scatterers in the solution. P(r) is usually calculated by the inverse Fourier transform of the cross section and it will be essential for the interpretation of the SAS data in the present work. 2.4 Diffraction Instruments In this section an overview will be presented about the instruments used for the collection of data in this work. 2.4.1 Neutron diffractometers IN3 IN3 is a three-axis spectrometer at the ILL (France), it was used for sample characterization. This technique provides access to the scattering function S(Q, w) in a large volume of the reciprocal space. However, only elastic measurements were performed. Three-axis instruments have a mobile rotational axis at both the sample and analyzer positions. The direction of the initial and final wavevectors with respect to the sample is defined by the angles of each axis. Any combination of kiand kfcan be selected as long as the vector triangle ~ ki−~ kf=~ Q can close. 36 Figure 2.14: Scheme of the three axis spectrometer IN3 at the ILL. Reproduced from the ILL website. For the experiments presented in this document a PG(002) monochromator was used delivering a λ= 3.3545 ˚ A−1, another PG(002) crystal was used as analyzer, 400collimation was used before and after the sample position and a PG filter was placed before the sample to filter high order contamination. The measurements were performed in reciprocal ˚ Angstr¨oms (˚ A−1) with an orthogonal co-ordinate system. D16 The diffractometer D16 at the ILL is used for small angle scattering, powder diffraction and single crystal studies. It uses a pyrolitic graphite monochromator, a beryllium filter, two sets of slits for incident beam collimation (one just after the monochromator and another just before the sample) and a square 3He detector of area 320 ×320 mm2. Fig. 2.15 presents a schematic of the instrument. This instrument was used for the collection of reciprocal space maps to structurally characterize the high oriented DNA fibers in PEG and ethanol solutions at room temperature. The wavelength was set to 4.5 ˚ A and the scattering from each sample was recorded in two different orientations: with the fiber axis parallel and perpendicular to the scattering plane. The first orientation allows to study periodic order in the sample along 37 Figure 2.15: Scheme of the diffractometer D16 at the ILL. Reproduced from the ILL website. the fiber axis and the latter orientation gives information about the lattice spacing of the sample in the direction perpendicular to the fiber axis. A cylindrical piece of vanadium, of length similar to the sample, was measured for every detector position to account for the efficiency of the detector. D19 D19 is a thermal diffractometer at the ILL, specially designed for studying large structures and fibers. D19 was configured with a graphite monochromator delivering an incident wavelength of 2.4 ˚ A. The monochromator-sample distance was 3.18 m. Pre-sample collimation and beam size were defined with two sets of squared slits (12×12 mm2) and a circular aperture (diameter of 10 mm). The slits were at 1.51 mand 2.49 mfrom the monochromator. The circular aperture was at 3.1mfrom the monochromator. High-order Bragg contamination was eliminated by using a graphite filter. D19 has a 120◦position-sensitive detector which was fixed throughout the experiment. There was no collimation between sample and detector. Fig. 2.16 presents a scheme of the instrument. A cylindrical piece of vanadium, 38 Figure 2.16: Scheme of the D19 diffractometer at the ILL. Reproduced from the ILL website. of length similar to the sample, was measured for every detector position to account for the efficiency of the detector. This instrument was used to study the diffraction pattern of samples of fiber DNA submerged in PEG solutions and ethanol-d6/2H2Omixtures as a function of temperature through the melting transition. Reciprocal space maps with the fiber axis within the scattering plane were collected at several temperatures between 20 ◦C and 110 ◦C. The stabilization time between measurements when the temperature was changed was 15 min. On this instrument two different sample environments were used: a) For the fibers submerged in PEG 6000 at 17% (w/w) two heaters were attached to opposite vertices of the square cassette. At room temperature the temperature stability was around 0.2 ◦C but thermal oscillations increased with temperature. Close to the melting temperature of this sample (≈95 ◦C) the stability was around ±1◦C. b) For the ethanol samples the sample environment was a cylindrical aluminum chamber with a flow of thermalized air. Stability of the sample temperature during the measurement was <0.1◦C over the entire temperature range. 39 The first step in the analysis was to reduce the raw data to reciprocal space maps. It was assumed that the most convenient way of presenting such maps was by defining a system of reciprocal coordinates with reference to the sample cassette. Such a reference system has been used in previous articles ([31],[45]). As presented in fig. 2.21 the momentum transfer vector ~ Qcan be expressed as ~ Q= ( ~ QH+~ QK+~ QL) where ~ QHis parallel to the axis of the DNA fibers, ~ QKis perpendicular to the axis and to the face of the cassette, lastly ~ QLis orthogonal to the previous two. In order to present the raw data in terms of QH,QKand QLeach detector image was first normalized to monitor and divided by the vanadium data corresponding to the same detector position (detector efficiency correction). Integrating over the height of the detector gave a map of intensity as a function of ωand 2θfor each detector position, an example can be seen in fig. 2.22a. In the case of D16 the different maps for each detector position were assembled together and in the parts in which two maps overlapped in the 2θ-ωspace an average was taken as the representative scattered intensity (fig. 2.22b). The ”ω-2θ” maps in fig. 2.22 present a clearly not natural dip in the intensity whose position evolves linearly with 2θ. It is an artifact due to the self attenuation of the sample when the scattering angle of the deflected neutrons is so that their direction is in the plane of the cassette. The data must be corrected for this. In order to do so the transmission factor of the sample was calculated using: T(ω, 2θ) = 1 AbZxZy e−µt(x,y,ω,2θ)dxdy ×1 cos ω(2.20) where Tis the transmission factor, µis the linear attenuation coefficient, Abis the area of the incident beam and tis the path length of a given set of neutrons through the sample in function of ω, 2θand (x,y) which is the point in the sample at which the scattering event occurred with reference to an arbitrary origin in one of the vertices of the sample ( fig. 2.23). The facor 1/cos ωwas included to account for the footprint of the beam on the sample as the sample ratated. Since the linear attenuation factor for the sample is not known, µwas firstly approximated by the linear attenuation factor of 2H2Oand them adjusted slightly for 46 (a) (b) Figure 2.21: a) and b) Schematic of the reciprocal coordinate system defined with respect to the DNA fiber axis. ~ QHis parallel to the fiber axis, ~ QKis perpendicular to the fiber axis and to the face of the cassette, ~ QLis orthogonal to both ~ QHand ~ QK.~ QSP is in the scattering plane and it matches ~ QHin the longitudinal orientation and ~ QLin the traversal orientation. 47 (a) D19 (b) D16 Figure 2.22: Scattered intensity as a function of ω(sample rotation) and 2θfor Na-DNA submerged in a PEG 6000 solution at as measured at room temperature on a) D19 and b) D16. the result to match the attenuation observed in the experimental data. An example of part of the calculation will be presented here. The integral was divided into different cases so that in each case the trajectory of the neutrons, t, is defined as a single function of x,y,ωand 2θ. The simplest case assumes that θ1<0 and θ1< θ2< θmax where θmax =atan(w−Bw 2d), as is highlighted in fig. 2.23. Under these assumptions every possible path of the scattered neutrons through the sample enters it by the face A, leaves the sample by face Cand the path length can be described as: t=d−y cos θ1 +y cos θ2 (2.21) Then Tis computed with eq. 2.20 with the limits for the integration in xbeing (w− Bw)/2< x < (w+Bw)/2 and in ybeing 0 < y < d. Fig. 2.24 shows an example of the result of the correction for both a single value of ω and the complete ω-2θmap. The corrected intensity map was then transform to the QH-QKspace for the data of the longitudinal orientation (fiber axis within scattering plane) or the QL-QKspace for 48 Figure 2.23: Geometry of the calculation of the transmission factor T.θ1=ω+ ∆θand ∆θ is an instrumental offset. wis the width of the sample, dis the thickness of the sample. Bw is width of the neutron beam. The center of the neutron beam is supposed to go though the middle of the sample in the front face. θmax is a limit for θ2in the example of the calculation of Tand it is described in the text. (a) (b) Figure 2.24: a) Example of ω-2θmap after the self attenuation correction. b) Intensity vs. 2θ for the raw data (blue), self-attenuation corrected data (black) and value of the transmission factor, T0, (red) for a given omega value. 49 Figure 2.25: Diagram of the scattering geometry relating the coordinates ωand 2θto the QH-QKspace. In the case of the transversal orientation the diagram would be identical and QHwould be replaced with QL. the transversal orientation (fiber axis normal to the scattering plane). This is done by transforming the ω-2θspace using the equations: QH,L =k(sin ω+ sin(2θ−ω)) QK=k(cos ω−cos(2θ−ω)) (2.22) where k= 2π/λ. These equivalences are apparent when following the scattering geometry of fig. 2.25. The final reciprocal maps for both orientations can be seen in fig. 2.26. The slight drop in the intensity which is observable in the upper left corner of fig. 2.26a proves that the attenuation correction is not perfect. Since such marginal defect is relatively far away from the features of interested studied in this work it can be reasonably assumed that its effect in the interpretation of the data is negligible. Before interpreting the data of the maps with the fiber axis normal to the scattering plane (transversal orientation) another reducing step was carried on. The data of these 50 (a) (b) Figure 2.26: Reciprocal space map of a DNA sample submerged in PEG solution as measured in D16 for both orientations: fiber axis in the scattering plane (a) and normal to the scattering plane (b). maps were summed over the sample rotation angles (ω) and plotted as a function of the 2θ of the magnitude of the scattering vector (Q) which are related through ec. 2.8). For the reciprocal maps collected with the fiber axis parallel to the scattering plane it was important to extract a representative data of a scan along the helix axis, i.e. a scan along QHwhen QK= 0. To get this, a narrow QK-range was chosen centered at QK= 0 (usually −0.04 < QK<0.04 ˚ A−1) Data whithin this range were extraxted and plotted against their QHvalues, disregarding the QKvalues. 2.5.2 Small angle neutron scattering The raw SANS patterns were corrected for environmental background using a blocked beam measurement. Defects in the sample and reference cells were accounted for with empty cell measurements. Afterwards the intensity in absolute units (cm−1) was obtained by using the formula which relates the experimental elastic signal with the differential cross section: Iel(~ Q) = I0η(λ)Tr(λ)∆Ω( dσ dΩ)el ⊗R(~ Q) (2.23) 51 where I0is the incident flux, ηis the efficiency of the detectors, Trthe transmission of the sample, ∆Ω is the solid angle of the detector with respect to the sample and R(~ Q) is the instrumental resolution. The experimentally detected intensity is smeared with respect to the real scattered intensity due to the finite size of the incoming beam, the wavelength resolution and the pixel size of the detector. R(~ Q) describes the distribution of the Q vectors at a given instrument configuration and corrects for this smearing. A sheet of plexiglass was measured in order to account for the detector efficiency (η) since it scatters isotropically, transmission of the sample was approximated by attenuating the beam and then measuring the direct transmitted beam at θ= 0. A monitor before the sample gave an estimation of the incident flux. A Gaussian function was assumed to described the instrument resolution function which has been proved reasonable in the past [46]. The GRASP (Graphical Reduction and Analysis SANS program) Matlab code package was used for applying a rectangular mask to the direct beam position and then integrate the data radially getting the final curves as intensity (cm−1) versus Q(˚ A). Then, using the scattering cross section and the GNOM program [47] the pair distribution function for each temperature was calculated. GNOM approximates P(r) using the regularization method which is based on minimizing the function: TG(P) = |I(q)−Zdmax 0 P(r)sin(Qr) Qr dr|2+XΥ(P) (2.24) where Υ(P) is an stabilizer containing a priori information about the solution. It is normally assume that Υ(P) = RdP(R) dr dr which requires P(R) to be a smooth function. Xis the regularization parameter. The larger Xis more attention is paid to the smoothness of the final P(r) and less to fitting the experimental data. The value of Xis crucial and there is not an accepted universal error-proof method to choose the value. GNOM search for the optima Xusing a perceptual criteria. With this criteria the program explore different Xvalues and estimates the plausibility of the solution by its smoothness, stability with respect to Xvariations and the absence of systematic variations. 52 The perceptual criteria is reported extensively in the book by Tikhonov and Arsenin [48] and well summarized in [49]. The GNOM estimations of Xvary for different SANS curves of a sample at different temperatures. The estimations fall in the range 0.58 <X<1.2. For consistency Xwas fixed to 1 for every SANS curve which gives reasonable results for all the data studied. Regarding the UV-Vis spectroscopy data recorded, since intensity of the UV-Vis radiation through the sample was monitored at each temperature (IS(T)) the absorbance of the sample can be calculated in function of temperature as: A(T) = log10(LS−DS IS(T)−DS ) (2.25) where LSis the so called light measurement or the intensity recorded when the sample position is empty (transmittance of 100%), DSis the dark measurement or intensity recorded when the beam is blocked (transmittance of 0%). 2.5.3 Small angle X-ray scattering For the SAXS case the reduction of the data is almost identical. The important difference is that the final data was normalized to absolute units using the diffraction of a glassy carbon standard as explained in [50]. The calculation of the P(r) for SAXS data was identical to the one of SANS. The configuration of the SAXS instrument had some advantages over the D22, for example the increased flux will allowed to perform the experiment with a fraction of the sample used for neutrons. However, there were not in-situ UV-Vis absortion measurements of the samples studied by SAXS. 53 Chapter 3 Literature review This chapter presents literature results which are relevant to this thesis as well as some of the models that will be use to analyze and interpret the data. 3.1 Previous diffraction studies in fiber DNA As described in the comprehensive book by Watson [51] X-ray diffraction studies on DNA fibers by Wilkins and Gosling showed that the DNA molecule can assume a highly periodic structure given that the fibers are kept moist. Frankling and Gosling were the first to develop optimal techniques to control the relative humidity of fibers [52] and they could obtain mode defined diffraction patterns which they designated A and B. They already detected that the pattern of a given fiber changes reversible when the water content of the sample is modified and that mixtures of A and B patterns exits which correspond to samples with a conformational mixture. Watson and Crick developed a two stranded model [53] which was able to explain the B diffraction pattern and later a more detailed analysis by Wilkins et al. [54] showed that both A and B patterns could be accounted for by the models of watson and Crick. 54 Since then, many groups greatly contributed to the overall knowledge of the characteristics of crystalline and semicrystaline fiber DNA and their A and B diffraction pattern as well as the A-to-B transition, a non complete list includes: Fuller et al. [55, 41]; Franklin and Gosling [56]; Langridge et al. [38]; Forsyth et al. [57]; Lindsay et al. [58] among others. Several comprehensive overviews in the topic can be found (e.g. [59]), the rest of the section will be focused in specific results that are specially relevant since they come from very similar experiments performed on almost identical samples with respect to the present work. 3.1.1 Conformation of humidified fibers. A and B form DNA as seen by neutron scattering As described in sec. 2.3.4 and above the diffraction pattern of A-form and B-form DNA differ dramatically and changes in the water content or hydration of the fibers can trigger a conformational B-to-A transition which is reversible. The conformation of the DNA under study must be taken into account for a correct interpretation of the scattering features. Valle-Orero et al. [60] studied recently highly oriented wet spun fibers humidified at several relative humidities using neutron scattering. They identified the main features which indicate a given sample is in B form, A form or a mixture of both conformations. Fig. 3.1 reproduced from [60] summarizes these results. The figure shows selected parts of the reciprocal space maps in longitudinal (fiber axis within the scattering plane) orientation. The maps represent the diffracted intensity in reciprocal space using the perpendicular coordinate system explained in sec. 2.5.1:(QH, QK, QL). Fig. 3.1a top shows a singular intense Bragg peak centered at (1.87,0,0) ˚ A−1which is characteristic of the B-form. This Bragg peak, associated with a d-spacing ≈3.4˚ A , is related with the long range order of the position of the base pairs along the molecular axis (base pair stacking). This feature will be the focus of the temperature dependence study by 55 a non random alignment of discrete charges on the opposite molecules. Expressions for the three components can be approximated if the two molecules are assumed to be identical although they still may rotate around its own axis independently. The whole mathematical derivation is long and can be found in [68] (part C, double helices). The final results are: fcyl 16π2ασ0 =1 2κ K1(κIad) K1(κRa)K1(κRa)(3.7) with Kn(x) being the modified bessel function of the second kind and order nth. The selfcorrelation term: fself 16π2ασ2 0 = ∞ X n=1 cos2(nΦs 2)Ω0 n,n(κnIad, κnRa) κn[K0 n(κnRa)]2(3.8) where κn=p(κ2+ (2π P)2n2), K0 n(x) = dKn(x)/dx and Φsis the azimuthal half-width of the minor groove (which is ≈0.4πfor B-DNA [69]) and Ω0 n,n is so that: Ω0 n,m(x, y) = ∞ X j=−∞ [K0 n−j(x)Kj−m(x) + Kn−j(x)K0 j−m(x)] J0 j(y) K0 j(y)(3.9) where Jnis the bessel function of the first kind order nth and J0 n(x) = dJn(x)/dx. fcross 16π2ασ2 0 = ∞ X n=1 (−1)ncos2(nΦn 2) cos[n(Φ1−Φ2)] K1(κnIad) κn[K0 n(κnRa)]2(3.10) where (Φ1−Φ2) is the relative rotation of the two identical molecules. For the calculations of the present work (Φ1−Φ2) was taking as the optimal relative angle which minimizes the cross correlation energy which can be calculated as: 62 (Φ1−Φ2) = arccos κ2 2cos2(Φ 2)[K0 2(κ2Ra)]2K0(κ1Iad) aκ2 1cos2(φs)[K0 1(κ1)Ra]2K0(κ2Iad)(3.11) this approximation holds for inter axial distances shorter than a critical separation of R∗, at larger distances the optimal angle is zero. R∗can be approximated as: R∗=1 κ2−κ1 ln4 cos2(Φs)[K0 1(κ1Ra)]2κ5/2 cos2(Φs/2)[K0 2(κ2Ra)]2κ5/2 2(3.12) Forces calculated with this model were proven to be consistent with experimental measurements form Parsegian and coworkers [67]. Note that under certain conditions this model predicts an attraction force between DNA molecules. DNA molecules are generally negatively charge in solution so this may look unreasonable. In a different publication Kornyshev and Leikin proved that an attractive resultant force can take place caused by an attraction of the phosphates of strands of one DNA with cations adsorbed in the grooves of another DNA when DNA is confined to dense aggregates [71]. 3.3 Melting transition The melting transition is usually characterized by the melting temperature, Tm.Tmis defined as the temperature at which half of the base pairs in the molecule are open. It is commonly used for addressing the stability of DNA and other nucleic acids [72, 73]. In long chain DNA the melting temperature depends mainly on the environmental conditions of the DNA like hydration level, ionic strength of the medium, the presence of other solutes in the surrondings and also the DNA-DNA interactions. Another feature that helps characterizing the transition is the cooperativity. The cooperativity of the transition is the tendency of the base pairs to open in contiguous segments. The cooperativity is usually quantified by the so called cooperativity factor which is the mean 63 number of base pairs that melt as a single thermodynamic entity [74]. In a highly cooperative transition, usually shown by short DNA molecules and specially synthetic polynucleotide duplexes (poly(dAdT) or poly(dGdC)), most of the base pairs of the molecule open as a whole at a single temperature. In a less cooperative transition, ascribed traditionally to long natural DNA, many domains in the molecules melt independently from each other at different temperatures. The cooperativity depends on the energy and entropy changes associated with the creation of the open regions between helical domains. The cooperativity can be accessed experimentally since the width of the melting transition (which can be measured, for example, by calorimetry as explained in sec. 2.2.5) is inversely proportional to its cooperativity. Thus narrower transitions are more cooperative [75]. 3.3.1 Effect of the confinement of DNA in the melting transition A prediction of how the intermolecular forces in dense DNA assemblies affect the melting transition was published by Cherstvy and Kornyshev [69]. They combined the theory of electrostatic interactions presented in sec. 3.2 (also see [68]) and the two-state one-dimensional Ising model of DNA melting [76]. The model was used to account for the difference in the free energy of base pairs in closed (Fc) and open (Fo) state. During the melting of a single molecule: Fo−Fc= ∆U−T∆S where Tis temperature, ∆Uis the heat of melting of a base pair and ∆Sis the entropy difference between closed and open states. ∆S > 0 because open base pairs have more degrees of freedom. At the melting temperature of this single molecule, Tm0, the number of open (No) and closed (Nc) base pairs is equal so: s=exp[(Fo−Fc)/(kBTm0)] = 1 (3.13) where kBis the Boltzmann constant. This model also includes a cooperativity factor σcoop =exp[−Fs/(kBT)] where Fsis the 64 energy required to create a open region between two intact closed regions. Smaller σcop values (larger Fs) corresponds to a more cooperative melting. Cherstvy and Kornyshev argued that if the force between DNA molecules is attractive this attraction stabilizes the close base pairs, thus it lowers the free energy in the closed state. Therefore the melting temperature must increasse for eq. 3.13 to still hold [69]. Following previous studies in the topic [77, 78] they modeled the interaction energy between parallel soft non-homologous DNA molecules (totally independent sequences) as: E(L) = a0L−La1[1 −lt/(2lc)] −a1l2 t[1 −el/lt]/(2lc) (3.14) where Lis the length of the molecules, lcis the helical coherent length (which has a value between 300-700 ˚ Afor DNA [79, 80]), lt=pCt/2a1and Ctis the torsional elastic modulus of DNA (usually taken as 3 ×10−18 J˚ A [81]) . a0(Iad) and a1(Iad) are the electrostatic interaction harmonic coefficients whose expressions can be found in the appendix of [69]. As in previous sections, Iad is the interaxial distance between molecules. Using eq. 3.14 Cherstvy and Kornyshev rewrote the free energy of the Ising model as the sum of the interaction energy of the closed fragments, the energy of the closed/open boundaries and the energy of all the DNA base pairs which allowed them to obtain an expression for the free energy as a function of No,Nc,T,Iad and nbwhich is the number of closed/open boundaries. Minimizing Fwith respect nand Nh. They derived two coupled equations which must be fulfilled at the melting temperature in a columnar DNA aggregate: (N 2nb−1)2=1 σcoop 1−2b/N 2(1 −nb)/N =exp(−1 2 6a(a0−a1) kBT) (3.15) where ais the distance between base pairs (3.4 ˚ Afor B form), nbis the number of closed/open boundaries and N=Nc+Nois the total number of base pairs. 65 If all the other parameters are constant given two interaxial distance: Iad1with melting temperature Tm1and Iad2with melting temperature Tm2this model predicts that : Tm2=Tm1 a0(Iad2)−a1(Iad2) a0(Iad1)−a1(Iad1)(3.16) 3.3.2 Effect of PEG in the melting transition To the best of our knowledge there are not previous studies on the melting of DNA fibers submerged in PEG solutions. However, the melting of DNA dissolved in many different PEG solutions was reported by different groups (e.g. [82, 83]) and the results are relevant to the present work. When PEG is dissolved in a DNA-water solution it decreases the water activity of the solution which in turn decreases the melting temperature of DNA because it changes the water structure around the DNA molecules [82]. This is believed to be the explanation for low-molecular weight PEGs and other polymers decreasing the melting temperature of DNA dissolved in solution. However, high molecular weight polymers increase the melting temperature of DNA in solution. The origin of such increase was said to be the excluded volume effect. This assumes that the volume of the solution unavailable to the DNA due to the PEG presence stabilizes the molecular conformation which occupies the smallest space, that is, the helix molecule [82, 83]. The decrease of the water activity still happens for the long chain polymers but its effect on the melting has been proven to be very small in comparison to the effect of the excluded volume [82]. A strong indication that the excluded volume effect is taking place is that the variation of Tmis changing dramatically with the molecular weight of the PEG [82, 73], as can be seen in fig. 3.3. Even though it is not patent, these results for DNA in solution are relevant for the case of DNA-fibers submerged in PEG solutions. If the PEG penetrates the fibers then the 66 Figure 3.3: Variation of Tmof E.coli DNA in solution with the molar concentration of the PEG 400 (squares), 1000 (circles), 3400 (triangles), 8000 (inverse triangles). Reproduced from [82]. sample is not much more different than a very concentration DNA solution and the excluded volume of the PEG will affect the melting transition of the fibers. On the contrary, if the PEG remains separated from the DNA, in the outside of the fibers, just a small fraction of the DNA molecules in the sample will be in contact with PEG molecules and the excluded volume effect will be negligible. 3.3.3 Effect of ethanol in the melting transition It is known that increasing concentrations of ethanol decrease the melting temperature of DNA in solution [84]. The main factors explaining this behavior are the increased electrostatic repulsions among phosphate groups of the helix due to the lowering of the dielectric constants of the ethanol solution as the ethanol concentration increases, the hydrophobic effect and the decreased water activity [84]. In the case of the fibers submerged in ethanol solutions there is not a phase separation as happens with PEG of a high enough molecular weight. Ethanol is a very small molecule in comparison with PEG (the molecular weigh of ethanol is 46.07 g/mol) and will penetrate the fibers as easily as the water molecules. There67 (a) (b) Figure 3.4: Melting temperature (filled circle) and width of the transition (open circle) for fiber submerged in ethanol solutions. a)Na-DNA and b)Li-DNA. Reproduced from [85]. fore the same factors which affect DNA in solution will for sure be present in the submerged fiber samples. Rupprecht et al. studied the melting transition of very similar DNA wet-spun fibers samples submerged in ethanol/water mixtures ([85],[86]). They used a mechanochemical method which can relate changes in the length of the submerged fibers strained by a weight with confomational and thermodynamical transitions of the DNA [87]. Fig. 3.4 summarizes their results for Na−and Li-DNA fibers. For Na-DNA (fig. 3.4a) Tmdecreases from around 60% to 88% ethanol concentration ([EtOH]) but there is a local maximum at around 75%. The width of the transition decreases slightly from 60% to 70% and drops steeply at around 75% [EtOH]. These seemingly coupled changes in the behavior of Tmand the width were related with the B-to-A form transition of the secondary structure of the DNA (section 2.3.4). Rupprecht et al. linked the effect of the B-to-A transition on Tmand width to the stronger inter-helical interactions that the A-form exhibits with respect to the B-form in aggregated DNA [88]. 68 For [EtOH] higher than 90% the changes in Tmand width were related with a transition to P-form DNA [89], a very stable and dehydrated DNA form which is not of interest for the present work. For Li-DNA fibers (fig. 3.4b) the Tmdecreases monotonically until around 83%. The width stays constant from 70% to 75% and then decreases steadily. The raise in Tmand width after ≈82% is again related with the transition to the P-form. In these samples a B-to-C transition was detected at around 80% ethanol. These transitions were also detected by X-ray scattering in [61] (B-to-A) and in [62] (B-to-C) as explained in sec. 3.1.2. Rupprecth et al. measured samples submerged in ethanol solutions in a rather extensive range (0.3-3 M) of salt concentrations (NaCl for Na-DNA fibers and LiCl for Li-DNA fibers). They found no variance of the melting transition with salt concentration in this range [87]. 3.4 Models of DNA and the melting transition 3.4.1 Peyrard-Bishop-Dauxois model The one dimensional Peyrard-Bishop-Dauxois (PBD) model [90], [91] was used to analize the part of the neutron data. The model is able to predict melting curves of complex DNA molecules and solve the dynamical properties associated to the formation and stability of the denaturation bubbles [92]. A simple version of the model describes a DNA molecule as Nbase pairs placed in a 1D disordered chain with a mean separation of a, fig. 3.5. The state of each base pair is described by a single real variable, yn, which is the stretching of the base pair perpendicular to the molecular axis with respect to its equilibrium position. ynranges from 0 to +∞. The Hamiltonian of such a system is: 69 Figure 3.5: Graphical representation of the PBD model. ynis the stretching of the nth base pair, ais the mean distance between consecutive base pairs, xnis the local structure deviation for the nth base pair, Wis a potential describing inter-pair interaction and Vis a potential accounting for the interactions between the two bases within the pair nth. Hy= N−1 X j=1 W(yj, yj+1) + N X j=1 Vj(yj) (3.17) where yjrepresents the stretching of the jth base pair caused by the transverse displacement of the bases. W(yj, yj+1) is a potential describing the stacking interaction between adjacent bases [93]: W(yj, yj+1) = 1 2k[1 + ρe−b(yj+yj+1)](yj−yj+1)2(3.18) where kis a coupling constant, ρis the relative strength of the nonlinear base stacking and bis the inverse range of the nonlinear base stacking. Vjdescribes the intra-pair potential in the jth base pair and takes into account the hydrogen-bonding, electrostatic interactions between phosphate groups and solvent effects. It is usually taken as a Morse potential: Vj(yj) = Dj[1 −e−αjyj] (3.19) with Djand αjbeing respectively the depth and inverse range of the potential. Four 70 different parameters were necessary for describing the two kinds of base pairs:DAT ,αAT and DGC,αGC. The model can be used to calculated the size distribution of the closed segments of DNA which would be instrumental for the analysis of the diffraction data presented in this work. A detailed description of this calculation has been reported elsewhere [7]. Here only main steps of the process are presented. A quantitative definition of a closed base pair is needed to calculate the size of the closed regions at a given temperature (T) . Base pair jis considered closed if yj< ycwhere yc corresponds to a stretching well on the plateau of the Morse potential. The statistical weight of a given configuration of the molecule thermalised at temperature Tis[7]: zT=Zyf1 yl1 dy1···ZyfN ylN dyN·exp−Hy(y1,··· , yN)/kBT(3.20) where kBis the Boltzmann constant and yland yfdefine the configuration. If yl=−∞ and yf=∞for all j, the molecules explore the whole configurational space and zT=Z where Zis the partition function. ylj = 0 and yfj =ycdefine a configuration in which the base pair jis closed. If ylj =ycand yfj =∞define a configuration in which base pair jis open. The integrals associated with all configurations can be easily calculated as a series of mono-dimensional integrlas because the model is one-dimensional and restricted to nearest neighbor coupling. [7] The probability of madjacent base pairs being closed starting with the site iis then: P(m, i) = zT(y1,··· , yi−1, yi< yc, yi+1 < yc,··· , yi+m−1< yc, yi+m,···)/Z (3.21) Eq. 3.21 calculates the statistical weight of configurations where restrictions on the integration range were imposed for all sites belonging to the closed region and no restrictions 71 (a) (b) (c) (d) (e) (f) Figure 4.1: X-ray diffraction photographs of DNA fibers. Fibers equilibrated with an atmosphere of 75% RH a) Na-DNA and b) Li-DNA. Fibers submerged in ethanol solutions: c) Na-DNA 60% , d) Na-DNA 70%, e) Li-DNA 20% f) Li-DNA 70%. The momentum coordinate system is defined by QHvs. QKwhere QHis parallel to the molecular axis and QKis perpendicular to it. 78 4.2 Room temperature study with neutrons 4.2.1 Fibers submerged in PEG solutions Five samples of Na-DNA submerged in PEG solutions were studied by neutron scattering at room temperature. The solutions contained: PEG 6000 at 17% (w/w) (PEG6K-17%); PEG 6000 at 20% (PEG6K-20%); PEG6K-40%; PEG 8000 at 15% (PEG8K-15%); and PEG 8000 at 20% (PEG8k-20%). As a reference, Na-DNA fibers humidified at 92% RH in a 2H2O atmosphere were also measured (Na-humid). The left panels of fig. 4.2 shows the reciprocal space maps for the Na-humid fibers. Fig. 4.2a is the map of the longitudinal orientation (fiber axis within the scattering plane). Fig. 4.2c is the map of the transversal orientation (fiber axis perpendicular to the scattering plane). The maps represent the diffracted intensity in reciprocal space using the perpendicular coordinate system explained in sec. 2.5.1: (QH, QK, QL). Na-fibers at this RH are expected to be in the semicristaline B-form of DNA [98, 60]. Indeed, fig. 4.2a shows a singular intense Bragg peak centered at (1.87,0,0) ˚ A−1(the 10th layer Bragg peak) which is characteristic of the B-form as discussed previously (sec. 3.1.1). The transversal reciprocal map shown in fig 4.2c is qualitatively identical to the results presented in 3.1.1 and also suggest that the sample is in the B-form. It shows two ringlike features, one strong and centered around Q= 0.5˚ A−1and another much weaker at around Q= 0.57 ˚ A−1. These reflexions are related to the semicrystalline packing of the DNA molecules in the direction perpendicular to the fiber axis [60, 23]. The fibers submerged in PEG solutions all showed very similar features and only the data of the PEG6k-17% sample are shown in fig. 4.2b and 4.2d as model examples. The submerged samples have substantially more incoherent scattering in comparison to the humid fibers due to the presence of protonated PEG and so the signal-to-noise ratios of the Bragg peaks are smaller. The features may also be broader in the sample rotation angle, suggesting that 79 some orientation of the fibers has been lost. However, the results are qualitatively identical to the humid fibers. This means that the fibers submerged in PEG solutions are also in the B-form and most of the long range order of the fibers is not lost during the submersion. Similar results have been reported previously by Wildes et al. [12]. Fig. 4.3 shows the low-Qpart of the reciprocal space map in longitudinal orientation for the Na-humid and PEG6K-17% fibers. The maps are featureless for these sample except for the halo of the direct beam in the left bottom corner. This result is surprising since previous studies in very similar samples concluded that an additional Bragg peak in this region, centered at (QH, QK) = (0.25,0.3), was another reflexion related with the B-form (sec. 3.1.1 and [60]). This featured has not been detected in these or other samples measured in the present work. This suggest that the peak at (0.25,0.3) was related with some specific crystalline arrangement of the samples studied in [60] but does not seem to be a universal feature of the B-form of DNA. The data of the transversal reciprocal space maps were used to calculate the interaxial distance between molecules (Iad) for every sample and thus to gauge the effect of the PEG solution on the confinement of the molecules. The data of these maps were summed over the sample rotation angles for equal Qvalues and plotted as a function of the magnitude of Q(the scattering vector). Fig. 4.4 shows the results. The peaks for the submerged samples are shifted to lower Qvalues with respect to those of the Na-humid fibers. This suggest an increase in the lattice parameters which is consistent with the fibers swelling when submerged. B-form DNA fibers are believed to have a hexagonal space group, as shown for B-form Na-DNA at 92% RH by Langridge and Wilson [38] and for samples submerged in PEG solution by Podgornik et al. [11]. The two peaks can be indexed as the 110 and 200 reflexions respectively from the hexagonal lattice. The d-spacing related with a given peak is d= 2π/QCwhere QCis the center of the peak and the relation between the Miller indices and the lattice parameter a, corresponding to the axis-to-axis distance between two molecules, is 80 (a) (b) (c) (d) Figure 4.2: Reciprocal space maps of the Na-DNA fibers in the longitudinal (top) and transversal (botton) orientations. a) and c) are the maps for fibers humidified to 92% RH. b) and d) are maps for fibers submerged in a PEG6K-17% solution. Data measured in D16. 81 (a) (b) Figure 4.3: Low Q-part of the reciprocal space maps of the longitudinal orientation for a) the Na-humid fibers and b) the fibers submerged in PEG6k-17%. Data measured in IN3. (a) (b) Figure 4.4: Sum of the intensity over the sample rotation angles of the transversal reciprocal space maps for constant scattering vector as a function of Q. The curves have been shifted vertically for clarity. Red lines are the fit to the data. Data on the left were measured on D16, data on the right on WOMBAT. 82 Sample Iad (˚ A) ∆a aHu (%) PEG6k-17% 28.24 ±0.05 14.54 ±0.91 PEG8k-15% 26.92 ±0.06 9.18 ±0.99 PEG8k-20% 26.11 ±0.04 5.90 ±0.81 PEG6k-20% 25.48 ±0.03 3.33 ±0.70 PEG6K-40% 24.08 ±0.03 −2.35 ±0.62 Humid fibers 24.66 ±0.09 0 Table 4.1: Percentage increase in the intermolecular spacing for Na-DNA fibers submerged in PEG solutions With Respect to the Humidified Fibers. a=d(4 3(h2+kh +k2))1/2(4.1) The centers of the peaks for each sample were determined by fitting two Gaussian functions with a linear background. The results of the fits can be seen in fig. 4.4. The lattice parameter of the Na-humid sample was calculated using the average afrom both peaks. The result was aHu = 24.66 ±0.09 ˚ A, which is consistent with previous results [38]. The intermolecular distances for the other samples were computed analogously and the percentage increase in intermolecular distance with respect to the humidified fibers was calculated. Table 4.1 shows the values of the percentage increase and the interaxial distance (Iad) for each sample. All the samples swelled under submersion (Iad increased) except for PEG6K-40% in which the osmotic pressure compressed the fibers to Iad shorter than that of the Na-humid fibers. 4.2.2 Fibers submerged in ethanol solutions Six samples submerged in deuterated ethanol solutions were investigated with neutrons at room temperature: Na-DNA in 60% ethanol-d6 (v/v) with 0.1M NaCl (Na-60%-0.1); NaDNA in 66% with 0.1 M NaCl (Na-66%-0.1); Na-DNA in 66% with 0.01 M NaCl(Na-66%- 0.01); Li-DNA in 20% (Li-20%); Li-DNA in 60%(Li-60%); and Li-DNA in 80% (Li-80%). 83 All the solutions for lithium samples had a LiCl concentration of 0.1Mand so it has not been included in the code of the sample. As a reference for the lithium samples, Li-DNA fibers humidified at 75% RH (Li-humid) were also measured. Ethanol mixtures present some advantages over polymer solutions for the studies of DNA fibers using neutron scattering: a) they do not contain long-chain polymers which contribute to the scattering of the sample and could mask the signal of the DNA. b) fully deuterated ethanol is easily accessible while fully deuterated PEG is prohibitively expensive. Minimizing the amount of 1Hin the sample is important for neutron scattering since it contributes to the incoherent scattering and degrades the peak-signal-to-noise ratio. As shown in sec. 4.1 the Na-fibers submerged in ethanol undergo a B-to-A transition due to the ethanol drastically reducing the water activity of the solution [61]. Fig. 4.5 shows a longitudinal reciprocal space map for Na-66%-0.1. It shows off-axis peaks characteristic of the A-form DNA as presented in sec. 3.1.1. This is consistent with the X-ray measurements presented in previous sections and with the literature (sec. 4.1 and [61]) which proved that the ethanol-induced B-to-A transition happens at ethanol concentrations between 60%-70%. It is important to notice that the 10th layer peak still remains although it is much weaker. The superposition of Band A-form features indicates that the sample is a mixture of conformations. Most of the molecules are in A-form but some of them are still hydrated enough to be in B-form. It can be said that the sample has ”B-form contamination”. As presented in sec. 3.1.1 evidence of conformational mixtures were previously detected using neutron scattering and other techniques. The influence of the salt concentration on the amount of ethanol needed to cause the A-to-B transition has been previously reported [58]. Higher salt content seems to favor the A-form. Neutron data support this. Fig. 4.6a shows the high-Qpart of the longitudinal reciprocal map for the Na-66%-0.01 sample. The 10th layer Bragg peak is strong and the off axis peaks are weak. Fig. 4.6b show the low-Qpart of the map. A Bragg peak appears at (QH, QK) = (0.45,0.3) which is usually related with A-form DNA (sec. 3.1.1). These results suggest this sample is composed predominantly by B-DNA with some A-form contamination 84 Figure 4.5: Reciprocal space map in longitudinal orientation of the Na-66%-0.1 sample. Measured in IN3. in opposition to the similar sample with 0.1M NaCl. The lower NaCl content of this sample seems to increase the number of molecules which remain in the B-form. Fig. 4.6c shows the 10th layer peak for the Na-60%-0.1 sample. It suggests that this sample is in the B-form which is consistent with the previous presented X-ray data but some very weak off-axis features may be asserted to exist at (QH, QK) = (1.6,0.5) ˚ A−1and (1.6,−0.5) ˚ A−1. In addition, the low-Qpart of the longitudinal reciprocal space map (shown in fig. 4.6d) shows clearly the A-form Bragg peak mentioned above. It seems like the Na60%-0.1 sample has some A-form contamination even though it was not appreciable in the X-ray images. Similar measurements proved that Li-DNA fibers show a pure B-form at ethanol concentrations up to 80% (compare fig. 4.6e and 4.6f with sec 3.1.1). Hereafter Li-DNA fibers submerged in ethanol will be considered to be in a pure B-form. On the contrary, Na-DNA fibers submerged in ethanol concentrations equal or above 60% ethanol in volume would be considered to have some degree of A/B mixture of conformations. The effect of the submersion of the Naand Li-DNA samples in ethanol on the interaxial 85 (a) (b) (c) (d) (e) (f) Figure 4.6: Longitudinal reciprocal space maps (left:high-Q, right:low-Q) of: Na-66%-0.01 [(a), and (b)]; Na-60%-0.1 [(c), (d)]; and Li-80% [(e) and (f)]. Measured in IN3. 86 distance (Iad) was addressed using the same procedure as for the PEG samples. Reciprocal space maps in the transversal orientation were measured and the intensity was summed over the sample rotation angles (for constant Q) and plotted as the magnitude of Q. Fig. 4.7 shows representative examples of the reciprocal space maps collected on D16 to gauge the intermolecular distance of the samples submerged in ethanol solutions along with the humidified Li-fibers. Fig. 4.7a is identical to fig. 3.2a with three ring-like reflections, one strong and centered at Q≈0.3˚ A−1and two weaker ones at Q > 0.3˚ A−1. In the maps of the samples submerged in ethanol a feature can be seen at around 0.3˚ A−1which was not present in their PEG counterparts (fig. 4.4). For the Li-DNA fibers the radial distribution of this new feature is homogeneous. For the Na-DNA fibers, there is arguably a spot of higher intensity centered at approximately (QL, QK) = (0.3,0) which is similar to the peak observed in fig. 3.2b, the pattern of a pure A-form sample. This is another proof that the Na-DNA fibers submerged in ethanol have a mixture of conformations A and B. The result of the summation over the rotation angle for equal Qs for the ethanol samples can be seen in fig. 4.8. The data of the Li-fibers humidified at 75% RH (black in fig. 4.8a) show at least three clear reflexions at approximately 0.3, 0.58 and 0.68 ˚ A−1. The other Li-samples show corresponding reflexions. For all Li-fibers the reflexion at 0.3˚ A−1is composed of two peaks which are very close. This is patent for the Li-20% sample and it is suggested for the rest of the samples due to the tail of the reflexion in the low-Qpart and the asymmetry of the reflexion. Therefore there are four reflexions to consider in each curve related with Li-samples. These curves are rather different from what was observed for the same measurements for PEG samples. The double-peak feature is not presented in the PEG samples and the previously observed strong peak at around 0.5˚ A−1appears much weaker in the ethanol samples. It has been reported that Li-DNA fibers humidified at 75% RH have an orthorhombic packing structure of its molecules with two molecules per unit cell in equivalent positions (0,0,1 6) and (1 2,1 2,−1 6) [38]. The different values in the z-axis mean that neighboring molecules are displaced with respect to each other along the fiber axis. In an orthorombic lattice the 87 were prepared with an identical buffer (sec. 2.1.1). The PEG-concentration range for the studied samples was 5 < C%<40 where C%is the PEG concentration in weight percent. Three other types of samples were measured in addition to fibers submerged in PEG solutions: fibers equilibrated in a humid atmosphere with 92% relative humidity (Na-humid fibers); the same DNA used for the preparation of the fibers (salmon testes) dissolved in the buffer used to prepare the PEG solution; and fibers submerged in the buffer. Note that submersion in PEG-free buffer caused partial dissolution of the fibers, but due to the relatively low solubility of the DNA in water (10 mg/ml for a saline buffer according to the provider) most of the DNA remained in fiber form. The calorimetry data for every sample showed a well defined single-peak related with the excess heat capacity of the melting transition. Fig. 4.9a shows representative examples of the data. It displays the specific heat as a function of temperature for the humid fibers and fibers submerged in a solution of PEG6k-20%, along with the respective fits to the curves using a Gaussian function and the fraction of closed base pairs (fDS) calculated using eq. 2.6. The melting temperatures, Tm, are highlighted. Fig. 4.9b shows the Tmof: the humid fibers (92% RH); the DNA dissolved in the buffer; the fibers submerged in PEG-free buffer; and of the submerged fibers in PEG solution as a function of PEG concentration ([PEG]). DNA molecules dissolved in solution are less confined than the DNA molecules of the fibers submerged in the PEG-free buffer. Except for that, the DNA of both samples are subjected to the same conditions (hydration, ionic environment etc). The Tmof DNA fibers submerged in buffer is higher than Tmfor the DNA dissolved in the same buffer. Therefore it is probable that confinement is the origin of the higher Tmfor the submerged fibers. A similar effect was reported previously in [99], in this study the transition between DNA dispersed in solution and an aggregated liquid-crystalline state increased the Tmmeasured by differential scanning calorimetry. More recently, consistent results were published in [100] where a shift of the DNA melting temperature of several degrees occurred due to the aggregation of DNA molecules. As explained in sec. 3.3.1, interaction between densely packed DNA molecules 94 (a) (b) (c) Figure 4.9: a) The heat capacity per unit mass, ∆c, for Na-DNA fibers equilibrated in an atmosphere and 92% RH and submerged in a solution of PEG6k-20% w/w is plotted with solid thick black lines, the solid thin red lines represent the fit to the data, the blue dashed lines are the fraction of closed base pairs as a function of temperature. The Tms are highlighted. b) Melting temperature measured of a dilute solution of DNA, DNA fibers humidified at 92% RH, fibers submerged in buffer and fibers submerged in solutions of PEG1k, PEG6k and PEG8k as a function of the [PEG]. c) Width of the transition for the same samples of panel b). The green line marks the value of the width for the humid fibers. Error bars represent the standard deviation of measurements on identical samples. 95 can theoretically increase Tm. The Tmfor PEG samples were consistently higher than for fibers submerged in buffer with no PEG. Tmincreases linearly with [PEG] and the trend is equivalent (within error bars) for PEG6K and PEG8K. The behavior of Tmas PEG1K concentration increases is appreciably different. Similar effects were reported for DNA dissolved in PEG solutions [82, 83] and were explained via the excluded volume effect (sec. 3.3.2). The excluded volume could be the main effect explaining the stabilization caused by PEG1K. PEG1K is significantly shorter than PEG6K which is supposedly the shorter PEG which is excluded from the DNA fibers ([67] and sec. 3.1.3). If the PEG1K can penetrate the fibers it will share the same space as the DNA and the sample will be qualitatively similar to a very dense DNA solution in which the excluded volume would be an important factor. However, for PEG6K and PEG8K it is reasonable to assume, based on previous evidence, that the PEG molecules did not penetrate the fibers [11] and thus only a small percentage of the DNA molecules in the sample are in contact with PEG molecules. Knowing that the width of the macroscopic DNA fibers is ≈0.5mm, if one assumes that the DNA molecules forming the fiber have a hard diameter of 20 ˚ A and they are closely packed so that there is no separation between molecules, the percentage of DNA molecules in the surface of the fibers can be roughly estimated as less than 1%. Therefore the excluded volume and specific interactions of the PEG with DNA cannot affect significantly the melting transition. Moreover, the trend of Tmas [PEG] is increased seems to be the same for PEG6K and PEG8K which is consistent with the excluded volume having a insignificant effect in the transition ([82] and sec. 3.3.2). When DNA fibers are submerged in PEG6K and PEG8K solutions, there is a well defined average interaxial distance which decreases as [PEG] increases (due to the osmotic pressure of the solution which grows with [PEG]) as can be seen in table 4.1 and also in [10, 11]. Therefore the confinement in these samples is increasing with [PEG]. As presented in sec. 3.3.1 it may be the main factor in the increase of Tmof the samples submerged in high 96 Parameter Value κ−19.63 ˚ A Ra9˚ A P34 ˚ A Φs0.8π a3.4˚ A θf0.8 s80 fc0.4 σ016.8µC/cm2 Table 4.4: Parameters used in the calculation of f/(16π2ασ0) and the theoretical melting temperature. Note that the value of κ−1 here was used only for the calculation of the intermolecular foce. It was adjusted for the calculation of Tm(see text). molecular weight PEG solutions. This idea can be further explored by combining the calorimetry data for Tmwith the interaxial distance (Iad) measured by neutrons and the models of DNA confinement developed by Kornyshev and Leikin presented in sec. 3.2. Fig. 4.10b shows a comparison of this model with our experimental data. The magnitude f/(16π2ασ0) is proportional to the interactive force between two DNA molecules as predicted by the model [68]; calculated using equations 3.6. The parameters used are presented in table 4.4. (They are Ra,P, Φsand κ−1 or Debye length). The values for Raand Pare reasonable for B-form DNA, 0.8πis a usually accepted value from the literature [68] and the Debye lenght was calculated based on the salt content of the solution (0.1M NaCl) as done in [101]. The model predicts an attractive force between molecules which increases as the interaxial distance decreases. Fig. 4.10 shows that both Tmand the width of the transition are quite correlated with the interaction force over most of the range studied which supports the idea of the confinement being the main factor in the effect of the PEG in the fiber samples. This correlation does not hold at Iad = 28.24 ˚ A. Within the model the attraction between 97 (a) (b) Figure 4.10: a) Left scale: Blue squares are the melting temperatures measured by calorimetry as a function of the interaxial distance between molecules (Iad). Right scale: the red line is proportional to the absolute value of the attractive force between molecules predicted by eq. 3.6. b) Left axis: Blue squares are the width of the melting transition measured by calorimetry as a function of Iad. Right axis: the red line is proportional to the force of the previous panel. 98 DNA molecules is closely related to the non-random alignment of opposite strands which is defined by the relative rotation of the two helices (Φ1-Φ2) [68]. The selection of Φ1-Φ2in the present calculation was based on a minimization of the interaction energy which holds at distances shorter than R∗, the critical separation, given by eq. 3.12. Substituting the parameters used for computing the force of fig. 4.10 into eq. 3.12 gives R∗≈29.32 ˚ A. This could certainly explained the breaking of correlation between experimental data and model at Iad = 28.24 ˚ A. Future works will try to improve the matching of model and experimental data by changing the approximation of Φ1-Φ2as R∗is approached. In addition to this qualitative comparison between theory and experiment, a theoretical prediction of the increase of Tmas Iad decreases was tried using eq. 3.16. The parameters used for this calculation were taken from the literature [69] and are presented in table 4.4 except for κ−1.θfis the fraction od DNA charge compensated by adsorbed cations, fcis the fraction of adsorbed cations in the minor groove of DNA and sis the dielectric constant of the solution (for which the value of water was taken). A Debye screening length of 9.63 ˚ A is a reasonable value for the salt concentration of the solutions the samples were submerged in. However, when used in eq. 3.16 it gave a very poor resemblance with the data. Fig. 4.11 shows a comparison of the theoretical and experimental Tmas a function of Iad for a calculation with κ−1= 88 ˚ A. Eq. 3.16 allows to predict the variation of Tmwhen Iad changes with respect to a reference Tm, which is highlighted in the figure, and for which the theoretical Tmis assumed to match exactly the experimental data. Fig. 4.11 shows that, with this large value for κ−1the model matches the data remarkably well. Theory and model differ for the Tmat 28.24 ˚ A, this prediction of Tmis based in the calculation of the force presented in fig. 4.10 (sec. 3.3.1 and [69]) so the range of applicability should be the same. Therefore it is not surprising that the prediction of Tmfails at Iad = 28.24 ˚ A. 99 Figure 4.11: Comparison between experimental and theoratical Tmas a function of Iad for a Debye screening length of 88 ˚ A. κ−1= 88 ˚ A relates to a solution with a salt concentration roughly two orders of magnitude lower that the expected Debye length for the solutions of the samples. The samples could exhibit a smaller ion activity than expected because of the presence of PEG which was not accounted for in the calculation of κ. However, a two orders of magnitude decrease in the ionic strength looks unreasonable. The model, which gets the Tmright just by changing one parameter, may have a relatively small shortcoming. 4.3.2 Fibers submerged in ethanol Calorimetry data were collected in Na/Li-DNA fibers submerged in ethanol solutions as a function of the ethanol concentrations between 20% and 85% (v/v). The solutions are described in sec. 2.1.1. All samples for the calorimetry study of this section contained 0.1 Mof the corresponding salt. Fig. 4.12a shows examples of calorimetric curves collected in Naand Li-DNA fibers submerged in ethanol solutions. The curves of Li-DNA fibers in the whole concentration range studied were qualitative identical to the PEG case with a single peak on a constant 100 background as seen in the figure for Li-60% ethanol (black squares). This is also the case for Na-DNA for ethanol concentrations up to 50%. However, at 60% ethanol (red circles) a tail appears at the high temperature side of the peak making it appreciably asymmetric and hinting at the existence of a second, weaker, contribution to the melting curve apart from the main strong peak. For Na-66% fibers (blue triangles in the figure) this second contribution to the melting curve is patent since there is a smaller melting peak at higher Twith respect to the strong main one. Na-DNA fibers showed some degree of A-form contamination when submerged in 60% or higher ethanol solutions (sec. 3.1.1 and sec. 4.2.2) while Li-DNA remained in B-form for the whole ethanol concentration range studied. These changes in the shapes of the melting curves for Na-DNA with increasing ethanol concentration are most probably related with the appearance of A-contamination and the increase of the number of molecules in A-form as the ethanol concentration is increased. Within this interpretation, it is reasonable to assume that most of the molecules in the Na-66%-0.01 were in B-form and underwent the melting transition with a melting temperature ≈63 ◦C. The fraction of the sample in A form remained in the helical form and melted at ≈70 ◦C(the center of the secondary peak). Two different melting temperatures could be unambiguously computed for curves exhibiting two clear and separated melting peaks. This is not the case in the samples of the present study. All the secondary peaks ascribed to the melting of the A-form domains are relatively very small and superimposed with the main peak. A melting temperature for A and B domains could still be roughly estimated by fitting two peaks to the curve. However, even for single peak curves, identifying the melting temperature with the center of the peak can introduce errors in the calculation [102]. In this work a singular Tm(calculated as explained in sec. 2.2.5) was ascribed to the double-peak samples. These values should be understood as weighted averages between the Tmof domains in B and A conformations for each sample. Special care must be taken if the Tmvalues reported here are to be analyzed quantitatively. For the qualitative discussion presented in this chapter the values are probably sufficient. On the contrary, calculating the width of the double-peak samples as the full width at 101 half maximum of a single peak (as described in sec. 2.2.5) would be quite meaningless. For all the Na-DNA fibers submerged in ethanol the width of the transition was calculated as the temperature change necessary to go from 25% to 75% open base pairs(using eq. 2.5). For a single-peak melting curve this is equivalent to take the full width at half maximum of the peak. This procedure was used before, with calorimetry and other techniques able to access the fraction of open base pairs, to compute the width of the transition [103]. Fig. 4.12b shows the value of the melting temperature and the width of the transition for the Na-DNA case. The melting temperature decreases from 0% until 70% ethanol and raises from 70% to 80% before decreasing again at 90%. Caution must be applied when taking into consideration the increase in Tmat 80% since only one point constitutes such increase. However, as explained previously (sec. 2.2.4) the presented values of Tmare the average of the measurement on three identical samples. Therefore we believe this increase is significant. The width of the transition is roughly constant until at least 50% ethanol and drops for higher concentrations. Fig. 4.12c shows the same data for Li-DNA fibers, in this case Tmdecreases monotonically (the local maximum in Tmdoes not exist) and the width increases significantly at 70% ethanol and then drops steeply at 80%. For the ethanol samples the main factors explaining the overall effect of the ethanol in the melting temperature is decreasing of the water activity and the dielectric constant of the solution as presented in sec. 3.3.3. The behavior of Tmand the width of the transition as a function of the ethanol concentration found in this work are qualitatively identical to what was reported by Rupprecht et al. (sec. 3.3.3) for very similar samples. The quantitative difference can be explained by differences in salt concentration of the solutions which affect both Tmand width [103]. Rupprecht et al. also found a B-to-A transition in Na-DNA (consistent with the scattering data of previous sections). They even suggested that a range of ethanol concentrations exist in which the fibers are a mixture of B and A form (fig. 3.4a and [88]) which relates to the A/B contamination found in the samples of this work. 102 (a) (b) Na-DNA (c) Li-DNA Figure 4.12: a) Examples of calorimetric curves of Na−and Li−DNA fibers submerged in ethanol solutions. Melting temperature and width of the transition for fibers submerged in ethanol solutions as a function of the ethanol concentration (v/v). 103 The total intensity for every temperature was fitted with the expression: I(QH) = I1+I2+IAl,P b (4.7) A0and Bwere not fit-parameters. Their values were calculated before fitting a given curve. For the D19 data the average values of the scattering signal for QH<0.6˚ A−1and QH>3.4˚ A−1were calculated and a line was drawn between the two values. A0and Bwere taken as respectively the intercept and slope of that line. For the WOMBAT data, Bwas set to zero and A0was determined by averaging the signal for QH<0.8˚ A−1. In addition, for the WOMBAT data the diffuse scattering was represented by a single rising step function so the term tanh(QH−Q2 s2) in eq. 4.5 related with the declining step was not included. The curves of the PEG solutions at room temperature were fitted using eq. 4.5. The results can be seen in fig. 4.14a and 4.14b. The values for the parameters of this fit (A1,Q1, s1,Q2,s2) were used as part of the initial set of values for fitting the DNA data at room temperature using eq. 4.7. The rest of initial values were chosen by visual comparison. For subsequent temperatures a two-stage process was used in order to get an accurate fit when the size of the Bragg peak and the diffuse contribution became comparable. For a given temperature above room T, the γfrom the fit of the previous temperature was used to define a range in QHcentered around the DNA Bragg peak (Q0−0.8γ≤Q≤Q0+0.8γ). In the first stage the parameters of the DNA Bragg peak (eq. 4.4) were fixed, data inside the previously defined range were ignored and eq. 4.7 was fitted using the results for the fit of the previous temperature as initial values for the parameters . In the second stage data outside the range were ignored, the parameters of eq. 4.5 and 4.6 were fixed to the fitted values of the first stage and the DNA Bragg peak was fitted with eq. 4.7. The two-stage process was then repeated twice per temperature. Each new iteration used the parameters of the previous iteration as initial parameters for the fit. After 3 iterations the parameters were stable. Examples of the final fits can be seen in fig. 4.14. The fitting is very consistent but should be interpreted with care at high temperatures, where the Lorentzian peak was so small in 110 comparison with the diffuse contribution that the general fit had trouble converging. At these temperatures the values for γand Q0were fixed to the values of the last temperature in which the fit converged and only I0was fitted. Fig. 4.15 shows a representative example of the temperature dependence of the parameters of the double-step function and of the center of the DNA Bragg peak (Q0). The center of the Bragg peak shifts slightly to smaller Qs as the temperature raises (fig. 4.15b) which is consistent with thermal expansion and the change in the average base pair distance due to the relaxation of the base stacking because of partial unwinding of the helix. Q0suddenly drops at T≈97 ◦C. This steep decrease could be associated to a partial untwist of the helix due to the great number of unstacked bases at this high temperature. With a sudden untwist the average distance between adjacent base pairs will grow fast and so the center of the Bragg peak will decrease. However, at this high temperature the peak is very small in comparison to the diffuse background therefore, as already mentioned, the interpretation of Q0and other fitted parameters must be done with care. Regarding the the parameters of the double-step, their evolution with Tis reasonable but it is very challenging to ascribe a physical meaning to them. The fitted values for eq. 4.6 (related with the aluminum and lead Bragg peaks) did not change within reasonable limits with Twhich is consistent with the fact that no significant changes were expected from the Al or Pb in the range of temperatures studied. Fig. 4.16 shows the evolution of the A0parameter with temperature for all the samples. A0(T) in this figure is normalized by its value at T= 20 ◦C to allow easy comparison between samples. A0(T) describes adequately the magnitude of the increase of the diffuse scattering with T. The figure proves that the diffuse contribution rises close to the melting temperature in every sample. The increase at the highest Treached is approximately 20% for the PEG6K-17% (measured at D19) and approximately 5% for the rest of the samples (measured at WOMBAT) . It is likely that this quantitative difference is due to the different instrument configurations. There are two factors likely to contribute to the difference: The first concerns the collimation between sample and analyser. D19 had no collimation 111 (a) (b) (c) Figure 4.15: Temperature dependence of the parameters of the double-step function and the center of the DNA Bragg peak for the PEG6K-17% sample as found by the fit. a) A1, b) Centers of the double step function (Q1and Q2) and of the Bragg peak (Q0). c) Gradients of the double step function (s1and s2). 112 Figure 4.16: Parameter A0from equation 4.5 as a function of the reduced temperature (T/Tm calculated in Celsius) normalized by its value at 20 ◦C for each sample. A0is the average of the intensity at low Qand represents the magnitude of the diffuse contribution. The curve of the PEG8k-20% sample is shifted downwards by 0.05 units for clarity. while WOMBAT used an oscillating collimator. In principle, an oscillating collimator limits only the scattering gauge volume of the sample. However, the diffuse scattering resembles, to first order, incoherent scattering while the scattering angles for the Bragg peaks are reasonably well self-collimated. The WOMBAT oscillating collimator also limits instantaneously the divergence of the scattered beam to 0.5◦, hence reducing an incoherent contribution relative to a coherent signal. This partly explains the larger diffuse signal in the D19 data. The second concerns the kinematic limits on the energy integration of the neutron instrument. Neither WOMBAT nor D19 had any means to analyze the final energy of the neutron. Both instruments therefore integrated over neutron energy transfers. The allowed energy and momentum transfers are limited by the energy of the incident neutrons, which was 14.20 meV for D19 and 3.83 meV for WOMBAT. D19 therefore integrated over a much larger energy window than WOMBAT. Fiber DNA has substantial spectral weight from 2 to 25 meV [104] , and D19 will capture these lattice dynamics where WOMBAT cannot. The dynamics of DNA will change substantially as the melting temperature is approached, giving a non-linear increase in the spectral weight for all Qand proportionately more diffuse scattering in the D19 data. 113 Fig. 4.16 also shows that the values for A0do not increase monotonically with temperature close to melting, particularly for the PEG6k-17% (black squares) and the PEG6k-20% (red circles) samples. The data shows small peaks in A0which may also be observed in fig. 4.13a and fig. 4.13b as vertical lines close to the temperature at which the Bragg peak disappears. As previously stated, the temperature stability at the melting temperatures for these samples was rather poor (sec. 2.4.1 and 2.4.1). The amplitude of the diffuse scattering increases steeply with temperature in this range. The pilot study [12] showed that the melting transition is, to some extent, reversible in these samples given that the melting is not complete. It is possible that the variations in A0are coupled with the temperature stability, and that the final registered values are indicative of the weighted average of the fluctuating intensity over the duration of the measurement. Fig. 4.17 shows the fitted I0and γas a function of temperature for the four samples. For all samples ,the intensities decreases rapidly and the peak effectively disappears over the range 0.95 ≤T/Tm≤1.05. For the WOMBAT data, the integrated intensities and widths stay roughly unchanged until close to the melting temperature, as seen in previous studies on humidified fibers [7, 8]. This suggests that, as for humidified fibers, long segments of DNA remain until the very last stages of melting. These define the width of the Bragg peak. At the temperature where these last segments denature, the intensity of the Bragg peak is so weak that it is lost in the diffuse scattering and any change in the width cannot be unambiguously determined from a fit. The PEG6k-17% sample measured on D19 shows a somewhat different behavior. Both I0 and γincrease steadily before the Tm. This difference in the behavior of the fitted parameters with respect to the WOMBAT data may be related to the different integration over neutron energy transfers for both instruments. An increase in the phonon dynamics with increasing temperature can manifest itself as an increasing width in the tails of a Bragg peak. Such effect would be more dramatic in D19 due to the expanded energy integration. Although a neutron inelastic scattering measurement would be necessary to prove the hypothesis, it appears likely that the increasing I0and γwith temperature seen on D19 are due to the increased dynamics of the fiber DNA as melting is approached. 114 (a) PEG6K-17% (b) PEG6K-20% (c) PEG8K-15% (d) PEG8K-20% Figure 4.17: Comparison between theory and experiment for the data of the sample submerged in PEG. PEG6k-17% a) was measured on D19, the other samples b)-d) on WOMBAT. A reduced temperature, T/Tm(calculated in Celsius) was used where Tmis the melting transition of the sample. In each panel the three upper curves relate to the scale in the left, they are the fitted integrated intensity, I0(blue open circles), the theoretical integrated intensity (thick red line) and the fraction of closed base pairs calculated with calorimetry (eq. 2.6) for a corresponding sample (black dashed line), the fitted integrated intensities have been divided by arbitrary numbers for easy comparison. The lower curves relate to the scale in the right, they are γ, the fitted width of the peak (black close circles), and the theoretical width of the peak (thin red line). 115 Analysis using the Peyrard-Bishop-Dauxious model The PBD model was used to make a quantitative analysis of the fit results, following a previously-reported procedure [7, 94]. The model can be used to calculated the probability that a base pair of a given sequence is closed at a given temperature. The probability of a given size distribution of closed segments can then be determined, as explained in sec. 3.4.1. The expected diffraction pattern, S(Q), from the sequence can then be calculated (as presented in sec. 3.4.1) and compared to the experiments. The parameters for the Hamiltonian the model uses to described the DNA molecule (eq. 3.17) were refined by comparing the calculated melting curve with the data from calorimetry. A segment of the genome of Atlantic Salmon reported previously [105] (10000 bases starting at site 50000) was chosen for the calculation. In the modeling Wwas assumed to be the same for all combinations of adjacent base pairs, which has been shown to be reasonable for describing the melting curves of long DNA molecules [7, 92]. The DNA sequence was taken into account only for the calculation of the intra-pair potential Vj. All values of the parameters of the Hamiltonian used to model the data, except for DAT and DGC, are the same as previously used in the study of humidified fibers [7]. They are shown in table 4.5. DAT and DGC represent the energy barrier for base pair dissociation and thus they are the main factor in setting the Tmof the theoretical melting curve. As shown in fig. 4.9b, the melting temperature when the fibers are submerged in the PEG solutions increases with PEG concentration. Thus DAT and DGC needed to be scaled to reproduced the melting temperature of each sample. The values for the depth of the Morse potential shown in table 4.5 (DAT,95,DGC,95) with the chosen sequence and parameters correspond to Tm= 95 ◦C. For a sample with a Tm=Tm,x in Celsius the value for DAT was scaled by: DAT,x =DAT,95(Tm,x + 273 95 + 273 ) (4.8) and an analogous expression was used for the value of DGC. 116 Parameters Value a3.4˚ A yc1.5˚ A k4.5 10−4eV/˚ A2 ρ50 b0.2 ˚ A−1 αAT 4.2 ˚ A−1 αGC 6.9 ˚ A−1 DAT,95 0.13150 eV DGC,95 0.17150 eV Table 4.5: Parameters used in the PBD model. Sample <Λ2>(˚ A) PEG6k-17% 0.45 PEG8k-15% 0.35 PEG8k-20% 0.33 PEG6k-20% 0.33 Humid fibers 0.18 Table 4.6: Standard deviation of the distance between consecutive base pairs used to calculated the S(~ Q) of each sample. Regarding the calculation of the theoretical S(Q) (sec. 3.4.1); a value of <Λ2>= 0.18 ˚ A, reported by Lavery et al. [106] , was used to model the melting of humidified DNA in previous works [7]. This value gave widths for the Bragg peak that were too small in comparison to the experiemntal value of the submerged samples. <Λ2>was increased to model the current data. The values used can be found in table 4.6. It is unlikely that the effects of the PEG can directly modify the standard deviation of the distance between base pairs along the molecule. More likely, the increase of <Λ2> accounted phenomenologically for other disorder effects, such as an increased variation of 117 the alignment of the molecules, when the fibers were submerged. The Debye-Waller factor, ∆, is a function of both < σ2>and <Λ2>and it is possible that the increased Bragg widths are at least partly due to thermal fluctuations that were not linear with temperature. However, without inelastic scattering data it is not possible to say whether the larger widths were due to increased structural disorder, increased thermal fluctuations, or a combination of both factors. The calculated S(~ Q) for each Twas fitted with eq. 4.4 to determine values for I0and γ as a function of Tthat could be compared to the experimental data. Fig. 4.17 shows a comparison of the experimental and theoretical integrated intensities and widths of the peaks for each sample along with the fractions of open base pairs calculated by calorimetry. The data are plotted as a function of reduced temperature, T/Tm, as there are differences between the temperatures recorded with neutrons and calorimetry due to different sample environments. Overall, the model matches all the data quantitatively. The agreement is excellent for the samples measured on WOMBAT. While the magnitudes for the model match the D19 data and the model does predict a linear increase in width with temperature, the model fails to adequately describe the gradient of the increasing width and of the integrated intensity with temperature below Tm. This may be an aspect of the modelling that does not fully capture the DNA phonon dynamics which, combined with the expanded energy integration on D19, are the possible cause of the increases in I0and γ. However, the magnitudes of the intensities and widths are matched and modelling may be regarded as satisfactory. Discussion The data are an improvement on the pilot study of DNA fibers submerged in PEG solutions [12]. The use of PEG solutions allowed the fibers to swell without losing their orientation. The neutron experiment was able to follow the evolution of the Bragg peak with temperature. The PBD model was able to describe the data, and the description was particularly good 118 for the WOMBAT data. The previous study showed that the transition is, to an extent, reversible [12]. In this sense, it is similar to a critical phase transition. The diffuse scattering in fig. 4.16 increases rapidly at the melting temperature. The PEG6k-17% and PEG6k-20% samples show departures from a monotonic increase in the diffuse scattering intensity close to the melting temperature. These measurements suffered from relatively large temperature fluctuations around the melting temperature, and it is likely that the recorded intensity variations are a result from the time-average of the concomitantly fluctuating diffuse signal. The measurements with better temperature stability at the melting transition did not show this anomalous intensity variations. These variations do not appear to be present in the integrated intensities of the Bragg peaks of the affected samples. A Bragg peak is due to coherent scattering from long-ranged, time-averaged order, while the diffuse scattering is more incoherent in nature. It may be that the diffuse scattering is dominated by the DNA dynamics, particularly of open base pairs, and its temperature dependence is driven by changes in the spectral weight. This hypothesis is consistent with the observation that D19, with the larger energy integration, shows a larger increase in the diffuse scattering. The PBD model uses one set of parameters for DNA and is able to satisfactorily reproduce all the data despite the change in confinement brought about by the osmotic pressure. This shows that the model is, within reasonable limits, insensitive to confinement of the DNA and establishes that the analysis shown in previous works [7, 8, 94] is sound. It is noteworthy that most of the parameters in table 4.5 are the same as those for the humidified fibers [7, 94] and for genomic DNA in solution [92]. The only differences lie in the values of DAT and DGC. Regarding the model, the unique effect of the submersion of the fibers in PEG solutions on the melting transition seems to be in adjusting the apparent dissociation energy of the base pairs. 119 before the melting temperature (T/Tm≈0.9) is observed. This looks significantly different that the steady (linear like) increase of the width of the PEG sample measured in D19 (fig. 4.17a). Discussion The experimental data presented in this section proves that the transition can be monitored equally well with neutron scattering in samples submerged in deuterated ethanol solutions with the advantage of the reduced incoherent scattering with respect to the samples with protonated PEG solutions. The increase in the diffuse scattering (quantified by the parameter A0plotted in fig. 4.21) is qualitatively identical to the data of PEG6K-17% which was also measured in D19. This indicates that the large increase of the diffuse scattering in the PEG6K-17% sample as T raises is not a sample-specific behavior and reinforces the idea that the magnitude of this increase is linked to the instrumental configuration. The double-step function seems to be in general less optimal to described the background of the ethanol samples. However, the fit of two samples (Na-66%-0.01 and Li-60%) is regarded as satisfactory and future attempts to reproduce the experimental data with the PBD model will be performed. It is expected that the parameters necessary to model the data of these samples will differ significantly from the PEG. The effective potential of the binding between the bases (related with DAT and DGC parameters) is affected by the repulsion between the DNA strands which is reduced by the presence of ions around the DNA. This electrostatic effect is strongly affected by the dielectric constant of the solvent which changes with the amount of ethanol added to the solution. Regarding the stacking of the bases, it is known to highly depend on the hydrophobic interactions [23] which must change in the presence of ethanol. For the Na-66%-0.01 sample the case is even more complex. A way to include the two peak melting in the relatively 126 (a) Na-60%-0.1 (b) Na-66%-0.01 (c) Li-60% Figure 4.22: Parameteres of the fit as a function of temperature for the ethanol samples: integrated intensity (I0, open blue circles) and width (γ, closed black squares) of the DNA Bragg peak placed at QH≈1.87 ˚ A−1; parameter A1of the double-step function (red triangles) which models the diffuse scattering. The dash black line represents the fraction of closed base pairs (fDS) calculated by calorimetry with eq. 2.6. 127 simple PBD model must be found. This would be a opportunity to test the limits of the model. Future experimental work will be focused on Li-DNA fibers since that will eliminate the A-contamination which may hinder the strength of the conclusions. Overall, the temperature dependence of the ethanol samples is consistent with previous data but shows some specifities that, we believe, justify further experiments and data analysis in these kind of samples. 128 Chapter 5 Widom-601 investigated by SAS 5.1 Room temperature study The bending and flexibility of DNA are of critical importance for many of its biological functions like gene regulation, protein-DNA interactions and DNA packing in viruses and eukaryote cells. However the actual magnitude, nature and origin of DNA flexibility is still an open problem. Kahn has reviewed recently experimental works on bending and twisting of DNA which used DNA ring closure, atomic force microscope and optical tweezers methods [107]. Discrepancies in the results of the different techniques showed that the flexibility of DNA is far from being understood [107]. The magnitude of the flexibility of DNA is usually accounted for by the persistence length (lp) which, within the Kratky-Porod model (section 3.4.2), is defined as the characteristic length in the correlation of the direction of the segments that describe the polymer. The lp of DNA was initially thought to be ≈500 ˚ A which would imply that DNA is hard to bend over shorter distances. However recent cyclization experiments [108], fluorescence resonance energy transfer measurements [109] and small angle X-ray scattering [110] performed on short 129 Figure 5.1: The 145 base-pair sequence investigated. The fragment in the rectangle is the strong positioning element, characteristic of this sequence. The TA fragments in red are the possible kink positions considered in the model. chain DNA revealed that DNA is likely to bend spontaneously over much shorter distances than 500 ˚ A. The worm-like chain model is a continuous version of the Kratky-Porod model and has been widely used for describing long chain DNA. However, the previously mentioned studies suggest that the worm-like chain may not be applicable to short chain sequences. Also, these studies point to the possibility that the persistence length depends on the length of the DNA. The close-packing of DNA inside the cell nucleus is a particular interesting event in which the flexibility of DNA is key to the biological function. The Widom-601 sequence, shown in fig. 5.1, has a strong histone positioning fragment which has great affinity to wind around a histone octamer to form a nucleosome which is a essential step of the packing of the genome in the cell nucleus. Crick and Klug tried to address the mechanism behind the considerable folding the DNA undergoes to form the chromatin. They showed in a pioneering study that DNA can form sharp kinks without a major disturbance of its structure [111]. Indeed, Kinks have been 130 found in the structure of short DNA chains wrapped around a nucleosome [112] but Crick and Klug also hypothesized that kinks could occur in solution. This hypothesis was never definitively confirmed. The Widom sequence has been previously studied under the effects of the strong interactions with histone proteins, [13] or attached to gold nanoparticles [110]. Investigation of the Widom sequence free in solution may provide the answer to the question of whether some intrinsic mechanical and/or geometrical properties of DNA are responsible for the strong positioning effect. The fundamental dilemma is whether the wrapping of DNA in nucleosomes requires a very high elastic energy, as the worm-like chain model suggests, or whether there is a sequence-dependent feature of DNA, like a enhanced local flexibility at the positioning site, that could explain or favour the positioning effect. Therefore the aim is to study DNA molecules containing the Widom sequence dissolved in solution. Small angle scattering can probe the shape of the molecules dispersed in the solution and, when used with an appropriate model, the geometry and flexibility of the molecules can be estimated. 2H2O-based solutions of Widom-601 DNA molecules were prepared as described in sec. 2.1.2. Neutron and X-rays small angle scattering (SANS and SAXS respectively) data of these samples were recorded and reduced as described in previously (sec. 2.5.2, 2.4.1, 2.4.2 and 2.5.3). The use of the two techniques gave independent and complementary data. SAXS gives a larger signal from a much smaller mass of DNA but X-rays are well-known to damage DNA during long exposures. X-ray damage can hinder the experiment but it can also be used as a validation of the analysis from undamaged-DNA data as it will be shown below. Neutrons are non-ionizing radiation and the damage they cause to the sample is negligible. However, since the available fluxes are many orders of magnitude smaller, a greater mass of DNA is needed to obtained a usable signal. Figure 5.2a presents the SANS and SAXS curves (I(q)) at room temperature. Fig. 5.2b shows the corresponding pair distribution function (P(r)), calculated as described in sec. 2.5.2. 131 (a) (b) Figure 5.2: a) SANS and SAXS data at room temperature; b) their corresponding P(r). The P(r) found by both techniques is qualitatively similar but there are some discrepancies. These are due to the differences in scattering length for neutrons and X-rays which arise from the different interaction mechanism of both radiations with matter (sec. 2.3.2). X-rays are more sensitive to heavier elements since the scattering length for them is proportional to the number of electrons in the atom. For neutrons hydrogen (which has a negative scattering length) has the highest contrast with the deuterated solvent and therefore the neutron data are more sensitive to the distribution of hydrogen in the sample. The two data sets show peaks around 20 ˚ A. For the X-ray data the peak is related to the phosphates in the outside of the double helix which are 20 ˚ A apart. The DNA has many protons distributed along its structure, thus for short distances neutron scattering of DNA is well approximated by the scattering by a bulk cylinder with a diameter of 20 ˚ A. Both P(r) curves show a rather flat region between 100 and 140 ˚ A. For r > 140 ˚ A the P(r) decrease steeply until they reach a plateau from 300 to 390 ˚ A before going to 0 for r > 400 ˚ A . The oscillations in the 300−390 ˚ A range in the SAXS data may be an artefact due to truncation in the measured Qrange which entails missing Fourier components in the P(r) calculation. However, the plateau is probably a real feature since it appears in both sets of data. The calculation of P(r) using the structure factor is a well-established procedure, which is based on a precisely defined mathematical connection between the functions (sec. 2.5.2). However, deriving the shape of the scattering molecules from P(r) is not an unambiguous 132 Figure 5.3: Representative examples of the output of the DAMMIF program. The dummy atoms show the estimation of the most likely shapes of the DNA in solution. process. The DAMMIF program [113], included in the ATSAS package, was used as a first step. DAMMIF starts from the P(r) function and uses simulated annealing to find the shape of a set of dummy objects which reproduce the P(r). DNA can have a great variety of conformations in solution and multiple runs lead to different final shapes. DAMMIF converges to either strongly curved structures or branched solutions when the P(r) shown in fig. 5.2b is studied. Fig. 5.3 shows representative examples of both cases. The in situ UV-Vis measurements collected in the SANS sample (sec. 2.4.1) ensures that the molecules were not partially denatured at room temperature. Therefore branching from individual molecules is not expected. The DAMMIF solution could still be explained if the sample contains a mixture of weakly curved and sharply bent molecules. In this case, the DAMMIF results would be due to a superposition of both conformations. The ab-initio shape reconstruction that DAMMIF used is not conclusive because it does not include a priori knowledge of the molecular properties. In order to extract further information from the scattering data a theoretical model was developed. An extension of the Kratky-Porod model ([96] and sec. 3.4.2) was used to analyze the P(r) curves. The model describes the conformations that the backbone of the DNA can adopt but not the internal structure of the molecule. A schematic of the model used can be 133 Figure 5.4: Schematic of the extended Kratky-Porod model used. The top part shows how the base pairs and segments were numbered and the bottom shows the definition for the bond and torsional rotation angles. found in fig. 5.4. The model describes a single DNA molecule as consisting of N+ 1 objects representing base pairs. They are separated by Nsegments of length a= 3.34 ˚ A which is the average base pair distance in B form DNA. The bond angles between the segments connecting the pairs may vary at each base pair. The local bending angle at site n, between segments n−1 and n, is θn. Torsional rotation is accounted for by means of a second set of angles, Φn, giving the dihedral angle between the plane containing segments n−1 and n and the plane containing segments nand n+ 1. The model allows to compute a Hamiltonian which accounts for the thermal fluctuations by means of the bending and torsional energy. The Hamiltonian is given by: H= N−1 X n=1 Kn[1 −cos(θn−θ0n)] + N−1 X n=2 Cn[1 −cos(Φn−Φ0n)] (5.1) where θ0nand Φ0nare local equilibrium values for the bending and torsional angles which can be different from zero, Knand Cnare constants related with the bending and torsional energy. Dimensionless variables were used in the calculations with the model. Distances were measured in units of a, and temperature was expressed in energy units relative to kBT 134 at room temperature. Thus T= 1 gives the properties of DNA at room temperature. For any given conformation of the model a theoretical P(r) can be determined by putting a unit scattering center at each base pair position. This is a good approximation for the SAXS data because the X-ray scattering from a base pair is dominated by the phosphorous atoms whose contribution (for r > 40 ˚ A) can be effectively mapped onto the center of the base pair. Considering the base pair as a unit scattering center is a worse approximation for the neutron data because neutrons are more sensitive to the distribution of protons which is much more homogeneous throughout the molecule with respect to the phosphorous atoms. Therefore the theoretical P(r) were compared to the SAXS data which, in addition, have better signal to noise ratio than SANS. The data were first modeled with the classical Kratky-Porod model which has Cn=θ0n=0 and assumes Kn=K=constant for every segment. In this situation the persistence length is lp=Ka. A persistence length of 500 ˚ A corresponds to K= 150. Fig. 5.5 shows a comparison between the experimental data from SAXS at room temperature and the result of the calculation of P(r) with these parameters (black line). This calculation has a very poor resemblance to the experimental data. The model gives a far better agreement if lp is decreased to 60 ˚ A. However, such a short persistence length seems fairly unrealistic. If the molecules were single stranded this persistence length could be adequate but the in situ UV-Vis absorption measurements performed confirmed that the sample was in helical form at room temperature. This suggests that, at least for short molecules (145 bp molecules), DNA cannot be modeled as a homogeneous Kratky-Porod polymer which agrees with the conclusions of the cyclization experiments [108]. It is not possible to perform a refinement of the model with all the parameters free because the parameter space is too large. A two-step process was adapted to circumvent this difficulty. First, a significant sample of geometric conformations able to reproduce the experimental P(r) was found. Then, parameters able to generate these geometrical conformations when the model was thermalized were explored. Monte-Carlo simulations were use to generate a large number of random conformations 135 (a) (b) Figure 5.8: (a) In situ UV-Vis absorption as a function of temperature. (b) P(r) from SANS at 25 and 79 ◦C. respect to the center of the molecule. For the SAXS/SANS experiment and for the model the two ends of the molecule are indistinguishable, therefore the 57 and 88 sites are almost equivalent. This is consistent with the fact that models with the kink at n= 57 give also good results. Wherever the kink was placed, the best agreement with the experiment was found with θK= 95 ◦in good agreement with the kink angle predicted by Crick and Klug [111]. The scattering from the DNA solution containing the Widom sequence was measured in function of temperature with in situ UV-Vis spectroscopy as described in previous chapters (sec. 2.4.1). Temperature-dependent data will be discussed extensively in the next section but it is interesting to highlight here some aspects of the data which reinforce the conclusions of the study with the model. Fig. 5.8a displays the UV-Vis absorbance of the sample in the 260 nm line which is usually used as reference to follow the unstacking of the base pairs due to temperature [116]. Fig. 5.8b shows a comparison of the P(r) of the SANS data at 25 and 79 ◦C . P(r) clearly changes due to the increase in temperature, it increases in the range 80 to 200 ˚ A and decreases to almost 0 for values greater than 300 ˚ A. The UV-Vis data show that around 20% of the base pairs are opened at 79 ◦C. The changes observed with respect to room Tare 142 related with the onset of the melting transition and an increase of the thermal fluctuations of the molecules. For the SAXS data the measurements showed a dependence on the exposure time. This was not observed in the neutron data with similar exposure times. Fig. 5.9 shows three data sets, one at 23 ◦C and two at 70 ◦C. The three data sets were measured on 2 aliquots of the same sample. One aliquot was measured for one hour at room temperature to obtain the data set labeled as 23 ◦C. Then this aliquot was thermalized at 70 ◦C (with the beam shut down) and measured for another hour to obtain the data set labeled as ”70 ◦C, short exposure”. Therefore before recording the short exposure data the sample was exposed to X-rays for 1 hour. The second aliquot was measured for one hour at three different temperatures before being thermalized at 70 ◦C for measuring the data labeled as ”70 ◦C, long exposure”. Therefore, before recording the long exposure data the sample was exposed to X-rays for 3 hours. The short exposure data (red line in 5.9 ) agree qualitatively with the high temperature SANS data of fig. 5.8b, showing changes with respect to room temperature happening in a similar range of Qwith a similar magnitude. The long exposure data (blue line in fig. 5.9) are very different from both the short exposure SAXS data and the high temperature SANS data. It is believed that X-ray damage due to the relatively long exposure time is the cause. At X-ray fluxes as low as the one used in this study the main mechanism by which X-rays damage DNA is single strand breaking due to free radicals generated by absorption of the X-rays by the buffer [117]. Single strand breaking will significantly increase the flexibility of the DNA molecules which can explain the changes on the experimental P(r) as a function of exposure time. This problem is not present in the neutron data since neutrons are not ionizing radiation. A conformational search was repeated using P(r) from the long exposure data (blue curve in fig. 5.9). The matching of the average P(r) of the 103selected conformations to the experimental data was again satisfactory and much better than trials with the classic Kratky-Porod model, even if torsional rigidity was included (fig. 5.10a). Fig. 5.10b shows 143 Figure 5.9: The P(r) at 23 ◦C and 70 ◦C as a function of time of exposure to X-ray radiation. The short exposure data is the result of a measurement after the sample was exposed to Xrays for 1 h. The long exposure data is the result of a measurement on an identical sample after the sample was exposed for 4 h. an histogram of the θnfor the selected conformations. In comparison to the room Thistogram (fig. 5.6a) the histogram for these data shows many more sites in which θncan be large. Although there is still a gap between the large and small θnvalues, the distribution of θnis much more homogeneous than in the room T case. This can be explained by the single strand breaks caused by the X-ray damage which would increase the local flexibility dramatically and create a more continuous distribution of bending angles. The diagram on the right of fig. 5.10b still shows a maximum in the 90◦-140◦, therefore a kink seems to persist in these conditions. In summary, the analysis of the scattering data suggested the existence of kinked Widom601 DNA molecules in the solution at room temperature. The presence of a gap between the low and high bending angles near the center of the molecules, observed in the results of the conformational search, proves that an enhanced local bending flexibility of the DNA molecules is not enough to explain the scattering data. Complementary cryomicroscopy experiments [118], able to provide direct imaging, could perhaps confirm this result and validate further the kink hypothesis made by Crick and Klug. 144 (a) (b) Figure 5.10: a) Same as fig. 5.6a for the 103conformations that provide the best matching with long-exposure SAXS data. b) Black circles are the SAXS P(r) measured in a sample at 70 ◦C after a long exposures to X-rays; the red line is the average P(r) for the 103 conformations which provided the best match to the experimental data; the full black line shows the P(r) calculated with the polymer model with parameters: Kn= 150, θ0n= 0, Cn = 0; the dashed black line is the P(r) for the same model if one takes into account the torsional rigidity (Cn = 2,φ0n= 0). 145 The results suggest that, besides energetic effects in the interaction between DNA and histone, mechanical effects may contribute to positioning. A kink in DNA would localize the histone octamer relative to the DNA and contribute to the binding. This investigation can also contribute to the open debate on the length-scale dependence of the DNA persistence length. Intrinsic curvature effects average out for long DNA molecules in experimental studies. However, that is not the case for short molecules and this can result in a reduction in the observed experimental persistence length of short DNA molecules. 5.2 Temperature-dependent study It has long been known that the persistent length of DNA decreases as temperature rises [119, 120]. Theoretical efforts have attempted to link the temperature dependence of lp with the thermally-induced base pair openings. Models which do not include the openings predict that lpvaries as 1/T, which disagrees with experiments [120]. Theodorakopoulos and Peyrard have included fluctuation openings using a combination of the Kratky-Porod and the PBD models [15]. The DNA molecules were described with an inhomogeneous Kratky-Porod model with soft and hard joints corresponding to open and closed base pairs. Statistical information about the state of each pair was provided by the PBD model [9]. Such an approach can be used to study the sequence effects on local flexibility [121] which may have important biological consequences. Moreover, the link between fluctuational openings and local flexibility provides evidence that the dynamical character of DNA is very important for the description of the molecule, even at temperatures well below the melting transition. Scattering data were used to try to experimentally test this theory. The samples used in sec. 5.1 were heated and their temperature-dependent small angle scattering was recorded, with in situ UV-Vis absorption spectroscopy for the SANS experiment. SAXS data presented here was recorded in samples which were exposed to X-ray for a maximum of one hour so the effect of the radiation damage can be neglected. The lpof the molecules can be estimated by fitting the small angle scattering curves 146 with an appropriate model. Theoretical predictions of lpcan be computed as in [15] with the advantage that the sequence of short artificial DNA is known and so the calculation of the statistical conformations of the molecules with the PBD model includes no arbitrary parameters. 5.2.1 SANS Fig. 5.11a shows an example of the SANS curve of the DNA solution at room temperature. SANS data for the buffer solution, measured under identical conditions, are also shown. The signal from the buffer is featureless and the signal from the DNA appears mostly at low Q due to the significant size of the molecules (145 base pairs relates to a length of around 485 ˚ A). Fig. 5.11b shows representative examples of the SANS curves at low and high temperature. The most patent change with temperature is an increase of the magnitude of the intensity at large Qas temperature rises. Fig. 5.11c shows the mean intensity of the scattering for Q > 0.17 ˚ A−1for the DNA and over the whole Qrange for the buffer plotted as a function of temperature. The buffer follows the same trend as the sample, so the increase in the scattering is not caused by the DNA molecules but by temperature-related changes in the solvent. Fig. 5.11d show the representative curves normalized by the average intensity of the curve for Q > 0.17˚ A−1. Once the difference in level is accounted for the curves show a quite similar shape even at the highest temperature reached (97◦C) where the UV-Vis absorption indicates that around 90% of the base pairs are open (fig. 5.8a). With only 10% of the molecule in the helical form, the molecule is expected to be extremely flexible in comparison with the room temperature molecules. Although not immediately obvious, the DNA signal does change with T. Fig. 5.12a shows the result of dividing the data at each temperature by the data at 15 ◦C . The divided data were fitted with straight lines. The gradients of the lines clearly change with T. Fig. 147 (a) (b) (c) (d) Figure 5.11: a) SANS curve of the DNA solution and of the buffer the DNA was dissolved in at room temperature in log-log scale. b) Representative SANS curves of the DNA solution at different temperatures in log-log scale. c) Value of the average intensity for Q > 0.17˚ A−1for the DNA sample and over the whole Qrange for the buffer as a function of temperature. d) Same curves of panel b) normalized by the average intensity of the curve for Q > 0.17˚ A−1, error bars were removed for the sake of clarity. 148 5.12b shows the gradient of the linear fits as a function of temperature alongside the UV-Vis absorbance of the DNA. The gradient increases with increasing temperature. This shows that scattering at larger Qs increases relative to the signal at low Qas temperature raises, therefore smaller length scales are more dominant in the average structure of the molecules. This could be due to a bending over short spatial lengths which is consistent with an increase in local flexibility of the molecules and thus with a decrease of lp. The fact that the U-Vis absorption seems to be correlated with the behavior of the gradient suggests that this effect is related with the pre-melting and melting of the molecules. Fits to the small angle scattering data as a function of the temperature were attempted using the commercial software package Sasview [122]. The model used was called ”flexible cylinder” and it describes the DNA molecule as a Kratky-Porod like chain (sec. 3.4.2) but the base pairs are represented as hard spheres (no overlap allowed) of radius Rinstead of dimensionless points. Thus the model accounts for self excluded volume effect when considering the conformations the molecule is allow to adopt and also for the effect of the radius of the DNA in the scattering pattern. The derivation of the fitting function is based on Monte-Carlo simulations which used this model. Pedersen and Schurtenberger fitted the simulations and used the results along with numerical approximations to derive a phenomenological expression of a scattering function for semiflexible chains (SWC(Q, L, lp)) which accounted for the excluded volume effect [123]. If the Lof the chain is significantly larger than the Rof the hard spheres the scattering can be expressed as a multiplication of two terms using the decoupling approximation [124], thus the scattered intensity from a DNA solution is: IWC(Q, L, lp, R) = Ds[(SLDDNA −SLDsol)2SW C(Q, L, lp)PCS(Q, R)] + Ib(5.4) where Dsis an scaling factor proportional to the DNA concentration, SLDDNA is the scattering length density for the DNA molecule , SLDsol is the scattering length density for 149 (a) (b) Figure 5.12: a) Examples of the result of normalizing the SANS curves of different temperatures to the data at 15 ◦C along with the linear fits (red lines). b) Slope of the linear fit to the normalized data and absorption of the sample as a function of temperature 150 (a) (b) Figure 5.13: Examples of the fit to the SANS data at 15 ◦C and 97 ◦C. a) Intensity vs Qin log-log scale. b) Experimental P(r) and P(r) of the fits, they have been shifted vertically for the sake of clarity. the solvent, Ibis a constant background, SWC(Q, L, lp) is described in [123] (section Method 3 with excluded volume) and SCS is the scattering function from the cross section of a rigid rod [125]: SCS(Q, R) = [2J1(QR) QR ]2(5.5) where J1is a Bessel function of the first kind. The instrumental smearing for SANS was accounted for by using dQ values for each Qwhich represented the standard deviation of Gaussian functions and were calculated as explained in [46]. The SLD for the solvent for neutrons (SLDsol,N ) was fixed to 5.754×10−6 ˚ A−2, the value of 2H2O[126]. Rwas fixed to 10 ˚ A and Lto 485 ˚ Awhich is reasonable for DNA molecules of 145 base pairs in solution. Dswas fitted at room temperature, the value found was 58.23 ±9.26. This value was fixed for the fit at other temperatures. Three parameters were fitted at every temperature lp,SLDDNA,X (SLD of DNA for X-rays) and Ib. 151