Liquid Crystal Phases of RNA Mononucleosides

Transcription

1 University of Colorado, Boulder CU Scholar Undergraduate Honors Theses Honors Program Spring 2018 Liquid Crystal Phases of RNA Mononucleosides Emily Hayden Follow this and additional works at: Part of the Biochemistry Commons, Biological and Chemical Physics Commons, Biophysics Commons, Condensed Matter Physics Commons, and the Optics Commons Recommended Citation Hayden, Emily, "Liquid Crystal Phases of RNA Mononucleosides" (2018). Undergraduate Honors Theses This Thesis is brought to you for free and open access by Honors Program at CU Scholar. It has been accepted for inclusion in Undergraduate Honors Theses by an authorized administrator of CU Scholar. For more information, please contact

2 Liquid Crystal Phases of RNA Mononucleosides by Emily Elizabeth Hayden A thesis submitted to the Faculty of the Honors Program of the University of Colorado in partial fulfillment of the requirements for the degree of Bachelor of Arts with Honors, Department of Physics Defended 03 April 2018 Examining Committee: Dr. Noel Clark, Department of Physics (Thesis Advisor) Dr. John Cumalat, Department of Physics Dr. Roy Parker, Department of Biochemistry

3 Abstract Deoxyribonucleic Acid (DNA) can form columnar liquid crystal phases in solutions of both short strand, base-pair oligomer solutions, and in solutions of single DNA Nucleoside Tri- Phosphates (dntp), the molecular constituents that make up helical DNA. The spontaneous phase transition to columnar liquid crystals by the dntps occurs without the necessity of the sugar-phosphate backbone of helical DNA, and exhibits key structural elements of biologic nucleic acids including long-range columnar stacking of base-pairs and Watson-Crick selectivity. This spontaneous increase in structural complexity is useful when discussing liquid crystal formation as relevant to the increasingly complexity of prebiotic life. Ribonucleic acid (RNA) and its nucleoside triphosphates (rntps) are the primary focus of this work, and they are closely related to DNA and the dntps discussed above. RNA differs from DNA in that, rather than containing a deoxyribose sugar, it contains a ribose sugar, which has two hydroxyl groups. These hydroxyl groups make the RNA less stable in solution because of its propensity for hydrolysis. This lack of stability makes RNA difficult to work with, but because it is considered an early precursor of DNA, it is interesting to study. This work is focused on the liquid crystals formed by the complementary rntps Cytidine Triphosphate (rctp) and Guanosine Triphosphate (rgtp). When placed into a solution, these molecules are able to bond with another to form base-pairs. The base-pairs may then stack on top of one another to shield their hydrophobic center from the surrounding solution. These stacks can then orient into a columnar LC phase, where this self-assembly further promotes the stabilization of the aggregates. i

4 Acknowledgements Thank you to all in the SMRC center at University of Colorado Boulder for help and guidance during this research project, especially Noel Clark, Greg Smith, Alexandra Duncan, and Adam Green. This work financially supported by NSF Biomolecular Materials Grants DMR and DMR , and NSF MRSEC Grant DMR XRD made possible by NSF MRSEC Grant No. DMR and DMR ii

5 Table of Contents Abstract... i Acknowledgements... ii Chapter 1 1.1) Introduction to DNA and RNA...2 DNA structure...2 RNA structure...5 Liquid Crystal Ordering of RNA and DNA...6 G-quartets and their Liquid Crystal Phases...7 RNA World Hypothesis ) Introduction to Liquid Crystals...9 Columnar Phase...11 Chapter 2 2.1) Materials and Preparation ) Polarized Light Microscopy (PLM)...13 Principles...13 Optical Textures of LCs...16 Nematic LCs...16 Columnar LCs...17 Birefringence...18 Microscopy Procedures ) X-ray Diffraction (XRD)...24 Principles...24 Diffraction Procedures...30 Chapter 3 3.1) Microscopy Data and Analysis...32 Birefringence Sign...32 Observed Phases...34 Phase Diagram ) X-ray Diffraction Data and Analysis...38 XRD Observations...38 iii

6 Chapter 4 Conclusions...45 References...46 Appendix I) Apparatus and Sample Information... A-i II) ratp and rutp Mixtures... A-i III) XRD Structural Summary... A-ii IV) Laue Diffraction... A-xi V) Concentration Calculation... A-xxii iv

7 List of Figures 1.1) DNA Helical Structure ) DNA Watson-Crick Base-Pairing ) DNA Nucleoside Triphosphates ) RNA Nucleoside Triphosphates ) A-form and B-form helices ) G-quartet Structure ) G-quartet columnar LCs ) Phases of matter ) Lyotropic Chromonic LC Structures (LCLCs) ) Columnar phase formed by discotics ) Index Ellipsoids ) Schlieren Textures ) Focal Conics ) Michel-Levy color chart ) Focal Conic Diagram ) Refractive Indices ) Sealed-cell diagram ) Diffusive cell ) Bragg Diffraction ) Hexagonal Lattice ) Unit Cell Hexagonal Lattice ) q 2 v. Concentration Slope Plot ) Theory Plot of GC base-pairs and G-quartets ) Flame-sealed capillary diagram ) Focal conic rotation ) Birefringence ) rctp+rgtp Phases ) Phase Diagram ) Composite WAXS ) Composite WAXS close-up ) Diffraction plot peak ) Theory vs. WAXS data ) SAXS v

8 3.10) WAXS rgtp 867 mg/ml III.1) Hexagonal Lattice Area... A-ii III.2) Unit Cell Area... A-iii III.3) Inverse Lattice Characteristic Vectors... A-iv III.4) Basis Vectors of Reciprocal Lattice... A-iv III.5) Periodicity of Column Spacing... A-v III.6) Unit Area... A-vi III.7) Column Spacing... A-vii III.8) Area of Parallelogram Derivation... A-vii III.9) Inverse Lattice Area... A-ix III.10) Plot of q 2 vs. concentration... A-x IV.1) Scattering arrangements... A-xi IV.2) Laue Diffraction... A-xii IV.3) Relationship between q-space vectors... A-xiv IV.4) Unit cell... A-xiv IV.5) 1D system... A-xvi IV.6) Unit cell in q-space... A-xvi IV.7) Body-centered Cubic Lattice... A-xvii IV.8) Face-centered Cubic Lattice... A-xvii IV.9) Face-centered Rectangular Lattice... A-xviii IV.10) Incoming and outgoing light... A-xix IV.11) Rectangular lattice as 2D unit cell... A-xxi vi

9 Chapter 1 Introduction Spontaneous molecular self-assembly due to columnar liquid crystal formation is of interest for fundamental biological materials, as it provides a framework for studying the increasing complexity of primordial molecules. Prior research has shown that long-strand DNA as well as its short-chain oligomers exhibit this phase transition [1, 2]. In addition, earlier work by our group has found that DNA monomers also exhibit the transition to columnar LC lattices, even in the absence of a sugar-phosphate backbone [3]. Because RNA is often considered the biological precursor of DNA, if its monomers also exhibit this selective self-assembly, it will advance our understanding of a pathway by which simple biological molecules may have increased in complexity. Because of the similarity between DNA and RNA NTPs (rntps), and the success in finding columnar liquid crystal phases in mixtures of dntps, the formation of similar liquid crystal phases in rntp mixtures is expected. Here the self-assembly behavior of these rntps is investigated by exploring aqueous mixtures of complementary rntps (rctp and rgtp, and ratp and rutp) for liquid crystal ordering. The observation of a columnar phase in these mixtures would serve to indicate that they are potential candidates for exploring the effect of liquid crystal ordering on self-assembly and ligation, without the need for polymerization. The remainder of this chapter provides background information on DNA and RNA, as well as the specific NTP monomers studied, followed by a discussion of liquid crystals. Chapter 2 is a discussion of the materials used in experimentation, as well as theoretical background for X-ray diffraction and polarized light microscopy analysis. Chapter 3 is a description of the data acquired, as well as an analysis of the data. Chapter 4 provides a summary of this work. 1

10 1.1) Introduction to DNA and RNA 1.1.1) DNA Structure Deoxyribonucleic Acid (DNA) is a fundamental building block of life. Within living cells, it takes the form of a double helix. The two strands making up the helix are right-handed, and, if they are uncoiled, their structure can be seen to be made up of nucleotides, which are composed of: a sugar, a phosphate group, and a base (Figure 1.1). Figure 1.1: The right-handed, double-helix structure of DNA. Each strand is composed of nucleotides, which pair as complementary bases to form the backbone of the DNA. The DNA bases are Adenine (A), Guanine (G), Cytosine (C) and Thymine (T). These bases bond with one another to form base pairs, with A bonding to T, and C bonding to G. This pairing is known as Watson-Crick pairing (Figure 1.2). 2

11 Figure 1.2: Watson-Crick pairing of the DNA bases, with Adenine and Thymine as one complementary base pair, and Cytosine and Guanine as another. This bonding of the base pairs forms the structural backbone of the DNA helix [4]. Adenosine and Guanine are purines, while Cytosine and Guanine are pyrimidines, which are smaller than the purines. The base pairs in this work are Mononuucleoside Triphosphates (NTPs). NTPs are formed by the four bases described above, A, T, C, and G, with a sugar and a triphosphate bonded to each base. The DNA NTPs (Figure 1.3) datp, dttp, dctp and dgtp; while the RNA NTPs (Figure 1.4) are ratp, rutp, rctp and rgtp. NTPs were chosen because of their increased solubility in aqueous solutions, and due to the ligation potential provided by the triphosphate tail [5]. 3

12 Figure 1.3: DNA Nucleoside Triphosphates (dntps). The center of each molecule is highly hydrophobic, while the sugar and triphosphate tails are hydrophilic. These aspects of the dntps result in stacking of their complementary base pairs. Figure 1.4: RNA Nucleoside Triphosphates (rntps). They differ from the dntps (figure 1.3) in the extra OH group attached to each sugar. Additionally, RNA is made up of Uracil in place of Thymine. 4

13 These NTPs can be modeled as flat disks with a hydrophobic center, and with the soluble sugar and phosphates on the ends of the molecule, which forms a hydrophilic ring around this center. This structure results in the helical arrangement of DNA, as well the shielding of the hydrophobic center from contact with the surrounding aqueous solution ) RNA Structure Ribonucleic acid (RNA) and its nucleoside triphosphates (rntps) (Figure 1.4) are the primary focus of this work, and they are closely related to DNA and the dntps discussed above. RNA differs from DNA in that, rather than containing a Deoxyribose sugar, it contains a Ribose sugar, which has two hydroxyl groups. These hydroxyl groups make the RNA less stable in solution because of their propensity for hydrolysis [6]. This lack of stability makes RNA difficult to work with, but, because it is considered an early precursor of DNA, there is a strong motivation to study it, specifically with regards to the RNA world hypothesis, which suggests RNA as the initial molecule for storing genetic information and catalyzing chemical reactions in cells [7]. Another difference from DNA is that RNA does not contain Thymine this is replaced by Uracil (U), which differs from Thymine only in that it lacks a methyl group. These differences have a pronounced effect on the shape of the RNA double helix. RNA tends to have a higher tilt of its bases as well as a shorter rise for the base pairs, and is generally in an A-form helix, in contrast to DNA which is able to form A, B or Z form helices, depending on formation conditions (Figure 1.5). 5

14 Figure 1.5: On the left is an example of an A-form helix, the form usually taken by RNA. Compared to the B-form on the right, one can see the higher-base tilt for the A-form, as well as a shorter rise for the base pairs. This difference in form for RNA is due to the presence of hydroxyl groups and the presence of Uracil and its missing methyl group, rather than Thymine [image courtesy of ATD Bio] ) Liquid Crystal (LC) ordering of RNA and DNA It has been shown in prior studies that short strands of DNA (as small as 4 base pairs) are capable of forming columnar liquid crystal (LC) phases in solution [8]. This self-assembly occurs due to the following steps: pairing of oligomers into duplexes, stacking of these duplexes into linear aggregates, and finally, condensation into LC domains through orientational and positional ordering [9, 10]. The stacks formed by the DNA oligomers lack the chemical bonds to form complete DNA helical strands; however, they share the structure and stacking of said DNA duplexes. This suggests liquid crystal ordering as a template for base-pair stacking and selfassembly, and thus for building larger, more complex molecules. To further analyze the LC behavior of DNA and its constituent parts, experiments have been performed that show that un-bonded DNA NTPs (dntps) placed into solution will bond with their complementary base (A-T, C-G) to form base-pairs, which then stack on one another to form columns that exhibit liquid crystal behavior [3]. This stacking occurs because the 6

15 hydrophobic cores of the molecules exclude water, while the phosphates and sugars of the base pairs, which are hydrophilic, remain in contact with the aqueous solution. The columnar liquid crystal phases formed by dntps are defined as lyotropic due to the strong concentration dependence of their formation. Within the LC domains that are formed, long-range ordering enhances the stability and concentration of end-to-end molecular contacts [3]. The LC ordering provides selectivity, molecular organization, and fluidity, which in turn promotes the polymerization of longer strands. The polymerization results in increased stability of the LC ordering, and a positive feedback occurs. This feedback is termed liquid crystal autocatalysis (LCA), and has been studied in depth in earlier work [3]. In addition to columnar liquid crystals formed by complementary DNA NTPs, Guanosine Triphosphate, GTP, can also form columnar LCs, due to the formation of G-quartets ) G-quartets and Their Liquid Crystal Phases The behavior of guanosine monophosphate in solution is to hydrogen-bond with itself to form tetramers known as G-quartets (Figure 1.6), which can then stack on one another to form tetraplex columns that exhibit columnar LC behavior (Figure 1.7) [11]. The ability of guanosinebased monomers to form G-quartets is applicable to the rgtp material used here. Because of its ability to pair with itself and self-assemble in LC columns, coexistence of a G-quartet columnar phase with a rctp+rgtp base-pair columnar phase is expected. However, determining which of these columnar phases tends to form at varying concentrations and temperatures is important to study, as either could serve as a template for ligation. 7

16 Figure 1.6: G-quartet structure formed when four rgtp molecules bond to one another by eight H-bonds, forming a highly stable tetramer. Figure 1.7: After G-quartets have formed, the flat assemblies are capable of stacking on one another as shown on the left. These stacks can be modeled as columns, which in turn order into a columnar lattice (right) ) RNA World Hypothesis The RNA world hypothesis states that DNA and protein-based life was preceded by more simplistic forms of RNA-based life. This hypothesis is based on the fact that RNA contains the 8

17 genetic sequences later present in DNA, and thus is generally considered its precursor [7]. Because of this hypothesis of RNA as an important precursor to DNA and increasingly complex life, the self-assembly of rntps into increasingly complex columnar liquid crystals is a candidate for ligation of RNA strands. This self-assembly could serve as a template for the RNA world and the origins of life. 1.2) Introduction to Liquid Crystals Liquid crystals (LCs) are partially ordered but still fluid phases of matter that occur between the liquid and the crystal phase. In the liquid phase, a material is isotropic, and its molecules have no orientational order in any direction of space. In contrast, a solid, crystalline material is entirely anisotropic and has both positional order and molecular orientational order. The LC phase between these two phases has attributes of both that make it a unique, interesting phase of matter. Liquid crystals exhibit a fluid-like randomness in at least one spatial direction, while also exhibiting orientational and/or positional order (Figure 1.8). Figure 1.8: Phases of matter, increasing in ordering from left to right. The rods are representative of asymmetric molecules. In an isotropic liquid (a), the molecules have no order. In a liquid crystal (b), there is some orientational and/or positional ordering, but it is not fully anisotropic. In a solid crystal (c), there is total anisotropy, and positional and molecular orientational ordering. 9

18 The liquid crystals discussed in this paper can be additionally classified per their morphology. Liquid crystals whose formation is dependent on temperature are classified as thermotropic, while liquid crystals that have a formation dependence on both temperature and concentration are lyotropic LCs. In the case of thermotropic LCs, if the temperature of the material is too high, the phases will melt and the material will be an isotropic liquid. On the other hand, if the temperature is very low, the material will have a high level of order, and will be solid. A similar dependence occurs for concentration: if the concentration of material in solution is too low, the molecules will not be capable of interacting due to their large separation distance and the formation of liquid crystals will not occur. If the concentration is too high, the material will be solid and not form LC phases as the molecules are too close to slide along one another. The temperature and concentration ranges at which liquid crystals form is unique to the molecule studied. The materials discussed in this paper are classified as lyotropic because of their strong concentration dependence, as well as their phase dependence on temperature. In addition to morphology classifications, there are varying types of liquid crystals, defined according to the level of order. Nematic (N) liquid crystals have the least amount of order, while Columnar (C) liquid crystals, the primary type of LC relevant to this work, exhibit higher order than nematics. The overall order of liquid crystals, is defined primarily by the molecular degree of ordering (Figure 1.9). 10

19 Figure 1.9: Lyotropic Chromonic Liquid Crystal Structures. In the Isotropic (I) phase (a), molecules are oriented randomly in solution, due to a concentration that is too low for liquid crystals to form, or due to a high thermal energy which also prevents ordering. If the concentration is high enough and/or the temperature low enough, the molecules begin to form chromonic aggregates, while still in the isotropic phase. Once the aggregates have grown to a point that their aspect ratio is large enough to break the isotropic tumbling symmetry, a nematic phase can form. In the nematic phase (b), the aggregates begin to grow, and end up with a uniform orientation throughout the phase domain. Finally, in the columnar phase (c), these uniformly oriented aggregates form a 2D lattice either hexagonal or square [12] ) Columnar Phase The liquid crystal phase that exhibits the highest level of ordering is the columnar phase, which is also the primary phase of interest in this work. The columnar phase can occur in lyotropic systems, like those discussed here, or in thermotropic systems. Materials in the columnar LC phase exhibit two-dimensional ordering, and can be simply modeled as rods or disks that stack on one another to form liquid-like columns that make up a 2D lattice, generally a square or hexagon. 11

20 Figure 1.10: Thermotropic hexagonal columnar phase formed by discotics (a) and lyotropic hexagonal columnar phase formed by cylindrical micelles (b), shown from above in a 2D plane normal to the cylinders [13]. Although these columns are highly ordered and maintain a 2-dimensional structure, they differ from crystalline structures by maintaining some degree of disorder the columns can slide with respect to one another, which lends to their liquid-like behavior. This analysis of columnar LC phases is applicable to the base-pairs from by RNA NTPs, which can be modeled as flat disks which stack on one another to form columns (Figure 1.10a). This form stacking is energetically favorable because it protects the hydrophobic core of the molecules from the surrounding aqueous environment, while the hydrophilic sugar-phosphate tails remain in contact with the solution. Chapter 2 Methods and Materials 2.1.1) Materials and Preparation RNA Nucleoside Triphosphates (100 millimolar ATP, UTP, CTP, GTP) were purchased from GE Healthcare Life Sciences and Jena Biosciences, and were used for all experimentation. 12

21 The rntps were stored in the freezer until ready to use, at which time they were brought to room temperature, then mixed and centrifuged to maintain a constant concentration throughout the aqueous solution. Once a homogeneous liquid mixture was achieved, a desired ratio of the samples was placed into an Eppendorf tube generally a 1:1 mixture of the complementary base pairs. The tube was then mixed and centrifuged, again to ensure a homogenous mixture. Two methods of drying were then used to evaporate the water from the sample material. Vacuum drying was used to dry many of the samples. Mixtures prepared in the Eppendorf tubes were deposited onto cut and weighed glass slides, ~25x30 mm, and placed into a vacuum until the water had evaporated from the solution and solid material remained on the slide. To ensure complete evaporation of the water from the sample, the glass slides were then placed in covered petri dishes and placed in the refrigerator overnight. Once fully dry, the glass slide with the material deposit was weighed, then compared to the original weight of the slide to determine the mass, in milligrams, of solid material. Lyophilization was also used to dry mixtures. They were transferred from the Eppendorf tubes to small glass vials, then placed into liquid nitrogen to freeze. Screw-top lids were then placed over the vials such that air could still escape, and placed into a large jar and finally onto the lyophilizer. Once dried, vials of dry material were stored in the refrigerator until use. Once dried, the materials were used for Polarized Light Microscopy (PLM) experiments (Chapter 2.2), or X-ray Diffraction (XRD) (Chapter 2.3). 2.2) Polarized Light Microscopy (PLM) 2.2.1) Principles The RNA NTP molecules observed in these experiments are too small to be directly observed using polarized light microscopy (PLM); however, this method of microscopy can 13

22 provide information regarding the structural detail of the liquid crystal phases the NTPs form. Because of the intrinsic anisotropy of the NTPs, when white light enters the sample, it gains a phase difference. This phase difference results in visible light, known as birefringence. This birefringence provides information regarding the structure of the materials. PLM can also provide data regarding the concentration and temperature parameters that determine LC formation. When light interacts with isotropic material, the index of refraction of the material is constant, and thus its polarization is unchanged. On the other hand, anisotropic materials can change the polarization of incoming light because there are two or more different refractive indices perpendicular to one another within the material, which will affect the two perpendicular polarizations of light separately. Liquid crystals have this property because their organizational order and polarization varies according to which axis is being probed by the light. This changes the velocity of the light propagating through the material, resulting in birefringence, which can be seen in PLM [14]. The materials in this paper are uniaxial, in that they are composed of molecules that have a single optical axis and two principal refractive indices [6]. Such uniaxial materials can be defined according to the sign of their birefringence either positive or negative as birefringence is defined by the difference between the refractive indices, and can be seen in visible colour in the microscope (Equation 2.1). n = n e n o = n II n Equation 2.1: Positive birefringence occurs when the refractive index parallel to the optical axis (n II ) is the larger of the two, while negative birefringence occurs when the refractive index perpendicular to the optical axis (n ) is larger (Figure 2.1). 14

23 Figure 2.1: Index ellipsoids showing the signs of birefringence for uniaxial materials, with the optical axis along the z-axis. (a) is for positive birefringence and (b) for negative birefringence [3]. The ellipsoids are not representative of actual molecules; rather, they are imaginary surfaces that depict the orientation and relative magnitude of refractive indices in a crystal [15]. Because of this singular optical axis, rotating a sample around the axis does not change the optical behavior observed. The two refractive indices for the uniaxial material are defined as the ordinary index, no, polarization perpendicular to the optical axis, and the extraordinary index, ne, polarization parallel to the optical axis. These two refractive indices result in the splitting of the incoming beam of light, with each resulting beam having a different direction and velocity, and having perpendicular polarization vectors. These beams are re-combined by the polarizing microscope, and the interference between the beams results in a visible, birefringent image. Because of two refractive indices, there is a phase difference between the beams, governed by Equation 2.2, which produces an image. This image can then be used to determine the structure of the material being observed. δ = 2π ƛ (n e n 0 )d Equation 2.2: d is the distance traveled into the material and ƛ the wavelength. This phase difference results in the birefringence of the material that makes it possible to visualize its structure using microscopy techniques. 15

24 2.2.2) Optical Textures of Liquid Crystals The birefringence of a material is directly correlated to its molecular structure, and therefore symmetry can be evaluated using the method of optical microscopy. Preparing samples of RNA and DNA NTPs for visualization with the microscope is essential for determining the presence of liquid crystal phases in the sample, as well as for evaluating the morphology of the LC domains. Other methods of observation are then important to confirm these microscopy observations. There are many structures that can be observed using PLM, including crystalline and liquid crystalline structures. The phase of interest for this work is the columnar LC phase, with optical properties described below, with a short discussion of the Nematic LC phase included ) Nematic LCs Materials with Nematic LC domains that are placed between untreated glass plates tend to orient such that the director is parallel to the glass plates. If the orientation throughout the material lacks homogeneity, Schlieren textures, optical inhomogeneities that occur due to path length differences, will be observed when the sample is placed between crossed polarizers, as in PLM experiments. The brushes visible in Schlieren textures (Figure 2.2) correspond to the extinction position of the director field, where the director coincides with either the polarizer or analyzer [16]. Figure 2.2 represents these director configurations as well as values assigned to the strength of the defects (given by ±1 and ±1/2). The positive sign (+) means that when the polarizer is rotated, the brushes rotate in the same direction as the polarizer. The negative sign (-) means the opposite the brushes rotate opposite of the direction of polarizer rotation [16]. Nematic textures are not observed in the materials studied here, and will not be analyzed further. 16

25 Figure 2.2: Schlieren textures exhibited by nematic liquid crystals when placed between untreated glass plates. The values and signs of s correspond to the strength of the defect within the material and the direction of rotation of the brushes under a crossed polarizer [16]. More detail regarding the nematic liquid crystal phase and its general properties can be found in Chapter ) Columnar LCs Columnar LCs are the primary phase of interest for the rntps in this work due to the fact that they are formed by both G-quartets and G-C base-pairs. The phases formed by both can be modeled as flat disks that stack on one another to form columns (c and c.1.1.4). The presence of columnar LC phases can be confirmed from the presence of focal conics and/or fanlike textures (Figure 2.3) observed using PLM. The director of the liquid crystal is important to understand why focal conics and fan-like textures are formed. When the optical axis of the molecule is aligned parallel to the polarizer or analyzer, extinction occurs, and the sample appears black. When the director is at a 45⁰ angle to the polarizer or analyzer, the light transmitted is at a maximum. Additionally, the columns that make up the LC phase tend to bend over large distances. This bend results in the fan-like or circular extinction patterns, known as 17

26 focal conics (Figure 2.3). When the crossed polarizers are rotated over the sample, the alignment of the director will also change, and the extinction patterns will rotate. Figure 2.3: On the left is an example of a focal conic occurring due to a columnar LC phase in an evaporative sample of a random sequence DNA 12mer. On the right, the different possible columnar structures and the relationship the extinction points and the director (n(r)) and polarizer direction is illustrated on the right (image on right courtesy of Noel Clark) ) Birefringence As discussed in section 2.2.1, the rctp and rgtp mixtures are uniaxial, and the sign of their birefringence can be determined using PLM. The color of these materials is a function of the thickness of the sample, which is summarized by a Michel-Levy chart (Figure 2.4). To determine the sign of the birefringence of the sample, a portion with a fan-like or focal conic texture is necessary, and rotation of the sample will result in a rotation of the extinction lines of the fan-texture. This occurs because, as the sample is rotated, the alignment of its optical axis with the polarizer and analyzer changes (see section and Figure 2.3). 18

27 Figure 2.4: The Michel-Levy color chart shows that the polarization colors visible under the microscope can be correlated to the thickness and birefringence of the sample (image courtesy of Olympus Scientific Solutions). Once an appropriate texture has been found, the principles of the Michel-Levy chart can be used to determine the sign of the birefringence. A quartz wedge compensator is inserted above the sample, but below the objective lens of the sample, at a 45-degree angle with respect to the polarizer and analyzer. The wedge compensator is designed such that the fast optical axis of the quartz can be oriented either parallel or perpendicular to the fast axis of the sample. The path difference between the fast and slow wave-fronts that traverse the wedge is a continuously varying function of the wedge thickness. As the wedge is moved across the sample over the varying wedge thicknesses, a succession of interference colors is visible. As noted in section 2.2.1, positive birefringence occurs when the refractive index parallel to the optical axis (n II ) is the larger of the two, while negative birefringence occurs when the refractive index perpendicular to the optical axis (n ) is larger. In other words, the polarization of the fast wave is perpendicular to the optical axis when the birefringence is positive, and the polarization of the slow wave is perpendicular to the optical axis when the birefringence is negative. 19

28 When the compensator is placed over the sample, it is adjusted until the isotropic portion of the sample is the magenta/deep-pink tone that occurs at the boundary between the first and second order (Figure 2.4). If the portions of the fan-like textures that are perpendicular to the compensator are shifted blue, and the portions that are parallel are shifted orange, the sign of the birefringence is negative the slow wave is perpendicular to the optical axis. The incoming beam of light is split, and the velocity difference between the two beams is increased. Determination of the sign of the birefringence provides information regarding the orientation of the optical axis of the LC columns (Figure 2.5). Figure 2.5: The circles represent focal conics, formed by the presence of columnar liquid crystals. The brushes occur due to the orientation of the anisotropy of the liquid crystals (Figure 2.3). In these diagrams, the green cylinders represent a single column, while the arrow in the direction of n(r) represents the director of the column. In a), the larger of the refractive indices is the one along the long axis of the bases that compose the column, which corresponds to negative birefringence. In b), the larger refractive index is that along the length of the column, corresponding to positive birefringence. For the materials considered in this work, the larger refractive index is expected to be along the length of the disk that makes up the column of the liquid crystal, perpendicular to the director 20

29 (Figure 2.6). This is known for DNA from previous work [3], and occurs due to the higher polarizability along this axis, compared with the axis parallel to the director. Figure 2.6: The 3D model on the left is a DNA AT base-pair, and on the right, is a simplified model of this molecule. The arrows on the right represent the refractive indices of the molecule. The refractive index that runs along the length of the molecule, perpendicular to the optical axis, is the larger of the two due to its higher polarizability. Therefore, the sign of the birefringence will indicate the orientation of the columns composed of these disks, within the LC phase. If the sign of the birefringence is found to be negative, then the columns are oriented as shown in Figure 2.5a, and have a long-range ordering, as shown in Figure 2.3. If the sign of the birefringence is positive, then the columns are oriented as in Figure 2.5b, and the long-range ordering is not discernible using these techniques. The long-range order associated with negative birefringence is relevant to the discussion of liquid crystal assembly as a motif by which molecules may have become increasingly complex over long-ranges ) Microscopy Procedures Samples for PLM observation were prepared one of two ways depending on the observations of interest. To determine initial information regarding the presence of birefringence and phases, evaporative cells were made. 0.5μL of a sample was loaded on a cut-glass slide using a micropipette, ~25x30 mm, which was placed on the Instec mk1000 hot stage connected to the Nikon Metaphot microscope. To encourage development of LC domains, the stage was initially set to 5⁰C, and Argon allowed to flow over the sample and the slide to encourage water 21

30 evaporation from the material. The sample was observed as water evaporated, and images of birefringence and/or LC domains taken using a Nikon D5000 camera. Once the material was nearly dry, another 0.5μL of solution was added, and again water was allowed to evaporate from the sample, and birefringence was photographed. This process was repeated using 2μL total of material. This method was used to establish if mixtures exhibited birefringence due to the presence of LC domains, and to approximate concentrations at which phases occurred. For microscopy observations requiring increased control, stability, and accurate concentration calculations, non-evaporative cells were prepared. 30μL of material was dried onto a glass slide (~25x30mm) to obtain 2-3 mg of solid material. A drop of heavy mineral oil placed over the dried material to seal, and a controlled amount of water brought into contact with the sample under this oil seal (Figure 2.7). Figure 2.7: Sealed cells of specific temperature were prepared for use in PLM experiments. The mineral oil and epoxy-sealed glass prevented evaporation over time. Concentration was initially determined according to Equation 2.3, with more detailed calculations of the concentration performed according to the method detailed in Appendix IV. 22

31 V H2 O = ( 1 C 1 ρ ) M Equation 2.3: V H2 O is the volume of water (in milliliters) to add to the solution to obtain the desired concentration, C. M is the mass (in milligrams) of material on the slide, and ρ is set as 1800 mg/ml, the density of the rntps. The sealed, hydrated samples formed thin films under the oil layer, and the water pipetted onto the sample and below the oil diffused into the sample. This diffusion resulted in a concentration gradient in the sample, within which birefringence and phases could develop in a stable environment (Figure 2.8). Additionally, by making non-evaporative cells, multiple experiments on temperature, stability and phase development could be performed without destroying the sample and without significant water loss and drying. Figure 2.8: As water diffuses into the oil-sealed rntp sample, a concentration gradient occurs. In the above figure, the dark portion is isotropic, and is an area that is predominantly water. This excess of water results in a concentration that is too low for the formation of LCs. The concentration gradient that occurs due to the spreading of the water allows for the analysis of various phases. 23

32 2.3) X-ray Diffraction (XRD) 2.3.1) Principles The order (structure) of a material can be probed using X-ray diffraction (XRD) techniques. Diffraction is the elastic scattering of X-ray radiation off electrons in a materials structure, in this case liquid crystals. The wavelets scattered from the different atomic interaction sites recombine and result in constructive or destructive interference. The type of interference that occurs is dependent on the relative phase of the wavelet, which is determined by the atomic interactions in material. The amplitude of the wavelet is further determined by the spatial distribution of said atoms. Thus, diffraction probes the structure of a material at an atomic level. While X-ray diffraction is useful for determining the underlying structure of a material, it is important to note that the image produced is not a physical image of the sample, but is a 2- dimensional Fourier transform of its structure. This is because x-rays are generally unaffected by refraction, and therefore cannot be focused using a lens. To understand the theory behind XRD techniques, it is useful to review Bragg diffraction, then use the basic tenants of this method to explain how more complex structures are probed. Bragg diffraction can be understood by visualizing an X-ray that enters a planar crystal, and is scattered by those planes (Figure 2.9). For such a material that is made up of planes, constructive interference will occur when the Bragg condition is met (Equation 2.4). 2d sin θ = nƛ Equation 2.4: In this equation, d is the spacing between the planes, θ the angle of incidence, n is an integer value, and ƛ is the wavelength. This equation states that, for constructive interference to occur, the angle θ between the plane and the x-ray must result in a path-length difference that is an integer multiple (n) of the wavelength (ƛ) of the x-ray. For other angles, there will be some level of destructive interference that occurs, and the resulting wave will have a reduced amplitude [14]. 24

33 Figure 2.9: Bragg Diffraction. Two identical beams enter a crystalline solid, where each is scattered by different atoms within the materials. The beam that travels further into the material travels and extra length of 2d sin θ. When this extra length traveled is equal to an integer multiple of the wavelength of the incident light, there is constructive interference. When it is equal to some other value, there is destructive interference. Bragg diffraction is a powerful theory, but does not allow for analysis of non-planar crystalline arrangements. To analyze more complex crystalline and semi-crystalline arrangements, the concepts of Laue diffraction are useful. Laue diffraction is similar to Bragg diffraction in that it relates the ingoing and outgoing waves that are diffracted by a crystal lattice; however, Laue diffraction does not require a planar arrangement in the structure, thus, it can be used to analyze more complex arrangements (Figure 2.10). 25

34 Figure 2.10: Columnar liquid crystal, with a hexagonal packing structure. Complex crystalline arrangements such as this can be analyzed using XRD and Laue diffraction. From this, the spacing of columns can be determined [17]. The columns that form columnar liquid crystals pack into geometric, 2-dimensional lattices, often in a square or hexagonal lattice pattern. Simplifying these structures to 2D allows them to be defined according to characteristic vectors, by which all remaining points can be defined. Each scattering object within the lattice that is defined by these characteristic vectors is considered a scatterer incoming X-rays will be scattered by each point. Molecules that are arranged in planes scatter the incoming X-rays as described by Bragg diffraction, mentioned above, while more complex arrangements that are arranged in a geometrically ordered, but not planar fashion will scatter the x-rays according to Laue Diffraction. Laue diffraction is discussed in detail in Appendix IV; however, the result of this analysis is an equation relating q-space diffraction spectra to real-space distances within a lattice. For the LC samples considered here, the hexagonal or square lattice of the columnar phase results in diffraction peaks representing the column-column spacing. These peaks are given in q-space, which is in units of inverse Angstrom, which is representative of the spacing within the reciprocal lattice. To determine the lattice dimensions of the LC phase, it is necessary to convert from q-space into real-space (Equation 2.6). 26

35 q = 2π d Equation 2.5: Derived explicitly in Appendix IV, this equation describes how the real-space and reciprocal space values are related. This analysis allows the materials in this work to be analyzed using powder diffraction. Powder diffraction results in rings that are representative of the intercolumn spacing, because these samples are composed of a large number of microdomains. When the x-ray interacts with a powder sample, all of the diffraction peaks will be visible, and will be averaged into a ring because of the many microdomains that each have a different angle of orientation with respect to the beam. As noted prior, the diffraction peaks that result from XRD are reciprocally related to the separation between the molecules in the LC structure. For small spacing values, d, the angle of orientation is large, and will be the larger ring on the output image. Because the materials in this work can form either GC base-pair columnar lattices or G- quartet lattices, a theoretical model of expected behavior is important for comparing to XRD data. The generalized, theoretical model relating inverse area, q 2, and concentration, in mg/ml is derived explicitly in Appendix III. The model relates lattice area (defined by the area occupied by a single column) (Figure 2.11) and inverse area (in q-space) to concentration (Figure 2.12). 27

36 Figure 2.11: The shaded region within the hexagonal lattice is a 2D area, defined as the area occupied by a single column. As concentration increases, the area should decrease as the columns become closer to one another. Figure 2.12: The model derived in Appendix III relates the inverse area of the lattice in reciprocal space to the concentration. The slope of the line is dependent on l u, the unit length of the periodicity of bases within the aggregate, columnar stack, which is given by the large q-space diffraction peak of the XRD spectra; and m u, the unit mass of the bases within the stack, which varies according to the materials observed. Values for columns formed by GC base-pairs, or by G-quartets, can be plugged into the model to find the relationship between concentration and inverse area for each type of columnar LC (Figure 2.13). 28

37 Figure 2.13: The theoretically derived relationship between q 2 and concentration for columnar LCs formed by GC base-pairs is plotted in orange, while that for G-quartets is plotted in purple. Both lines suggest a linear relationship between inverse space and concentration, which means that, in realspace, concentration and area are inversely related. The model suggests that, regardless of whether the lattice is formed by GC base-pairs or G- quartets, as concentration increases, q 2 also increases. Referencing Equation 2.6, one can see that this suggests an inverse relationship between concentration and the area occupied by a column. This makes logical sense: as concentration increases, the lattice area should decrease as the columns are pressed closer to one another. Additionally, it suggests that GC base-pairs have larger q 2 values by concentration than do the G-quartets. Because the area and q 2 are inversely related, this means that the lattices formed by GC base-pairs have a smaller area than those formed by G-quartets. 29

38 2.3.2) Spectroscopy Procedures Information regarding the materials used can be found in Chapter 1.1: Materials and Preparation. Once material was dried using vacuum drying or lyophilization, it was carefully placed into pre-weighed quartz glass capillaries with dimensions x 90 mm (Figure 2.14). Figure 2.14: Flame-sealed capillaries used for XRD experiments. The rntp and water mixture of a specific concentration was placed in the bottom, with the remainder of the capillary filled with air. Capillaries were more concentration stable then cells. The capillaries were then placed into a low-speed centrifuge for a four-minute cycle. The centrifuged capillary was then weighed, and the measured amount of material in the capsule recorded. A specific amount of water was then added to the capillary using a micropipette to obtain an estimate goal concentration (Equation 2.6). 30

39 V H2 O = M s ( 1 c 1 ρ ) Equation 2.6: M s is the mass of the solid material, c is the desired concentration in mg mg, and ρ is the concentration of the RNA, also in. ml ml The hydrated sample was again centrifuged, then weighed to determine the actual concentration for the sample. The capillary was then flame sealed, and allowed to sit at room temperature overnight to encourage diffusion of the sample throughout the water, and to obtain a constant concentration throughout. A goal concentration was decided by comparison to the concentrations at which DNA NTPs were found to exhibit phases [3]. In addition, dntps and rntps are at 100% by volume at concentrations of 1403 mg/ml. Due to difficulty in completely removing water from the hydrated samples during drying procedures, as well as the presence of sodium counter ions that effect the mass, Equation 2.7 had to be modified to account for these variances. To determine a precise concentration for each capillary, the actual values for the mass of material and liquid was measured during the preparation process, and a precise concentration calculated (Equation 2.7 and 2.8). See Appendix V for a derivation. C rv = m r V total = ( 1 ρ r + f + g [ V w + w 1 ]) ρ Na m m ρ w Equation 2.7: Adjusted concentration calculation for vacuum-dried material. Variables are defined in Appendix V. C r lyo = ( 1 ρ r + 1 f + (1 + f) k ρ m ) Na Equation 2.8: Adjusted concentration calculation for lyophilized material. Variables are defined in Appendix V. 31

40 The prepared capillaries were then examined using WAXS and/or SAXS XRD. Data obtained through this method was analyzed using the Nika 2S SDS program in Igor to obtain linear plots of the diffraction pattern intensity in q-space. The diffraction spacing was then converted from inverse Angstroms, in q-space, to nanometers using Equation 2.5. Chapter 3 Experiment and Analysis 3.1) Microscopy Data and Analysis The following section is a summary of the observations made of rctp and rgtp mixtures using PLM methods. The first section, 3.1.1, is an analysis of the birefringence of the materials, and is a discussion of the observed phases, and their concentration and temperature-dependence. The final section, 3.1.3, is a phase diagram formulated using the data observed in ) Birefringence Sign As discussed in section 2.2.5, the sign of the birefringence of a material can be calculated using Polarized Light Microscopy. Determination of the sign provides information regarding the orientation of the columnar stacks and their long-range ordering. A cell of rctp and rgtp at a 1:1 ratio was prepared at a concentration of 900 mg/ml, and the LC domains allowed to develop at 5, for a period of 72 hours. The sample was then placed onto the microscope (at 5 ), and a focal-conic domain found (Figure 3.1). Once a developed domain was found, the sign of the birefringence was determined (Equation 2.1) using a quartz wedge compensator. 32

41 Figure 3.1) The fan-like textures are evident at the border between the birefringent domain and the isotropic portion of the sample. a) the sample is oriented as shown with the crossed polarizer and analyzer. b) sample has been rotated with respect to the polarizer and analyzer, and the textures have rotated as well. c) and the fan like textures have shifted as well. d) the sample has been shifted 180 with respect to the polarizer and analyzer, and the brushes within the focal-conic texture have shifted fully as well. This is evidence of LC columnar domains, which can be used when determining the sign of the birefringence for the rctp and rgtp mixtures. Placement of the wedge compensator required the removal of the top-plate of the hot-stag. In order to account for convective heating, while maintaining a temperature of 5⁰, the temperature of the hot stage was reduced to 0, to ensure that the sample did not warm and result in melting and degradation of the textures. The wedge compensator was adjusted such that it was at a 45⁰ with respect to the polarizer and analyzer (Figure 3.2). The compensator was then shifted along 33

42 its length, while maintaining a 45 angle, until the isotropic area of the sample was magenta, indicating the boundary between the first and second order in the Michel-Levy chart (Figure 2.4). Figure 3.2: Once an appropriate domain in which focal-conic/fan-like textures existed was located, the quartz wedge compensator was placed into the microscope, over the sample, at a 45 degree angle to the polarizer and analyzer. The compensator was then shifted along its length until the isotropic region, on the right-hand side of the image, was a magenta color. The color of the portion of the focal-conics perpendicular to the compensator were shifted toward blue, while the portion parallel to the compensator were shifted orange. This shift suggests that the columns slow wave is perpendicular to the optical axis. Comparison of Figure 3.2 with the Michel-Levy chart in Figure 2.5, shows that these materials have a negative birefringence because the phase shift between the ordinary and extraordinary wave has been increased along the slow axis of the material (Figure 2.2 and section 2.2.1) 3.1.2) Observed Phases Based on analysis PLM data of rctp and rgtp samples, four distinct phases were observed: Isotropic (I), Isotropic and Columnar in coexistence (I+C), Columnar (C), and Columnar G-quartets (G) (Figure 3.3). Columnar phases formed by G-quartets were differentiated from those formed by GC base pairing by comparison to those formed by DNA GTP, confirmed by X-ray analysis, and for their high-melting temperature, indicative of high 34

43 stability (section 1.14). For the samples analyzed here, all were prepared with rctp and rgtp in solution at a 1:1 ratio, with the varying parameters being temperature (0 ⁰C to 80 ⁰C) and concentration ( mg/ml) of the NTPs in solution. Figure 3.3: Observed phases in the rctp+rgtp samples from left: Columnar (C) at 20 ⁰C; Isotropic and Columnar in Coexistence (I+C) at 30 ⁰C; Columnar G- quartets (G), at a range of 40 ⁰C 80 ⁰C; and Isotropic (I), at temperatures over 90 ⁰C. The sample shown began in the Columnar phase, and as the temperature was raised transitioned into the other phases shown. At high enough temperatures, the phases melt, and the sample becomes isotropic. As displayed in Figure 3.3, at sufficiently high concentrations (~900 mg/ml for this sample), samples tended to form LC phases near room temperature (20 ⁰C) and, as heat was applied to the sample, tended to shift to a state in which the material existed in a state where Isotropic and Columnar phases coexisted (30 ⁰C). At high enough temperatures, only phases formed by 35

44 columnar g-quartets existed with the Isotropic material (40 ⁰C 80 ⁰C). Eventually, a temperature was reached at which all phases melted, and the sample was fully isotropic (+90 ⁰C). Samples that were brought to a high enough temperature to melt fully into the isotropic phase were brought to a lower temperature, and phases would re-form. Using the methodology above for multiple samples, the concentration and temperature dependence of columnar LC formation for these materials was determined. Samples at various concentrations were prepared and analyzed using the methodology described above. Based on visual observations, samples with higher concentrations of rctp+rgtp tended to form LC phases with a higher melting temperature than samples of lower concentrations of material (c > ~850 mg/ml). Additionally, in samples with coexistence of rctp+rgtp columnar phase and g- quartet columnar phases, the LCs formed by the g-quartets had a much higher melting temperature, and, at high enough concentrations (~950 mg/ml), could not be melted by the application of high temperatures (90 ). Finally, for samples with low concentrations (<~700mg/mL), LC phases did not form at any temperature considered, and the sample remained Isotropic. These results are incorporated into the phase diagram given in Figure 3.4, section ) Phase Diagram Using the observations noted in section 3.1.2, a phase diagram of the 1:1 mixtures of rctp+rgtp at varying concentrations was made (Figure 3.4). At very low concentrations (<~800 mg/ml, or < 60% by volume), the solution remained isotropic at all temperatures. In addition, for samples that formed phases at low temperatures, the phases were melted and the sample became isotropic at high temperatures. The temperatures at which samples shifted from exhibiting LC phases to being fully isotropic, was dependent on the concentration, with higher 36

45 concentration samples having a higher temperature at which they melted. The point at which the bi-phase occurred, I+C, was confined to small temperature ranges, and represented the change in phase from Columnar to Isotropic during heating, or vice versa during cooling. The Columnar phase occurred at concentrations from ~700 mg/ml to ~900 mg/ml, and at temperatures within a range that was dependent on concentration. The columnar g-quartet phase occurred at high concentrations, and was present at very high temperatures due to the high stability and level of ordering of the quartets. Figure 3.4: This phase diagram shows that mixtures of rctp+rgtp exhibit a columnar LC phase formed by complementary GC base-pairs and G-quartets within a small region of temperature and concentration. The shaded areas correspond to the range at which each phase (Isotropic, Columnar, Isotropic+Columnar in coexistence, and G-quartets) occurs. Above a certain concentration, G-quartet LC phases overwhelm the sample due to their high stability. Some phase coexistence may occur at these high concentrations, but further XRD analysis is necessary. The increase in thermal stability of these mixtures with increasing concentration is also noticeable. As the concentration of material increases, melting from a columnar phase to the isotropic becomes difficult. This is again due to the presence of the G-quartet LC phase, which are strongly stabilized by the presence of eight H-bonds. 37

46 From visual analysis of the 1:1 rctp+rgtp samples, it was determined that the formation of rctp+rgtp LC phases is strongly dependent on both concentration and temperature. Additionally, the high melting temperature of columnar G-quartet phases suggests they are more stable than the columnar phase formed by GC base-pairs. These G-quartets tend to be present in samples at high concentrations. Finally, the isotropic phase occurs at low concentrations and at high temperatures. 3.2) X-ray Diffraction Data and Analysis This section is a summary of XRD observations made on the rctp and rgtp mixtures, as well as samples of rgtp alone. The diffraction of these samples provides insight into the structural spacing of columnar LCs, as well as information on the intermolecular spacing. This information regarding the structure of the domains will show what sort of lattice is formed by the columnar domains, as well as whether GC base pairs, G-quartets, or a coexistence of both is forming columnar phases ) XRD Observations X-ray Diffraction techniques were used to further probe the concentration and temperature dependent phases observed using PLM techniques; additionally, the columnar spacing and lattice structure can be determined using these techniques by measuring electron density modulations. For the three 1:1 samples of rctp+rgtp shown in Figure 3.5, Wide-Angle X-ray Scattering (WAXS) resulted in diffraction spectra that showed two prominent peaks. One of the peaks occurred in the small-angle q-range of approximately 0.20 Å Å 1. This corresponds to large molecular spacing in real space. The second peak that occurred in each 38

47 sample occurred in the wide-angle q-range, with values in the range of 1.8 Å Å 1, which corresponds to smaller molecular spacing in real space. Figure 3.5: Composite image of the diffraction peaks of three samples of rctp+rgtp at a 1:1 ratio. The concentration of each sample is given in mg/ml in the upper right-hand corner of the image, with each sample color-coded. The diffraction peaks occur in the small-angle range at approximately 0.20 Å Å 1, and in the wide-angle at Å 1. The q-space values measured in Å 1 can be converted to real space using Equation 2.5 (section 2.3.1). For the small-angle range, Å 1 is equal to nm, which corresponds to the intercolumn spacing of the columnar LC lattice. In the wide-angle range, Å 1 is equivalent to nm, which is related to the molecular stacking height. Further analysis of the WAXS diffraction peaks in the small angle range provided more information on the approximate spacing of the peaks (Figure 3.6). The spacing of the peaks was plotted against the concentration of the sample, and a linear relationship was suggested (Figure 3.7). 39

48 Figure 3.6: WAXS diffraction from figure 3.2.1, with the small q-range in more detail. The location of the peak in the small angle appeared slightly different for each concentration, with higher concentrations suggesting a peak with a smaller real-space distance. The locations of the peaks are plotted in figure 3.2.2, with axes concentration vs. q. Figure 3.7: A plot of the diffraction peaks from figure 3.5. The error bars are given by the width of the diffraction peak. A best-fit line suggests that there is a linear relationship between the location of the peaks and the concentration of the sample. Because q-spacing is inversely related to real-space, this suggests that, at higher concentrations, the lattice spacing is smaller. This makes intuitive sense: as concentration is increased, the columns are closer to one another. Figure 3.7 suggests that, at lower concentrations, the lattice spacing is larger, and as the concentration increases, the spacing decreases. 40

49 To further analyze the small-q diffraction peaks, the theoretical model discussed in section (and derived in detail in Appendix III), was applied to the data in Figure 3.6. The peaks were plotted for q 2 against concentration, and compared to expected lattice area for GC base-pair or G-quartet columnar LCs (Figure 3.8). Figure 3.8: The black diamonds are plots of the peaks in Figure 3.6, plotted as q 2 in terms of concentration, c. Because of contaminants within the materials used, data that falls exactly on the theory line is not expected. Points directly below either line suggests that phases are occurring due only to that pairing. Because the points are above the G-quartet line but below the GC base-pair, the data suggests that the phases are formed primarily by G-quartets, with phase coexistence of GC base-pairs also occurring. The location of the q 2 vs. concentration values suggest that there is phase coexistence of G- quartet and GC base-pair columnar LC phases. Because of the inability to completely remove contaminants from these samples, some deviation from the theory line is expected. If the line data points fall entirely below the G-quartet theory line, then one can deduce that the phases are formed entirely by G-quartets, with contaminants resulting in slightly larger real space areas than 41

50 the theory predicts. If the points fell directly below the GC base-pair theory line, then one could similarly determine that the phases are occurring due to GC base-pairs. Their proximity to the G- quartet theory line suggests that the majority of the phase is occurring due to the G-quartets; however, because they are above the G-quartet theory line, there is a phase coexistence with some GC base-pair phase also occurring. To further probe the columnar spacing, the samples discussed above were analyzed using SAXS (Small-Angle X-Ray Scattering) diffraction to obtain increased detail into the small q- space diffraction peaks (Figures 3.9). All experiments were done at room temperature. Figure 3.9: SAXS diffraction for the sample shown in Figure 3.6. for an 842 mg/ml sample at room temperature. The WAXS peaks appeared at Å 1, and although similar peak values are suggested here, they are far less prominent then those found in WAXS analysis. Although the peaks that were observed in the small q-range in WAXS are suggested in each of these SAXS images, it is difficult to claim with certainty that they are in fact columnar spacing peaks. The samples have a high level of noise, as well as a distinct drop-off in intensity at ~

51 Å 1. Likely possibilities for this disparity are contamination issues with the XRD machine, or degradation of the sample during the time-frame in which the XRD machine was being repaired. In addition to observing rctp and rgtp samples using XRD, rgtp alone was also analyzed due to its ability to form LC phases on its own (Figure 3.10). The diffraction peaks of the rgtp alone could then be compared to those of the mixed samples to evaluate if columnar LCs were formed by base-pairs or g-quartets. Figure 3.10: An XRD image of rgtp, at a concentration of 867 mg/ml, observed at 25⁰C. The sharp peaks in the plot represent the q-spacing of the reciprocal lattice (c.2.3.1). The sharp peak at Å 1 is equivalent to approximately 6nm in real space, while the peak at Å 1, a harmonic of the first, is approximately 0.3nm. Finally, the sharp peak at 0.07 Å 1 is much larger than the atomic scale (~9nm), and therefore is probably due to noise. The sharp peak at Å 1 is indicative of the 2D lattice spacing formed by the G-quartet columnar LCs, and is equivalent to approximately 6nm in real space. The peak at Å 1 is a harmonic of the first peak, and therefore does not describe whether the lattice formed by the G- quartet columnar phase is hexagonal or square, although it does provide information that can be compared to other samples. The presence of harmonic peaks within the XRD data indicates wellcorrelated samples. Finally, the sharp peak at 0.07 Å 1 is much larger than the atomic scale 43

52 (~9nm), and therefore is probably due to noise. Further analysis into the concentration and temperature dependence of the G-quartet lattice would provide information regarding lattice geometry, that could then be compared to rctp and rgtp mixtures. Comparison of the peak at Å 1 in the rgtp sample in Figure 3.10 to the peaks in the rctp+rgtp mixtures shown in Figure 3.5 suggest that there are g-quartet columnar LCs present in the samples. 44

53 Chapter 4 Conclusion DNA is the foundational molecule for living organisms, as it is the carrier of genetic information. One of the ongoing mysteries of DNA is how such a complex structure could have self-assembled. Liquid crystals serve as a useful template for this process of DNA assembly into increasingly complex structures, which is an exciting discovery that provides insight into how early life may have evolved from simple molecules. RNA is a more simplistic molecule, that is generally considered a precursor to DNA, so a similar liquid crystal self-assembly motif would show how simple biological molecules may have evolved into life as we know it. Showing that the constituents of RNA (rntps) form base-pairs that then form columnar liquid crystals thus showing self-assembly in DNA precursors was the goal of this work. Using a combination of X-ray experiments and microscopy, we were able to show that, in mixtures of the complementary RNA base-pairs rctp and rgtp, columnar liquid crystals form spontaneously. Thorough analysis of these intricate formations, showed that RNA exhibits similar self-assembly behavior as DNA, which provides an exciting hypothesis for how prebiotic molecules may have self-assembled into more complex structures, forming RNA then DNA the building blocks of life. Further work researching the conditions for the formation of liquid crystals in RNA would provide more insight into how these complex molecules formed and how the selfassembly of complex molecules through this liquid crystal template may have been important in the origin of life. In addition, more analysis of the coexistence of columnar liquid crystals within these materials may also show which types of RNA structures form preferentially. 45

54 References [1] Livolant, F. Cholesteric liquid crystalline phases given by three helical biological polymers: DNA, PBLG and xanthan. A comparative analysis of their textures. J. Phys. France. 47(9), 9 Sep. 1986: DOI: /jphys: [2] Livolant, F., Levelut, A.M., Doucet, J., Benoit, J.P. The highly concentrated liquidcrystalline phase of DNA is columnar hexagonal. Nature 339, 26 June 1989: DOI: /339724a0. [3] Smith, G.P., Fraccia, T.P., Todisco, M., Zanchetta, G., Zhu, C., Hayden, E., Bellini, T., and Clark, N.A. Watson-Crick Base-Pairing and Duplex Stacking of Nucleic Acid Monomers in Aqueous Solution. Article submitted for publication, (2017). [4] Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., and Walter, P. The Structure and Function of DNA. Molecular Biology of the Cell. 4th edition. New York: Garland Science; [5] Rohatgi, R., Bartel, D., and Szostak, J. Kinetic and Mechanistic Analysis of Nonenzymatic, Template-Directed Oligoribonucleotide Ligation. J. Am. Chem. Soc. Vol. 118 (14). 10 April 1996: , DOI: /ja953712b. [6] Zanchetta, G. Liquid Crystalline Phases in Oligonucleotide Solutions. Doctoral Thesis. Universita degli Studi di Milano Web. 07 July [7] Joyce, G.F. The antiquity of RNA-based evolution. Nature. Vol July 2002: DOI: /418214a. [8] Nakata, M., Zanchetta, G., Chapman, B.D., Jones, C.D., Cross, J.O., Pindak, R., Bellini, T., and Clark, N.A. End-to-End Stacking and Liquid Crystal Condensation of 6 to 20 Base Pair DNA Duplexes. Science. Vol. 318, Issue Nov 2007: , DOI: /science [9] Strey, H., Parsegian, V. and Podgornik, R. Equation of State for DNA Liquid Crystals: Fluctuation Enhanced Electrostatic Double Layer Repulsion. Phys. Rev. Lett. Vol Feb. 1997: DOI: /PhysRevLett [10] Maniatis, T., Jeffrey, A. and van desandet, H. Chain Length Determination of Small Double-and Single-Stranded DNA Molecules by Polyacrylamide Gel Electrophoresis. Biochem., Vol. 14 (17). August 1975: [11] Davis, J.T. and Spada, G.P. Supramolecular architectures generated by self-assembly of guanosine derivatives. Chem. Soc. Rev. Vol. 36 (2). Feb. 2007: DOI: /B600282J. [12] Yamaguchi, Akihiro, "Self-Assembly of Lyotropic Chromonic Liquid Crystal Mixtures" (2015). Undergraduate Honors Theses

55 [13] Kleman, M. and Lavrentovich, O.D., Soft Matter Physics. New York: Springer-Verlag; DOI: /b [14] Senyuk, B. Liquid Crystals: A Simple View on a Complex Matter. SPIE Student Chapter at Kent State University. Kent State University. Web. 20 Sept [15] Zernike, Frits. Applied Nonlinear Optics. Wiley and Sons, [16] Dierking, Ingo. Textures of Liquid Crystals. Wiley-VCH, DOI: / [17] Seddon, J.M. (1998). Structural Studies of Liquid Crystals by X-Ray Diffraction. In Demus, D., Goodby, J., Gray, G. W., Spiess, H.-W. and Vill, V. (Eds), Handbook of Liquid Crystals Set, Wiley-VCH Verlag GmbH, Weinheim, Germany. Doi: / ch8ca. 47

56 Appendix I Apparatus and Sample Information The following is a list of the materials, their source and identification numbers, and a list of the instruments used in this project. RNA Mononucloside Triphosphates Jena Bioscience RNA Mononucleosides, 100mM solutions GE Healthcare Sciences RNA Mononucleosides, 100 mm solutions Instruments for PLM Measurements and Analysis Nikon Metaphot Microscope Nikon D5000 Camera Instec mk1000 Hot Stage Instruments for XRD Measurements and Analysis Forvis Technologies SAXS Instrument Nika 2D SAS Igor Macro analysis program Appendix II ratp and rutp Mixtures In addition to working with rctp and rgtp, the complementary bases ratp and rutp were also analyzed. Binary 1:1 samples of ratp+rutp were prepared and studied using the methodology noted above. Regardless of the concentration studied (Note what was looked at), and temperature parameter variation ( 20 < T < 80 C), liquid crystals did not form. Samples of this mixture only exhibited the isotropic phase, under all conditions considered. Adjustments to the ph of the ratp and rutp materials was done, and the experiments repeated. Addition of a Sodium Hydroxide solution allowed for an adjustment of the ph to one that was nearly neutral (7 ±.5). However, even with ph adjustments, liquid crystals did not A-i

57 form in any of the solutions, and they remained isotropic. The lack of liquid crystal formation in these complementary base-pairs solutions is indicative of selection, and is of interest for further research and discussion. Appendix III XRD Structural Summary X-ray diffraction data is given in term of a reciprocal q-space, which has units of Å 1. This output needs to be converted to real-space, which can be done in a few ways. The equations developed using Laue Diffraction provide information regarding the spacing within the structure being probed. Additionally, a theoretical model of the relationship between concentration and the area occupied by the material can be developed and compared to the q-space data. To develop the theoretical model, assume a hexagonal lattice, with a certain column thickness. Also assume that with an increase in concentration, there will be a decrease in spacing between the columns until space is filled entirely by the columns. Further, assume that the base stacking distance is unchanged, regardless of concentration. These assumptions fix the z-axis, but allow the area of the lattice to change with concentration (Figure III.1). Figure III.1: Each column is represented in this 2D model by blue circles. The area occupied by each column is equal to the area of the shaded parallelogram. A-ii

58 Because XRD data is given in q-space, one can relate the real-space area shown in Figure III.1 to an inverse area given by q 2. The goal is to relate the concentration in mg/ml to this q-space area. A generalized model relating q-space and real-space will provide the basis for expansion to more complex arrangements, such as the hexagonal lattice in this work. A face-centered rectangular cell in real space has objects placed at half-period intervals (Figure III.2). Figure III.2: The vectors a and b are the characteristic vectors of the unit cell. The objects, represented by circles, are related by a half-period of the characteristic vectors. The geometry of this cell results in a relationship between the real space and inverse space spacing (Equation III.1). d = 2π q Equation III.1: d is the distance between objects in real space, while q is the spacing in inverse space. Because of the relationship given by Equation 1, and the half-periodicity of the real-space unit cell, the inverse cell will have objects that are related by 2 times the period (Figure III.3). A-iii

59 Figure III.3: The characteristic vectors of this inverse-space lattice are equal. The objects, denoted by solid black circles, have a periodicity of two. The layout shown above results in inverse-space and real-space orientations that are mathematically convenient to calculate, due to their periodicity that can be determined using Equation III.1. For the reciprocal lattice given by Figure III.2, the basis vectors do not point to objects, as in the real-space lattice; they point to omissions, which occur when waves cancel one another out, due to two objects sharing a frequency (Figure III.4). Figure III.4: The arrows, basis-vectors for this lattice, pointing from the observation point, denoted by x, point toward omissions in the lattice. These omissions occur when waves cancel one another out, due to objects sharing a frequency. A-iv

60 The reciprocal lattice is easier to evaluate because XRD data is given in q-dimensions. However, relating it to real-space allows for the development of a theoretical model of concentration and lattice area. For the materials in this work, a columnar liquid crystal occurs due to the stacking of base-pair or G-quartet units. The hexagonal lattice spacing of these columnar LCs is expected to change with concentration, but the z-axis column spacing is unchanged with concentration (Figure III.5). This value, denoted by l u, is related to the large-q peaks in the X-ray diffraction spectra. Figure III.5: A single column that forms parts of the columnar liquid crystal lattice. The spacing between disks, formed by GC base-pairs or G-quartets, is fixed throughout the columns within the lattice, and is independent of the concentration parameter. The unit cells in these materials are the parallelograms occupied by a single column (Figure III.6). Thus, there is one object (column) per area, and per volume. A-v

61 Figure III.6: A hexagonal lattice with the area of the parallelogram, shaded in blue, is occupied by a single unit. The relationship between this area, A, and the concentration, in mg/ml, is of interest. Because each unit cell is occupied by one column, in the x-y plane, the concentration of interest is the unit-mass concentration (Equation III.2). c = m v = m u l u A Equation III.2: Unit-mass concentration, per area of the parallelogram in the hexagonal lattice. Mass per volume is the general form, which is expanded on the right to be in terms of unit mass, m u, the z-axis column spacing, l u, and the area of the parallelogram, A. The area, A, in real-space is necessary to relate this equation to the q-space XRD results, and can be determined using a geometric argument (Figure III.7). A-vi

62 Figure III.7: Spacing between columns is given by the characteristic vectors, a and b. The side length of the parallelogram is given by l. From this diagram, one can see that a = lx. Deriving b requires further geometrical analysis. Because the objects within the lattice are related to the neighboring object by a distance l, each triangle formed by three objects, is an equilateral triangle. This symmetry allows for the calculation of the second characteristic vector (Figure III.8). Figure III.8: The triangle formed by three objects within the lattice, denoted by the dashed line on the left-hand image, is an equilateral triangle, with side length l. The length of vector b, is related to this triangle in that it is equal to 2 times the height (b = 2x). By dividing the triangle into a triangle, as shown on the right, x = 3 2 l, and therefore b = 3 l y. A-vii