Two-dimensional crystals and

CNTs own excellent materials properties. DNA is an excellent molecule to construct macromolecular networks because it is easy to synthesize, with a high specificity of interaction, and is conformationally flexible. The complementary base-paring properties of DNA molecules have been used to make two-dimensional crystals and prototypes of DNA computers and electronic circuits (Yan et al., 2002 Batalia et al., 2002). Therefore functionalization of CNTs with DNA molecules has great potential for applications such as developing nanodevices or nanosystems, biosensors, electronic sequencing, and gene transporters. 

Many important biological substances do not form crystals. Among these are most membrane proteins and fibrous materials like collagen, DNA, filamentous viruses, and muscle fibers. Some membrane proteins can be crystallized in matrices of lipid and studied by X-ray diffraction (Chapter 3, Section III.D), or they can be incorporated into lipid films (which are in essence two-dimensional crystals) and studied by electron diffraction. I will discuss electron diffraction later in this chapter. Here I will examine diffraction by fibers. 

Maunsbach, A.B., Skriver, E., Hebert, H. (1991). Two-dimensional crystals and three-dimensional structure of Na,K-ATPase analyzed by electron microscopy. In The Sodium Pump Structure, Mechanism, and Regulation (Kaplan, J.H. De Weer, P., eds.), pp. 159-172, The Rockefeller University Press, New York. 

Only recently was the first higfr-resolution atomic structure of a G-protein-coupled receptor solved, namely that of rhodopsin, although lower-resolution spatial structural information based on two-dimensional crystals and electron diffraction and NMR structures was available.3.4 This information makes it certain that all heptahelical receptors have the same topological arrangement of the polypeptide chains. The amino- and carboxy-termini are oriented in the same way, with the amino-terminus outside and carboxy-terminus on the cytoplasmic side. Valuable structural relationships between different G-protein-coupled receptors for hormones have also come to light, mainly thanks to comparisons of cDNA-derived sequences. ... 

Fig. 16. Three-dimcnsioiiiil structure of pea LHC II determined at 16 A resolution by electron microscopy of two-dimensional crystals and image analysis (Kiihlbrandt et al. [198,199]).

Equation (5.3.3) is analogous to the Peierls-Landau free energy expression for a two-dimensional crystal, and leads to a logarithmic divergence of the mean square fluctuation as Writing the free energy in terms of the Fourier components of u... 

Bonaccorso F, Colombo L, Yu G, Stoller M, Tozzini V, Ferrari AC, Ruoff RS, Pellegrini V (2015) Graphene, related two-dimensional crystals, and hybrid systems for eneigy conversion and storage. Science 347 6217... 

CS. The true two-dimensional crystal with chains oriented vertically exists at low T and high ir in the CS phase. This structure exhibits long-range translational order. 

Fig. Vn-2. Conformation for a hypothetical two-dimensional crystal, (a) (lO)-type planes only. For a crystal of 1 cm area, the total surface firee energy is 4 x lx 250 = 1000 eigs. (b) (ll)-type planes only. For a crystal of 1-cm area, the total surface free eneigy is 4 x 1 x 225 = 900 ergs, (c) For the shape given by the Wulff construction, the total surface free energy of a 1-cm crystal is (4 x 0.32 x 250) + (4 x 0.59 x 225) = 851 ergs, (d) Wulff construction considering only (10)- and (ll)-type planes.

Surface states can be divided into those that are intrinsic to a well ordered crystal surface with two-dimensional periodicity, and those that are extrinsic [25]. Intrinsic states include those that are associated with relaxation and reconstruction. Note, however, that even in a bulk-tenuinated surface, the outemiost atoms are in a different electronic enviromuent than the substrate atoms, which can also lead to intrinsic surface states. Extrinsic surface states are associated with imperfections in the perfect order of the surface region. Extrinsic states can also be fomied by an adsorbate, as discussed below. 

In some Hquid crystal phases with the positional order just described, there is additional positional order in the two directions parallel to the planes. A snapshot of the molecules at any one time reveals that the molecular centers have a higher density around points which form a two-dimensional lattice, and that these positions are the same from layer to layer. The symmetry of this lattice can be either triangular or rectangular, and again a positional distribution function, can be defined. This function can be expanded in a two-dimensional Fourier series, with the coefficients in front of the two... 

For cubic crystals, which iaclude sUicon, properties described by other than a zero- or a second-rank tensor are anisotropic (17). Thus, ia principle, whether or not a particular property is anisotropic can be predicted. There are some properties, however, for which the tensor rank is not known. In addition, ia very thin crystal sections, the crystal may have two-dimensional characteristics and exhibit a different symmetry from the bulk, three-dimensional crystal (18). Table 4 is a listing of various isotropic and anisotropic sUicon properties. Table 5 gives values for the more common physical properties and for some of the thermodynamic properties. Figure 5 shows some thermal properties. 

Figure 12.3 Two-dimensional crystals of the protein bacteriorhodopsin were used to pioneer three-dimensional high-resolution structure determination from electron micrographs. An electron density map to 7 A resolution (a) was obtained and interpreted in terms of seven transmembrane helices (b).

It has been shown by FM that the phase state of the lipid exerted a marked influence on S-layer protein crystallization [138]. When the l,2-dimyristoyl-OT-glycero-3-phospho-ethanolamine (DMPE) surface monolayer was in the phase-separated state between hquid-expanded and ordered, liquid-condensed phase, the S-layer protein of B. coagulans E38/vl was preferentially adsorbed at the boundary line between the two coexisting phases. The adsorption was dominated by hydrophobic and van der Waals interactions. The two-dimensional crystallization proceeded predominately underneath the liquid-condensed phase. Crystal growth was much slower under the liquid-expanded monolayer, and the entire interface was overgrown only after prolonged protein incubation. 

There are three kinds of diffusion (i) within the isotropic phase (ii) the interface (between the isotropic and the crystalline phases) and (iii) the crystalline phase. In the case of a polymer system, the topological nature of polymer chains assumes an important role in all three kinds of diffusion, which has been shown in the chain sliding diffusion theory proposed by Hikosaka [14,15]. It is obvious that any nucleus (a primary nucleus and a two-dimensional nucleus) and a crystal can not grow or thicken without chain sliding diffusion. 

The upgrade of a frequency-domain fluorescence lifetime imaging microscope (FLIM) to a prismless objective-based total internal reflection-FLIM (TIR-FLIM) system is described. By off-axis coupling of the intensity-modulated laser from a fiber and using a high numerical aperture oil objective, TIR-FLIM can be readily achieved. The usefulness of the technique is demonstrated by a fluorescence resonance energy transfer study of Annexin A4 relocation and two-dimensional crystal formation near the plasma membrane of cultured mammalian cells. Possible future applications and comparison to other techniques are discussed. 

The book thus embraces an extended study on a variety of issues within the theory of orientational ordering and phase transitions in two-dimensional systems as well as the theory of anharmonic vibrations in low-dimensional crystals and dynamic subsystems interacting with a phonon thermostat. For the sake of readability, the main theoretical approaches involved are either presented in separate sections of the corresponding chapters or thoroughly scrutinized in appendices. The latter contain the basic formulae of the theory of local and resonance states for a system of bound harmonic oscillators (Appendix 1), the theory of thermally activated reorientations and tunnel relaxation of orientational... 

Lyuksyutov, A. Naumovets and V. Pokrovsky, Two-Dimensional Crystals, Academic Press, New York, 1992. 66 ... 

Lyotropic lamellar (La) liquid crystals (LC), in a form of vesicle or planar membrane, are important for membrane research to elucidate both functional and structural aspects of membrane proteins. Membrane proteins so far investigated are receptors, substrate carriers, energy-transducting proteins, channels, and ion-motivated ATPases [1-11], The L liquid crystals have also been proved useful in the two-dimensional crystallization of membrane proteins[12, 13], in the fabrication of protein micro-arrays[14], and biomolecular devices[15]. Usefulness of an inverted cubic LC in the three-dimensional crystallization of membrane proteins has also been recognized[16]. 

Photosystem I is a membrane pigment-protein complex in green plants, algae as well as cyanobacteria, and undergoes redox reactions by using the electrons transferred from photosystem II (PS II) [1], These membrane proteins are considered to be especially interesting in the study of monomolecular assemblies, because their structure contains hydrophilic area that can interact with the subphase as well as hydrophobic domains that can interact either with each other or with detergent and lipids [2], Moreover, studies with such proteins directly at the air-water interface are expected to be a valuable approach for their two-dimensional crystallization. 

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