STRUCTURE AND STRUCTURAL STABILITY

The structure and structural stability of globular proteins in aqueous solution are the result of various interactions inside the protein molecule, between the protein and the water, and among the water molecules (Norde 2003a). The... 

The theory of atoms in molecules192 recovers all the fundamental concepts of chemistry, of atoms and functional groups with characteristic properties, of bonds, of molecular structure and structural stability, and of electron pairs and their role in molecular geometry and reactivity. The atomic principle of stationary action extends the predictions of quantum mechanics to the atomic constituents of all matter, the proper open systems of quantum mechanics. All facets of the theory are predictive and, as a consequence, the theory can be employed in many fields of research at the atomic level, from the design and synthesis of new drugs and catalysts, to the understanding and prediction of the properties of alloys. 

The set of molecular graphs in Fig. 3.6 exemplify the principal ideas of structure and structural stability. The initial and final structures are each represented by a unique molecular graph, one which persists over a range of nuclear motions. These structures are stable. They arc separated by a structure whose molecular graph is intermediate in form and, since it exists for only a single nuclear geometry along the reaction path, is unstable. 

Hydrocarbon molecules are used to illustrate the definitions of structure and structural stability introduced above and also the manner in which the properties of the electronic charge density at a bond critical point can be used to summarize the important physical characteristics of a bonded interaction between atoms (Bader et al. 1983). Figure 3.7 gives the molecular graphs for saturated hydrocarbon molecules with widely varying equilibrium structures, beginning with acyclic molecules both branched and unbranched, followed by cyclic and bicyclic molecules, and ending with a number of so-called... 

The definition of structure and structural stability for a molecular system as presented above is an example of the application of a general mathematical theory of structural stability. This work has evolved, under the general headings of differential topology and qualitative dynamics, a theory of... 

The atomic forms defined by the topology of the charge density are open systems and their boundaries, as defined in real space, satisfy the quantum condition for an open system. Thus all of the properties of an atom in a molecule or a crystal employed in the atomic classification of the properties of matter are predicted by quantum mechanics. The same topological properties of the charge density which define the atom also lead to the definition of bonds, structure and structural stability and the whole of the molecular structure hypothesis is given a basis in physics. ... 

III. STRUCTURE AND STRUCTURAL STABILITY A. The Molecular Structure Concept... 

Proteins are the most abundantly occurring natural polyampholytes. In addition to their amphoteric character, proteins are amphiphilic heteropolymers. The distribution of the monomers (the various amino acid residues) determines the amphiphi-licity and charge distribution and is therefore largely responsible for the 3D structure of a protein molecule in aqueous solution. Principles governing the protein structure and structural stability are treated in more detail in Chapter 13. 

Polymer molecules, which by their mere size belong to the colloid family, are described in Chapter 12. Special attention is paid to polymer-solvent interaction and its influence on the structure adopted by polymer molecules. Proteins are a special class of biopolymers. Because of their central role in biological systems, a full chapter (Chapter 13) is dedicated to describing their three-dimensional structure and structure stability in an aqueous environment. It is shown that the compact structures of globular protein molecules is the result of intramolecular self-assembly. 

The topological definition of an atom and the associated ideas of structure and structural stability are introduced in Section 2. These ideas can be presented in a pictorial and qualitative manner. The quantum definition of an open system and its identification with the topological atom are presented in Section 3. The consequences of this identification are explored without presenting its derivation, the approach that must necessarily be followed in this general introduction to the theory. 

Within this category, the greases are divided into those based on simple soaps and those based on complex soaps. The latter generally have better high temperature and structural stability properties under high mechanical shear they also have higher resistance to water than their simple soap-based counterparts. 

It is known, the residual austenite is not a stable structure and after some time is transformed into a bainite structure, so elements used for calibrating sorting thresholds will be unstable, and thus unrealiable Thus special reference samples showing structure stability should be used. 

Glansdorff P and Prigogine I 1971 Thermodynamio Theory of Structure, Stability and Fluctuations (London Wiley-Interscience)... 

Aers G C and Inglesfield J E 1989 Electric field and Ag(OOI) surface electronic structure Surf. Sc/. 217 367 Colbourn E A and Inglesfield J E 1991 Effective charges and surface stability of O on Cu(OOI) Phys. Rev. Lett. 66 2006... 

Haynes C A and Norde W 1995 Structural stabilities of adsorbed proteins J. Colloid Interface Sci. 169 313-28... 

Zoungrana T, FIndenegg G FI and Norde W 1997 Structure, stability and activity of adsorbed enzymes J. Colloid Interfaoe So/. 190 437-48... 

The results of the derivation (which is reproduced in Appendix A) are summarized in Figure 7. This figure applies to both reactive and resonance stabilized (such as benzene) systems. The compounds A and B are the reactant and product in a pericyclic reaction, or the two equivalent Kekule structures in an aromatic system. The parameter t, is the reaction coordinate in a pericyclic reaction or the coordinate interchanging two Kekule structures in aromatic (and antiaromatic) systems. The avoided crossing model [26-28] predicts that the two eigenfunctions of the two-state system may be fomred by in-phase and out-of-phase combinations of the noninteracting basic states A) and B). State A) differs from B) by the spin-pairing scheme. 

The system provides an opportunity to test our method for finding the conical intersection and the stabilized ground-state structures that are formed by the distortion. Recall that we focus on the distinction between spin-paired structures, rather than true minima. A natural choice for anchors are the two C2v stmctures having A2 and B, symmetry shown in Figures 21 and 22 In principle, each set can serve as the anchors. The reaction converting one type-I structirre to another is phase inverting, since it transforms one allyl structure to another (Fig. 12). 

By analogy to additions of divalent carbon to the Cio aromatic framework, the molecule Cgi was expected to have the norcaradi-ene (II) or the cycloheptatriene (III) structure. Although an X-ray structure was not available, the UV-visible spectrum, NMR spectrum, and cyclic voltammetry supported the cycloheptatriene (III) structure. The researchers then calculated the relative molecular mechanics energies of II and III and found the cycloheptatriene structure stabilized by 31 kcal/mol with respect to the norcaradi-ene structure. Although the calculations do not confirm the structures, they provide additional supporting evidence. 

A sample can be complex in one of two ways. It might be a single substance with a very complex chemical structure, or it might contain several substances of varying polarity, volatility, and thermal stability. 

Noncovalent Forces Stabilizing Protein Structure. Much of protein engineering concerns attempts to alter the stmcture or function of a protein in a predefined way. An understanding of the underlying physicochemical forces that participate in protein folding and stmctural stabilization is thus important. 

The most frequent of the domain structures are the alpha/beta (a/P) domains, which consist of a central parallel or mixed P sheet surrounded by a helices. All the glycolytic enzymes are a/p structures as are many other enzymes as well as proteins that bind and transport metabolites. In a/p domains, binding crevices are formed by loop regions. These regions do not contribute to the structural stability of the fold but participate in binding and catalytic action. 

Glycine residues have more conformational freedom than any other amino acid, as discussed in Chapter 1. A glycine residue at a specific position in a protein has usually only one conformation in a folded structure but can have many different conformations in different unfolded structures of the same protein and thereby contribute to the diversity of unfolded conformations. Proline residues, on the other hand, have less conformational freedom in unfolded structures than any other residue since the proline side chain is fixed by an extra covalent bond to the main chain. Another way to decrease the number of possible unfolded structures of a protein, and hence stabilize the native structure, is, therefore, to mutate glycine residues to any other residue and to increase the number of proline residues. Such mutations can only be made at positions that neither change the conformation of the main chain in the folded structure nor introduce unfavorable, or cause the loss of favorable, contacts with neighboring side chains. 

Figure 17.11 Structure of EMPl dimer from x-ray crystallography. In the presence of EBP, the EMPl peptide forms a dimer. Each monomer (shown in red and blue) forms a p hairpin structure stabilized by hydrogen bonds (red dashes) and a disulfide bond (yellow).

The pyromellitic dianhydride is itself obtained by vapour phase oxidation of durene (1,2,4,5-tetramethylbenzene), using a supported vanadium oxide catalyst. A number of amines have been investigated and it has been found that certain aromatic amines give polymers with a high degree of oxidative and thermal stability. Such amines include m-phenylenediamine, benzidine and di-(4-amino-phenyl) ether, the last of these being employed in the manufacture of Kapton (Du Pont). The structure of this material is shown in Figure 18.36. 

Staeking faults and sometimes proper polytypism are found in many inorganic compounds - to pick out just a few, zinc sulphide, zinc oxide, beryllium oxide. Interest in these faults arises from the present-day focus on electron theory of phase stability, and on eomputer simulation of lattice faults of all kinds investigators are attempting to relate staeking-fault concentration on various measurable character-isties of the compounds in question, such as ionicity , and thereby to cast light on the eleetronic strueture and phase stability of the two rival structures that give rise to the faults. 

Because these stability measurements pertain to the gas phase, it is important to consider the effects that solvation might have on the structure-stability relationships. Hydride affinity values based on solution measurements can be derived from thermodynamic cycles that relate hydrocarbon p T, bond dissociation energy and electrochemical potentials. The hydride affinity, AG, for the reaction... 

The mid-block monomers are primarily isoprene and butadiene. These diolefins can polymerize in several ways. The isomeric structure of the final polymer has a strong impact on its properties and thermal stability. Isomeric composition is easily varied by changing the polymerization solvent or adding complexing agents. The typical isomeric structures for isoprene and butadiene mid-blocks are shown in Fig. 2. 

Fig. 6. Freeman and Lewis stabilized structure and the likely results of orr/to-polymerization. As polymerization consumes o-hydroxymethyl groups, the hydrogen-bonded species cannot fomi.

We showed the possible existence of various forms of helically coiled and toroidal structures based on energetic and thermodynamic stability considerations. Though the formation process of these structures is not the subject of this work, the variety of patterns in the outer and inner surface of the structures indicates that there exist many different forms of stable cage carbon structures[10-19]. The molecules in a onedimensional chain, or a two-dimensional plane, or a three-dimensional supermolecule are possible extended structures of tori with rich applications. 

The relation of rates of reduction with NaBH4 to variations in structure in a wide variety of monocyclic and bridged bicyclic compounds has also been discussed for example, a methyl a to a ketone slows the rate of reduction. Brown ° stated that reactions should not be discussed in terms of axial and equatorial attack, since the rates simply reflect differences in the energies of the possible transition states and not enough is known about the transition state to analyze it. He accepted th concepts of SAC and PDC, but preferred to call them steric strain contrpl and product stability control. ... 

The immunoglobulin structure in Figure 6.45 represents the confluence of all the details of protein structure that have been thus far discussed. As for all proteins, the primary structure determines other aspects of structure. There are numerous elements of secondary structure, including /3-sheets and tight turns. The tertiary structure consists of 12 distinct domains, and the protein adopts a heterotetrameric quaternary structure. To make matters more interesting, both intrasubunit and intersubunit disulfide linkages act to stabilize the discrete domains and to stabilize the tetramer itself. 

---