Hole models

Fig. 2 The dependence on q of the non-zero eigenvalues of the two-dimesional, three-hole model described in the text shows the rapid onset of escape Grom wells as soon as q exceeds unity and the saturation at higher values of q. Also shown is the logarithm of the ratio of the two non-zero eigenvalues.

Detailed structure determinations of GCN4 and other coiled-coil proteins have shown that the a helices pack against each other according to the "knobs in holes" model first suggested by Francis Crick (Figure 3.5). Each side chain in the hydrophobic region of one of the a helices can contact four side chains from the second a helix. The side chain of a residue in position "d"... 

Figure 3.S Schematic diagram of packing side chains In the hydrophobic core of colled-coll structures according to the "knobs In holes" model. The positions of the side chains along the surface of the cylindrical a helix Is pro-jected onto a plane parallel with the heUcal axis for both a helices of the coiled-coil. (a) Projected positions of side chains in helix 1. (b) Projected positions of side chains in helix 2. (c) Superposition of (a) and (b) using the relative orientation of the helices In the coiled-coil structure. The side-chain positions of the first helix, the "knobs," superimpose between the side-chain positions In the second helix, the "holes." The green shading outlines a d-resldue (leucine) from helix 1 surrounded by four side chains from helix 2, and the brown shading outlines an a-resldue (usually hydrophobic) from helix 1 surrounded by four side chains from helix 2.

In most four-helix bundle structures, including those shown in Figure 3.7, the a helices are packed against each other according to the "ridges in grooves" model discussed later in this chapter. However, there are also examples where coiled-coil dimers packed by the "knobs in holes" model participate in four-helix bundle structures. A particularly simple illustrative example is the Rop protein, a small RNA-binding protein that is encoded by certain plasmids and is involved in plasmid replication. The monomeric sub unit of Rop is a polypeptide chain of 63 amino acids built up from two... 

Figure 3.8 Schematic diagram of the dimeric Rop molecule. Each subunit comprises two a helices arranged in a coiled-coil structure with side chains packed into the hydrophobic core according to the "knobs in holes" model. The two subunits are arranged in such a way that a bundle of four a helices is formed.

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

Taylor, C.P.S. 1977. The EPR of low spin heme complexes. Relation of the fg hole model to the directional properties of the g tensor, and a new method for calculating the ligand field parameters. Biochimica et Biophysica Acta 491 137-149. 

Yaron, D., Moore, E.E., Shuai, Z., Bredas, J.L. Comparison of density matrix renormalization group calculations with electron-hole models of exciton binding in conjugated polymers. J. Chem. Phys. 1998, 108(17), 7451. 

It is worthwhile to mention the ample use of screening final states models in understanding core levels as well as valence band spectra of the oxides. The two-hole models, for instance, which have been described here, are certainly of relevance. Interpretational difference exists, for instance, on the attribution of the 10 eV valence band peak (encountered in other actinide dioxides as well), whether due to the non-screened 5f final state, or to a 2p-type characteristics of the ligand, or simply to surface stoichiometry effects. Although resonance experiments seem to exclude the first interpretation, it remains a question as to what extent a resonance behaviour other than expected within an atomic picture is exhibited by a 5 f contribution in the valence band region, and to what extent a possible d contribution may modify it. In fact, it has been shown that, for less localized states (as, e.g., the 3d states in transition metals) the resonant enhancement of the response is less pronounced than expected. 

One attempt to remedy the limitations of the 2D model, and yet retain its simplicity, is the so-called hole model [25] which represents a simple static way to average over this distribution of barriers. If the variation of barrier height with these spectator variables is given as (X, Y, i), ), then the 6D dissociation probability S6D is approximated in terms of the 2D S2D as... 

The hole model of a typical organic molecule is useful for all liquids with the exception of systems in which the H-bond interaction plays an important role. In this case the interaction becomes orientation dependant. This effect is most significant for liquid water. The degree of H-bond interaction on the total intermolecular energy is — in the case of water at room T — about 2/3 of the total energy (about 8 kcal/mol of 11.6 kcal/mol). Therefore, water is the most pronounced liquid of the H-bonded type. A large section of organic chemistry consists of molecules with H-bonds especially in biochemistry, pharmaceutical chemistry and plant protection chemistry. 

Plakida N.M., Hayn R., and Richard J.L., (1995). Two-band singlet-hole model for the copper oxide plane. Phys. Rev. B 51 16599-16607. 

The hole model for molecular liquids was elaborated by Furth [12], who supposed that the free volume of a liquid is not distributed uniformly between its molecules like in crystals, but is concentrated like some holes which can disappear in one place and appear in another place. These holes are in permanent motion, so that the situation is different from the jumps of the holes in a crystal. The appearance and disappearance of the holes in a liquid are a result of the fluctuations connected with thermal movements. These holes in liquids have no definite shape and size they can increase or decrease spontaneously. Furth [12] tried to calculate a large number of properties of the liquids viscosity, compressibility, thermal expansion, thermal conductivity, but the results were not successful. However, Furth obtained a precise result of the calculation of the volume change by melting and the entropy of melting. 

The most important deficiency of this theory is the fact that the notion of holes has not an exact definition. Also, the hole model does not contain any... 

It is not surprising that attempts have been made to derive equations of state along purely theoretical lines. This was done by Flory, Orwoll and Vrij (1964) using a lattice model, Simha and Somcynsky (1969) (hole model) and Sanchez and Lacombe (1976) (Ising fluid lattice model). These theories have a statistical-mechanical nature they all express the state parameters in a reduced dimensionless form. The reducing parameters contain the molecular characteristics of the system, but these have to be partly adapted in order to be in agreement with the experimental data. The final equations of state are accurate, but their usefulness is limited because of their mathematical complexity. 

Cao, H., Zhang, R., Yuan, J.P., Huang, C.M., Jean, Y.C., Suzuki, K., Oh-daira, T. (1998) Free-volume hole model for position formation in polymers surface studies . J. Phys. Cond. Mart. 10. 10429. 

The Hole Model A Fused Salt Is Represented as Full of Holes as a Swiss Cheese... 

One of the models that can be used to approximately predict the properties of molten salts is called the hole model. The outstanding fact that led to this model is the large volume of fusion (10-20%) exhibited by simple salts on melting (Fig. 5.17). The basic idea of this rather artificial model is that within the liquid salt are tiny volume... 

Fig. 5.17. The hole model with randomly located and variable-sized holes in the liquid.

Although this model of a liquid was suggested independently of the results obtained from computer modeling, the imagined picture of the hole model in Fig. 5.17 closely resembles the picture (Fig 5.14) from Woodcock and Singer s model derived from the Monte Carlo approach. 

To quantify the hole model, it is necessary to calculate a distribution function for the hole sizes. This is a plot of the number of holes per unit volume as a function of their size. As a first step toward this calculation, one can consider a particular hole in a liquid electrolyte and ask What are the quantities (or variables) needed to describe this hole This problem can be resolved by means of a formulation first published by Fiirthin 1941. 

Fig. 5.21. The basis of the hole model of Furth is the anabgy between (a) a hole in a liquid and (b) a bubble in a liquid. An...

USING A HOLE MODEL TO UNDERSTAND TRANSPORT PROCESSES IN SIMPLE IONIC LIQUIDS... 

Some facts about transport processes in molten salts have been mentioned (Section 5.6). Whether a hole model (Section 5.4) can provide an interpretation of these must now be examined. First it is necessary to cast the model into a form suitable for the prediction of transport properties. The starting point is the molecular-kinetic expression (Appendix 5.3) for the viscosity ij of a fluid, i.e.,... 

Fig. 5.45. According to the hole model, viscous drag arises from the momentum transferred between moving fluid layers when holes jump from one layer to another.

How Consistent with Experimental Values Is the Hole Model for Simple Molten Salts ... 

An example of the ability of this Fiirth hole model to reproduce experimental data numerically without previous appeal to experimental values of similar systems is shown in Table 5.32, which gives a comparison of experimental expansivities with the values that the hole theory yields. An interesting aspect of the evidence supporting the usefulness of this model is the relation of the (cell) free volume (Fig. 5.47) to the volume of the expansion of melting. This free volume, in the sense referred to here, is... 

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