Structure-function optimization

Fetisova Z G, Borisov A Y and Fok M V 1985 Analysis of structure-function correlations in light-harvesting photosynthetic antenna—structure optimization parameters J. Theoret. Biol. 112 41-75... 

Standard shapes for composite stiffeners are not likely to occur for most aerospace applications. There, the value and function of the structure warrant optimizing the stiffener design. In contrast, for more everyday applications such as scaffolding, stairways, and walkways in chemical plants, competitive pressures lead to a situation where compromises in stiffener efficiency are readily accepted (overdesign) in order to achieve lower cost than would be associated with optimum design. 

One of the goals of Localized Molecular Orbitals (LMO) is to derive MOs which are approximately constant between structurally similar units in different molecules. A set of LMOs may be defined by optimizing the expectation value of an two-electron operator The expectation value depends on the n, parameters in eq. (9.19), i.e. this is again a function optimization problem (Chapter 14). In practice, however, the localization is normally done by performing a series of 2 x 2 orbital rotations, as described in Chapter 13. 

Krier M, de Araujo-Junior JX, Schmitt M, Duranton J, Justiano-Basaran H, Lugnier C, Bourguignon JJ, Rognan D. Design of small-sized libraries by combinatorial assembly of linkers and functional groups to a given scaffold application to the structure-based optimization of a phosphodiesterase 4 inhibitor. J Med Chem 2005 48 3816-22. 

Selection of the form of an empirical model requires judgment as well as some skill in recognizing how response patterns match possible algebraic functions. Optimization methods can help in the selection of the model structure as well as in the estimation of the unknown coefficients. If you can specify a quantitative criterion that defines what best represents the data, then the model can be improved by adjusting its form to improve the value of the criterion. The best model presumably exhibits the least error between actual data and the predicted response in some sense. 

A speculative proposal was made thirty years ago by Schmid and Krenmayr77, namely that a nitrosyl ion solvated, but not covalently bonded, by a water molecule may be involved in these systems. This hypothesis was investigated theoretically in 1984 by Nguyen and Hegarty78 who carried out ab initio SCF calculations of structure and properties employing the minimal STO-3G basis set, a split-valence basis set plus polarization functions. Optimized geometries of six planar and two nonplanar forms were studied for the nitrosoacidium ion. The lowest minimum of molecular electrostatic potential... 

The structure-function relationship of the indole-indoline binary alkaloids was relegated to obscurity until the recent achievement of methodologies for their complete syntheses (see Chapter 2, this volume). Our work with C-20 congeners of VBL has established that the complex interactions between this molecule and tubulin or microtubules can be modified by structural alteration. The various, concentration-dependent reactions of VBL with the microtubule system in vitro are sensitive to subtle modifications at a single molecular locus. In addition, these reactions are distinctive on a mechanistic level as seen from the unique activity profiles of most of our C-20 alkyl congeners. At first light, we can look toward the future with secured optimism. 

Optimization problems in crystallographic structure refinement are seldom convex, that is very rarely characterized by a unimodal function/(x). Regularization of a two-atom model is an example of such a unimodal function. Fig. 11.2a. in contrast. Fig. 11.2b shows a profile of a function for modelling an amino acid side chain - the peaks correspond to the possible rotamers. In this case, the shape of the function/(x) is called multimodal. Such functions arise naturally in structural macromolecular optimization problems and possess a highly complex multiminima energy landscape that does not lend itself favourably to standard robust optimization techniques. 

Critical periods are those in which the synaptic circuitry of a given brain region becomes stabilized in a functionally optimized conformation. The cerebral cortex and other brain structures contain functional maps for the activities characteristic of a species. The best example is the ocular dominance columns and other physical and functional characteristics of the circuitry within the visual cortical system that process information derived from the left and right visual fields, producing a map of the visual world. Other internal maps exist for the body (somatosensory, motor corti-... 

End view of energy-optimized parallel tetramer of the sodium channel helix 3. Colors light blue, a-carbon backbone red, acidic residues blue, basic residues yellow, polar and neutral residues and purple, lipophilic residues. This view is from the intracellular face of the membrane, at which the N terminus of each segment is predicted to be located. (From M. Montal, Proteins Structure, Function, and Genetics, vol. 8, University of California Press at San Diego, La Jolla, Calif., p. 226.)... 

Structures were optimized at the theoretical level described in Table 1, footnote a. Final energies were obtained by using multi-reference configuration interaction (MRCI) wave functions including single and double excitations from die reference wave functions. cFrom Reference 8. 

A simple analysis of eq 17 shows the general aspects of the structure-function relations expected to control /3. This demonstration is simplistic in its lack of explicit bridge orbital structure, but it demonstrates the compromises needed to optimize Consider... 

As a starting point for structural cost optimization, Clariant first of all has an optimized production network design that leverages scale effects and regional advantages. Second, a review of truly value-creating functions, processes, and process steps is performed on a regular basis. 

The results of MO calculations depend on the nature of the basis set and on the extent to which polarization functions are evaluated. Open-shell systems, such as the radical cations discussed here, inherently present greater difficulties. Typically the structures are optimized at a somewhat lower level of theory then the extrema so identified are subjected to single point calculations at higher levels of theory, including polarization functions. To confirm the identity of an extremum as a minimum, an analysis of the vibrational frequencies is carried out at an advanced level of theory. A single imaginary frequency typically disqualifies an extremum as a minimum. 

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