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Underdetermined structures

I. A. Vakser, Biopolymers, 39, 455-464 (1996). Low-Resolution Docking Prediction of Complexes for Underdetermined Structures. [Pg.167]

It is also possible to satisfy this relation and have the structure be underdetermined and locally over determined. Examples of two-dimensional structures are shown in Table 1. [Pg.51]

A geodesic structure with any non-triangular faces is underdetermined, since adding the struts needed to make all faces triangles will add constraints. [Pg.53]

In microwave spectroscopy, the situation is characterized by the fact that the number of independent pieces of observable data is often restricted to three rotational constants, while the number of degrees of freedom—3N-6 or 3N-5, where N is the number of atoms—can be significantly larger. The number of independent experimental rotational constants can be effectively increased by recording the spectra of isotopically substituted species, but that is not always possible. Thus, structural studies by microwave spectroscopy are often seriously underdetermined and extraneous information is useful in aiding the spectroscopic assignment. [Pg.141]

Structures determined by spectroscopic means are generally underdetermined in that the number of variables is similar to or greater than the number of observations. In such cases, the energy-minimized structures can be used to aid in the refinement of the structure or as a check on the geometry[51]. Applications of molecular mechanics modeling to the determination of solution structures is described in detail in Chapters 6, 7, and 9. Such approaches are fundamental to the determination of macromolecu-lar structures by NMR spectroscopy. [Pg.174]

Another feature of the superconductivity effort has been that most has been devoted to detailed studies of existing materials rather than wide-ranging searches for new compositions. Substantially enhanced properties are necessary if high temperature superconductors are to have a major impact in the commercial sector. The assumption has been that detailed understanding will lead to improved superconductors. Usually, this has not occurred. The complexities of these underdetermined solid state systems restrict the ability to design improved structures. [Pg.131]

Describing the ensemble of conformations would imply knowing the structure and the relative population of each conformer in solution. In many cases this problem is underdetermined, since the number of NMR-derived experimental restraints is smaller than the degrees of freedom of the system. In consequence,... [Pg.103]

The generalized cylinder representation of a macromolecule is a much sparser description of the system than is the full set of Cartesian or internal coordinates which define the position of every atom. The generalized cylinder representation leaves the molecular structure seriously underdetermined. It is eventually necessary to recover an estimate of all the atomic coordinates for more detailed study. Here is where DOCENT takes on some of the features of an expert system, which must make plausible judgments without complete information. [Pg.102]

Whatever model is used, the problem with equation (1) is that it is intrinsically underdetermined since it contains the product of interaction and spectral density terms. The usual solution is to examine relaxation at different temperatures and assume a function (usually exponential) for the temperature dependence of the correlation times. This is problematic in foods, as the structure of food is typically very temperature dependent. The alternative is directly to determine the spectral density function of the material by determining 7, over a wide range of frequencies. This may be done by using fast field cycling NMR. [Pg.132]

The indene bioconversion network proposed for Rhodococcus sp. KYI (Fig. 4) using the induction studies with radiolabeled indene can be used to write five independent mass balances to describe six intracellular fluxes (Table 3). This yields an underdetermined system for the fluxes of the KYI network requiring that at least one flux be directly measured to calculate uniquely the remaining network fluxes. It is further desirable to measure directly additional fluxes to generate redundancies that can be used to confirm the structure of the proposed bioreaction network, validate the flux estimates, and help detect gross measurement errors, if present. [Pg.94]

With a model that has on the order of 180 factors, we need to solve for over 16,000 covariances. Factor returns series include, in many cases, less than 30 to 40 periods. With such a small sample size compared to the number of factors, we have a severely underdetermined problem and are virtually assured that the covariance forecasts will show a large degree of spurious linear dependence among the factors. One consequence is that it becomes possible to create portfolios with artificially low risk forecasts. The structure of these portfolios would be pecu-... [Pg.743]

Multiple Conformations Ensembles. When multiple conformations are present, the problem rapidly becomes underdetermined. For example, if a nucleotide can exist in two major conformational states, with x(N)P(N) and x(S)P(S) where the glycosidic torsion angles in the N and S sugar states are not equal, each conformation will have its own characteristic NOEs and coupling constants. For n bases, there are 2" conformations, and the contribution of each one to the ensemble will depend on its population. Even for a dinucleotide, there are at least 4 conformations (viz. SS, SN, NS, NN), which multiplies the number of structural parameters to be determined fourfold, plus four equilibrium constants. There are not enough independent NMR data to determine all of these parameters and the problem is underdetermined. In this situation, the best that can be hoped for is to derive a set of structures that in some way represent the ensemble of structures that is present in solution. [Pg.111]

In addition, assumptions about symmetry are often made in analysis of diffraction data (both gas and condensed phases) and of rotation constants. Consider Ceo, discussed in the previous section. Of course, it makes sense to assume that this molecule has icosahedral symmetry, but this is still an assumption. Electron diffraction cannot prove the symmetry, although large differences in distances between otherwise identical atom pairs would be obvious. If we were to define the structure without symmetry restriction, we would have to refine (3 x 60) — 6 = 174 structural parameters and this would clearly be an underdetermined problem. The assumption of symmetry, which is not just a guess but is supported in this case by theory and spectroscopic data, reduces the problem to the very tractable problem of refining only two parameters. [Pg.315]


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Problems with underdetermined structures

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