Conformation-dependent value functions

Conformation-dependent Value Functions and Fitness Landscapes... 

For each combination of atoms i.j, k, and I, c is defined by Eq. (29), where X , y,. and Zj are the coordinates of atom j in Cartesian space defined in such a way that atom i is at position (0, 0, 0), atomj lies on the positive side of the x-axis, and atom k lies on the xy-plaiic and has a positive y-coordinate. On the right-hand side of Eq. (29), the numerator represents the volume of a rectangular prism with edges % , y ., and Zi, while the denominator is proportional to the surface of the same solid. If X . y ., or 2 has a very small absolute value, the set of four atoms is deviating only slightly from an achiral situation. This is reflected in c, which would then take a small absolute value the value of c is conformation-dependent because it is a function of the 3D atomic coordinates. 

Conformational energies as function of rotational angles over two consecutive skeletal bonds for both meso and racemic diads of poly(Af-vinyl-2-pyrrolidone) are computed. The results of these calculations are used to formulate a statistical model that was then employed to calculate the unperturbed dimensions of this polymer. The conformational energies are sensitive to the Coutombic interactions, which are governed by the dielectric constant of the solvent, and to the size of the solvent molecules. Consequently, the calculated values of the polymeric chain dimensions are strongly dependent on the nature of the solvent, as it was experimentally found before. 

The conformational dependence of the 33S isotropic a in dimethyldisulphide, (CH3)2S2, has been studied by HF calculations using the IGLO method.121 (CH3)2S2 is a good model for the disulphide linkage in polypeptides and proteins. 33S a has been calculated as a function of the dihedral angle C-S-S-C. Predicted chemical shifts vary between —84.4 ppm (< C-S-S-C = 0°) and —42.3 ppm (Calculated values refer to CS2 and cannot be converted to the SO4 scale, since the absolute shielding of the SQj anion has not been reported... 

This expansion contains only seven terms. This expression means that only seven conformational energy values have to be determined for retaining all the main features of potential energy surface of pyrocatechin. These seven conformations have to be conveniently chosen in order to avoid linear dependency. In particular, the 90 , 90 and 90 , -90 conformations have to be considered in order to take accurately into account the cog wheel effect. This particularity is often forgotten by the spectroscopists when they determine the V/i term, i.e, the Aff of the potential energy function (111). 

Figure 3.17 Birefringence as a function of the eigenvalue of the velocity gradient tensor, G, for planar flows generated in a four-roll mill, for dilute solutions of polystyrenes of three different molecular weights in polychlorinated biphenyl solvent. Here G is the strain rate and a the flow type parameter. For planar extension, a — 1 and G = is the extension rate for simple shear, a = 0 and G = y is the shear rate. The different symbols correspond to a values of 1.0 (0)> 0.8 (A), 0.5 (-1-), and 0.25 (diamonds). The curves are theoretical predictions from the FENE dumbbell model, including conformation-dependent drag (discussed in Section 3.6.2.2.2). (From Fuller and Leal 1980, reprinted with permission from Steinkopff Publishers.)...

Figure 3-21 Distribution of bead mass as a function of position downstream of the tether point of a DNA molecule of length L -67.2 tm for various velocities measured in experiments similar to those described in the caption to Fig. 3-1. The lines are the predictions of Monte Carlo molecular simulations using the elastic force from the worm-like chain model, Eq. (3-57), and conformation-dependent drag, as described in the text. The value of the parameter fcoii/ ksT — 4.8 sec(/im) is obtained from the diffusivity measurements of Smith et al. (1995) Crod/ a = 9.1 sec(/Ltm) 2 is obtained from Eq. (3-62) for a fully stretched filament (From Larson et al. 1997, reprinted with permission from the American Physical Society.)...

In solution, nucleotides (and polynucleotides) exist as an equilibrium between several conformers and it is possible to modify this equilibrium by changing the physico-chemical properties of the solution [14][19]. The variation of the chemical shifts which are measured are then function of the variations of all the different conformational parameters of the nucleotide and it was not possible up to now to determine from experiment the role of a given conformational parameter in the value of the chemical shift of a given nucleus. The theoretical determination of the conformational dependence of chemical shifts is for the moment/ to our knowledge/ the only tool which can give information on the chemical shift of each individual proton as a function of each individual conformational parameter of the molecule. Ue have... 

For molecules with an even number of electrons, the spin function has only single-valued representations just as the spatial wave function. For these molecules, any degenerate spin-orbit state is unstable in the symmetric conformation since there is always a nontotally symmetric normal coordinate along which the potential energy depends linearly. For example, for an - state of a C3 molecule, the spin function has species da and E that upon... 

This is a linear equation, and we can thus expect kobs to track linearly with inhibitor concentration for an inhibitor conforming to the mechanism of scheme B. As illustrated in Figure 6.4, a replot of kobs as a function of [/] will yield a straight line with slope equal to k3 and y-intercept equal to k4. It should be noted that in such an experiment the measured value of k3 is an apparent value as this association rate constant may be affected by the concentration of substrate used in the experiment, depending on the inhibition modality of the compound (vide infra). Hence the apparent value of Ki (Kfw) for an inhibitor of this type can be calculated from the ratio of... 

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