Distance bound calculation

Figure 4 Procedure for upper and lower distance bound calculation in ISIS/3D ...

A distance geometry calculation consists of two major parts. In the first, the distances are checked for consistency, using a set of inequalities that distances have to satisfy (this part is called bound smoothing ) in the second, distances are chosen randomly within these bounds, and the so-called metric matrix (Mij) is calculated. Embedding then converts this matrix to three-dimensional coordinates, using methods akin to principal component analysis [40]. 

Figure 3 Flow of a distance geometry calculation. On the left is shown the development of the data on the right, the operations, d , is the distance between atoms / and j Z. , and Ujj are lower and upper bounds on the distance Z. and ZZj, are the smoothed bounds after application of the triangle inequality is the distance between atom / and the geometric center N is the number of atoms (Mj,) is the metric matrix is the positional vector of atom / 2, is the first eigenvector of (M ,) with eigenvalue Xf,. V , r- , and ate the y-, and -coordinates of atom /. (1-5 correspond to the numbered list on pg. 258.)...

Throughout the torsion angle dynamics calculation the list of van der Waals lower distance bounds is updated every 50 steps using a cutoff of 4.2 A for the interatomic distance. 

Distance geometry uses a four-stage process to derive a conformation of a molecule [Crippen 1981 Crippen and Havel 1988]. First, a matrix of upper and lower interatomic distance bounds is calculated. This matrix contains the maximum and minimum values periiutted to each interatomic distance in the molecule. Values are then randomly assigned to each interatomic distance between its upper and lower bounds. In the third step, the distance matrix is converted into a trial set of Cartesian coordinates, which in the fourth step are then refined. 

A subsequent study considered two selected possible conformations for ASYN bound to SUVs, namely an extended helix and the horseshoe structure. Theoretically expected spin-spin distance distributions for doubly labeled ASYN taking the possible rotamers of the spin labels into account were calculated. This enabled one to identify label positions in the crucial location close to the potential linker region between the two horseshoe helices which would allow distinguishing between these conformations by CW EPR distance measurements. CW EPR spectra of correspondingly labeled ASYN bound to POPC SUVs were measured and, using the theoretical distance distributions, calculated. The authors interpreted their results in... 

Gas-phase spectroscopic measurements [115] had been unable to clearly determine the structure of the H2S dimer, but had offered the suggestion of a linear or bifurcated geometry. Frisch et al. [94] compared these two theoretically and found indications that the bifurcated structure represents a transition state on the surface, about 1 kJ/mol higher in energy than the linear structure. The dimer is only very weakly bound, by less than 6 kJ/mol and by an even smaller amount (3.3 kJ/mol) when zero-point vibrational energies are considered. Accentuating the weakness of the interaction, the S S distance was calculated to be quite long at 451.4 pm. 

System Setup and MC Details. To correspond to the experimental conditions, the fep calculations were performed in the isothermal, isobaric (NPT) ensemble at 25 °C and 1 atm. Furthermore, the solvents were chloroform for the calixarene and dichloromethane for the calixpyrrole. The calculations employed periodic boundary conditions and 12-A spherical cutoffs based on the C-C distance for solvent pairs and on the distance between the solvent molecule s carbon atom and a well distributed set of solute atoms. If any of these interatomic distances is below the cutoff, the entire solute-solvent interaction is included. For the calixarene, the unbound and bound calculations used 626 and 127 chloroform molecules, respectively, and the corresponding numbers were 327 and 127 dichloromethane molecules for the smaller calixpyrrole. A rectangular cell, ca. 39 X 46 X 48 A, contained the calixarene, ion and chloroform, while a cubic box ca. 33 A on a side was used for the calixpyrrole complexes. Each window involved ca. 2 x 10 configurations of equilibration followed by 2 x 10 configurations of averaging for... 

Distances between the tight Mn site and the Cr of various complexes were determined using EPR and NMR data. From the diminution elicited by paramagnetic Cr on the EPR transitions of bound Mn +, a distance was calculated using the Leigh theory because the results suggested a dipolar relaxation phenomenon similar to that observed with glutamine synthetase. The data that were evaluated were at a Mn PPase ratio of more than 0.26, where 95% of the Mn was in E-Mn complex. 

We can now proceed to the generation of conformations. First, random values are assigne to all the interatomic distances between the upper and lower bounds to give a trial distam matrix. This distance matrix is now subjected to a process called embedding, in which tl distance space representation of the conformation is converted to a set of atomic Cartesic coordinates by performing a series of matrix operations. We calculate the metric matrix, each of whose elements (i, j) is equal to the scalar product of the vectors from the orig to atoms i and j ... 

Physical Properties. The absorption of x-rays by iodine has been studied and the iodine crystal stmcture deterrnined (12,13). Iodine crystallizes in the orthorhombic system and has a unit cell of eight atoms arranged as a symmetrical bipyramid. The cell constants at 18°C (14) are given in Table 1, along with other physical properties. Prom the interatomic distances of many iodine compounds, the calculated effective radius of the covalently bound iodine atom is 184 pm (15). 

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