Collinearity rule

The three-module system found in all ACV synthetases correlates well with the sequential condensation, epimerization, and hydrolytic release of the tripeptide. At first sight, the arrangement of domains and modules fits perfectly the collinearity rule found in the majority of NRPS systems, which implies that the linear sequence of domains corresponds to the sequence of reactions of the pathway [40,45],... 

To a first approximation, the composition of the distillate and bottoms of a single-feed continuous distillation column lies on the same residue curve. Therefore, for systems having separatrices and multiple regions, distillation composition profiles are also constrained to lie in specific regions. The precise boundaries of these distillation regions are a function of reflux ratio, but they are closely approximated by the RCM separatrices. If a separatrix exists in a system, a corresponding distillation boundary also exists. Also, mass balance constraints require that the distillate composition, the bottoms composition, and the net feed composition plotted on an RCM for any feasible distillation be collinear and spaced in relation to distillate and bottoms flows according to the well-known lever rule. 

It is of some interest to compare the different structures resulting from linear monomers (HF)2 (bent) and (HCN)2 (collinear). In both dimers, the observed intermolecular separations11 are such that rule 7 is ineffective, even for the collinear structure of (HCN)2, where steric effects might be expected to be important. As already seen in Section 5.2.1 and... 

After mixing with the entrainer C, the new feed becomes the point m,. The mixing operation is represented by the segment f,-C, the position of m, depending on the ratio entrainer/initial mixture given by the lever rule. Suppose that we would like to separate A of good purity by a first split. The distillate is described by the point d, close to the vertex of A. The bottom product is marked by the point b, collinear with d, and m,. Both d, and b, will be situated on the same residue curve. In addition, the position of b, must obey a hard constraint imposed by the distillation boundary it cannot go beyond. Thus, high purity A can be obtained, but the maximum recovery is dictated by the distillation boundary. 

A study directed toward understanding when gas phase dynamics closely resembles the dynamics of the same reaction in solution was performed by Li and Wilson. io In this work, they used a model asymmetric A -t- BC reaction. By using an asymmetric reaction, Li and Wilson were able to test the validity in the solution phase of the Evans—Polanyi rule,3n which has proven to be quite useful in understanding gas phase reaction dynamics. The Evans-Polanyi rule states for a collinear A -t- BC reaction, that if the barrier to reaction is located early in the reaction coordinate, then translational excitation of the reactants is necessary to climb this barrier and vibrational excitation of the products will result. Conversely, a late barrier to reaction requires vibrational excitation of the reactants and results in translational excitation of the products. This rule has been validated numerous times in the gas phase and is an ideal example of how a simple rule can explain the dynamics of a large number of reaction systems. 

Logical construction rules are tangent, parallel, perpendicular, concentric, continuous, coincident, symmetric, intersected, point on element, collinear, connect, and equal (Figure 7-21). 

The momentum conservation law rules the direction of photons, as well. In the case of two-photon annihilation, photons must depart collinearly and the three-photon annihilation determines a plane in which photons should stay. This strict rule is usually altered slightly by... 

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