Multiplicity profiles region

A prior distribution for sequence profiles can be derived from mixtures of Dirichlet distributions [16,51-54]. The idea is simple Each position in a multiple alignment represents one of a limited number of possible distributions that reflect the important physical forces that determine protein structure and function. In certain core positions, we expect to get a distribution restricted to Val, He, Met, and Leu. Other core positions may include these amino acids plus the large hydrophobic aromatic amino acids Phe and Trp. There will also be positions that are completely conserved, including catalytic residues (often Lys, GIu, Asp, Arg, Ser, and other polar amino acids) and Gly and Pro residues that are important in achieving certain backbone conformations in coil regions. Cys residues that form disulfide bonds or coordinate metal ions are also usually well conserved. 

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. 

Fig. 9.4. (a) The dependence of the stationary-state concentration of reactant A at the centre of the reaction zone, a (0), on the dimensionless diffusion coefficient D for systems with various reservoir concentrations of the autocatalyst B curve a, / = 0, so one solution is the no reaction states a0i>8 = 0, whilst two other branches exist for low D curves b and c show the effect of increasing / , unfolding the hysteresis loop curve d corresponds to / = 0.1185 for which multiplicity has been lost, (b) The region of multiple stationary-state profiles forms a cusp in the / -D parameter plane the boundary a corresponds to the infinite slab geometry, with b and c appropriate to the infinite cylinder and sphere respectively. 

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