Catalytic calculations

We have previously calculated conformational free energy differences for a well-suited model system, the catalytic subunit of cAMP-dependent protein kinase (cAPK), which is the best characterized member of the protein kinase family. It has been crystallized in three different conformations and our main focus was on how ligand binding shifts the equilibrium among these ([Helms and McCammon 1997]). As an example using state-of-the-art computational techniques, we summarize the main conclusions of this study and discuss a variety of methods that may be used to extend this study into the dynamic regime of protein domain motion. 

The procedure is computationally efficient. For example, for the catalytic subunit of the mammalian cAMP-dependent protein kinase and its inhibitor, with 370 residues and 131 titratable groups, an entire calculation requires 10 hours on an SGI 02 workstation with a 175 MHz MIPS RIOOOO processor. The bulk of the computer time is spent on the FDPB calculations. The speed of the procedure is important, because it makes it possible to collect results on many systems and with many different sets of parameters in a reasonable amount of time. Thus, improvements to the method can be made based on a broad sampling of systems. 

A flame-ionization, total hydrocarbon analyzer determines the THC, and the total carbon content is calculated as methane. Other methods include catalytic combustion to carbon dioxide, which may be deterrnined by a sensitive infrared detector of the nondispersive type. Hydrocarbons other than methane and acetylene are present only in minute quantities and generally are inert in most appHcations. 

In the presence of 6-iodo-l-phenyl-l-hexyne, the current increases in the cathodic (negative potential going) direction because the hexyne catalyticaHy regenerates the nickel(II) complex. The absence of the nickel(I) complex precludes an anodic wave upon reversal of the sweep direction there is nothing to reduce. If the catalytic process were slow enough it would be possible to recover the anodic wave by increasing the sweep rate to a value so fast that the reduced species (the nickel(I) complex) would be reoxidized before it could react with the hexyne. A quantitative treatment of the data, collected at several sweep rates, could then be used to calculate the rate constant for the catalytic reaction at the electrode surface. Such rate constants may be substantially different from those measured in the bulk of the solution. The chemical and electrochemical reactions involved are... 

F. W. Kaiser and co-workers, Optim tion of an Electrically-Heated Catalytic Converter System—Calculations and Application, SAE 930384, Society of Automotive Engineers, Warrendale, Pa., 1993. 

A final important area is the calculation of free energies with quantum mechanical models [72] or hybrid quanmm mechanics/molecular mechanics models (QM/MM) [9]. Such models are being used to simulate enzymatic reactions and calculate activation free energies, providing unique insights into the catalytic efficiency of enzymes. They are reviewed elsewhere in this volume (see Chapter 11). 

All criteria proposed here are constructed such that if absolutely no gradient of a particular type exists, then the value of the corresponding criterion is zero. For fast catalytic processes this is not reasonable to expect and therefore a value judgment must be made for how much deviation from zero can be ignored. For the dimensionless expressions the Damkdhler numbers are used as these are applied to each particular condition. The approach is that the Damkdhler numbers can be calculated from known system values, which are related to the unknown driving forces for the transport processes. 

Commercial or production reactors for heterogeneous catalytic processes are versions of the so-called integral reactors, so the fundamental process of design is integration. In particular, the necessary catalyst-filled reactor volume must be calculated that will give a desired production rate. This then includes finding conditions to achieve the desired production, at a certain selectivity and minimal operating costs and investment, to maximize the return on investment. 

Catalytic crackings operations have been simulated by mathematical models, with the aid of computers. The computer programs are the end result of a very extensive research effort in pilot and bench scale units. Many sets of calculations are carried out to optimize design of new units, operation of existing plants, choice of feedstocks, and other variables subject to control. A background knowledge of the correlations used in the "black box" helps to make such studies more effective. 

Chaput, Jeminet and Juillard measured the association constants of several simple polyethylene glycols with Na", K", Cs", and Tl". Phase transfer catalytic processes and most biological processes are more likely to involve the first two cations rather than the latter two, so we will confine the discussion to these. Stability constants for the dimethyl ethers of tetra-, penta-, hexa-, and heptaethylene glycols were determined poten-tiometrically in anhydrous methanol solution and are shown in Table 7.1. In the third column of the table, the ratio of binding constants (Ks/K s) is calculated. Note that Simon and his coworkers have referred to this ratio as the selectivity constant. ... 

These rate constants are for the hydrolysis of cinnamic anhydride in carbonate buffer, pH 8.45, total buffer concentration 0.024 M, in the presence of the catalysts pyridine, A -methylimidazole (NMIM), or 4-dimethylaminopyridine (DMAP). In the absence of added catalyst, but the presence of buffer, the rate constant was 0.005 24 s . You may assume that only the conjugate base form of each catalyst is catalytically effective. Calculate the catalytic rate constant for the three catalysts. What is the catalytic power of NMIM and of DMAP relative to pyridine ... 

Figure 1.4 Catalytic C-N-O cycle for conversion of H to He. The times quoted are the calculated half-lives for the individual steps at 1.5 X 10 K.

During studies on ditryptophan derivatives, an interesting acid-induced cy-cHzation has been discovered. The 10-membered ring 37 was thus subjected to acidic conditions to produce the indolocarbazole derivative 38 (Scheme 6). Interestingly, calculations performed on the precursor 37 indicated that the lowest energy conformation resembled that of the diastereomer of 38, which was never observed. An additional experiment furnished the parent system 1 on treatment of 38 with a catalytic amount of acid. A TFA-induced formation of an indolo[2,3-<3]carbazole was also observed from a related acyclic 2,2 -connected tryptophan dimer (99JOC8537). 

Yamamoto et al. have developed a catalytic enantioselective carbo-Diels-Alder reaction of acetylenic aldehydes 7 with dienes catalyzed by chiral boron complexes (Fig. 8.10) [23]. This carbo-Diels-Alder reaction proceeds with up to 95% ee and high yield of 8 using the BLA catalyst. The reaction was also investigated from a theoretical point of view using ab-initio calculations at a RHF/6-31G basis set. 

The Conradson test (ASTM D-189) measures carbon residue by evaporative and destructive distillation. The sample is placed in a preweighed sample dish. The sample is heated, using a gas burner, until vapor ceases to burn and no blue smoke is observed. After cooling, the sample dish is reweighed to calculate the percent carbon residue. The test, though popular, is not a good measure of the cokeforming tendency of FCC feed because it indicates thermal, rather than catalytic, coke. In addition, the test is labor intensive and is usually not reproducible, and the procedure tends to be subjective. 

The simplest case to be analyzed is the process in which the rate of one of the adsorption or desorption steps is so slow that it becomes itself rate determining in overall transformation. The composition of the reaction mixture in the course of the reaction is then not determined by kinetic, but by thermodynamic factors, i.e. by equilibria of the fast steps, surface chemical reactions, and the other adsorption and desorption processes. Concentration dependencies of several types of consecutive and parallel (branched) catalytic reactions 52, 53) were calculated, corresponding to schemes (Ila) and (lib), assuming that they are controlled by the rate of adsorption of either of the reactants A and X, desorption of any of the products B, C, and Y, or by simultaneous desorption of compounds B and C. 

The results obtained showed, again, that the form of the rate equations and the values of their constants, obtained by the study of isolated reactions, are valid also in the coupled system. This was also confirmed by the observed agreement between the calculated and the experimental integral data (94)- Kinetic results and the analysis of the effect of reaction products revealed that adsorption of the reaction components was competitive and that all the compounds involved in the three reactions were adsorbed on the same sites of the catalytic surface. 

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