Ordered Sequential Reactions

Thus far only reactions involving a single substrate have been considered. Most enzymatic reactions have two substrates. Unlike chemical processes, the sequence in which the substrates bind to the enzyme may be important. If two substrates, A and B, bind in a specific order (e.g., A binds first) as illustrated in Equation 11.37 the mechanism is called ordered sequential. 

Following a protocol analogous to the one used in developing Equations 11.32 through 11.36, the apparent rate constant and its isotope effects can be calculated  

One important difference between Equations 11.35 and 11.39 is that in the latter case the commitment is a function of the concentration of the second substrate (i.e. the one which binds second and is labeled B in Equation 11.37, while in Equation 11.35 it is not. 

Equation 11.39 reduces to 11.35 when steps labeled with rate constants ks-k7 are lumped together and treated as a unit, e.g.  

Equation 11.40 is a special case of a more general mechanism discussed below in which substrates bind to the enzyme randomly. However, to finish discussion of the sequential ordered mechanism, Equation 11.37, we simplify as before, by assuming that binding processes are isotopically insensitive. Equation 11.39 becomes  

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In a sequential reaction, all the substrates must be bound to the enzyme before any release of product can occur. Sequential systems can be either ordered or random. In an ordered sequential reaction, substrates must bind to the enzyme in a particular order, whereas in a random sequential system, substrates may bind to the enzyme in any order. In reaction schemes, substrates are usually abbreviated as A, B, C, and D in the order that they bind to the enzyme, whereas products are abbreviated as P, Q, R, and S in the order that they leave the enzyme. Sequential binding of substrates is a consequence of their orientation within the enzyme active site. 

Valuable insights into how DNA polymerases process their substrates were obtained as a result of detailed kinetic studies of the enzymes. Benkovic and coworkers employed rapid quenching techniques to study the kinetics of transient intermediates in the reaction pathway of DNA polymerases [5]. Intensive studies revealed that E. coli DNA polymerase I follows an ordered sequential reaction pathway when promoting DNA synthesis. Important aspects of these results for DNA polymerase fidelity are conformational changes before and after the chemical step and the occurrence of different rate-limiting steps for insertion of canonical and non-canonical nucleotides. E. coli DNA polymerase I discriminates between canonical and non-canonical nucleotide insertion by formation of the chemical bond. Bond formation proceeds at a rate more than several thousand times slower when an incorrect dNTP is processed compared with canonical nucleotide insertion. 

Steady-state kinetics have been used to determine the kinetic mechanisms of many of these enzymes. The questions that have been primarily addressed are the sequence of steps that occur in substrate binding prior and subsequent to the catalytic reaction and the potential formation of covalent enzyme intermediates. Classical interpretation of kinetic analyses has been the determination of the relevant reactions occurring via a random or an ordered sequential reaction, or if the reaction is a double-displacement or Ping-Pong reaction. In the former case, phosphoryl transfer occurs in the ternary complex that contains enzyme, phosphoryl donor, and phosphoryl acceptor. In the latter case, enzyme reacts with... 

The first situation, for parallel pathways, is illustrated by Eq. (6-9), the reaction between H2O2 and I". The limiting order with respect to [H+] increases from zero to one as [H+] increases. The second situation, for sequential reactions, is illustrated by Eq. (6-14). The order with respect to [Fe2+] falls from two to one with increasing [Fe2+], and that with respect to [Fe3 r ] from zero to negative one with increasing [Fe3+]. 

Saddle point. 170 Salt effects. 206-214 Scavenging (see Reactions, trapping) Second-order kinetics. 18-22, 24 in one component, 18-19 in two components (mixed), 19-22 Selectivity. 112 Sensitivity analysis. 118 Sensitivity factor, 239-240 Sequential reactions (see Consecutive reactions)... 

For a number of reasons, there are some important limitations to the extension of this principle. Biodegradation—as opposed to biotransformation—of complex molecules necessarily involves a number of sequential reactions each of whose rates may be determined by complex regulatory mechanisms. For novel compounds containing structural entities that have not been previously investigated, the level of prediction is necessarily limited by lack of the relevant data. Too Olympian a view of the problem of rates should not, however, be adopted. An overly critical attitude should not be allowed to pervade the discussions—provided that the limitations of the procedures that are used are clearly appreciated and set forth. In view of the great practical importance of quantitative estimates of persistence to microbial attack, any procedure—even if it provides merely orders of magnitude—should not be neglected. 

At about the same time, hydroxamic adds and oximes were found to react directly with organophosphorus compounds.85 2-PAM I was found to react In vitro with sarin with marked deviation from first-order kinetics that suggested that the reaction actually consists of (at least) two sequential reactions. Green showed that quatemlzed pyridine aldoximes react with an organophosphorus (OP) compound In three steps ... 

A substrate analog will frequently inhibit only one of the two forms of a multisubstrate enzyme with a ping-pong mechanism.1 72 Reciprocal plots made for various inhibitor concentrations consist of a family of parallel lines reminiscent of uncompetitive inhibition. Observation of such parallel line plots can support a ping-pong mechanism for an enzyme but cannot prove it because in some cases parallel lines are observed for inhibition of enzymes acting by an ordered sequential mechanism. The following question arises naturally for any ordered bimolecular reaction (Eq. 9-43) Of the... 

Reactions in which all the substrates bind to the enzyme before the first product is formed are called sequential. Reactions in which one or more products are released before all the substrates are added are called ping-pong. Sequential mechanisms are called ordered if the substrates combine with the enzyme and the products dissociate in an obligatory order. A random mechanism implies no obligatory order of combination or release. The term rapid equilibrium is applied when the chemical steps are slower than those for the binding of reagents. Some examples follow. 

Multicomponent reactions (MCRs) are processes that involve sequential reactions among three or more reactant components that co-exist in the same reaction mixture. In order to be efficient, MCRs rely on components that are compatible with each other and do not undergo alternative irreversible reactions to form other products or by-products. 

If the von Smoluchowski rate law (Eq. 6.10) is to be consistent with the formation of cluster fractals, then it must in some way also exhibit scaling properties. These properties, in turn, have to be exhibited by its second-order rate coefficient kmn since this parameter represents the flocculation mechanism, aside from the binary-encounter feature implicit in the sequential reaction in Eq. 6.8. The model expression for kmn in Eq. 6.16b, for example, should have a scaling property. Indeed, if the assumption is made that DJRm (m = 1, 2,. . . ) is constant, Eq. 6.16c applies, and if cluster fractals are formed, Eq. 6.1 can be used (with R replacing L) to put Eq. 6.16c into the form... 

Reductive dimerization of ketones Aromatic -unsaturated ketones are reduced and dimerized to 1,5-hexadienes by sequential reaction with LiAIH4, Fe3(CO)i2, and HCl. The effectiveness of iron carbonyls shows the order Fe3(CO), 2 > Fe2(CO)y > FeiCO). ... 

The efficiency of this sequential reaction significantly depends on the layering sequence used for the two kinds of enzymes. When GA and GOD are applied in the correct order for the reaction to occur (GA in the first layer and GOD in the second layer), the reaction efficiency is high. Reversing the en-... 

PA-824." The overall yield of the target compound was nearly tripled and the amount of solvent used was reduced by one third. A reduction in energy usage was also noted, as the extent of solvent removal between steps (in order to perform sequential reactions in different media) was significantly reduced. This study therefore demonstrates the great potential that solvent free reactions hold for complex organic procedures. 

It has been shown that the suggested. sequential reaction scheme, A - B -< C, fully explains the phenomena observed for Vanadium removal from Kuwait AR at industrially relevant conditions. However, it has also been shown that the A - B reaction controls the Vanadium removal in most of the reactor, and this implies that, in practical terms, the overall HDV reaction can be considered as a simple first order reaction with Qv values as effectiveness factors. 

The same author found that under controlled humidity conditions degradation was first order at 23 to 90% relative humidity (RH) and 64 to 90°C for trihydrate and at 50 to 90% RH and 40 to 70°C for sodium salt, although at 23% RH sequential reactions occurred with the sodium salt [40], The logarithm of the first order rate constants at a fixed temperature increased linearly with RH [40] or with the logarithm of the vapour pressure [41], confirming the importance of water for the degradation of these compounds. 

A reference vanadium deposition experiment is carried out in order to assess the influence of quinoline and HjS. Quinoline showed to decrease the rate of metal removal, the amount of vanadium deposited is lower as compared to the reference experiment. The shape of the vanadium deposition profiles is similar in both cases. A deposition maximum is observed in the centre of the pellet, indicating that the vanadium deposition process is not diffusion limited and that a sequential reaction mechanism applies for VO-TPP HDM. Low H2S partial pressure resulted in different vanadium deposition profiles as a function of the axial position in the reactor. At the inlet of the reactor, similar shaped profiles as the reference experiment were found, however, at the outlet of the reactor a shift towards M-shaped profiles was found indicating a diffusion limited vanadium deposition proeess. This shift in vanadium deposition profiles is explained by the build-up of the last intermediate resulting in a higher metal deposition rate. 

The deposited solid is the final result of all these subprocesses. The rate of the subprocess varies in a wide range. For these sequential reactions or subprocesses the overall deposition rate is controlled by the slowest subprocess. In this section the CH3SiCl3-H2 deposition system has been chosen as the system for discussion in both homogeneous chemical reactions and heterogeneous chemical reactions in order to give a more in-depth understanding of the kinetics of a chosen CVD process. 

It would be beyond our present scope to try to cover the detail of the theory of systems of first order reactions, but the basic ideas are so simple and elegant that it seems a pity that they should pass completely unnoticed. A simple eicample will show the main features. We shall take the reversible sequential reaction A B C and add a further reaction A, thus turning it into the triangular system... 

Sequential Reactions. In sequential reactions, all substrates must bind to the enzyme before any product is released. Consequently, in a bisubstrate reaction, a ternary complex of the enzyme and both substrates forms. Sequential mechanisms are of two types ordered, in which the substrates bind the enzyme in a defined sequence, and random. 

In the random sequential mechanism, the order of the addition of substrates and the release of products is random. An example of a random sequential reaction is the formation of phosphocreatine and ADP from ATP and creatine, which is catalyzed by creatine kinase (p. 416). 

If the orders of reaction in the reactants are positive, a broad RTD will diminish the reactor performance (lower the conversion at a given space velocity). The loss in performance can become considerable at high conversions for reactions with high reaction orders. If the target product is an intermediate in a sequential reaction network, selectivity and yield may be quite sensitive to back-mixing. 

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