Rate-limiting bottlenecks

Consider the series reaction A—>B—>C. If the first step is very much slower than the second step, the rate of formation of C is controlled by the rate of the first step, which is called the rate-determining step (rds), or rate-limiting step, of the reaction. Similarly, if the second step is the slower one, the rate of production of C is controlled by the second step. The slower of these two steps is the bottleneck in the overall reaction. This flow analogy, in which the rate constants of the separate steps are analogous to the diameters of necks in a series of funnels, is widely used in illustration of the concept of the rds. 

Rate-limiting step (Section 11.4) The slowest step in a multistep reaction sequence. The rate-limiting step acts as a kind of bottleneck in multistep reactions. 

Generally, the stratum corneum is considered to be the rate limiting layer of the skin with regard to transdermal drug absorption. However, for the invasion of very lipophilic compounds, the bottleneck moves from the stratum corneum down to the viable, very hydrophilic layer of the epidermis, due to substances reduced solubility in this rather aqueous layer [14],... 

Often an improvement in one section of a line or plant will cause the rate-limiting section to shift to either an upstream or downstream process. These types of projects often have considerable value associated with them because of the multiple bottlenecks that exist. 

The skeletal or short mechanism is a minimum subset of the full mechanism. All species and reactions that do not contribute significantly to the modeling predictions are identified and removed from the reaction mechanism. The screening for redundant species and reactions can be done through a combination of reaction path analysis and sensitivity analysis. The reaction path analysis identifies the species and reactions that contribute significantly to the formation and consumption of reactants, intermediates, and products. The sensitivity analysis identifies the bottlenecks in the process, namely reactions that are rate limiting for the chemical conversion. The skeletal mechanism is the result of a trade-off between model complexity and model accuracy and range of applicability. 

So far we have considered a system with two reservoirs separated by one bottleneck in general a polyatomic system wil1 have many reservoirs in its configuration space, and the location of the critical bottleneck or bottlenecks will be unknown. Here we will first distinguish critical and rate-limiting bottlenecks from less important ones, and then discuss several more or less heuristic methods for for finding bottlenecks. 

Definition of Critical and Rate-Limiting Bottlenecks" The hypothesis of local equilibrium within the reservoirs means that the set of transitions from reservoir to reservoir can be described as a Markov process without memory, with the transition probabilities given by eq. 4. Assuming the canonical ensemble and microscopic reversibility, the rate constant Wji, for transitions from reservoir i to reservoir j can be written... 

In flashing light, there are limitations on the minimum and maximum times between flashes. The rate-limiting step in turnover of PSII is exchange of quinone for quinol, which occurs at the QB site. Consequently, the electron acceptors will produce a bottleneck if the time between... 

The removal of kinetic bottlenecks by removing regulation and/or by amplifying the genes that code for the rate-limiting enzymes. Alternatively, the WT enzymes may be replaced by mutated or heterologous ones with a different control architecture. 

The concept of the rate limiting step in a sequence of chemical transfer mations is conventionally associated with a bottleneck. It is hardly pos sible to provide a consistent mathematical definition of a bottleneck in terms of classical chemical kinetics, but the concept of the rate controlling step can be defined easily. 

The maximum difference of thermodynamic rushes is, obviously, corre spondent to the occurrence of the bottleneck in the stepwise reaction. Therefore, the rate limiting step in a sequence of chemical transformations is naturally to define as some elementary step with the maximum differ ence of thermodynamic rushes (or that has nearly the same chemical potentials) of the reaction groups involved in the transformation. Horiuti first mentioned this specificity of the stepwise reaction bottleneck. 

Figure 1.7 An example of the interrelation of the bottleneck created by the rate-limiting step of a consecutive set of monomolecular transformations with the decrease in thermodynamic rushes of consecutive thermalized in intermediates Y. The stationary rate of the overall stepwise reaction here should be VE = 2(R P).

Some specific features of catalytic reactions, which are identified via the microkinetic analysis and are what make catalytic and noncatalytic reac tions qualitatively different, are discussed following. One is possible nonco incidence of the rate limiting steps (the process bottleneck ) and rate determining steps, the parameters of the latter being directly present in the expressions that describe the stationary rate of the stepwise process. 

It is evident here that the rate-limiting stage (the reaction "bottleneck") that is the step with the largest difference of the stationary values of chemical potentials (thermodynamic rushes) of the interacting reaction groups is the one with minimal s,. This is identical to the case of the chain of noncatalytic transformations (1.54). 

We must emphasize that the condition R > P satisfies inequality (4.13) at both 81 > 82 and 81 < 82, which means that the rate-determining stage in Gase a appears to be step 2, no matter which step of the stepwise process is the actual rate-limiting one (the "bottleneck") ... 

Given that the bottleneck establishing the rate of chlorine-induced ozone destruction is, to first order, the concentration of the rate limiting chlorine free radical in the dominant catalytic cycle destroying odd oxygen, it is essential to establish the propensity of the stratosphere for partitioning total chlorine into the rate limiting radical form. This ratio of CIO to total chlorine as a function of altitude is a quantity of first order importance. 

As illustrated in the previous section, the kinetics associated with an ET process may be complex when diffusion or relaxation processes create dynamic bottlenecks. In limiting cases, however, a simple model based on transition state theory (TST) suffices. According to TST, the system maintains thermal equilibrium between different positions along the reaction coordinate [87]. We consider the TST rate constant for electron transfer after some preliminary comments about state manifolds and energetics. 

The singlet-singlet energy transfer between the central zinc porphyrin in the antenna of 60 and the free base porphyrin ( 3) is slow (240 ps) compared with that among the zinc porphyrins (ki) (50 ps). Thus, the rate constant is a bottleneck that limits the quantum yield of the final charge-separated state (Pzp)3-Pzc-P -C6o . Structural modifications are envisioned to improve the performance of this antenna-reaction center device. 

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