Bottleneck intermediate

To illustrate how a complex mechanism described in terms of ODEs may be approximated by a simpler system in which delays are included, we consider a sequence of coupled irreversible first-order reactions. Epstein (1990) analyzed this system by introducing the concept of a bottleneck intermediate, a generalization of the notion of a rate-determining step. 

The above analysis suggests an algorithm for defining the subset [A ) p o. p of bottleneck intermediates. Let a(0) — 1, and let (/ ) be the index of that species / such that k/ is the smallest rate constant, that is. 

Again, if is the smallest of the remaining rate constants, we are done, / = 1, and there is a single bottleneck intermediate. If not, we continue the process until we are left with ki as the smallest remaining rate constant. The set of bottleneck intermediates is then complete. 

Except for a brief transient period, the DDE model, eqs. (10.29), reproduces the exponential decay of the reactant A the rise and fall, after a delay, of each of the bottleneck intermediates Aa(p), and the delayed buildup of the product A which constitute the essential aspects of the dynamics of the full system represented by eqs. (10.26). The model we have just treated is not particularly interesting in terms of its chemistry. It does, however, suggest that an approach based on treating systems with many intermediates in terms of DDE models with just a few key intermediates and delays that incorporate the effects of the nonessential intermediates may be worth exploring. The key problem to be solved in implementing such an approach lies in deriving relationships analogous to eq. (10.30) between the parameters of the system and the delay times. 

Kinetic data provide information only about the rate-determining step and steps preceding it. In the hypothetical reaction under consideration, the final step follows the rate-determining step, and because its rate will not affect the rate of the overall reaction, will not appear in the overall rate expression. The rate of the overall reaction is governed by the second step, which is the bottleneck in the process. The rate of this step is equal to A2 multiplied by the molar concentration of intermediate C, which may not be directly measurable. It is therefore necessary to express the rate in terms of the concentrations of reactants. In the case under consideration, this can be done by recognizing that [C] is related to [A] and [B] by an equilibrium constant ... 

Kinetic modeling of the transient absorption spectra is necessary in order to obtain estimates of the lifetimes and rate constants associated with the evolution of the intermediates observed during the dissociation. A detailed description of the modeling may be found in our work on the picosecond photodissociation of the natural car-boxy- and oxy- heme complexes (3,4). The model is designed to treat the dissociation as a series of first or second order steps indicated in pathways I and II, ones that are consistent with the transient absorption data and with arguments based on bottlenecks... 

Once relaxation to the lowest excited singlet has occurred the next intermediate expected would be due to the bottleneck in the... 

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. 

The intrinsic instability of235 makes its existence difficult to prove intramolecular closure to 4-hydroxy-1-deoxyartemisinin 236 or simple aqueous hydrolysis leads to its destruction. If 235 (and related structures) were the bottleneck through which the artemisinin class exerted its antimalarial effect, then replacement of 0-13 by CH2 might give an isolable intermediate epoxide of greater stability, but also with lesser activity. 

A distinctive feature of these metrics is that they can be stacked along the whole product supply chain. In this way, ecological bottlenecks can be identified readily. For example, a chemical product that might appear as benign for the environment, could involve, in reality, highly toxic materials in some intermediate steps of manufacturing. 

Normally there is no need for an intermediate storage, but the pace to which nuclear submarines have been decommissioned has created bottlenecks which in turn resulted into a difficult situation. 

Second bottleneck lies in the transportation capacity fuel elements that have been unloaded stay for many years in pools or in containers stored in the open air by want of transportation capacity. Those de facto intermediate storage lack the safety environment that would have been asked for if they had been conceived from the beginning as storage facilities they also lack correct physical protection and -though spent fuel from submarine is not the easiest way to a nuclear weapon - could thus attract the attention of terrorist organizations. 

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