A bottleneck state

Alternatively, all four ATPs may bind, accumulating subtle conformational changes in the ring which trigger hydrolysis only once all of the ATPs are bound. Moreover, it is also possible that the ATPs are hydrolyzed in the burst phase, immediately before each subunit generates a step. Finally, it is also possible that the hydrolysis of ATP is decoupled between the subunits and that it can occur spontaneously on its own, independent of the chemical state of the rest of the ring. The burst structure would then be maintained by another kinetic state, a bottleneck state, which would force the motor to wait until the necessary hydrolysis had occurred. A similar set of arguments can be made for the location of ADP release, with the result that ADP may be released in either the burst or dwell phase. 

As a result of possible recrossings of the transition state, the classical RRKM lc(E) is an upper bound to the correct classical microcanonical rate constant. The transition state should serve as a bottleneck between reactants and products, and in variational RRKM theory [22] the position of the transition state along q is varied to minimize k E). This minimum k E) is expected to be the closest to the truth. The quantity actually minimized is N (E - E ) in equation (A3.12.15). so the operational equation in variational RRKM theory is... 

Since chemical reactions usually show significant nonadiabaticity, there are naturally quantitative errors in the predictions of the vibrationally adiabatic model. Furthermore, there are ambiguities about how to apply the theory such as the optimal choice of coordinate system. Nevertheless, this simple picture seems to capture the essence of the resonance trapping mechanism for many systems. We also point out that the recent work of Truhlar and co-workers24,34 has demonstrated that the reaction dynamics is largely controlled by the quantized bottleneck states at the barrier maxima in a much more quantitative manner than expected. 

The SQ method extracts resonance states for the J = 25 dynamics by using the centrifugally-shifted Hamiltonian. In Fig. 20, the SQ wavefunc-tion for a trapped state at Ec = 1.2 eV is shown. The wavefunction has been sliced perpendicular to the minimum energy path and is plotted in the symmetric stretch and bend normal mode coordinates. As anticipated, the wavefunction shows a combination of one quanta of symmetric stretch excitation and two quanta of bend excitation. The extracted state is barrier state (or quantum bottleneck state) and not a Feshbach resonance. 

Since the submission of this article in 2002, there has been a great deal of new work published on the subject of resonances and quantum bottleneck states in chemical reactions. Unfortunately, a discussion of these exciting new results was not possible here. 

A kinetic term introduced by Ray to designate the bottleneck in a steady-state enzyme kinetic pathway as that step in which the enzyme form accumulates in highest concentration at saturating substrate concentration. Highest accumulation of this enzyme reflects the fact that this species faces the highest barrier that precedes an irreversible step in the forward direction. 

Transition state theory (1), the traditional way of calculating the frequency of infrequent dynamical events (transitions) involving a bottleneck or saddle point, typically had to call on both these approximations before yielding quantitative predictions. 

Transition-state theory is based on two assumptions, the existence of both a dynamic bottleneck and a preceding equilibrium between a transition-state complex and reactants. Eq. (2.4) results, where k denotes the observed reaction rate constant, k the transmission coefficient, and v the mean frequency of crossing the barrier. 

A second scenario is provided by barrier-type resonances (sometimes referred to as quantum bottleneck states [QBS]), which do not rely on the internal excitation of the collision complex for their existence. In fact, barrier resonances are observed even when there is no well in Vad(s n). Collisional time delay occurs near the barrier maximum simply because the motion along the s-coordinate slows down passing over the barrier, as in the lower... 

We have shown that an accessible conical intersection forms a bottleneck that separates the excited state branch of a nonadiabatic photochemical reaction path from the ground state branch, thus connecting the excited state reactant to two or more products on the ground state surface via a branching of the... 

Pick a disease-state management service. Develop a process diagram for this service. What stages of this process do you expect to create bottlenecks What resources would be necessary in each step of the process ... 

To that end, variational transition-state theory has been introduced, which is based on Wigner s variational theorem, Eq. (5.10). When a saddle point exists, it represents a bottleneck between reactant and products. It is the point along the reaction coordinate where we have the smallest rate of transformation from the reactant to products. This can be seen from Eq. (7.50), where it should be noted that only the sum of states G (E ) changes as the reaction proceeds along the reaction coordinate. We have the smallest sum of states of the activated complex G (E ) on top of the barrier because at this point the available energy E is at a minimum see Fig. 7.3.3. 

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