Two-state reaction

An additional surprise is, that the reaction rates of these spontaneous back-reactions 153 - 152 (X = Br, Cl) are temperature-independent between 8.5 and 25 K. In our opinion this unusual kinetic behavior might be the outcome of a double two-state reaction involving a surface crossing with the triplet state of... 

CI2 was used in the last chapter to exemplify the basic kinetics of two-state reactions. The small fraction that folds slowly because of cis —> trans peptidyl-proline isomerization is ignored in the following discussion. CI2 folds according to first-order kinetics from a relatively open denatured state, with a half-life of some 10 ms.25 Some mutants fold 10 times faster. 

Figure 11 Simulation of line shapes of a reaction according to the binding model (a) Two-state reaction, (b) Two-state reaction with one intermediate and (c) Two-state reaction with two possible intermediates. Protein concentration is 0.1 mM. Titration in equal steps until an equimolar amount of ligand is reached (0, 0.01, 0.02. .. 0.1 mM). The signals of P and PL are separated by Av = 150 Hz. The sequential steps in the titration change color from black to gray.

Fig. 25 Potential energy surfaces for the most feasible two-state reaction pathways for ethylene dimerization catalyzed by Cr(II)OH (If), via either a Cr-carbene mechanism or a metallacycle mechanism determined at the M06 level of theory. Also shown are the crossing points optimized at CASSCF level. The triplet metallacycle reaction pathway is depicted in blue, and the triplet Cr-carbene reaction pathway is shown in dark red. The quintet parts are in black. Energies are in kcal moP and relative to il. Bond lengths are in angstroms. Angles are in degrees...

The theory for a reversible two-state reaction predicts the same two dec times at all emission wavelengths. This is illustrated in Ae left-hand panel of Figure 18.8 for 2-naphthol at pH 3.0 at this pH, the same decay times were... 

Qi iwe 2 sigmoidal curve not unlike that observed with spectroscopic probes. If ris expressed relative to the midpoint temperature, T , where Ku = 1(AG° = 0 and a = 0.5), then the term C in Eqs. (5) and (6) is A plus the change in heat capacity (ACp) at Tm. Note that for a two-state reaction, T represents the maximum in but not Subtraction of from C" " provides... 

The calorimetric and van t Hoff enthalpies should be the same for a two-state reaction N U) that proceeds from completely folded to unfolded protein. It is often argued that the AHcai/AH h ratio indicates whether or not a reaction is two-state. However, care must be taken in application of this criterion. Marginally stable proteins may not be completely folded at the beginning of a thermal melt (Fig. 1, thin solid line), and then the measured AHcai will be less than AH even if the unfolding is two-state. Similarly, such data can yield an apparent T that is not an accurate reflection of where AG fo = 0 (see also ref. 45). 

I T) is linear before and after the transition, with a sigmoidal transition in between. An equilibrium constant is obtained from the progress curve at any temperature Tas commonly done with spectroscopic data s [see Eq. (18) below a two-state reaction can be assumed for this purpose without introducing significant error], and a(r) is calculated using Eq. (7). is calculated according to Eq. (5) using a(T) and... 

Fig. 4.9 The two-state reaction manifold as formulated by Shade and coworkers [68,69]. The ferryl radical cation of compound I (7) has two unpaired electrons in iron d orbitals and one in the Si2u porphyrin orbital. This electron configuration can give rise to either a quartet state ( Aju) if all spins are unpaired or a doublet if the spin of the electron in the aju orbital is inverted. A hydrogen atom is abstracted fi om the substrate in the first step of the reaction and an electron is transferred to either the iron, producing the ferrous state (as shown), or to the porphyrin, neutralizing the radical cation. A quartet or doublet state is...

The Marcus equation for nonadiabatic electron-transfer reactions (Eq. B5.3.4), and the Forster theory that we discussed in Chap. 7 apply only to systems with weak intermolecular interactions, which we now can define more precisely as meaning that H21 lh steady-state approximation to the stochastic Liouville equation for a two-state reaction in this limit From Eqs. (BIO.1.15), (10.29a), (10.29b), and (10.30), we have... 

Figure 5.6 Demonstration of the correlation between the ground-state activation free energy (AG ) and the height of the intersection between free energy functionals of the diabatic surfaces in a two-state reaction model. If the curve Ajj which describes the free energy of the state Fj, is shifted relative to A92 as shown in the figure, the activation energy (i.e. the relative energy of the transition state 2-3) will increase by approximately AAG2-.3[ ,(X)]=Ap3(X) — A3j(X)-...

So far we have been largely concerned with two state reactions. The exceptions to this were steady states and equilibria of enzyme reactions and ligand binding to multiple sites. In this and the next chapter we are concerned with rates of transition between a larger number of states of complex systems. An important statement about multi-state systems, which will recur in different forms, is that ... 

Ai/< ai and Ai/y.H. should be identical if the transition proceeds as a two-state reaction. The latter quantity is the so-called van t Hoff enthalpy and represents the standard enthalpy change of a one-step reaction. For a reaction of the type N nD the van t Hoff enthalpy can be approximately calculated by... 

In this paper, we compare quantum scattering, TSH-A and TSH-D results for several two-state reaction path models which describe the O + H2 reaction, and related reactions. Eleven model potentials have been considered, so as to determine the influence of triplet-singlet crossing location, the singlet well depth, and the size and coordinate dependence of the spin-orbit coupling. 

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