Occupancy equilibrium

Expressions relating the equilibrium occupancy of any state in this mechanism to agonist concentration can be derived as described in Chapter 1. If we define the equilibrium constants for agonist binding as K = kffk+1 and K2 = k 2lk+2 and a constant E describing the efficiency of channel opening (equivalent to efficacy) as E= (l a, then the equilibrium occupancy of the open state (A2R ) will be ... 

An expression for the equilibrium occupancy of pARt can again be obtained using the methods outlined in Chapter 1. A potential complication is that this mechanism contains a cycle, so the product of the reaction rates in both clockwise and counterclockwise directions should be equal in order to ensure the principle of microscopic reversibility is maintained. In this case, microscopic reversibility is maintained. Thus,... 

Notice that the channel opening rate is now denoted ( /. Because the channel can only open from the A2R state, the effective opening rate, ( /, is obtained by multiplying the real opening rate (5 by the equilibrium occupancy of A2R ... 

For part (d), substituting into Eq. (6.55) allows the equilibrium occupancy of AR to be calculated at 300 and 800 pM ACh. The results are 0.503 and 0.565, respectively. Therefore, at 300 pM, the calculated pAR is close to that observed experimentally. However, at 800 pM, the calculated p lft is higher than observed. Reasons for this result include the possibility that desensitization is affecting the popm at higher [A], In addition, the mechanism used to derive Eq. (6.55) may not be correct (as would be the case if a desensitized state must be added to the mechanism). 

Here akg is the annihilation operator of an electron in state fc, with spin s and energy eaks on large dot a. a = 1,..., M, na = J2ks aLafcs> an< fhe parameter K sets dot a1 s equilibrium occupancy. 

Temperature variations of equilibrium order parameters rp and r 2, and equilibrium occupation numbers n3, n2 and n3, shown in Figs. 2, are determined following the scheme [1], All numerical calculations have been performed for LaH2 27 (i.e. for c = 0.27), indicated in Fig. 1 by an arrow. 

This simple model is not exact because it takes no account of the occupancy of the defects, which is different from the equilibrium occupancy. The time-of-flight measurement of the trapping rates is performed with few excess carriers, so that the trap occupancy is the same as in equilibrium, but in a steady state photoconductivity experiment, and the demarcation energies are often far from midgap. The trap occupancy is calculated from the rate equations for band tail electrons and holes... 

Here Ti(T) ordered implies calculation of the sum [Zj0H ny(T)(r/6)] in (6) using the determined values of equilibrium occupation numbers ni(T), n2(T) and n3(T), while Ti(T) disordered implies replacement of the above sum by the expression [c Yj0H (r7 6)] at all temperatures. As it can be seen from Fig. 4b the difference delta seems to be very small to be registered in the measurements. 

The population coP of the state that pumps the system does not appear in the rate expression (9.88), however it determines the observed flux through Eqns (9.90) or (9.92). In the particular application (Section 17.2.2) to the problem of electronic conduction, when the left and right continua represent the free electron states of metal electrodes coP will be identified as the Fermi-Dirac equilibrium occupation probability at energy Eo, /(Eq) = [exp(( o — ti /kBT) + 1] where is the chemical potential of the corresponding electrode. 

Figure 1.22. The equilibrium occupation probabilities for Stone-Wales stacks up to stack 7 as a function of the total energy relative to Buckminsterfullerene.

Figure 1.28. Equilibrium occupation probabilities of the (NaCOssCP nanocrystals computed using the harmonic superposition method.

Figure 7 demonstrates the regularity band of PP in the Raman spectrum and the relative phonon occupation number for the extended excited bonds, Nj/No, and that for the compressed excited bonds, Nq/Nq, where No is the equilibrium occupation number. It is clear that Nj/No > 1 and Np/No < 1. N is related with temperature by the expression [61] ... 

Here, Vj stands for the volume of site j. The solute concentration c is then simply the sum over the equilibrium occupation numbers e, per unit volume. 

If a combustible gas R reacts with the adsorbed oxygen species, a steady state occupancy 0 of the surface state is established, which is less than the equilibrium occupancy in air. The following mechanism can be assumed ... 

We calculated the free energies of all the minima in order to determine the equilibrium probability distribution (see Section IV.C.2). We found that the several hundred lowest free energy minima have about the same free energy, and that no single minimum has an equilibrium occupation probability which exceeds 0.004. This is in stark contrast with unsolvated tetra-alanine, where the ground state had an equilibrium occupation probability of 0.748, and the lowest three potential energy states accounted for 0.936 of the total equilibrium probability. 

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