Partition folding

From the description of the kinetic partitioning mechanism (KPM) given above it follows that generically the time dependence of the fraction of molecules that have not folded at time t, is given by... 

For these sequences the value of Gj, is less than a certain small value g. For such sequences the folding occurs directly from the ensemble of unfolded states to the NBA. The free energy surface is dominated by the NBA (or a funnel) and the volume associated with NBA is very large. The partition factor <6 is near unify so that these sequences reach the native state by two-state kinetics. The amplitudes in (C2.5.7) are nearly zero. There are no intennediates in the pathways from the denatured state to the native state. Fast folders reach the native state by a nucleation-collapse mechanism which means that once a certain number of contacts (folding nuclei) are fonned then the native state is reached very rapidly [25, 26]. The time scale for reaching the native state for fast folders (which are nonnally associated with those sequences for which topological fmstration is minimal) is found to be... 

The likelihood function is an expression for p(a t, n, C), which is the probability of the sequence a (of length n) given a particular alignment t to a fold C. The expression for the likelihood is where most tlireading algorithms differ from one another. Since this probability can be expressed in terms of a pseudo free energy, p(a t, n, C) x exp[—/(a, t, C)], any energy function that satisfies this equation can be used in the Bayesian analysis described above. The normalization constant required is akin to a partition function, such that... 

Nys, G. G., Rekker, R. F. Statistical analysis of a series of partition coefficients with special reference to the predictability of folding of drug molecules. Introduction of hydrophobic fragmental constants (/-values). Chim. Therap. 1973, 8, 521-535. 

Figure 4. Fits of lattice strain model to experimental mineral-melt partition coefficients for (a) plagioclase (run 90-6 of Blundy and Wood 1994) and (b) elinopyroxene (ran DC23 of Blundy and Dalton 2000). Different valence cations, entering the large cation site of each mineral, are denoted by different symbols. The curves are non-linear least squares fits of Equation (1) to the data for each valence. Errors bars, when larger than symbol, are 1 s.d. Ionic radii in Vlll-fold coordination are taken from Shannon (1976).

The simplest proxy to identify is that of Ba for Ra. As noted above, both are heavy alkaline earths, which form large divalent cations. They exclusively enter large cation sites with at least Vlll-fold coordination. There are a large number of Ba partition coefficients for the major rock-forming minerals over a wide range of conditions, which make it an ideal proxy. 

Actinium is similarly easy to find a proxy for. It forms large trivalent cations with an ionic radius of 1.12 A in Vl-fold coordination. This is somewhat larger than La (1.032 A), which we will adopt as a proxy. The partitioning behavior of the lanthanides (denoted collectively Ln) is sufficiently well understood to make this a prudent choice. In some minerals, however, the larger size of Ac, may place it onto a larger lattice site than the lanthanides. This possibility should be considered for minerals with very large cation sites, such as amphiboles and micas. 

Orthopyroxene has a Vl-fold Ml site and a Vl-fold M2 site. Both are predominantly filled by Mg and Fe. The smaller Ml site shares many characteristics with the clinopyroxene Ml site. It is therefore reasonable to assume that no U-series cations, including Pa (see above) enter that site. We will confine our discussion to the octahedral M2, which is smaller than the equivalent (Vni-fold) clinopyroxene site, even after allowing for the different coordination number. Consequently most of the U-series elements have very low orthopyroxene-melt partition coefficients. 

Schmidt et al. (1999) report Dpb of 0.034-0.045 for two experiments with leucite lamproite melt composition for a basanitic melt composition La Tourrette et al. (1995) give Z)pb = 0.10. In all three cases Z)pb consistently falls below, by a factor of 3, the parabola defined by the other 2+ cations, as previously noted for several other minerals. Here the implication is that the effective Xll-fold ionic radius of Pb is slightly smaller than the value given in Table 2, i.e., closer in size to rsr. Upb/Usr is between 0.6 and 1.2, in these experiments. In the PIXE partition study of Ewart and Griffin (1994) for acid volcanic rocks, Z)pb ranges from 0.21 to 2.1 (3 samples), with Upb/Usr of 0.29 to 2.9. Until there are further experimental determinations of Upb, or better constraints on its ionic radius, we suggest that Z)pb = E>sr-... 

One of the striking features about as constrained above, is that it is almost identical to the ionic radius of Pa in Vlll-fold coordination, suggesting that Pa will readily partition into zircon. However, until there are experimental data with which to... 

Figure 24. Lattice strain model applied to zircon-melt partition coefficients from Hinton et al. (written comm.) for a zircon phenocryst in peralkaline rhyolite SMN59 from Kenya. Ionic radii are for Vlll-fold coordination (Shannon 1976). The curves are fits to Equation (1) at an estimated eraption temperature of 700°C (Scaillet and Macdonald 2001). Note the excellent fit of the trivalent lanAanides, with the exception of Ce, whose elevated partition coefficient is due to the presence of both Ce and Ce" in the melt, with the latter having a much higher partition coefficient into zircon. The 4+ parabola cradely fits the data from Dj, and Dy, through Dzi to Dih, but does not reproduce the observed DuIDjh ratio. We speculate that this is due to melt compositional effects on Dzt and (Linnen and Keppler 2002), and possibly other 4+ cations, in very silicic melts. Because of its Vlll-fold ionic radius of 0.91 A (vertical line), Dpa is likely to be at least as high as Dwh, and probably considerably higher.

For weak acids, e.g., salicylic acid, the dependency on a pH gradient becomes complex since both the passive diffusion and the active transport process will be dependent on the proton concentration in the apical solution [61, 63, 98, 105] and a lowering of the pH from 7.4 to 6.5 will increase the apical to basolateral transport more than 20-fold. Similarly, for weak bases such as alfentanil or cimetidine, a lowering of the pH to 6.5 will decrease the passive transport towards the basolateral side [105]. The transport of the ionizable compound will, due to the pH partition hypothesis, follow the pKa curve. 

The latter type of compounds should preferably carry either one type I unit or at most two units (positioned as far apart as possible), and have an elongated structure (which does not fold as verapamil, for example) with a small cross-sectional area, Ad- The first type of compounds is expected to be transported slowly, whereas the second type may not be transported. Table 20.2 summarizes the drug properties relevant for transporter binding and lipid partitioning of a substrate (modulator or inhibitor) of P-gp. Inspection of the information contained in Table 20.2 shows that the synthesis and membrane incorporation of inhibitors with a low number of H-bond acceptor patterns should be simpler and more efficient than that of inhibitors with a large number of patterns. 

In summary, there now exists a body of data for the reactions of carbocations where the values of kjkp span a range of > 106-fold (Table 1). This requires that variations in the substituents at a cationic center result in a >8 kcal mol-1 differential stabilization of the transition states for nucleophile addition and proton transfer which have not yet been fully rationalized. We discuss in this review the explanations for the large changes in the rate constant ratio for partitioning of carbocations between reaction with Bronsted and Lewis bases that sometimes result from apparently small changes in carbocation structure. 

The net effect of the two orrAo-methyl groups at Me-[10+] is a 4200-fold decrease in the rate constant ratio As/Ap for partitioning of the carbocation between nucleophilic addition of solvent and proton transfer.27... 

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