Barrier passage

The key quantity in barrier crossing processes in tiiis respect is the barrier curvature Mg which sets the time window for possible influences of the dynamic solvent response. A sharp barrier entails short barrier passage times during which the memory of the solvent environment may be partially maintained. This non-Markov situation may be expressed by a generalized Langevin equation including a time-dependent friction kernel y(t) [ ]... 

D., Vander Heyden, Y. Classification tree models for the prediction of blood-brain barrier passage of drugs. /. Chem Inf. Model. 2006, 46, 1410-1419. 

We consider the reactive solute system with coordinate x and its associated mass p, in the neighborhood of the barrier top, located at x=xi=0, and in the presence of the solvent. We characterize the latter by the single coordinate. v, with an associated mass ps. If the solvent were equilibrated to x in the barrier passage, so that there is equilibrium solvation and s = seq(x), the potential for x is just -1/2 pcc X2, where (, , is the equilibrium barrier frequency [cf. (2.2)]. To this potential we add a locally harmonic restoring potential for the solvent coordinate to account for deviations from this equilibrium state of affairs ... 

But the entire conception here is that of equilibrium solvation of the transition state by the Debye ionic atmosphere, and closer inspection [51] indicates that this assumption can hardly be justified indeed, time scale considerations reveal that it will nearly always be violated. The characteristic time for the system to cross the reaction barrier is cot, 0.1 ps say. On the other hand, the time required for equilibration of the atmosphere is something like the time for an ion to diffuse over the atmosphere dimension, the Debye length K- this time is = 1 ns for a salt concentration C= 0.1M and only drops to lOps for C 1M. Thus the ionic atmosphere is perforce out of equilibrium during the barrier passage, and in analogy with ionic transport problems, there should be an ionic atmosphere friction operative on the reaction coordinate which can influence the reaction rate. 

These aspects were examined in a study [51] which employed a generalized Debye-Falkenhagen description for the ionic atmosphere dynamical friction and GH theory for the rate. It was found that, while indeed the atmosphere is almost never equilibrated during the barrier passage and to a large extent is frozen on this time scale, the atmosphere frictional derivations from the equilibrium solvation TST result... 

Lipophilicity is of prime importance in the design of drugs. Indeed, it controls many parameters such as absorption, biological barrier passage (and consequently transport into organs and cells), and also interaction with the macromolecular target (cf. Chapter 3). 

Although in vitro GR 175737 is less potent (pKi = 8.2) than clobenpropit (pK = 9.8), in vivo GR 175737 shows a higher activity (ED3o 1.4 mg/kg) in an ex vivo binding assay than clobenpropit (ED50 = 10.3 mg/kg) [20], Apparently the bioavailability of GR 174737 is much better than clobenpropit and the authors postulated that this observed difference might be caused by the relative ease of blood-brain-barrier passage. 

This expression is expected to be valid if the time scale of the damping (tv ) is larger than that of the motion on the barrier height (1/ B). In contrast to the high-friction case, the barrier passage is negligibly perturbed and thus the motion of the particle to the product well is not hindered. In this case the rate is independent of the coupling between the heat bath and the particle. 

Ayre SG, Skaletski B, Mosnaim AD (1989) Blood-brain barrier passage of azidodiymidine in rats Effect of insulin. Res Comm Chem Padi Pharmacol 63 45—52. 

Absorption Distribution Metabolism Excretion GI tract, lungs, skin Storage in tissues (plasma proteins, liver and kidney, fat, bone), blood-brain barrier, passage across the placenta, membrane permeability Liver, lungs, kidney, brain, phase I, phase II metabolism Urinary, fecal, exhalation, milk, sweat, sahva... 

Antoniou, D., Caeatzouias, S., Kalyanaeaman, C., Mincer, J. S., Schwartz, S. D. (2002) Barrier passage and protein dynamics in enzymatically catalyzed reactions, Eur. J. Biochem. 269, 3103-3112 and many cited therein. 

The slow variable treatment of the particle relaxation process Xf(S) xf=o(S) of section II.B may be adapted to barrier crossing by making the following reinterpretations (a) x is taken as the reaction coordinate of a solute system undergoing barrier passage (b) W S]x) is taken as the system s reaction coordinate potential of mean force (c) m is taken as the reduced mass factor for reaction coordinate motion and (d) xf S) and Xf=o S) are taken, respectively, as the transition state x and product well xp values of x. Given these transcriptions, the process Xf(5) —>Xf=o( 5) is reinterpreted as the reactive barrier passage x xp. 

The fast variable nature of liquid phase reactions is illustrated in Figure 3.3. There we reproduce a plot of Wilson and co-workers [14b] derived from MD studies of their model aqueous 5/vl reaction. In Figure 3.3 the average reaction coordinate kinetic energy jmx computed from an ensemble of reactive trajectories is plotted as a function of time t. Notice that as early as — 1 ps before x is reached, mx is 25 times the mean thermal value j kT while in the last 0.1 ps before barrier passage j mx becomes as large as 45 times jkT. Thus, the average reaction coordinate speed x can be... 

To do this we adapt the short time treatment of particle relaxation to barrier crossing by making transpositions like those given at the start of Section III. Namely, (a) x is reinterpreted as the solute s reaction coordinate (b) V S x) as its reaction coordinate instantaneous potential (c) m as its reaction coordinate reduced mass factor and (d) the process Xf(S) Xf=o(5 ) as the reactive barrier passage x —> xp. 

Thus, according to the short time Eq. (3.51), the barrier passage frequency is expected to track with comip and to approach the sharp barrier limiting value comip as mip —> oo. In contrast, (recall Section III.B) according to the Grote-Hynes Eq. (3.47), x+ is expected to track with pmf and apparently to approach the sharp barrier limiting value x+ —> pmf as PMF cc. A comparison of the last three columns in Table IV shows that it is Eq. (3.51) not Eq. (3.47), which is in accord with the MD results. 

This assumption implies that memory of origin is lost after barrier passage. As a consequence, transition-state theory contains no information on the product. This is illustrated in the following example. The reaction of an oxygen atom and hydroxy radical can leave two different products... 

---