Concave Substrates

In many cyclic or bicyclic molecules a stereo structure is present in which one can identify a convex and a concave side. Because reactions usually take place in such a way that the reacting reagent is exposed to the least possible steric hindrance, convex/concave substrates are generally react on their convex side. 

It should be noted that the methods reviewed below can be applied not only to a planar substrate but also to convex and concave substrates. They can also be applied to an inner wall surface of a cylinder if it can be illuminated by propagating light. Furthermore, they can be used for a variety of materials, such as glasses, erystals, ceramics, metals, plastics, and so on. Since a high optical power is not required, visible LEDs can be employed as low-power-consumption light sources. 

Some studies have reported an initiation efficiency of 3-8.5% for concave substrates within ordered mesoporous silica nanoparticles, with mesopore diameter ranging from 1.8 to 2.3 nm [88, 89]. Another study reported 22-37% initiation efficiency when SI-ATRP was conducted in ordered mesoporous silica with 15 nm... 

Termination is unavoidable in ATRP systems because of the very nature of radicals. Termination in SI-ATRP is highly dependent on the geometry of the substrates. For example, the confined environment of concave substrate leads to closer proximity of polymer chains, which could lead to higher possibility of termination. On flat or convex substrates, the termination could occur via multiple modes. The modes of termination and experimental data supporting the role of termination in kinetics of SI-ATRP are discussed in the following sections. 

In the case of systems involving concave substrates, such as porous particles or cylindrical channels, the confinement effect is expected to be much more severe than that for flat substrates. In addition to the obvious mass transport issue that results from a more confined space, the probability of termination could also increase. Therefore, a less living and less controlled polymerization is expected in systems involving concave substrates. 

Multiple studies have reported a population of shorter grafted polymer chains with broader distribution in comparison with free/solution polymer chains [88, 89, 113]. Gorman et al. conducted SI-ATRP from a silicon wafer, porous silicon, and anodically etched aluminum oxide. The results were compared with those of ATRP conducted in solution under similar conditions. The grafted polymer chains from a flat substrate were shown to be shorter than the free chains formed in the parallel solution polymerization. The polymers obtained from concave substrates have an even lower molecular weight and broader distribution. 

Fig. 8 Molecular weight distributions of grafted chains for Sl-ATRP of MMA from a concave substrate. Detailed experimental conditions are provided in the original literature. Mp i indicates the molar mass at the peak for the living chains. (1) 50%, Mp,i= 16,320 g/mol (2) 62%, Mpj = 21,880 g/mol (5)91%,Mpj = 30,020 g/mol. The lower peak (Mp = 2500 g/mol) indicates the presence of dead chains. Reprinted with permission from Pasetto et al. [89]...

Simulation of polymerization from a concave substrate could prove to be a challenging task because of the complexity of the system. However, Liu et al. used coarse-grained molecular dynamic simulation to investigate the effect of curvature on polymer growth and dispersity [90]. Unfortunately, the polymerization was considered to be a perfectly living polymerization (i.e., in the absence of termination and other side reactions), thus it does not help in elucidating the role of termination in SI-ATRP. 

Plots devised by Dixon to determine K, for tight-binding inhibitors, (a) A primary plot of v versus total inhibitor present ([/Id yields a concave line. In this example, [S] = 3 x Km and thus v = 67% of Straight lines drawn from Vo (when [/It = 0) through points corresponding to Vq/2, Vq/3, etc. intersect with the x-axis at points separated by a distance /Cj app/ when inhibition is competitive. When inhibition is noncompetitive, intersection points are separated by a distance equivalent to K. The positions of lines for n = 1 and n = 0 can then be deduced and the total enzyme concentration, [EJt, can be determined from the distance between the origin and the intersection point of the n = 0 line on the x-axis. If inhibition is competitive, this experiment is repeated at several different substrate concentrations such that a value for K, app is obtained at each substrate concentration. (b) Values for app are replotted versus [S], and the y-intercept yields a value for /Cj. If inhibition is noncompetitive, this replot is not necessary (see text)... 

Competitive, 249, 123, 146, 190 [partial, 249, 124 progress curve equations for, 249, 176, 180 for three-substrate systems, 249, 133, 136] competitive-uncompetitive, 249, 138 concave-up hyperbolic, 249, 143 dead-end, 249, 124 [for bireactant kinetic mechanism determination, 249, 130-133 definition of kinetic constants, 249, 220-221 effects on enzyme progress curves, nonlinear regression analysis, 249, 71-72 inhibition constant evaluation, 249, 134-135 kinetic analysis with, 249, 123-143 one-substrate systems, 249, 124-126 unireactant systems, theory,... 

Selected entries from Methods in Enzymology [vol, page(s)] Theory, 63, 159-162 activation effect, 63, 174, 175 analysis, 63, 140, 159-183 burst, 64, 20, 203, 215 enzyme concentration, 63, 175-177 hysteresis, 64, 197, 200-204 limitations, 63, 181-183 plotting, 63, 177-180 practical methods, 63, 175-177 reversible inhibitor action, 63, 163-175 reversible reaction, 63, 171-175 simulation of, 63, 180 advantages and disadvantages, 249, 61-62 analysis, in kinetic models of inhibition, 249, 168-169 concave-down, 249, 156 concave-up, 249, 156 with enzyme-product complex instability, 249, 88 with enzyme-substrate instabil-... 

Inside the cell, numerous chemical processes take place at the same time. The cell solves the problem of generating a large number of different molecules at the same time with a high selectivity by the use of enzymes. The selectivity of these proteins is largely determined by their geometry. Also the selectivity of another class of proteins, the receptors, is influenced by geometrical features. Receptors and enzymes have in common that they are equipped with concave structures such as clefts or cavities [1] in which substrate molecules are bound or chemically modified. 

When the concave reagents are compared to other reactions in Supramole-cular Chemistry a distinct difference must be noted Most other approaches try to bind the substrate in a host first. Then this complex reacts with a reagent which either is present in solution or attached to the host. For concave reagents and concave catalysts, however, there is no need for binding of the educt. In contrast, the protonation reactions can be interpreted as a reagent (H ) host complex. 

By my remarks I wanted to emphasize the importance of concavity of enzymes as a feature that determines the specificity and stereospecificity. I didn t want to say that it is a feature that is necessary for all enzymes. However, starting with a globular convex substrate, a concave active site allows a strategic distribution of a number of small and large interactions that make the enzyme specific and stereospecific. 

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